Why Invest in Bonds?
1. LG 1
In contrast to stocks, bonds are liabilities—publicly traded IOUs where the bondholders are actually lending money to the issuer. Bonds are publicly traded, long-term debt securities. They are issued in various denominations, by a variety of borrowing organizations, including the U.S. Treasury, agencies of the U.S. government, state and local governments, and corporations. Bonds are often referred to as fixed-income securities because the payments made by bond issuers are usually fixed. That is, in most cases the issuing organization agrees to pay a fixed amount of interest periodically and to repay a fixed amount of principal at maturity.
Like stocks, bonds can provide two kinds of income: (1) current income and (2) capital gains. The current income comes from the periodic interest payments paid over the bond’s life. The capital gains component is a little different. Because the companies issuing bonds promise to repay a fixed amount when the bonds mature, the interest payments that bonds make do not typically rise in step with a firm’s profits the way that stock dividends often do, which is another reason bonds are known as fixed-income securities. By the same token, a company’s stock price tends to rise and fall dramatically with changes in the firm’s financial performance, but bond prices are less sensitive to changes in a company’s profits. However, bond prices do rise and fall as market interest rates change. A basic relationship that you must keep in mind is that interest rates and bond prices move in opposite directions. When interest rates rise, bond prices fall, and when rates drop, bond prices move up. We’ll have more to say about this relation later in the chapter, but here’s the intuition behind it. Imagine that you buy a brand-new bond, issued by a company like GE, paying 5% interest. Suppose that a month later market rates have risen, and new bonds pay investors 6% interest. If you want to sell your GE bond, you’re likely to experience a capital loss because investors will not want to buy a bond paying 5% interest when the going rate in the market is 6%. With fewer buyers interested in them, GE bonds will decline in value. Happily, the opposite outcome can occur if market rates fall. When the going rate on bonds is 4%, your GE bond paying 5% would command a premium in the market. Taken together, the current income and capital gains earned from bonds can lead to attractive returns.
A wide variety of bonds are available in the market, from relatively safe issues (e.g., General Electric bonds) sought by conservative investors to highly speculative securities (e.g., Sirius XM bonds) appropriate for investors who can tolerate a great deal of risk. In addition, the risks and returns offered by all types of bonds depend in part upon the volatility of interest rates. Because interest rate movements cause bond prices to change, higher interest rate volatility makes bond returns less predictable.
Other bonds have special features designed to appeal to certain types of investors. Investors in high tax brackets who want to shelter income from taxes find tax-exempt bonds appealing. Bonds issued by state and local government entities, called municipal bonds, pay interest that is not subject to federal income taxation, so these bonds have special appeal to investors in high tax brackets. Interest on U.S. Treasury bonds is exempt from state income tax, so taxpayers from states with high income tax rates may have particular interest in these bonds. Despite the term fixed income, some bonds make interest payments that vary through time according to a formula. In a sense, the term fixed income is still appropriate for these bonds because the formula that determines their interest payments is contractually fixed. For example, governments in the United States and many other countries issue inflation-indexed bonds with interest payments that rise with inflation. As the inflation rate changes, the payments on these bonds will change, but investors know in advance exactly how the interest payments will adjust as inflation occurs. Those bonds appeal to investors who want some protection from the risk of rising inflation.
A Brief History of Bond Prices, Returns, and Interest Rates
Interest rates drive the bond market. In fact, the behavior of interest rates is the most important influence on bond returns. Interest rates determine not only the current income investors will receive but also the capital gains (or losses) they will incur. It’s not surprising, therefore, that bond-market participants follow interest rates closely. When commentators in the news media describe how the market has performed on a particular day, they usually speak in terms of what happened to bond yields (i.e., what happened to interest rates) that day rather than what happened to bond prices.
Figure 10.1 provides a look at interest rates on bonds issued by U.S. corporations and the U.S. government from 1963 through 2014. It shows that rates on both types of bonds rose steadily through the 1960s and 1970s, peaking in 1982 at more than three times their 1963 levels. Rates then began a long downward slide, and by 2014 the rates were not that different from their 1963 levels. Keep in mind that rising interest rates lead to falling bond prices, so prior to the 1980s investors who held bonds that had been issued in the 60s and 70s realized capital losses if they sold their bonds after
Figure 10.1 The Behavior of Interest Rates over Time, 1963 through 2014
Interest rates rose dramatically from 1963 to 1982 before starting a long-term decline that continued through 2014. Rates on corporate bonds tend to mirror rates on government bonds, although corporate rates are higher due to the risk of default by the issuing corporation. Note that the gap, or “spread,” between U.S. corporate bond and U.S. Treasury bond yields has been particularly wide following the 2008 financial crisis.
(Source: Board of Governors of the Federal Reserve System (US), Moody’s Seasoned Aaa Corporate Bond Yield© [AAA], retrieved from FRED, Federal Reserve Bank of St. Louis https://research .stlouisfed.org/fred2/series/AAA/ , May 20, 2015. Board of Governors of the Federal Reserve System (US), 10-Year Treasury Constant Maturity Rate [DGS10], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/DGS10/ , May 20, 2015.)
interest rates had risen. By the same token, investors who purchased bonds when interest rates were high earned capital gains from selling their bonds after market interest rates had declined.
Figure 10.1 shows that rates on corporate and government bonds tend to move together, but corporate bond rates are higher. Higher rates on corporate bonds provide compensation for the risk that corporations might default on their debts. The difference between the rate on corporate bonds and the rate on government bonds is called the yield spread, or the credit spread. When the risk of defaults on corporate bonds increases, the yield spread widens, as it did in 2008. The average annual yield spread for triple-A corporate bonds over the 52 years shown in Figure 10.1 was about 1%, the average from 1987 through 2014 was nearly 1.4%, and the average from 2008 through 2014 was 1.8%. Because changes in the credit spread are tied to the risk of default on corporate bonds, prices of these bonds are not completely insensitive to a company’s financial performance. When a company’s performance improves, investors recognize the default risk is falling, so the credit spread falls and the company’s bond prices rise. When a firm’s financial results deteriorate, default risk rises, the credit spread increases, and the company’s bond prices fall. Even so, bond prices are nowhere near as sensitive to a firm’s financial results as are stock prices.
Historical Returns
As with stocks, total returns in the bond market are made up of both current income from the bond’s interest payments and capital gains (or losses) from changes in the bond’s value. Table 10.1 lists beginning-of-year and end-of-year bond yields and the total returns for 10-year U.S. government bonds from 1963 through 2014. The beginning-of-year yield represents the return that investors buying 10-year Treasury bonds require at the start of each year, and likewise the end-of-year yield represents the interest rate required by purchasers of 10-year bonds at the end of the year. Note how different the beginning-of-year yields can be from the end-of-year yields. For example, the year 2009 began with 10-year bond investors requiring a 2.3% return, but by the end of that year the required return on 10-year bonds had gone up to 3.9%. Notice the effect that this increase in interest rates had on the total return that investors earned on 10-year bonds in 2009. An investor who purchased a bond in January of 2009 received interest payments based on the bond’s 2.3% yield, but they also experienced a capital loss during the year because 10-year bond yields increased (remember, bond prices go down when interest rates go up). The total return on 10-year bond in 2009 was −10.8%, which simply means that the capital loss on bonds that year far exceed the 2.3% in interest income that bondholders received.
During a period of rising rates, total returns on bonds include capital losses that can sometimes exceed the bonds’ current interest income, resulting in a negative total return. Total returns on U.S. Treasury bonds were negative in 10 out of 52 years, and as Table 10.1 shows, the years with negative total returns on bonds were years in which bond yields rose: That is, the end-of-year yield was higher than the beginning-of-year yield.
Fortunately the inverse relationship between bond prices and yields can work in favor of investors too. Consider 2008. At the beginning of that year, the required return on bonds was 4.0%, but by the end of the year the required return had fallen to 2.3%. Notice that the total return earned by bond investors that year was 19.9%. In other words, bondholders earned about 4% in interest income, but they also earned a large capital gain (almost 16%) because interest rates fell during the year. As Table 10.1 shows, the years with the highest total returns on bonds are almost always years in which bond yields fell during the year.
Table 10.1 Historical Annual Yields and Total Returns for Treasury Bonds
(Source: Board of Governors of the Federal Reserve System (US), 10-Year Treasury Constant Maturity Rate [DGS10], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/DGS10/ , May 20, 2015.)
|
Year |
Beginning-of-Year T-Bond Yield |
End-of-Year T-Bond Yield |
T-Bond Total Return |
Year |
Beginning-of-Year T-Bond Yield |
End-of-Year T-Bond Yield |
T-Bond Total Return |
|
1963 |
3.9% |
4.1% |
1.5% |
1989 |
9.1% |
7.9% |
17.3% |
|
1964 |
4.1% |
4.2% |
3.6% |
1990 |
7.9% |
8.1% |
6.9% |
|
1965 |
4.2% |
4.7% |
0.8% |
1991 |
8.1% |
6.7% |
17.8% |
|
1966 |
4.7% |
4.6% |
4.7% |
1992 |
6.7% |
6.7% |
6.8% |
|
1967 |
4.6% |
5.7% |
−3.3% |
1993 |
6.7% |
5.8% |
13.2% |
|
1968 |
5.7% |
6.2% |
2.3% |
1994 |
5.8% |
7.8% |
−7.8% |
|
1969 |
6.2% |
7.9% |
−5.4% |
1995 |
7.8% |
5.6% |
24.8% |
|
1970 |
7.9% |
6.5% |
17.8% |
1996 |
5.6% |
6.4% |
−0.6% |
|
1971 |
6.5% |
5.9% |
11.0% |
1997 |
6.4% |
5.8% |
11.5% |
|
1972 |
5.9% |
6.4% |
2.1% |
1998 |
5.8% |
4.7% |
14.4% |
|
1973 |
6.4% |
6.9% |
3.0% |
1999 |
4.7% |
6.5% |
−8.3% |
|
1974 |
6.9% |
7.4% |
3.5% |
2000 |
6.5% |
5.1% |
16.7% |
|
1975 |
7.4% |
7.8% |
5.0% |
2001 |
5.1% |
5.1% |
5.5% |
|
1976 |
7.8% |
6.8% |
14.5% |
2002 |
5.1% |
3.8% |
15.2% |
|
1977 |
6.8% |
7.8% |
0.2% |
2003 |
3.8% |
4.3% |
0.3% |
|
1978 |
7.8% |
9.2% |
−1.0% |
2004 |
4.3% |
4.2% |
4.5% |
|
1979 |
9.2% |
10.3% |
2.0% |
2005 |
4.2% |
4.4% |
3.0% |
|
1980 |
10.3% |
12.4% |
−1.3% |
2006 |
4.4% |
4.7% |
1.9% |
|
1981 |
12.4% |
14.0% |
4.3% |
2007 |
4.7% |
4.0% |
10.1% |
|
1982 |
14.0% |
10.4% |
35.9% |
2008 |
4.0% |
2.3% |
19.9% |
|
1983 |
10.4% |
11.8% |
2.0% |
2009 |
2.3% |
3.9% |
−10.8% |
|
1984 |
11.8% |
11.6% |
13.4% |
2010 |
3.9% |
3.3% |
8.5% |
|
1985 |
11.6% |
9.0% |
27.9% |
2011 |
3.3% |
1.9% |
16.0% |
|
1986 |
9.0% |
7.2% |
21.3% |
2012 |
1.9% |
1.8% |
2.9% |
|
1987 |
7.2% |
8.8% |
−3.1% |
2013 |
1.8% |
3.0% |
−8.9% |
|
1988 |
8.8% |
9.1% |
6.9% |
2014 |
3.0% |
2.2% |
10.8% |
We can use the return data from Table 10.1 to look at average bond returns over different periods, as shown below:
|
Period |
Average Annual Total Returns |
|
5 years: 2010–2014 |
5.9% |
|
10 years: 2005–2014 |
5.3% |
|
20 years: 1995–2014 |
6.9% |
|
30 years: 1985–2014 |
8.5% |
These figures show that the last 30 years were generally good to bond investors. This was mostly due to the fact that the U.S. economy was in a sustained period of declining interest rates, which in turn produced hefty capital gains and above-average returns. In fact, in 14 of the last 30 years, bonds earned double-digit total returns. Whether market interest rates will (or even can) continue on that path is, of course, the big question. Given the current record low yields, most market observers expect yields to begin rising over the next several years, leading to capital losses and below-average returns on bonds.
Bonds versus Stocks
Compared to stocks, bonds are generally less risky and provide higher current income. Bonds, like stocks, are issued by a wide range of companies as well as various governmental bodies, so investors can construct well-diversified portfolios with bonds, just as they do with stocks. On the other hand, compared to stocks, the potential for very high returns on bonds is much more limited, even though the last two decades have been exceptional for bonds.
Figure 10.2 illustrates some of the performance differences between stocks and bonds by showing how a $10,000 investment in either stocks or bonds would have grown from 1990 through 2014. Although the investment in bonds slightly outpaced stocks in the early 1990s, investors in stocks were far better off in the late 1990s as the equity market boomed. Stocks peaked in August 2000 and then fell sharply. Stocks fell even more after the terrorist attacks on September 11, 2001, and they eventually hit bottom in September 2002. By the end of 2002, the bond investment was back in front, but only for a brief time. Stocks quickly recovered much of the ground that they had lost, peaking again in October 2007, only to have the U.S. housing bubble burst and the financial crisis begin. With the stock market in free fall in 2008 the bond market investment again took over the lead, and it would remain there for more than four years. After the financial crisis began to ease, stocks began a rocky rebound, and by the end of 2014, the $10,000 investment in stocks had grown to more than $60,000, whereas the money invested in bonds had grown to just over $48,000.
Figure 10.2 illustrates that over the last 25 years, stocks have outperformed bonds, but it also illustrates that stock returns are much more volatile than bond returns. If stocks are riskier, then investors should, on average, earn higher returns on stocks than on bonds, and we know from the historical evidence that stocks have outperformed bonds over long horizons. Still, Figure 10.2 shows that bonds can outperform stocks for a long time. For example, the cumulative returns on bonds far outpaced returns on stocks from July 2000 all the way through 2014. An investor who purchased $10,000 in bonds in July 2000 would have accumulated more than $21,200 by the end of 2014, whereas a $10,000 investment in stocks would have grown to just $13,900 over the same period.
The biggest differences in returns between stocks and bonds usually come during bear markets when stock returns are negative. In part, this reflects a phenomenon called “flight to quality” in which investors pull their funds out of the stock market to invest in less risky securities such as bonds. For example, while Figure 10.2 shows that investors in stocks lost roughly 40% of their money in 2008, Table 10.1 shows that government bond investors made about 20% that year.
Many investors argue that even if bonds earn lower returns than stocks on average, that’s a low price to pay for the stability that bonds bring to a portfolio. The fact is, bond returns are far more stable than stock returns, plus they possess excellent portfolio diversification properties. As a general rule, adding bonds to a portfolio will, up to a point, reduce the portfolio’s risk without dramatically reducing its return. Investors don’t buy bonds for their high returns, except when they think interest rates are heading down. Rather, investors buy them for their current income and for the stability they bring to a portfolio.
Figure 10.2Comparative Performance of Stocks and Bonds, 1990 through 2014
This graph shows what happened to $10,000 invested in bonds and $10,000 invested in stocks over the 25-year period from January 1990 through December 2014. Clearly, while stocks held a commanding lead going into the 21st century, the ensuing bear market more than erased that advantage. That pattern repeated itself as stocks outperformed bonds from early 2003 to late 2007, only to fall sharply through the end of 2008. From early 2009 through the end of 2012, stocks took a bumpy path toward rebounding, and from there stocks continued to climb at a rapid pace through 2014.
Note: Performance figures and graphs are based on rates of return and include reinvested current income (dividends and interest) as well as capital gains (or losses); taxes have been ignored in all calculations.
Exposure to Risk
Like all other investments, bonds are subject to a variety of risks. Generally speaking, bonds are exposed to five major types of risk: interest rate risk, purchasing power risk, business/financial risk, liquidity risk, and call risk.
· Interest Rate Risk. Interest rate risk is the most important risk that fixed-income investors face because it’s the major cause of price volatility in the bond market. For bonds, interest rate risk translates into market risk, meaning that the behavior of interest rates affects nearly all bonds and cuts across all sectors of the market, even the U.S. Treasury market. When market interest rates rise, bond prices fall, and vice versa. As interest rates become more volatile, so do bond prices.
· Purchasing Power Risk. Inflation erodes the purchasing power of money, and that creates purchasing power risk. Naturally, investors are aware of this, so market interest rates on bonds compensate investors for the rate of inflation that they expect over a bond’s life. When inflation is low and predictable, bonds do pretty well because their returns exceed the inflation rate by an amount sufficient to provide investors with a positive return, even after accounting for inflation’s effect on purchasing power. When inflation takes off unexpectedly, as it did in the late 1970s, bond yields start to lag behind inflation rates, and the interest payments made by bonds fail to keep up. The end result is that the purchasing power of the money that bond investors receive falls faster than they anticipated. That’s what the term purchasing power risk means. Of course, risk cuts both ways, so when the inflation rate falls unexpectedly, bonds do exceptionally well.
· Business/Financial Risk. This is basically the risk that the issuer will default on interest or principal payments. Also known as credit risk, or default risk, business/financial risk has to do with the quality and financial health of the issuer. The stronger the financial position of the issuer, the less business/financial risk there is to worry about. Default risk is negligible for some securities. Historically, investors have viewed U.S. Treasury securities as being free of default risk, although the growing debt of the United States has raised some concern about the potential for a default. For other types of bonds, such as corporate and municipal bonds, default risk is a much more important consideration.
· Liquidity Risk. Liquidity risk is the risk that a bond will be difficult to sell quickly without cutting the price if the investor wants to sell it. In some market sectors, this can be a big problem. Even though the bond market is enormous, many bonds do not trade actively once they are issued. U.S. Treasury bonds are the exception to the rule, but most corporate and municipal bonds are relatively illiquid.
· Call Risk. Call risk, or prepayment risk, is the risk that a bond will be “called” (retired) long before its scheduled maturity date. Issuers often prepay their bonds when interest rates fall. (We’ll examine call features later.) When issuers call their bonds, the bondholders get their cash back and have to find another place for their funds, but because rates have fallen, bondholders have to reinvest their money at lower rates. Thus, investors have to replace high-yielding bonds with much lower-yielding bonds.
Watch Your Behavior
Buffet’s Bonds Bomb Even the most savvy investors make mistakes. Warren Buffett recently acknowledged that one of his biggest mistakes was purchasing $2 billion in bonds issued by Energy Future Holdings Corporation. A prolonged drop in natural gas prices hurt the company’s prospects, and in 2012 the value of Buffett’s bonds was less than $900 million.
The returns on bonds are, of course, related to risk. Other things being equal, the more risk embedded in a bond, the greater the expected return. The risks of investing in bonds depend upon the characteristics of the bond and the entity that issued it. For example, as we’ll see later in the chapter, there’s more interest rate risk with a long-term bond than with a short-term bond. In addition, for particular bonds, the characteristics that affect risk may have offsetting effects, and that makes risk comparisons of bonds difficult. That is, one issue could have more interest rate and call risk but less credit and liquidity risk than another issue. We’ll examine the various features that affect a bond’s risk exposure as we work our way through this chapter.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 10.1 What appeal do bonds hold for investors? Give several reasons why bonds make attractive investment outlets.
2. 10.2 How would you describe the behavior of market interest rates and bond returns over the last 50 years? Do swings in market interest rates have any bearing on bond returns? Explain.
3. 10.3 Identify and briefly describe the five types of risk to which bonds are exposed. What is the most important source of risk for bonds in general? Explain.
Essential Features of a Bond
1. LG 2
2. LG 3
A bond is a long-term debt instrument that carries certain obligations (the payment of interest and the repayment of principal) on the part of the issuer. Bondholders are lenders, not owners, so they are not entitled to any of the rights and privileges associated with common stock, such as the right to vote at shareholders’ meetings. But bondholders do have a number of well-defined rights and obligations that together define the essential features of a bond. We’ll now take a look at some of these features. When it comes to bonds, it’s especially important for investors to know what they’re getting into, for many seemingly insignificant features can have dramatic effects on a bond’s return.
Bond Interest and Principal
Bonds make periodic interest and principal payments. Most bonds pay interest every six months, although some make monthly interest payments, and some pay interest annually. A bond’s coupon is the annual interest income that the issuer will pay to the bondholder, and its par value , principal , or face value is the amount of capital that the borrower must repay at maturity. For instance, if a bond with a par value of $1,000 pays $60 in interest each year, we say that $60 is the coupon. The coupon rate is the dollar coupon divided by the bond’s par value, and it simply expresses the interest payment that the bond issuer makes as a percentage of the bond’s par value. In the case of the $1,000 par value bond paying an annual $60 coupon, the coupon rate is 6% (i.e., $60 ÷ $1,000)(i.e., $60 ÷ $1,000). If the bond makes semiannual payments, there would be a $30 interest payment every six months. Likewise, if the bond made monthly payments, the $60 coupon would be paid as 12 equal monthly interest payments of $5. The bond’s current yield measures the interest component of a bond’s return relative to the bond’s market price. The current yield equals the annual coupon divided by the bond’s current market price.
Example
Suppose that a 6% bond with a $1,000 par value is currently priced in the market at $950. You can calculate the bond’s current yield as follows:
$1,000 × 0.06$950=0.0632=6.32%$1,000 × 0.06$950=0.0632=6.32%
Notice that the 6.32% current yield is greater than the bond’s coupon rate. That’s because the bond’s market price is below its par value. Note that a bond’s market price need not, and usually does not, equal its par value. As we have discussed, bond prices fluctuate as interest rates move, yet a bond’s par value remains fixed over its life.
Maturity Date
Unlike common stock, all debt securities have limited lives and will mature on some future date, the issue’s maturity date . Whereas bond issuers may make interest payments annually or semiannually over the life of the issue, they repay principal only at maturity. The maturity date on a bond is fixed. It not only defines the life of a new issue but also denotes the amount of time remaining for older, outstanding bonds. Such a life span is known as an issue’s term to maturity. For example, a new issue may come out as a 25-year bond; five years later, it will have 20 years remaining to maturity.
We can distinguish two types of bond offerings based on the issuer’s plans to mature the debt: term and serial bond issues. A term bond issue has a single, fairly lengthy maturity date for all of the bonds being issued and is the most common type of bond issue. A serial bond issue, in contrast, has a series of bonds with different maturity dates, perhaps as many as 15 or 20, within a single bond offering. For example, in an offering of 20-year term bonds issued in 2015, all the bonds have a single maturity date of 2035. If the bonds were offered as serial bonds, they might have different maturity dates, extending from 2016 through 2035. At each of these maturity dates, a certain portion of the issue (i.e., a certain number of bonds) would mature.
Debt instruments with different maturities go by different names. A debt security that’s originally issued with a maturity of 2 to 10 years is known as a note , whereas a bond technically has an initial term to maturity of more than 10 years. In practice, notes are often issued with maturities of 5 to 7 years, whereas bonds normally carry maturities of 20 to 30 years, or more.
Practice Pricing Bonds
Principles of Bond Price Behavior
The price of a bond is a function of the bond’s coupon, its maturity, and the level of market interest rates. Figure 10.3 captures the relationship of bond prices to market interest rates. Basically, the graph reinforces the inverse relationship that exists between bond prices and market rates: Lower rates lead to higher bond prices.
Figure 10.3 also shows the difference between premium and discount bonds. A premium bond is one that sells for more than its par value. A premium results when market interest rates drop below the bond’s coupon rate. A discount bond , in contrast, sells for less than par value. The discount is the result of market interest rates being greater than the issue’s coupon rate. Thus, the 10% bond in Figure 10.3 trades at a premium when the market requires 8% but at a discount when the market rate is 12%.
When a bond is first issued, it usually sells at a price that equals or is very close to par value because bond issuers generally set the coupon rate equal or close to the market’s required interest rate at the time of the issue. Likewise, when the bond matures—some 15, 20, or 30 years later—it will once again be priced at its par value. What happens to the price of the bond in between is of considerable interest to most bond investors. In this regard, the extent to which bond prices move depends not only on the direction of change in market interest rates but also on the magnitude of such change. The greater the moves in interest rates, the greater the swings in bond prices.
However, bond price volatility also varies according to an issue’s coupon and maturity. Bonds with lower coupons and/or longer maturities have more price volatility and are more responsive to changes in market interest rates. (Note in Figure 10.3 that for a given change in interest rates—for example, from 10% to 8%—the largest change in price occurs when the bond has the greatest number of years to maturity.) Therefore, if investors expect a decline in interest rates, they should buy bonds with lower coupons and longer maturities to maximize capital gains. When interest rates move up, they should do just the opposite: Purchase bonds with high coupons and short maturities. This choice will minimize the price decline and act to preserve as much capital as possible.
The maturity of an issue has a greater impact on price volatility than the coupon does. For example, suppose there are two bonds that both pay an 8% coupon rate and currently sell at par value. One bond matures in 5 years while the other matures in 25 years. Look what happens to the bond prices when market rates change:
|
|
Percentage Change in the Price of an 8% |
|||||
|
|
Coupon Bond When Market Interest Rates Change |
|||||
|
Interest Rate Change |
−3% |
−2% |
−1% |
+1% |
+2% |
+3% |
|
Bond Maturity (yr) |
|
|
|
|
|
|
|
5 |
13.0% |
8.4% |
4.1% |
−3.9% |
−7.6% |
−11.1% |
|
25 |
42.3% |
25.6% |
11.7% |
−9.8% |
−18.2% |
−25.3% |
The prices of both bonds rise when interest rates fall, but the effect is much larger for the 25-year bond. Similarly, both bonds fall in value when rates rise, but the 25-year bond falls a lot more than the 5-year bond does. Such behavior is universal with all fixed-income securities and is very important. It means that if investors want to reduce their exposure to capital losses or, more to the point, to lower the price volatility in their bond holdings, then they should buy bonds with shorter maturities.
Figure 10.3 The Price Behavior of a Bond
A bond will sell at its par value so long as the prevailing market interest rate remains the same as the bond’s coupon—in this case, 10%. However, even when the market rate does not equal the coupon rate, as a bond approaches its maturity, the price of the issue moves toward its par value.
Quoting Bond Prices
Unlike stocks, the vast majority of bonds—especially corporate and municipal bonds—rarely change hands in the secondary markets. As a result, with the exception of U.S. Treasury and some agency issues, bonds are not widely quoted in the financial press, not even in the Wall Street Journal. Prices of all types of bonds are usually expressed as a percent of par, meaning that a quote of, say, 85 translates into a price of 85% of the bond’s par value or $850 for a bond with a $1,000 par value (most corporate and municipal bonds have $1,000 par values). Also, the price of any bond depends on its coupon and maturity, so those two features are always a part of any price quote.
In the corporate and municipal markets, bond prices are expressed in decimals, using three places to the right of the decimal. Thus, a quote of 87.562, as a percent of a $1,000 par bond, converts to a price of $875.62. Similarly, a quote of 121.683 translates into a price of $1,216.83. In contrast, U.S. Treasury and agency bond quotes are stated in thirty-seconds of a point (where 1 point equals $10). For example, a website might list the price of a T-bond at 94:16. Translated, that means the bond is priced at 94 16/32, or 94.5% of par—in other words, at $945.00. With government bonds, the figures to the right of the colon show the number of thirty-seconds embedded in the price. Consider another bond that’s trading at 141:08. This bond is being priced at 141 8/32, or 141.25% of par. Thus, the price of this bond in dollars is $1,412.50.
Call Features—Let the Buyer Beware!
Consider the following situation: You’ve just made an investment in a newly issued 25-year bond with a high coupon rate. Now you can sit back and let the cash flow in, right? Well, perhaps. Certainly, that will happen for the first several years. But if market interest rates drop, it’s also likely that you’ll receive a notice from the issuer that the bond is being called—that the issue is being retired before its maturity date. There’s really nothing you can do but turn in the bond and invest your money elsewhere. Every bond is issued with a call feature , which stipulates whether and under what conditions a bond can be called in for retirement prior to maturity.
Basically, there are three types of call features:
1. A bond can be freely callable, which means the issuer can prematurely retire the bond at any time.
2. A bond can be noncallable, which means the issuer is prohibited from retiring the bond prior to maturity.
3. The issue could carry a deferred call, which means the issue cannot be called until after a certain length of time has passed from the date of issue. In essence, the issue is noncallable during the deferment period and then becomes freely callable thereafter.
Call features allow bond issuers to take advantage of declines in market interest rates. Companies usually call outstanding bonds paying high rates and then reissue new bonds at lower rates. In other words, call features work for the benefit of the issuers. When a bond is called, the net result is that the investor is left with a much lower rate of return than would be the case if the bond could not be called.
Investors who find their bonds called away from them often receive a small amount of extra compensation called the call premium . If the issue is called, the issuer will pay the call premium to investors, along with the issue’s par value. The sum of the par value plus the call premium represents the issue’s call price . This is the amount the issuer must pay to retire the bond prematurely. Call premiums often amount to as much as a year’s worth of interest payments, at least if the bond is called at the earliest possible date. As the bond gets closer to maturity, the call premium gets smaller. Using this rule, the initial call price of a 5% bond could be as high as $1,050, where $50 represents the call premium.
In addition to call features, some bonds may carry refunding provisions . These are much like call features except that they prohibit the premature retirement of an issue from the proceeds of a lower-coupon bond. For example, a bond could come out as freely callable but nonrefundable for five years. In this case, brokers would probably sell the bond as a deferred refunding issue, with little or nothing said about its call feature. The distinction between nonrefundable and noncallable is important. A nonrefundable bond can still be called at any time as long as the money that the company uses to retire the bond prematurely comes from a source other than a new, lower-coupon bond issue.
Sinking Funds
Another provision that’s important to investors is the sinking fund , which stipulates how the issuer will pay off the bond over time. This provision applies only to term bonds, of course, because serial issues already have a predetermined repayment schedule. Not all (term) bonds have sinking-fund requirements, but for those that do, the sinking fund specifies the annual repayment schedule that will be used to pay off the issue. It indicates how much principal will be retired each year.
Sinking-fund requirements generally begin one to five years after the date of issue and continue annually thereafter until all or most of the issue is paid off. Any amount not repaid (which might equal 10% to 25% of the issue) would then be retired with a single “balloon” payment at maturity. Unlike a call or refunding provision, the issuer generally does not have to pay a call premium with sinking-fund calls. Instead, the bonds are normally called at par for sinking-fund purposes.
There’s another difference between sinking-fund provisions and call or refunding features. That is, whereas a call or refunding provision gives the issuer the right to retire a bond prematurely, a sinking-fund provision obligates the issuer to pay off the bond systematically over time. The issuer has no choice. It must make sinking-fund payments in a prompt and timely fashion or run the risk of being in default.
Secured or Unsecured Debt
A single issuer may have a number of different bonds outstanding at any given time. In addition to coupon and maturity, one bond can be differentiated from another by the type of collateral behind the issue. Bonds can be either junior or senior. Senior bonds are secured obligations, which are backed by a legal claim on some specific property of the issuer. Such issues include the following:
· Mortgage bonds , which are secured by real estate
· Collateral trust bonds , which are backed by financial assets owned by the issuer but held in trust by a third party
· Equipment trust certificates , which are secured by specific pieces of equipment (e.g., boxcars and airplanes) and are popular with railroads and airlines
· First and refunding bonds , which are basically a combination of first mortgage and junior lien bonds (i.e., the bonds are secured in part by a first mortgage on some of the issuer’s property and in part by second or third mortgages on other properties).
Note that first and refunding bonds are less secure than, and should not be confused with, straight first-mortgage bonds.
Junior bonds , on the other hand, are backed only by the promise of the issuer to pay interest and principal on a timely basis. There are several classes of unsecured bonds, the most popular of which is a debenture . For example, a major company like Hewlett-Packard could issue $500 million worth of 20-year debenture bonds. Being a debenture, the bond would be totally unsecured, meaning there is no collateral backing up the obligation, other than the good name of the issuer. For that reason, highly regarded firms have no trouble selling billion-dollar debenture bond issues at competitive rates.
Subordinated debentures can also be found in the market. These issues have a claim on income secondary to other debenture bonds. Income bonds , the most junior of all bonds, are unsecured debts requiring that interest be paid only after a certain amount of income is earned. With these bonds, there is no legally binding requirement to meet interest payments on a timely or regular basis so long as a specified amount of income has not been earned. These issues are similar in many respects to revenue bonds found in the municipal market.
Bond Ratings
To many investors, an issue’s agency rating is just as important in defining the characteristics of a bond as are its coupon, maturity, and call features. Bond rating agencies are institutions that perform extensive financial analysis on companies issuing bonds to assess the credit risk associated with a particular bond issue. The ratings that these agencies publish indicate the amount of credit risk embedded in a bond, and they are widely used by fixed-income investors. Bond ratings are essentially the grades that rating agencies give to new bond issues, where the letter grade corresponds to a certain level of credit risk. Ratings are an important part of the municipal and corporate bond markets, where issues are regularly evaluated and rated by one or more of the rating agencies. The three largest and best-known rating agencies are Moody’s, Standard & Poor’s, and Fitch.
How Ratings Work
When a new bond issue comes to the market, a staff of professional credit analysts from the rating agencies estimates the likelihood that the bond issuer will default on its obligations to pay principal and interest. The rating agency studies the financial records of the issuing organization and assesses its prospects. As you might expect, the firm’s financial strength and stability are very important in determining the appropriate bond rating. Although there is far more to setting a rating than cranking out a few financial ratios, a strong relationship does exist between the operating results and financial condition of the firm and the rating its bonds receive. Generally, higher ratings are associated with more profitable companies that rely less on debt as a form of financing, are more liquid, have stronger cash flows, and have no trouble servicing their debt in a prompt and timely fashion.
Table 10.2 lists the various ratings assigned to bonds by two of the three major services. In addition to the standard rating categories noted in the table, Moody’s uses numerical modifiers (1, 2, or 3) on bonds rated Aa to Caa, while S&P uses plus (+) and minus (−) signs on the same rating classes to show relative standing within a major
Table 10.2 Bond Ratings
(Source: Moody’s Investors Service and Standard & Poor’s Ratings Services.)
|
Moody’s |
S&P |
Definition |
|
Aaa |
AAA |
High-grade investment bonds. The highest rating assigned, denoting extremely strong capacity to pay principal and interest. Often called “gilt-edge” securities. |
|
Aa |
AA |
High-grade investment bonds. High quality but rated lower primarily because the margins of protection are not quite as strong as AAA bonds. |
|
A |
A |
Medium-grade investment bonds. Many favorable investment attributes, but elements may be present that suggest susceptibility to adverse economic changes. |
|
Baa |
BBB |
Medium-grade investment bonds. Adequate capacity to pay principal and interest but possibly lacking certain protective elements against adverse economic conditions. |
|
Ba |
BB |
Speculative issues. Only moderate protection of principal and interest in varied economic times. |
|
B |
B |
Speculative issues. Generally lacking desirable characteristics of investment bonds. Assurance of principal and interest may be small. |
|
Caa |
CCC |
Default. Poor-quality issues that may be in default or in danger of default. |
|
Ca |
CC |
Default. Highly speculative issues, often in default or possessing other market shortcomings. |
|
C |
|
Default. These issues may be regarded as extremely poor in investment quality. |
|
|
C |
Default. Rating given to income bonds on which no interest is paid. |
|
|
D |
Default. Issues actually in default, with principal or interest in arrears. |
rating category. For example, A+ (or A1) means a strong, high A rating, whereas A− (or A3) indicates that the issue is on the low end of the A rating scale.
Note that the top four ratings (Aaa through Baa, or AAA through BBB) designate investment-grade bonds . Such ratings are highly coveted by issuers because they indicate financially strong, well-run companies. Companies and governmental bodies that want to raise money by issuing bonds save money if they have an investment-grade rating because investors will accept lower yields on these bonds. Bonds with below-investment-grade ratings are called high-yield bonds , or junk bonds . The issuers of these bonds generally lack the financial strength that backs investment-grade issues. Most of the time, when the rating agencies assign ratings to a particular bond issue, their ratings agree. Sometimes, however, an issue carries different ratings from different rating agencies, and in that case the bond issue is said to have a split rating . For example, an issue might be rated Aa by Moody’s but A or A+ by S&P. These split ratings are viewed simply as “shading” the quality of an issue one way or another.
Also, just because a bond receives a certain rating at the time of issue doesn’t mean it will keep that rating for the rest of its life. Ratings change as the financial condition of the issuer changes, as the example involving Automated Data Processing at the start of this chapter illustrates. In fact, all rated issues are reviewed regularly to ensure that the assigned rating is still valid. Many issues do carry a single rating to maturity, but it is not uncommon for ratings to be revised up or down, and the market responds to rating revisions by adjusting bond yields accordingly. For example, an upward revision (e.g., from A to AA) causes the market yield on the bond to drop, reflecting the bond’s improved quality. By the same token, if a company’s financial condition deteriorates, ratings on its bonds may be downgraded. In fact, there is a special name given to junk bonds that once had investment-grade ratings—fallen angels. Although it may appear that the firm is receiving the rating, it is actually the issue that receives it. As a result, a firm’s different issues can have different ratings. The senior securities, for example, might carry one rating and the junior issues another, lower rating.
Investor Facts
Some Big-Name Junk Junk bonds are low-rated debt securities that carry a relatively high risk of default. You’d expect to find a bunch of no-name companies issuing junk bonds, but that’s not always the case. Here’s a list of some of the familiar companies (and their Moody’s rating) whose bonds were rated as junk in the summer of 2015:
· General Motors (Ba)
· JC Penney (Ba1)
· Sprint Corp (B)
· Toys R Us (Caa)
· Sears (Caa)
· Clear Channel Communications (Ca)
These fallen angels are still promptly servicing their debt. The reason they’ve been slapped with low ratings is that their operating earnings lack the quality and consistency of high-grade bonds. Why invest in these bonds? For their high returns!
What Ratings Mean
Investors pay close attention to agency ratings because ratings are tied to bond yields. Specifically, the higher the rating the lower the yield, other things being equal. For example, whereas an A-rated bond might offer a 6.5% yield, a comparable AAA issue would probably yield something like 6%. Furthermore, a bond’s rating has an impact on how sensitive its price is to interest rate movements as well as to changes in the company’s financial performance. Junk bond prices tend to respond more when a company’s financial position improves (or deteriorates) than prices of investment-grade bonds do.
Perhaps most important, bond ratings serve to relieve individual investors of the drudgery of evaluating the investment quality of an issue on their own. Large institutional investors often have their own staff of credit analysts who independently assess the creditworthiness of various corporate and municipal issuers. Individual investors, in contrast, have little if anything to gain from conducting their own credit analysis. After all, credit analysis is time-consuming and costly, and it demands a good deal more expertise than the average individual investor possesses. Two words of caution are in order, however. First, bear in mind that bond ratings are intended to measure only an issue’s default risk, which has no bearing whatsoever on an issue’s exposure to interest rate risk. Thus, if interest rates increase, even the highest-quality issues go down in price, subjecting investors to capital losses. Second, ratings agencies do make mistakes, and during the recent financial crisis, their mistakes made headlines.
Famous Failures in Finance Rating Agencies Miss a Big One
Mortgage-backed securities, essentially debt instruments with returns that depended upon payments on an underlying pool of residential real estate mortgages, played a central role in the financial crisis that began in 2007 and the Great Recession that followed. Moody’s and Standard & Poor’s provided ratings on these instruments, just as they did with corporate bonds. Rating these securities was much more complex than rating corporate bonds for a variety of reasons, among them the fact that rating agencies knew relatively little about the creditworthiness of the individual homeowners whose mortgages were in the pool. The rating agencies gave many mortgage-backed securities investment-grade ratings, and those ratings prompted investors of all kinds, including large financial institutions, to pour money into those assets. As real estate prices began to decline, the values of “toxic” mortgage-backed securities plummeted. That led to the failure of Lehman Brothers and bailouts of other large financial institutions.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 10.4 Can issue characteristics (such as coupon and call features) affect the yield and price behavior of bonds? Explain.
2. 10.5 What is the difference between a call feature and a sinking-fund provision? Briefly describe the three types of call features. Can a bond be freely callable but nonrefundable?
3. 10.6 What is the difference between a premium bond and a discount bond? What three attributes are most important in determining an issue’s price volatility?
4. 10.7 Bonds are said to be quoted “as a percent of par.” What does that mean? What is one point worth in the bond market?
5. 10.8 What are bond ratings, and how can they affect investor returns? What are split ratings?
6. 10.9 From the perspective of an individual investor, what good are bond ratings? Do bond ratings indicate the amount of market risk embedded in a bond? Explain.
The Market for Debt Securities
1. LG 4
2. LG 5
Thus far, our discussion has dealt with basic bond features. We now shift our attention to a review of the market in which these securities are traded. To begin with, the bond market is chiefly over-the-counter in nature, as listed bonds represent only a small portion of total outstanding obligations. In addition, this market is far more stable than the stock market. Indeed, although interest rates—and therefore bond prices—do move up and down over time, when bond price activity is measured daily, it is remarkably stable. Two other things that stand out about the bond market are its size and its growth rate. From a $250 billion market in 1950, it has grown to the point where, at the end of 2014, the amount of bonds outstanding in the United States totaled $39 trillion! That makes the U.S. bond market quite a bit larger than the size of the U.S. stock market.
Here’s what the U.S. bond market looked like at the end of 2014:
|
|
Amount Outstanding ($ trillions) |
|
Treasury bonds |
12.5 |
|
Agency bonds |
2.0 |
|
Municipal bonds |
3.7 |
|
Corporate bonds |
7.8 |
|
Mortgage-backed bonds |
8.7 |
|
Asset-backed bonds |
1.3 |
|
Other |
2.9 |
|
Total |
39.0 |
|
(Source: Securities Industry and Financial Markets Association, “U.S. Bond Market Issuance and Outstanding,” 2014.) |
Major Market Segments
There are bonds available in today’s market to meet almost any investment objective and to suit just about any type of investor. As a matter of convenience, the domestic bond market is normally separated into four major segments, according to type of issuer: Treasury, agency, municipal, and corporate. As we shall see, each sector has developed its own features, as well as its own trading characteristics.
An Advisor’s Perspective
Bill Harris Founder, WH Cornerstone Investments
“For us there are really three categories: treasuries, municipals, and corporate bonds.”
MyFinanceLab
Treasury Bonds
“Treasuries” (or “governments,” as they are sometimes called) are a dominant force in the fixed-income market. If not the most popular type of bond, they certainly are the best known. In addition to T-bills (a popular short-term debt security), the U.S. Treasury issues notes and bonds. It also issues inflation-indexed securities.
More about Treasury Bills
All Treasury obligations are of the highest quality because they are all backed by the “full faith and credit” of the U.S. government. This backing, along with their liquidity, makes them very popular with individual and institutional investors both in the United States and abroad. Indeed, U.S. Treasury securities are traded in all the major markets of the world, from New York to London to Sydney and Tokyo.
Treasury notes are issued with maturities of 2, 3, 5, 7, and 10 years, whereas Treasury bonds carry 30-year maturities. All Treasury notes and bonds pay interest semiannually. Interest income from these securities is subject to normal federal income tax but is exempt from state and local taxes. The Treasury today issues only noncallable securities; the last time it issued callable debt was in 1984. It issues its securities at regularly scheduled auctions, the results of which are widely reported by the financial media (see Figure 10.4 ). The Treasury establishes the initial yields and coupons on the securities it issues through this auction process.
Investors participating in an auction have a choice of two bidding options—competitive and noncompetitive. Investors who place competitive bids specify the yield that they are willing to accept (and hence, the price that they are willing to pay). Investors submitting competitive bids may be allocated securities in any given auction depending on how their bids compare to bids submitted by others. In a noncompetitive bid, investors agree to accept securities at the yield established in the auction. To conduct an auction, the Treasury first accepts all noncompetitive bids and then accepts competitive bids in ascending order in terms of their yield (i.e., descending order in terms of price) until the quantity of accepted bids reaches the full offering amount. All bidders receive the same yield as the highest accepted bid.
Figure 10.4 Auction Results for a 30-Year Treasury Bond
Treasury auctions are closely followed by the financial media. The number of competitive bids submitted generally far exceeds the number accepted; in this case only 45% of the competitive bids were accepted and issued bonds.
(Source: Department of the Treasury, Bureau of Public Debt, Washington, DC 20239, May 14, 2015.)
Famous Failures in Finance Yield Spreads Approach Records
One interesting indicator of the state of the economy is the yield spread between low-risk government bonds and high-risk junk bonds issued by corporations. During the 1990–1991 recession, this yield spread set a record of 10.5%. That means that if investors require a 3% interest rate on government bonds, then they will demand a 13.5% rate on the most risky corporate bonds. In 2008 the junk bond credit spread widened again, reaching a new high of 14.68%, eclipsing the 1990s record. Interestingly, both of these episodes corresponded with a major crisis in the investment banking industry. In 1990 it was the failure of Drexel Burnham Lambert and the fall of junk-bond king Michael Milken that led to wide spreads on junk bonds. In 2008 the yield spreads reflected investors’ concerns following the 2007 failure of Lehman Brothers and bailouts of several other large financial institutions. In part due to the growing crisis in Europe, junk bond credit spreads began climbing again in 2011. Although the spread topped 7% in October of 2011, as of early 2015 it has remained below this level.
(Source: New York University Salomon Center and FRED Economic Data, St. Louis Fed.)
Inflation-Protected Securities
The newest form of Treasury security (first issued in 1997) is the Treasury Inflation-Protected Securities , also known as TIPS. They are issued with 5-, 10-, and 30-year maturities, and they pay interest semiannually. They offer investors the opportunity to stay ahead of inflation by periodically adjusting their returns for any inflation that has occurred. The adjustment occurs through the bond’s principal or par value. That is, the par value rises over time at a pace that matches the inflation rate. Coupon payments rise, too, because the coupon rate is paid on the inflation-adjusted principal.
Example
Suppose you purchased a 30-year TIPS with a par value of $1,000 and a 2% coupon rate. If there is no inflation, you expect to receive $20 in interest per year (i.e.,$1,000×0.020)(i.e., $1,000 × 0.020), paid in two $10 semiannual installments. However, one year after you purchased the bond, inflation has caused the prices of goods and services to increase by 3%. The par value of your bond will increase by 3% to $1,030, and your interest payments will rise to $20.60 per year (i.e.,$1,030×0.02)(i.e., $1,030 × 0.02). Notice that your interest payments have increased by 3%, thus compensating you for the inflation that occurred while you held the bond.
Because this type of bond offers payments that automatically adjust with inflation, investors do not have to guess what the inflation rate will be over the bond’s life. In other words, TIPS eliminate purchasing power risk. Because they are less risky than ordinary bonds, TIPS generally offer lower returns than ordinary Treasury bonds do.
Agency Bonds
Agency bonds are debt securities issued by various agencies and organizations of the U.S. government, such as the Federal Home Loan Bank, the Federal Farm Credit Systems, the Small Business Administration, the Student Loan Marketing Association, and the Federal National Mortgage Association. Although these securities are the closest things to Treasuries, they are not obligations of the U.S. Treasury and technically should not be considered the same as Treasury bonds. Even so, they are very high-quality securities that have almost no risk of default. In spite of the similar default risk, however, these securities usually provide yields that are slightly above the market rates for Treasuries. Thus, they offer a way to increase returns with little or no real difference in risk.
Famous Failures in Finance Implicit Guarantee Becomes Explicit
Debt securities issued by agencies such as the Federal National Mortgage Association (Fannie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac) have generally had an implicit guarantee from the federal government, meaning that investors believed that the government would not allow a default on any of these instruments even if they were not “officially” backed by the full faith and credit of the U.S. government as Treasury bills, notes, and bonds are. In 2007 as residential mortgage defaults began to rise, Fannie Mae and Freddie Mac came under severe financial distress. On September 7, 2008, the federal government effectively took over these institutions, injecting $100 billion of new capital into each to stabilize them and to reassure investors that these giants of the mortgage industry, who held or guaranteed about $5.5 trillion in residential mortgage debt, would not disappear. Although the capital infusion helped initially, investor confidence in the two government-sponsored enterprises was rocked again on August 8, 2011, when their credit ratings were downgraded. Standard & Poor’s said that the downgrade reflected their “direct reliance on the U.S. government,” which had seen its own credit rating downgraded three days earlier.
There are basically two types of agency issues: government-sponsored and federal agencies. Six government-sponsored organizations and more than two dozen federal agencies offer agency bonds. To overcome some of the problems in the marketing of many relatively small federal agency securities, Congress established the Federal Financing Bank to consolidate the financing activities of all federal agencies. (As a rule, the generic term agency is used to denote both government-sponsored and federal agency obligations.)
Table 10.3 presents selected characteristics of some of the more popular agency bonds. As the list of issuers shows, most of the government agencies support either agriculture or housing. Although agency issues are not direct liabilities of the U.S. government, a few of them do carry government guarantees and therefore represent the full faith and credit of the U.S. Treasury. Even those issues that do not carry such guarantees are viewed as moral obligations of the U.S. government, implying it’s highly unlikely that Congress would allow one of them to default. Agency issues are normally noncallable or carry lengthy call deferment features.
Municipal Bonds
Municipal bonds (also called munis) are issued by states, counties, cities, and other political subdivisions (such as school districts and water and sewer districts). This is a $3.7 trillion market today, and it’s the only segment of the bond market where the individual investor plays a major role: More than 40% of municipal bonds are directly held by individuals. These bonds are often issued as serial obligations, which means the issue is broken into a series of smaller bonds, each with its own maturity date and coupon.
Municipal bonds (“munis”) are brought to the market as either general obligation or revenue bonds. General obligation bonds are backed by the full faith, credit, and taxing power of the issuer. Revenue bonds , in contrast, are serviced by the income generated from specific income-producing projects (e.g., toll roads). The vast majority of munis today come out as revenue bonds, accounting for about 75% to 80% of the new-issue volume. Municipal bonds are customarily issued in $5,000 denominations.
The distinction between a general obligation bond and a revenue bond is important because the issuer of a revenue bond is obligated to pay principal and interest only if a sufficient level of revenue is generated. If the funds aren’t there, the issuer does not have to make payment on the bond. General obligation bonds, however, must be
Table 10.3 Characteristics of Some Popular Agency Issues
|
|
|
|
Tax Status * |
||
|
Type of Issue |
Minimum Denomination |
Initial Maturity |
Federal |
State |
Local |
|
* T = taxable; E = tax-exempt. |
|||||
|
** Mortgage-backed securities. |
|||||
|
Federal Farm Credit System |
$ 1,000 |
13 months to 15 years |
T |
E |
E |
|
Federal Home Loan Bank |
$10,000 |
1 to 20 years |
T |
E |
E |
|
Federal Land Banks |
$ 1,000 |
1 to 10 years |
T |
E |
E |
|
Farmers Home Administration |
$25,000 |
1 to 25 years |
T |
T |
T |
|
Federal Housing Administration |
$50,000 |
1 to 40 years |
T |
T |
T |
|
Federal Home Loan Mortgage Corp. ** (“Freddie Mac”) |
$25,000 |
18 to 30 years |
T |
T |
T |
|
Federal National Mortgage Association ** (“Fannie Mae”) |
$25,000 |
1 to 30 years |
T |
T |
T |
|
Government National Mortgage Association ** (GNMA—“Ginnie Mae”) |
$25,000 |
12 to 40 years |
T |
T |
T |
|
Student Loan Marketing Association (“Sallie Mae”) |
$10,000 |
3 to 10 years |
T |
E |
E |
|
Tennessee Valley Authority (TVA) |
$ 1,000 |
5 to 50 years |
T |
E |
E |
|
U.S. Postal Service |
$10,000 |
25 years |
T |
E |
E |
|
Federal Financing Corp. |
$ 1,000 |
1 to 20 years |
T |
E |
E |
serviced in a timely fashion irrespective of the level of tax income generated by the municipality. Obviously, revenue bonds involve more risk than general obligations, and because of that, they provide higher yields.
Some municipal bonds are backed by municipal bond guarantees , though these have become much less common than they once were. With these guarantees, a party other than the issuer assures the bondholder that payments will be made in a timely manner. The third party, in essence, provides an additional source of collateral in the form of insurance, placed on the bond at the date of issue, which is nonrevocable over the life of the obligation. This additional collateral improves the quality of the bond. The three principal insurers are the Assured Guaranty Corp., Municipal Bond Investors Assurance Corporation, and the American Municipal Bond Assurance Corporation. These guarantors will normally insure any general obligation or revenue bond as long as it carries an S&P rating of BBB or better. Municipal bond insurance results in higher ratings and improved liquidity for these bonds, which are generally more actively traded in the secondary markets. Insured bonds are more common in the revenue market, where the insurance markedly boosts their attractiveness. That is, whereas an uninsured revenue bond lacks certainty of payment, a guaranteed issue is very much like a general obligation bond because the investor knows that principal and interest payments will be made on time.
An Advisor’s Perspective
Ryan McKeown Senior VP–Financial Advisor, Wealth Enhancement Group
“The most popular investments with tax advantages are municipal bonds.”
MyFinanceLab
Tax Advantages
The most important unique feature of municipal securities is that, in most cases, their interest income is exempt from federal income taxes. That’s why these issues are known as tax-free, or tax-exempt, bonds. Normally, municipal bonds are also exempt from state and local taxes in the state in which they were issued. For example, a California issue is free of California tax if the bondholder lives in California, but its interest income is subject to state tax if the investor resides in Arizona. Note that capital gains on municipal bonds are not exempt from taxes.
Individual investors are the biggest buyers of municipal bonds, and the tax-free interest that these bonds offer is a major draw. When investors think about buying municipal bonds, they compare the tax-free yield offered by the municipal bond and compare it to the after-tax yield that they could earn on a similar taxable bond.
Example
Suppose you are in the 25% tax bracket, so each dollar of interest that you earn triggers $0.25 in taxes, allowing you to keep $0.75. Suppose a tax-free municipal bond offers a yield of 6%. What yield would a taxable bond have to offer to give you the same 6% return after taxes that you could earn on the municipal bond? The after-tax yield on a taxable bond is just the stated yield times one minus the tax rate:
After-taxyield = Yield on taxable bond × (1−tax rate)After-tax yield = Yield on taxable bond × (1−tax rate)
If you desire an after-tax yield of 6% (because that’s what the municipal bond offers) and your tax rate is 25%, then we can calculate the yield that you would need to earn on a taxable bond as follows:
0.06=Yieldontaxablebond×(1−0.25)Yieldontaxablebond=0.06÷(1−0.25)=0.080.06=Yield on taxable bond × (1−0.25) Yield on taxable bond = 0.06÷(1−0.25)=0.08
If the taxable bond offers 8% and the municipal bond offers 6%, then you are essentially indifferent to the choice between the two securities as long as they are similar in terms of risk (and not counting any tax benefit on your state income taxes). Notice that this value is highlighted in Table 10.4 .
Table 10.4 shows how the yield that a taxable bond would have to offer to remain competitive with a municipal bond depends on the investor’s marginal tax rate. Intuitively, the tax break that municipal bonds offer is more appealing to investors in higher tax brackets who face higher marginal tax rates. For these investors, taxable bonds are not very attractive unless their yields are much higher than the yields on municipal bonds. To put it another way, investors facing high tax rates will gladly purchase municipal bonds even if they offer yields that are somewhat lower than yields on taxable bonds. For example, Table 10.4 shows that an investor in the 10% tax bracket would be indifferent to the choice between a municipal bond offering a 6% yield and a taxable bond offering a slightly higher 6.67% yield. In contrast, an investor in the 35% tax bracket would prefer the 6% municipal bond unless the yield on the taxable bond was much higher at 9.23%. Not surprisingly, investors subject to high tax rates are the main purchasers of municipal bonds. Individuals in lower tax brackets generally do not
Excel@Investing
Table 10.4 Taxable Equivalent Yields for Various Tax-Exempt Returns
|
|
Tax-Free Yield |
|||||
|
Federal Tax Bracket |
5% |
6% |
7% |
8% |
9% |
10% |
|
10% |
5.56% |
6.67% |
7.78% |
8.89% |
10.00% |
11.11% |
|
15% |
5.88% |
7.06% |
8.24% |
9.41% |
10.59% |
11.76% |
|
25% |
6.67% |
8.00% |
9.33% |
10.67% |
12.00% |
13.33% |
|
28% |
6.94% |
8.33% |
9.72% |
11.11% |
12.50% |
13.89% |
|
33% |
7.46% |
8.96% |
10.45% |
11.94% |
13.43% |
14.93% |
|
35% |
7.69% |
9.23% |
10.77% |
12.31% |
13.85% |
15.38% |
|
39.6% |
8.28% |
9.93% |
11.59% |
13.25% |
14.90% |
16.56% |
invest as heavily in municipal bonds because for them, the higher yield on taxable bonds more than offsets the benefit of earning tax-free income. The favorable tax status given to municipal bonds allows state and local governments to borrow money at lower rates than they would otherwise be able to obtain in the market.
Taxable Equivalent Yields
As you can see from the previous example and from Table 10.4 , it is possible to determine the return that a fully taxable bond would have to provide in order to match the return provided by a tax-free bond. The taxable yield that is equivalent to a municipal bond’s lower, tax-free yield is called the municipal’s taxable equivalent yield . The taxable equivalent yield allows an investor to quickly compare the yield on a municipal bond with the yield offered by any number of taxable issues. The following formula shows how to calculate the taxable equivalent yield given the yield on the municipal bond and the investor’s tax rate.
Taxable equivalent yield = Yield on municipal bond1−Marginal federal tax rateTaxable equivalent yield = Yield on municipal bond1−Marginal federal tax rateEquation10.1
For example, if a municipal offered a yield of 6.5%, then an individual in the 35% tax bracket would have to find a fully taxable bond with a yield of 10.0% (i.e., 6.5%÷(1−0.35)=10.0%6.5%÷(1−0.35)=10.0%) to reap the same after-tax returns as the municipal.
Note, however, that Equation 10.1 considers federal income taxes only. As a result, the computed taxable equivalent yield applies only to certain situations: (1) to states that have no state income tax; (2) to the investor who is looking at an out-of-state bond (which would be taxable by the investor’s state of residence); or (3) to the investor who is comparing a municipal bond to a Treasury (or agency) bond—in which case both the Treasury and the municipal bonds are free from state income tax; (4) to taxpayers with income levels low enough such that they are not subject to the 3.8% tax on net investment income that was passed as part of the Affordable Care Act. Under any of these conditions, the only tax that’s relevant is federal income tax, so using Equation 10.1 is appropriate.
But what if you are comparing an in-state bond to a corporate bond? In this case, the in-state bond would be free from both federal and state taxes, but the corporate bond would not. As a result, Equation 10.1 would not calculate the correct taxable equivalent yield. Instead, you should use a form of the equivalent yield formula that considers both federal and state income taxes:
Taxable equivalent yield for both federal and state taxes = Municipalbondyield1−[Federaltaxrate+Statetaxrate(1−Federaltaxrate)]Taxable equivalent yield for both federal and state taxes = Municipal bond yield1−[Federal tax rate+State tax rate (1−Federal tax rate)]Equation10.2
Notice that the inclusion of state taxes means that the denominator of Equation 10.2 is slightly smaller than the denominator of Equation 10.1 , which in turn means that the taxable equivalent yield will be higher with state taxes as part of the analysis. Intuitively this makes sense because if municipal bonds offer tax advantages at both the federal and state levels, then taxable yields must be even higher to remain competitive.
Example
Suppose your marginal federal tax rate is 35% and your state income tax rate is 3%. There is a municipal bond issued by your state that offers a yield of 6.305%. According to Equation 10.2 , the taxable-equivalent yield is 10%:
0.063051−[0.35+0.03(1−0.35)]=0.100.063051−[0.35+0.03(1−0.35)]=0.10
Just to confirm that this is correct, suppose you purchased a $1,000 bond paying a 10% coupon rate. In the first year, you would receive $100 in interest income that is fully taxable at both the state and federal levels. Remember that taxes paid to state governments may be deducted from income before you pay federal taxes. How much of the $100 coupon payment will you have to pay in combined federal and state taxes?
|
Income |
$100.00 |
|
State taxes (3%) |
−$3.00 |
|
Taxable income (federal) |
$97.00 |
|
Federal taxes (35%) |
−$33.95 |
|
Net |
$ 63.05 |
After paying $3 in state taxes and $33.95 in federal taxes, you get to keep $63.05 of the bond’s $100 coupon payment. Given that you paid $1,000 for the bond, your return is 6.305%. In other words, as you found by using Equation 10.2 , a 6.305% yield on a tax-free bond is equivalent to a 10% yield on a taxable bond.
Notice that if there had been no state tax in this example, the taxable equivalent yield would have been 9.7%. That’s not a huge difference, but the difference would be higher for a higher state tax rate, and some U.S. states have tax rates as high as 11%.
Corporate Bonds
Corporations are the major nongovernmental issuers of bonds. The market for corporate bonds is customarily subdivided into four segments based on the types of companies that issue bonds: industrials (the most diverse of the groups), public utilities (the dominant group in terms of volume of new issues), transportation, and financial services (e.g., banks, finance companies). In the corporate sector of the bond market investors can find bonds from high-quality AAA-rated issues to junk bonds in or near default, and there is also a wide assortment of bonds with many different features. These range from first-mortgage obligations to convertible bonds (which we’ll examine later in this chapter), debentures, subordinated debentures, senior subordinated issues, capital notes (a type of unsecured debt issued by banks and other financial institutions), and income bonds. Companies pay interest on corporate bonds semiannually, and sinking funds are fairly common. The bonds usually come in $1,000 denominations and are issued on a term basis with a single maturity date of 10 years or more. Many corporate bonds, especially the longer ones, carry call deferment provisions that prohibit prepayment for the first 5 to 10 years. Corporate issues are popular with individuals because of the steady, predictable income that they provide.
Investor Facts
A Very Long Caterpillar Caterpillar Inc., took advantage of historically low interest rates by selling bonds in May 2014. Caterpillar’s bonds promised a yield of about 4.8%, which was not remarkable at the time. What was remarkable about their bond issue was its maturity. Caterpillar’s bonds were set to mature in 2064, 50 years after they were issued. Even that maturity wasn’t the company’s longest. In 1997 Caterpillar issued bonds that it did not plan to retire until 2097, 100 years later.
(Source: Mike Cherney and Vipal Monga, “Caterpillar Sells 50-Year Bonds,” May 5, 2014, http://www .wsj.com/articles/SB10001424052702304831304579544304288532382 , accessed July 13, 2015.)
While most corporate issues fit the general description above, one that does not is the equipment trust certificate, a security issued by railroads, airlines, and other transportation concerns. The proceeds from equipment trust certificates are used to purchase equipment (e.g., jumbo jets and railroad engines) that serves as the collateral for the issue. These bonds are usually issued in serial form and carry uniform annual installments throughout. They normally carry maturities that range up to about 15 years, with the maturity reflecting the useful life of the equipment. Despite a near-perfect payment record that dates back to pre-Depression days, these issues generally offer above-average yields to investors.
Specialty Issues
In addition to the basic bonds described above, investors can choose from a number of specialty issues—bonds that possess unusual issue characteristics. These bonds have coupon or repayment provisions that are out of the ordinary. Most of them are issued by corporations, although they are being used increasingly by other issuers as well. Four of the most actively traded specialty issues today are zero-coupon bonds, mortgage-backed securities, asset-backed securities, and high-yield junk bonds. All of these rank as some of the more popular bonds on Wall Street.
Zero-Coupon Bonds
As the name implies, zero-coupon bonds have no coupons. Rather, these securities are sold at a discount from their par values and then increase in value over time at a compound rate of return. Thus, at maturity, they are worth more than their initial cost, and this difference represents the bond’s return. Other things being equal, the cheaper the zero-coupon bond, the greater the return an investor can earn: For example, a bond with a 6% yield might cost $420, but one with a 10% yield might cost only $240.
Because they do not have coupons, these bonds do not pay interest semiannually. In fact, they pay nothing at all until the issue matures. As strange as it might seem, this feature is the main attraction of zero-coupon bonds. Because there are no coupon payments, there is no need to worry about reinvesting interest income twice a year. Instead, the rate of return on a zero-coupon bond is virtually guaranteed to be the yield that existed at the time of purchase as long as the investor holds the bond to maturity. For example, in mid-2015, U.S. Treasury zero-coupon bonds with 10-year maturities were available at yields of around 2.5%. For around $780, investors could buy a bond that would be worth $1,000 at maturity in 10 years. That 2.5% yield is a rate of return that’s locked in for the life of the issue.
The foregoing advantages notwithstanding, zeros do have some serious disadvantages. One is that if market interest rates move up, investors won’t be able to participate in the higher return. (They’ll have no interest income to reinvest.) In addition, zero-coupon bonds are subject to tremendous price volatility. If market rates climb, investors will experience a sizable capital loss as the prices of zero-coupons plunge. (Of course, if interest rates drop, investors who hold long-term zeros will reap enormous capital gains.) A final disadvantage is that the IRS has ruled that zero-coupon bondholders must pay tax on interest as it accrues, even though investors holding these bonds don’t actually receive interest payments.
Zeros are issued by corporations, municipalities, and federal agencies. Actually, the Treasury does not issue zero-coupon bonds. Instead, it allows government securities dealers to sell regular coupon-bearing notes and bonds in the form of zero-coupon securities known as Treasury strips . Essentially, the interest and principal payments are stripped from a Treasury bond and then sold separately as zero-coupon bonds. For example, a 10-year Treasury note has 20 semiannual interest payments, plus 1 principal payment. These 21 cash flows can be sold as 21 different zero-coupon securities, with maturities that range from 6 months to 10 years. The minimum par value needed to strip a Treasury note or bond is $100 and any par value to be stripped above $100 must be in a multiple of $100. Treasury strips with the same maturity are often bundled and sold in minimum denominations (par values) of $10,000. Because there’s an active secondary market for Treasury strips, investors can get in and out of these securities with ease just about anytime they want. Strips offer the maximum in issue quality, a wide array of maturities, and an active secondary market—all of which explains why they are so popular.
Mortgage-Backed Securities
Simply put, a mortgage-backed bond is a debt issue that is secured by a pool of residential mortgages. An issuer, such as the Government National Mortgage Association (GNMA), puts together a pool of home mortgages and then issues securities in the amount of the total mortgage pool. These securities, also known as pass-through securities or participation certificates, are usually sold in minimum denominations of $25,000. Although their maturities can go out as far as 30 years, the average life is generally much shorter (perhaps as short as 8 years) because many of the mortgages are paid off early.
As an investor in one of these securities, you hold an undivided interest in the pool of mortgages. When a homeowner makes a monthly mortgage payment, that payment is essentially passed through to you, the bondholder, to pay off the mortgage-backed bond you hold. Although these securities come with normal coupons, the interest is paid monthly rather than semiannually. Actually, the monthly payments received by bondholders are, like mortgage payments, made up of both principal and interest. Because the principal portion of the payment represents return of capital, it is considered tax-free. The interest portion, however, is subject to ordinary state and federal income taxes.
Mortgage-backed securities (MBSs) are issued primarily by three federal agencies. Although there are some state and private issuers (mainly big banks and S&Ls), agency issues dominate the market and account for 90% to 95% of the activity. The major agency issuers of mortgage-backed securities (MBSs) are:
· Government National Mortgage Association (GNMA). Known as Ginnie Mae, it is the oldest and largest issuer of MBSs.
· Federal Home Loan Mortgage Corporation (FHLMC). Known as Freddie Mac, it was the first to issue pools containing conventional mortgages.
· Federal National Mortgage Association (FNMA). Known as Fannie Mae, it’s the leader in marketing seasoned/older mortgages.
One feature of mortgage-backed securities is that they are self-liquidating investments; that is, a portion of the monthly cash flow to the investor is repayment of principal. Thus, investors are always receiving back part of the original investment capital, so that at maturity, there is no big principal payment. To counter this effect, a number of mutual funds invest in mortgage-backed securities but automatically reinvest the capital/principal portion of the cash flows. Mutual fund investors therefore receive only the interest from their investments and their capital remains fully invested.
Collateralized Mortgage Obligations
Loan prepayments are another problem with mortgage-backed securities. In fact, it was in part an effort to diffuse some of the prepayment uncertainty in standard mortgage-backed securities that led to the creation of collateralized mortgage obligations (CMOs) . Normally, as pooled mortgages are prepaid, all bondholders receive a prorated share of the prepayments. The net effect is to sharply reduce the life of the bond. A CMO, in contrast, divides investors into classes (called tranches, which is French for “slice”), depending on whether they want a short-, intermediate-, or long-term investment. Although interest is paid to all bondholders, all principal payments go first to the shortest tranche until it is fully retired. Then the next class in the sequence becomes the sole recipient of principal, and so on, until the last tranche is retired.
Basically, CMOs are derivative securities created from traditional mortgage-backed bonds, which are placed in a trust. Participation in this trust is then sold to the investing public in the form of CMOs. The net effect of this transformation is that CMOs look and behave very much like any other bond. They offer predictable interest payments and have (relatively) predictable maturities. However, although they carry the same AAA ratings and implicit U.S. government backing as the mortgage-backed bonds that underlie them, CMOs represent a quantum leap in complexity. Some types of CMOs can be as simple and safe as Treasury bonds. Others can be far more volatile—and risky—than the standard MBSs they’re made from. That’s because when putting CMOs together, Wall Street performs the financial equivalent of gene splicing. Investment bankers isolate the interest and principal payments from the underlying MBSs and rechannel them to the different tranches. It’s not issue quality or risk of default that’s the problem here, but rather prepayment, or call, risk. Even if all of the bonds are ultimately paid off, investors don’t know exactly when those payments will arrive. Different types of CMO tranches have different levels of prepayment risk. The overall risk in a CMO cannot, of course, exceed that of the underlying mortgage-backed bonds, so in order for there to be some tranches with very little (or no) prepayment risk, others have to endure a lot more. The net effect is that while some CMO tranches are low in risk, others are loaded with it.
Investors discovered just how complex and how risky these securities could be as the financial crisis unfolded in 2007 and 2008. As homeowner defaults on residential mortgages began to rise, the values of CMOs plummeted. Trading in the secondary market dried up, so it was difficult to know what the underlying values of some CMOs really were. Investment and commercial banks that had invested heavily in these securities came under intense pressure as doubts about their solvency grew into a near panic. Everyone wanted to know which institutions held these “toxic assets” on their balance sheets and how large their losses were on these instruments. Lehman Brothers, Bear Stearns, Merrill Lynch, and many other financial institutions went bankrupt or were acquired under distress by other institutions, and the federal government poured hundreds of billions of dollars into the banking system to try to prevent total collapse.
Asset-Backed Securities
The creation of mortgage-backed securities and CMOs quickly led to the development of a new market technology—the process of securitization , whereby various lending vehicles are transformed into marketable securities, much like a mortgage-backed security. In recent years, investment bankers sold billions of dollars’ worth of pass-through securities, known as asset-backed securities (ABS) , which are backed by pools of auto loans, credit card bills, and home equity lines of credit (three of the principal types of collateral), as well as computer leases, hospital receivables, small business loans, truck rentals, and even royalty fees.
These securities, first introduced in the mid-1980s, are created when an investment bank bundles some type of debt-linked asset (such as loans or receivables) and then sells to investors—via asset-backed securities—the right to receive all or part of the future payments made on that debt. For example, GMAC, the financing arm of General Motors, is a regular issuer of collateralized auto loan securities. When it wants to get some of its car loans off its books, GMAC takes the monthly cash flow from a pool of auto loans and pledges them to a new issue of bonds, which are then sold to investors. In similar fashion, credit card receivables are regularly used as collateral for these bonds (indeed, they represent the biggest segment of the ABS market), as are home equity loans, the second-biggest type of ABS.
Investors are drawn to ABSs for a number of reasons. These securities offer relatively high yields, and they typically have short maturities, which often extend out no more than five years. A third reason that investors like ABSs is the monthly, rather than semiannual, principal/interest payments that accompany many of these securities. Also important to investors is their high credit quality. That’s due to the fact that most of these deals are backed by generous credit protection. For example, the securities are often overcollateralized: the pool of assets backing the bonds may be 25% to 50% larger than the bond issue itself. A large fraction of ABSs receive the highest credit rating possible (AAA) from the leading rating agencies.
Junk Bonds
Junk bonds (or high-yield bonds, as they’re also called) are highly speculative securities that have received low, sub-investment-grade ratings (typically Ba or B). These bonds are issued primarily by corporations and also by municipalities. Junk bonds often take the form of subordinated debentures, which means the debt is unsecured and has a low claim on assets. These bonds are called “junk” because of their high risk of default. The companies that issue them generally have excessive amounts of debt in their capital structures and their ability to service that debt is subject to considerable doubt.
Probably the most unusual type of junk bond is something called a PIK bond . PIK stands for payment in kind and means that rather than paying the bond’s coupon in cash, the issuer can make annual interest payments in the form of additional debt. This “financial printing press” usually goes on for five or six years, after which time the issuer is supposed to start making interest payments in real money.
Why would any rational investor be drawn to junk bonds? The answer is simple: They offer very high yields. Indeed, in a typical market, relative to investment-grade bonds, investors can expect to pick up anywhere from two to five percentage points in added yield. For example, in June of 2015, investors were getting roughly 6.5% yields on junk bonds, compared to just under 4% on investment-grade corporates. Obviously, such yields are available only because of the correspondingly higher exposure to risk. Junk bonds are subject to a good deal of risk, and their prices are unstable. Indeed, unlike investment-grade bonds, whose prices are closely linked to the behavior of market interest rates, junk bonds tend to behave more like stocks. As a result, the returns are highly unpredictable. Accordingly, only investors who are thoroughly familiar with the risks involved, and who are comfortable with such risk exposure, should purchase these securities.
A Global View of the Bond Market
Globalization has hit the bond market, just as it has the stock market. Foreign bonds have caught on with U.S. investors because of their high yields and attractive returns. There are risks with foreign bonds, of course, but high risk of default is not always one of them. Instead, the big risk with foreign bonds has to do with the impact that currency fluctuations can have on returns in U.S. dollars.
The United States has the world’s biggest bond market, accounting for a little less than half of the global market. Following the United States is Japan, China, and several countries in the European Union (principally Germany, Italy, and France). Together these countries account for more than 90% of the world bond market. Worldwide, various forms of government bonds (e.g., Treasuries, agencies, and munis) dominate the market.
U.S.-Pay versus Foreign-Pay Bonds
There are several ways to invest in foreign bonds. From the perspective of a U.S. investor, we can divide foreign bonds into two broad categories on the basis of the currency in which the bond is denominated: U.S.-pay (or dollar-denominated) bonds and foreign-pay (or non-dollar-denominated) bonds. All the cash flows—including purchase price, maturity value, and coupon income—from dollar-denominated foreign bonds are in U.S. dollars. The cash flows from non-dollar bonds are designated in a foreign currency, such as the euro, British pound, or Swiss franc.
Dollar-Denominated Bonds
Dollar-denominated foreign bonds are of two types: Yankee bonds and Eurodollar bonds. Yankee bonds are issued by foreign governments or corporations or by so-called supernational agencies, like the World Bank and the InterAmerican Bank. These bonds are issued and traded in the United States; they’re registered with the SEC, and all transactions are in U.S. dollars. Not surprisingly, Canadian issuers dominate the Yankee-bond market. Buying a Yankee bond is really no different from buying any other U.S. bond. These bonds are traded on U.S. exchanges and the OTC market, and because everything is in dollars, there’s no currency exchange risk to deal with. The bonds are generally very high in quality (which is not surprising, given the quality of the issuers) and offer highly competitive yields to investors.
Eurodollar bonds , in contrast, are issued and traded outside the United States. They are denominated in U.S. dollars, but they are not registered with the SEC, which means underwriters are legally prohibited from selling new issues to the U.S. public. (Only “seasoned” Eurodollar issues can be sold in this country.) The Eurodollar market today is dominated by foreign-based investors (though that is changing) and is primarily aimed at institutional investors.
Foreign-Pay Bonds
From the standpoint of U.S. investors, foreign-pay international bonds encompass all those issues denominated in a currency other than dollars. These bonds are issued and traded overseas and are not registered with the SEC. Examples are German government bonds, which are payable in euros; Japanese bonds, issued in yen; and so forth. When investors speak of foreign bonds, it’s this segment of the market that most of them have in mind.
Foreign-pay bonds are subject to changes in currency exchange rates, which can dramatically affect total returns to U.S. investors. The returns on foreign-pay bonds depend on three things: (1) the level of coupon (interest) income earned on the bonds; (2) the change in market interest rates, which determines the level of capital gains (or losses); and (3) the behavior of currency exchange rates. The first two variables are the same as those that drive U.S. bond returns. They are, of course, just as important to foreign bonds as they are to domestic bonds. Thus, if individuals are investing overseas, they still want to know what the yields are today and where they’re headed. It’s the third variable that separates the return behavior of dollar-denominated from foreign-pay bonds.
We can assess returns from foreign-pay bonds by employing the following equation:
Total return (in U.S. dollars)=[Ending value of bond in foreign currency + Amount of interest received in foreign currencyBeginning value of bond in foreign currency×Exchange rate at end of holding periodExchange rate at beginning of holding period]−1.00Total return (in U.S. dollars) = [Ending value of bond in foreign currency + Amount of interest received in foreign currencyBeginning value of bond in foreign currency×Exchange rate at end of holding periodExchange rate at beginning of holding period]−1.00Equation10.3
For example, assume a U.S. investor purchased a Swedish government bond, in large part because of the attractive 7.5% coupon it carried. If the bond was bought at par and market rates fell over the course of the year, the security itself would have provided a return in excess of 7.5% (because the decline in rates would provide some capital gains). However, if the Swedish krona (SEK) fell relative to the dollar, the total return (in U.S. dollars) could have actually ended up at a lot less than 7.5%, depending on what happened to the U.S.$/SEK exchange rate. To find out exactly how this investment performed, you could use the equation above. Like foreign stocks, foreign-pay bonds can pay off from both the behavior of the security and the behavior of the currency. That combination, in many cases, means superior returns to U.S. investors. Knowledgeable investors find these bonds attractive not only because of their competitive returns but also because of the positive diversification effects they have on bond portfolios.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 10.10 Briefly describe each of the following types of bonds: (a) Treasury bonds, (b) agency issues, (c) municipal securities, and (d) corporate bonds. Note some of the major advantages and disadvantages of each.
2. 10.11 Briefly define each of the following and note how they might be used by fixed-income investors: (a) zero-coupon bonds, (b) CMOs, (c) junk bonds, and (d) Yankee bonds.
3. 10.12 What are the special tax features of (a) Treasury securities, (b) agency issues, and (c) municipal bonds?
4. 10.13 Describe an asset-backed security (ABS) and identify some forms of collateral used with these issues. Briefly note how an ABS differs from an MBS. What is the central idea behind securitization?
5. 10.14 What’s the difference between dollar-denominated and non-dollar-denominated (foreign-pay) bonds? Briefly describe the two major types of U.S.-pay bonds. Can currency exchange rates affect the total return of U.S.-pay bonds? Of foreign-pay bonds? Explain.
Convertible Securities
1. LG 6
In addition to the many types of bonds covered in the preceding material, there is still another type of fixed-income security that merits discussion at this point—namely, convertible bonds . Issued only by corporations, convertibles are different from most other types of corporate debt because even though these securities may start out as bonds, they usually end up as shares of common stock. That is, while these securities are originally issued as bonds (or even preferred stock), they contain a provision that gives investors the option to convert their bonds into shares of the issuing firm’s stock. Convertibles are hybrid securities because they contain attributes of both debt and equity. But even though they possess the features and performance characteristics of both fixed-income and equity securities, convertibles should be viewed primarily as a form of equity. That’s because most investors commit their capital to such obligations not for the yields they provide but rather for the potential price performance of the stock side of the issue. In fact, it is always a good idea to determine whether a corporation has convertible issues outstanding whenever you are considering a common stock investment. In some circumstances, the convertible may be a better investment than the firm’s common stock. (Preferred stocks represent another type of hybrid security because they too have features and characteristics of both equity and fixed-income securities.)
Convertibles as Investment Outlets
Convertible securities are popular with investors because of their equity kicker —the right to convert these bonds into shares of the company’s common stock. Because of this feature, the market price of a convertible has a tendency to behave very much like the price of its underlying common stock. Convertibles are used by all types of companies and are issued either as convertible bonds (by far the most common type) or as convertible preferreds. Convertibles enable firms to raise equity capital at fairly attractive prices. That is, when a company issues stock in the normal way (by selling more shares in the company), it does so by setting a price on the stock that’s slightly below prevailing market prices. For example, it might be able to get $25 for a stock that’s currently priced in the market at, say, $27 a share. In contrast, when it issues the stock indirectly through a convertible issue, the firm can set a price that’s above the prevailing market—for example, it might be able to get $35 for the same stock. In this case, convertible bond investors will only choose to convert their bonds into shares if the market price of the shares subsequently increases above $35. As a result, the company can raise the same amount of money by issuing a lot less stock. Thus, companies issue convertibles not as a way of raising debt capital but as a way of raising equity. Because they are eventually converted into shares of the issuing company’s common stock, convertibles are usually viewed as a form of deferred equity .
Convertible bonds and convertible preferreds are both linked to the equity position of the firm, so they are usually considered interchangeable for investment purposes. Except for a few peculiarities (e.g., preferreds pay dividends rather than interest and do so quarterly rather than semiannually), convertible bonds and convertible preferreds are evaluated in much the same way. Because of their similarities, the discussion that follows will be couched largely in terms of bonds, but the information and implications apply equally well to convertible preferreds.
Convertible Notes and Bonds
Firms usually issue convertible bonds as subordinated debentures attached with the provision that within a stipulated time period, the bond may be converted into a certain number of shares of the issuing company’s common stock. Convertible notes are just like convertible bonds except that the debt portion of the security carries a shorter maturity—usually of 5 to 10 years. Other than the life of the debt, there is no real difference between the convertible notes and bonds. They’re both unsecured debt obligations, and they’re usually subordinated to other forms of debt.
Generally speaking, little or no cash is exchanged between investors and issuing firms at the time of conversion. Convertible bondholders merely trade in the convertible bond (or note) for a stipulated number of shares of common stock. For example, assume that a certain convertible security recently came to the market, and it carried the provision that each $1,000 note could be converted into shares of the issuing company’s stock at $50 a share. Thus, regardless of what happens to the market price of the stock, investors can redeem each note for 20 shares of the company’s stock ($1,000÷$50=20shares)($1,000÷$50=20 shares). So, if the company’s stock is trading in the market at, say, $65 a share at the time of conversion, then an investor could convert a $1,000 debt obligation into $1,300 worth of stock (20×$65=$1,300)(20×$65=$1,300). Not surprisingly, this conversion privilege comes at a price: the low coupon (or dividend) that convertibles usually carry. That is, when new convertible issues come to the market, their coupons are normally just a fraction of those on comparable straight (nonconvertible) bonds. Indeed, the more attractive the conversion feature, the lower the coupon.
Actually, while it’s the bondholder who has the right to convert the bond at any time, more often than not, the issuing firm initiates conversion by calling the bonds—a practice known as forced conversion . To provide the corporation with the flexibility to retire the debt and force conversion, most convertibles come out as freely callable issues, or they carry very short call deferment periods. To force conversion, the corporation would call for the retirement of the bond and give the bondholder two options: Either convert the bond into common stock or redeem it for cash at the stipulated call price (which, in the case of convertibles, contains very little call premium). As long as the convertible is called when the market value of the stock exceeds the call price of the bond (which is almost always the case), seasoned investors would never choose the second option. Instead, they would opt to convert the bond, as the firm wants them to. Then they can hold the stocks if they want to or they can sell their new shares in the market (and end up with more cash than they would have received by taking the call price). After the conversion is complete, the bonds no longer exist; instead, there is additional common stock in their place.
Conversion Privilege
The key element of any convertible is its conversion privilege , which stipulates the conditions and specific nature of the conversion feature. To begin with, it states exactly when the debenture can be converted. With some issues, there may be an initial waiting period of six months to perhaps two years after the date of issue, during which time the security cannot be converted. The conversion period then begins, and the issue can be converted at any time. The conversion period typically extends for the remaining life of the debenture, but in some instances, it may exist for only a certain number of years. This is done to give the issuing firm more control over its capital structure. If the issue has not been converted by the end of its conversion period, it reverts to a straight-debt issue with no conversion privileges.
From the investor’s point of view, the most important piece of information is the conversion price or the conversion ratio. These terms are used interchangeably and specify, either directly or indirectly, the number of shares of stock into which the bond can be converted. The conversion ratio denotes the number of common shares into which the bond can be converted. The conversion price indicates the stated value per share at which the common stock will be delivered to the investor in exchange for the bond. When you stop to think about these two measures, it becomes clear that a given conversion ratio implies a certain conversion price, and vice versa.
Example
Suppose that a certain $1,000 convertible bond stipulates a conversion ratio of 40, which means that the bond can be converted into 40 shares of common stock. In effect, if you give up your $1,000 bond in exchange for 40 shares, you are essentially buying 40 shares of stock for $1,000, or $25 per share. In other words, the conversation ratio of 40 is equivalent to a conversion price of $25. (One basic difference between a convertible debenture and a convertible preferred relates to conversion ratio: The conversion ratio of a debenture generally deals with large multiples of common stock, such as 15, 20, or 30 shares. In contrast, the conversion ratio of a preferred is generally very small, often less than one share of common and seldom more than three or four shares.)
The conversion ratio is normally adjusted for stock splits and significant stock dividends. As a result, if a firm declares, say, a 2-for-1 stock split, the conversion ratio of any of its outstanding convertible issues also doubles. And when the conversion ratio includes a fraction, such as 33.5 shares of common, the conversion privilege specifies how any fractional shares are to be handled. Usually, the investor can either put up the additional funds necessary to purchase another full share of stock at the conversion price or receive the cash equivalent of the fractional share (at the conversion price).
LYONs
Leave it to Wall Street to take a basic investment product and turn it into a sophisticated investment vehicle. That’s the story behind LYONs, which some refer to as “zeros on steroids.” Start with a zero-coupon bond, throw in a conversion feature and a put option, and you have a LYON (the acronym stands for liquid yield option note). LYONs are zero-coupon convertible bonds that are convertible, at a fixed conversion ratio, for the life of the issue. Thus, they offer the built-in increase in value over time that accompanies any zero-coupon bond (as it moves toward its par value at maturity), plus full participation in the equity side of the issue via the equity kicker. Unlike most convertibles, there’s no current income with a LYON (because it is a zero-coupon bond). On the other hand, however, it does carry an option feature that enables investors to “put” or sell the bonds back to the issuer (at specified values). That is, the put option gives investors the right to redeem their bonds periodically at prespecified prices. Thus, investors know they can get out of these securities, at set prices, if they want to.
Although LYONs may appear to provide the best of all worlds, they do have some negative aspects. It is true that LYONs provide downside protection (via the put option feature) and full participation in the equity kicker. But like all zero-coupon bonds, they don’t generate current income. And investors have to watch out for the put option. Depending on the type of put option, the payout does not have to be in cash—it can be in stocks or bonds. One other important issue to be aware of is that because the conversion ratio on the LYON is fixed, the conversion price on the stock increases over time. This occurs because the value of the zero-coupon bond increases as it reaches maturity. Thus, the market price of the stock had better go up by more than the bond’s rate of appreciation or investors will never be able to convert their LYONs.
Sources of Value
Because convertibles are fixed-income securities linked to the equity position of the firm, they are normally valued in terms of both the stock and the bond dimensions of the issue. Thus, it is important to both analyze the underlying common stock and formulate interest rate expectations when considering convertibles as an investment outlet. Let’s look first at the stock dimension.
Convertible securities trade much like common stock whenever the market price of the stock starts getting close to (or exceeds) the stated conversion price. When that happens, the convertible will exhibit price behavior that closely matches that of the underlying common stock. If the stock goes up in price, so does the convertible, and vice versa. In fact, the absolute price change of the convertible will exceed that of the common because of the conversion ratio, which will define the convertible’s rate of change in price. For example, if a convertible carries a conversion ratio of, say, 20, then for every dollar the common stock goes up (or down) in price, the price of the convertible will move in the same direction by roughly that same multiple (in this case, $20). In essence, whenever a convertible trades as a stock, its market price will approximate a multiple of the share price of the common, with the size of the multiple being defined by the conversion ratio.
Investor Facts
Busted Convertibles —Investors choose convertibles for the upside potential that they provide. Convertibles are very popular in rising equity markets, when their prices move more like stocks than bonds. What happens when stock prices take a nosedive? If the price of the stock that underlies the convertible falls well below the bond’s conversion price, then the conversion feature is nearly irrelevant, and you become the proud owner of a busted convertible—an issue that behaves more like a bond than a stock.
When the market price of the common is well below the conversion price, the convertible loses its tie to the underlying common stock and begins to trade as a bond. When that happens, the convertible becomes linked to prevailing bond yields, and investors focus their attention on market rates of interest. However, because of the equity kicker and their relatively low agency ratings, convertibles generally do not possess high interest rate sensitivity. Gaining more than a rough idea of what the prevailing yield of a convertible obligation ought to be is often difficult. For example, if the issue is rated Baa and the market rate for this quality range is 9%, then the convertible should be priced to yield something around 9%, plus or minus perhaps half a percentage point. Because of the interest and principal payments that they offer, convertible bonds essentially have a price floor, meaning that convertible values generally cannot drop as much as the underlying stock can. If a company experiences financial problems that cause its stock price to drop dramatically, the firm’s convertible bonds will retain much of their value because investors are still entitled to receive interest and principal payments. That is, the price of the convertible will not fall to much less than its price floor because at that point, the issue’s bond value will kick in.
Measuring the Value of a Convertible
In order to evaluate the investment merits of convertible securities, investors should consider both the bond and the stock dimensions of the issue. Fundamental security analysis of the equity position is, of course, especially important in light of the key role the equity kicker plays in defining the price behavior of a convertible. In contrast, market yields and agency ratings are used in evaluating the bond side of the issue. But there’s more: In addition to analyzing the bond and stock dimensions of the issue, it is essential to evaluate the conversion feature itself. The two critical areas in this regard are conversion value and investment value. These measures have a vital bearing on a convertible’s price behavior and therefore can have a dramatic effect on an issue’s holding period return.
Conversion Value
In essence, conversion value indicates what a convertible issue would trade for if it were priced to sell on the basis of its stock value. Conversion value is easy to find:
Conversion value=Conversion ration×Current market price of the stockConversion value = Conversion ration × Current market price of the stockEquation10.4
Example
Suppose that a particular convertible bond has a conversion ratio of 20. If the price of the company’s stock is $60 per share, then the conversion value of the bond is $1,200 (i.e.,20×$60)(i.e., 20×$60).
Sometimes analysts use an alternative measure that computes the conversion equivalent , also known as conversion parity . The conversion equivalent indicates the price at which the common stock would have to sell in order to make the convertible security worth its present market price. The conversion equivalent is calculated as follows:
Conversion equivalent = Current market price of the convertible bondConversion ratioConversion equivalent = Current market price of the convertible bondConversion ratioEquation10.5
Example
If a convertible bond has a current market price of $1,400 and a conversion ratio of 20, the conversion equivalent of the common stock would be $70 per share (i.e., $1,400÷20)(i.e., $1,400÷20). Although convertible bonds can trade above par value simply because of a decline in interest rates, as a practical matter, it would be unusual for a bond to trade as high as $1,400 based only on an interest rate drop. Accordingly, you would expect the current market price of the common stock in this example to be at or near $70 per share in order to support a convertible trading at $1,400.
Conversion Premium
Convertible issues seldom trade precisely at their conversion values. Rather, they usually trade at prices that exceed the bond’s underlying conversion value. The extent to which the market price of the convertible exceeds its conversion value is known as the conversion premium. The absolute size of an issue’s conversion premium is found by taking the difference between the convertible’s market price and its conversion value (per Equation 10.4 ). To place the premium on a relative basis, simply divide the dollar amount of the conversion premium by the issue’s conversion value. That is,
Conversion premium (in $) = Current market price of the convertible bond−Conversion valueConversion premium (in $) = Current market price of the convertible bond−Conversion valueEquation10.6
where conversion value is found according to Equation 10.4 .
Then
Conversion premium (in %)= Conversion premium (in $)Conversion valueConversion premium (in %) = Conversion premium (in $)Conversion valueEquation10.7
Example
Suppose that a convertible bond trades at $1,400 and its conversion value equals $1,200. This bond has a conversion premium of $200 (i.e., $1,400−$1,200)$200 (i.e., $1,400−$1,200). That $200 represents a conversion premium of 16.7% relative to the bond’s conversion value.
Conversion premiums are common in the market and can often amount to 30% to 40% (or more) of an issue’s conversion value. Investors are willing to pay a premium because of the added current income that a convertible provides relative to the underlying common stock and because of the convertible’s upside potential. An investor can recover this premium either through the added current income or by selling the issue at a premium equal to or greater than that which existed at the time of purchase. Unfortunately, the latter source of recovery is tough to come by because conversion premiums tend to fade away as the price of the convertible goes up. That means that if an investor purchases a convertible for its potential price appreciation, then he must accept the fact that all or a major portion of the price premium is very likely to disappear as the convertible appreciates over time and moves closer to its true conversion value. Thus, if he hopes to recover any conversion premium, it will probably have to come from the added current income that the convertible provides.
Payback Period
The size of the conversion premium can obviously have a major impact on investor return. When picking convertibles, one of the major questions investors should ask is whether the premium is justified. One way to assess conversion premium is to compute the issue’s payback period , a measure of the length of time it will take to recover the conversion premium from the extra interest income earned on the convertible. Because this added income is a principal reason for the conversion premium, it makes sense to use it to assess the premium. The payback period can be found as follows:
Payback period=Conversion premium (in $)Annual interest income from the convertible bond−Annual dividend income from the underlying common stockPayback period=Conversion premium (in $)Annual interest income from the convertible bond−Annual dividend income from the underlying common stockEquation10.8
In this equation, annual dividends are found by multiplying the stock’s latest annual dividends per share by the bond’s conversion ratio.
Example
In the previous example, the bond had a conversion premium of $200. Assume this bond (which carries a conversion ratio of 20) has an 8.5% coupon ($85 per year), and the underlying stock paid dividends this past year of 50 cents a share. Given this information, you can use Equation 10.8 to find the payback period.
Payback period=$200$85−(20×$0.50)=$200$85−($10.00)=2.7yearsPayback period = $200$85−(20×$0.50)=$200$85−($10.00)=2.7 years
In essence, you would recover the premium in 2.7 years (a fairly short payback period).
As a rule, everything else being equal, the shorter the payback period, the better. Also, watch out for excessively high premiums (of 50% or more). Indeed, to avoid such premiums, which are difficult to recover, most experts recommend that investors look for convertibles that have payback periods of five to seven years, or less. Be careful when using this measure, however. Some convertibles will have very high payback periods simply because they carry very low coupons (of 1% to 2%, or less).
Investment Value
The price floor of a convertible is defined by its bond properties and is the focus of the investment value measure. It’s the point within the valuation process where we focus on current and expected market interest rates. Investment value is the price at which the bond would trade if it were nonconvertible and if it were priced at or near the prevailing market yields of comparable nonconvertible bonds.
We will cover the mechanics of bond pricing in more detail later, but suffice it to say at this point that the investment value of a convertible is found by discounting the issue’s coupon stream and its par value back to the present, using a discount rate equal to the prevailing yield on comparable nonconvertible issues. In other words, using the yields on comparable nonconvertible bonds as the discount rate, find the present value of the convertible’s coupon stream, add that to the present value of its par value, and you have the issue’s investment value. In practice, because the convertible’s coupon and maturity are known, the only additional piece of information needed is the market yield of comparably rated issues.
For example, if comparable nonconvertible bonds were trading at 9% yields, we could use that 9% return as the discount rate in finding the present value (i.e., “investment value”) of a convertible. Thus, if a particular 20-year, $1,000 par value convertible bond carried a 6% annual coupon rate, its investment value (using a 9% discount rate) can be found using a financial calculator as shown in the margin.
Calculator Use
Based on the information given, $60 is entered as the interest payment amount, PMT; the $1,000 par value is entered as the future value, FV; the time till maturity, 20 years, is entered, N; and the yield of 9% is entered for the discount rate, I. Push the compute key, CPT, and then the present value key, PV, to find that the resulting value of the convertible would be about $726. This figure indicates how far the convertible will have to fall before it hits its price floor and begins trading as a straight-debt instrument.
Other things being equal, the greater the distance between the current market price of a convertible and its investment value, the farther the issue can fall in price and, as a result, the greater the downside risk exposure.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 10.15 What is a convertible debenture? How does a convertible bond differ from a convertible preferred?
2. 10.16 Identify the equity kicker of a convertible security and explain how it affects the value and price behavior of convertibles.
3. 10.17 Explain why it is necessary to examine both the bond and stock properties of a convertible debenture when determining its investment appeal.
4. 10.18 What is the difference between conversion parity and conversion value? How would you describe the payback period on a convertible? What is the investment value of a convertible, and what does it reveal?
Assignment Content
1.
Top of Form
Complete the following Case Problems from Fundamentals of Investing:
· Case Problem 10.1: Max and Veronica Develop a Bond Investment Program, Questions A-E (page 422)
· Case Problem 10.2: The Case of the Missing Bond Ratings, Questions A-C (page 423)
· Case Problem 11.1: The Bond Investment Decisions of Dave and Marlene Carter, Questions A-B (page 463)
· Case Problem 11.2: Grace Decides to Immunize Her Portfolio, Questions A-F (page 464).
Format your submission consistent with APA guidelines.
Submit your assignment.
Bottom of Form
The Behavior of Market Interest Rates
1. LG 1
2. LG 2
Recall from earlier discussions that rational investors try to earn a return that fully compensates them for risk. In the case of bondholders, that required return (ri) has three components: the real rate of return (r*), an expected inflation premium (IP), and a risk premium (RP). Thus, the required return on a bond can be expressed by the following equation:
ri=r*+IP+RPri=r*+IP+RPEquation11.1
The real rate of return and inflation premium are external economic factors, which together equal the risk-free rate (rf). To find the required return, we need to consider the unique features and properties of the bond issue itself that influence its risk. After we do this, we add a risk premium to the risk-free rate to obtain the required rate of return. A bond’s risk premium (RP) will take into account key issue and issuer characteristics, including such variables as the type of bond, the issue’s term to maturity, its call features, and its bond rating.
Together, the three components in Equation 11.1 (r*, IP, and RP) drive the required return on a bond. Recall in the previous chapter that we identified five types of risks to which bonds are exposed. All of these risks are embedded in a bond’s required rate of return. That is, the bond’s risk premium addresses, among other things, the business and financial (credit) risk characteristics of an issue, along with its liquidity and call risks, whereas the risk-free rate (rf) takes into account interest rate and purchasing power risks.
Because these interest rates have a significant bearing on bond prices and yields, investors watch them closely. For example, more conservative investors watch interest rates because one of their major objectives is to lock in high yields. Aggressive traders also have a stake in interest rates because their investment programs are often built on the capital gains opportunities that accompany major swings in rates.
Keeping Tabs on Market Interest Rates
The bond market is not a single market. Rather, it consists of many different sectors. Similarly, there is no single interest rate that applies to all segments of the bond market. Instead, different interest rates apply to different segments. Granted, the various rates do tend to drift in the same direction over time, but it is also common for yield spreads (interest rate differentials) to exist among the various market sectors. Some important factors to keep in mind when you think about interest rates on bonds are as follows:
· Municipal bonds usually offer the lowest market rates because of their tax-exempt feature. As a rule, their market yields are about 20% to 30% lower than corporate bond yields.
· In the municipal sector, revenue bonds pay higher rates than general obligation bonds.
· In the taxable sector, Treasury securities have the lowest yields (because they have the least risk), followed by agency bonds and then corporate bonds, which provide the highest returns.
Famous Failures in Finance Signs of a Recession
When short-term interest rates on treasury bills exceed the rates on long-term treasury bonds, watch out. That is often the precursor to a recession. This “inversion” in the relationship between short-term and long-term rates has occurred prior to each of the last five U.S. recessions. Just as important, this indicator has rarely issued a false recession warning signal.
· Issues that normally carry bond ratings (e.g., municipals or corporates) generally display the same behavior: the lower the rating, the higher the yield.
· Most of the time, bonds with long maturities provide higher yields than short-term issues. However, this rule does not always hold. When short-term bond yields exceed yields on longer-term bonds, as they did in February 2006, that may be an early signal that a recession is coming.
· Bonds that are freely callable generally pay the highest interest rates, at least at date of issue. These are followed by deferred call obligations and then by noncallable bonds, which offer lower yields.
Watch Your Behavior
Anchoring on Credit Spreads The credit spread is the difference in yield between a risky bond and a safe bond. In theory, credit spreads are determined by forward-looking economic fundamentals that measure a borrower’s capacity to repay its debts. A recent study found that borrowers and lenders appear to focus excessively (i.e., to anchor) on past deal terms when setting spreads for a new bond issue. The study found that when a firm’s most recent past debt issue had a credit spread that was higher than an upcoming issue, the interest rate on the upcoming deal was higher than fundamentals could justify. In other words, both the firm and its lenders were anchored to the older, higher interest rate.
(Source: Casey Dougal, Joseph Engelberg, Christopher A. Parsons, & Edward D. Van Wesep, “Anchoring on Credit Spreads,” Journal of Finance, June 2015.)
As an investor, you should pay close attention to interest rates and yield spreads. Try to stay abreast of both the current state of the market and the future direction of market rates. Thus, if you are a conservative (income-oriented) investor and think that rates have just about peaked, that should be a signal to try to lock in the prevailing high yields with some form of call protection. (For example, buy bonds, such as Treasuries or AA-rated utilities that are noncallable or still have lengthy call deferments.) In contrast, if you’re an aggressive bond trader who thinks rates have peaked (and are about to drop), that should be a clue to buy bonds that offer maximum price appreciation potential (low-coupon bonds that still have a long time before they mature).
But how do you formulate such expectations? Unless you have considerable training in economics, you will probably need to rely on various published sources. Fortunately, a wealth of such information is available. Your broker is an excellent source for such reports, as are investor services like Moody’s and Standard & Poor’s. Also, of course, there are numerous online sources. Finally, there are widely circulated business and financial publications (like the Wall Street Journal, Forbes, Business Week, and Fortune) that regularly address the current state and future direction of market interest rates. Predicting the direction of interest rates is not easy. However, by taking the time to read some of these publications and reports regularly and carefully, you can at least get a sense of what experts predict is likely to occur in the near future.
What Causes Rates to Move?
Although the determination of interest rates is a complex economic issue, we do know that certain forces are especially important in influencing rate movements. Serious bond investors should make it a point to become familiar with the major determinants of interest rates and try to monitor those variables, at least informally.
Watch Your Behavior
Money Illusion An investment that offers a high interest rate may seem attractive, but remember it’s the real return, after inflation, that matters. Although interest rates were very high in the late 1970s, so was the inflation rate, and many bond investors earned negative real returns during that period.
In that regard, perhaps no variable is more important than inflation. Changes in the inflation rate, or to be more precise, changes in the expected inflation rate, have a direct and profound effect on market interest rates. When investors expect inflation to slow down, market interest rates generally fall as well. To gain an appreciation of the extent to which interest rates are linked to inflation, look at Figure 11.1 . The figure plots the behavior of the interest rate on a 10-year U.S. Treasury bond and the inflation rate from 1963 to 2014. The blue line in the figure tracks the actual inflation rate over time, although as we have already noted, the expected inflation rate has a more direct effect on interest rates. Even so, there is a clear link between actual inflation and interest rates. Note that, in general, as inflation drifts up, so do interest rates. On the other hand, a decline in inflation is matched by a similar decline in interest rates. Most of the time, the rate on the 10-year bond exceeded the inflation rate, which is exactly what you should expect. When that was not the case, such as in the 1970s and more recently in 2012, investors in the 10-year Treasury bond did not earn enough interest to keep up with inflation. Notice that in 2009 as the U.S. struggled to recover from the Great Recession, the inflation rate was negative and the Treasury yields dropped sharply. On average, the 10-year Treasury yield exceeded the inflation rate by about 2.4 percentage points per year.
Figure 11.1 The Impact of Inflation on the Behavior of Interest Rates
The behavior of interest rates has always been closely tied to the movements in the rate of inflation. Since 1963 the average spread between the U.S. 10-year Treasury rate and inflation is 2.4 percentage points. This spread fluctuates quite a bit over time. Some extreme examples occurred in 1974 when the rate of inflation exceeded the 10-year Treasury rate by 4.1 percentage points and in 1985 when 10-year Treasury rates outpaced inflation by 8 percentage points.
In addition to inflation, five other important economic variables can significantly affect the level of interest rates:
· Changes in the money supply. An increase in the money supply pushes rates down (as it makes more funds available for loans), and vice versa. This is true only up to a point, however. If the growth in the money supply becomes excessive, it can lead to inflation, which, of course, means higher interest rates.
· The size of the federal budget deficit. When the U.S. Treasury has to borrow large amounts to cover the budget deficit, the increased demand for funds exerts an upward pressure on interest rates. That’s why bond market participants become so concerned when the budget deficit gets bigger and bigger—other things being equal, that means more upward pressure on market interest rates.
· The level of economic activity. Businesses need more capital when the economy expands. This need increases the demand for funds, and rates tend to rise. During a recession, economic activity contracts, and rates typically fall.
· Policies of the Federal Reserve. Actions of the Federal Reserve to control inflation also have a major effect on market interest rates. When the Fed wants to slow actual (or anticipated) inflation, it usually does so by driving up interest rates, as it did repeatedly in the mid- and late 1970s. Unfortunately, such actions sometimes have the side effect of slowing down business activity as well. Likewise, when the Federal Reserve wants to stimulate the economy, it takes action to push interest rates down, as it did repeatedly during and after the 2008-2009 recession.
· The level of interest rates in major foreign markets. Today investors look beyond national borders for investment opportunities. Rising rates in major foreign markets put pressure on rates in the United States to rise as well; if U.S. rates don’t keep pace, foreign investors may be tempted to dump their dollars to buy higher-yielding foreign securities.
Living Yield Curve
The Term Structure of Interest Rates and Yield Curves
Bonds having different maturities typically have different interest rates. The relationship between interest rates (yield) and time to maturity for any class of similar-risk securities is called the term structure of interest rates . This relationship can be depicted graphically by a yield curve , which shows the relation between time to maturity and yield to maturity for a group of bonds having similar risk. The yield curve constantly changes as market forces push bond yields at different maturities up and down.
Types of Yield Curves
Two types of yield curves are illustrated in Figure 11.2 . By far, the most common type is curve 1, the red upward-sloping curve. It indicates that yields tend to increase with longer maturities. That’s partly because the longer a bond has to maturity, the greater the potential for price volatility. Investors, therefore, require higher-risk premiums to induce them to buy the longer, riskier bonds. Long-term rates may also exceed short-term rates if investors believe short-term rates will rise. In that case, rates on long-term bonds might have to be higher than short-term rates to attract investors. That is, if investors think short-term rates are rising, they will not want to tie up their money for long at today’s lower rates. Instead, they would prefer to invest in a short-term security so that they can reinvest that money quickly after rates have risen. To induce investors to purchase a long-term bond, the bond must offer a higher rate than investors think they could earn by buying a series of short-term bonds, with each new bond in that series offering a higher rate than the one before.
Figure 11.2 Two Types of Yield Curves
A yield curve plots the relation between term to maturity and yield to maturity for a series of bonds that are similar in terms of risk. Although yield curves come in many shapes and forms, the most common is the upward-sloping curve. It shows that yields increase with longer maturities.
Occasionally, the yield curve becomes inverted, or downward sloping, as shown in curve 2, which occurs when short-term rates are higher than long-term rates. This curve sometimes results from actions by the Federal Reserve to curtail inflation by driving short-term interest rates up. An inverted yield curve may also occur when firms are very hesitant to borrow long-term (such as when they expect a recession). With very low demand for long-term loans, long-term interest rates fall. In addition to these two common yield curves, two other types appear from time to time: the flat yield curve, when rates for short- and long-term debt are essentially the same, and the humped yield curve, when intermediate-term rates are the highest.
Plotting Your Own Curves
Yield curves are constructed by plotting the yields for a group of bonds that are similar in all respects but maturity. Treasury securities (bills, notes, and bonds) are typically used to construct yield curves. There are several reasons for this. Treasury securities have no risk of default. They are actively traded, so their prices and yields are easy to observe, and they are relatively homogeneous with regard to quality and other issue characteristics. Investors can also construct yield curves for other classes of debt securities, such as A-rated municipal bonds, Aa-rated corporate bonds, and even certificates of deposit.
Historical Yield Curves
Figure 11.3 shows the yield curves for Treasury securities on March 7, 2007, and March 16, 2015. To draw these curves, you need Treasury quotes from the U.S. Department of the Treasury or some other similar source. (Note that actual quoted yields for curve 1 are highlighted in yellow in the table below the graph.) Given the required quotes, select the yields for the Treasury bills, notes, and bonds maturing in approximately 1 month, 3 months, 6 months, and 1, 2, 3, 5, 7, 10, 20, and 30 years. That covers the full range of Treasury issues’ maturities. Next, plot the points on a graph whose horizontal (x) axis represents time to maturity in years and whose vertical (y) axis represents yield to maturity. Now, just connect the points to create the curves shown in Figure 11.3 . You’ll notice that curve 1 is upward sloping, while curve 2 is downward sloping. Downward-sloping yield curves are less common,
Figure 11.3 Yield Curves on U.S. Treasury Issues
Here we see two yield curves constructed from actual market data obtained from the U.S. Department of the Treasury. Curve 2 shows a less common downward-sloping yield curve. The yields that make up the more common upward-sloping curve 1 are near U.S. record low levels.
(Source: U.S. Department of the Treasury, June 4, 2015.)
thankfully so because they often signal an upcoming recession. For example, the downward-sloping yield curve shown in Figure 11.3 signaled the Great Recession that officially ran from December 2007 to June of 2009. While curve 1 is the more typical upward-sloping yield curve, it nonetheless reflects the historically low interest rates that prevailed as the U.S. economy recovered from a deep recession.
Explanations of the Term Structure of Interest Rates
As we noted earlier, the shape of the yield curve can change over time. Three commonly cited theories—the expectations hypothesis, the liquidity preference theory, and the market segmentation theory—explain more fully the reasons for the general shape of the yield curve.
Expectations Hypothesis
The expectations hypothesis suggests that the yield curve reflects investor expectations about the future behavior of interest rates. This theory argues that the relationship between short-term and long-term interest rates today reflects investors’ expectations about how interest rates will change in the future. When the yield curve slopes upward, and long-term rates are higher than short-term rates, the expectations hypothesis interprets this as a sign that investors expect short-term rates to rise. That’s why long-term bonds pay a premium compared to short-term bonds. People will not lock their money away in a long-term investment when they think interest rates are going to rise unless the rate on the long-term investment is higher than the current rate on short-term investments.
For example, suppose the current interest rate on a 1-year Treasury bill is 5%, and the current rate on a 2-year Treasury note is 6%. The expectations hypothesis says that this pattern of interest rates reveals that investors believe that the rate on a 1-year Treasury bill will go up to 7% next year. Why? That’s the rate that makes investors today indifferent between locking their money away for 2 years and earning 6% on the 2-year note versus investing in the 1-year T-bill today at 5% and then next year reinvesting the money from that instrument into another 1-year T-bill paying 7%.
|
Investment Strategy |
(1) Rate Earned This Year |
(2) Rate Earned Next Year |
(3) Return over 2 Years [(1)+(2)][(1)+(2)] |
|
Buy 2-year note today |
6% |
6% |
12% |
|
Buy 1-year T-bill, then reinvest in another T-bill next year |
5% |
7% |
12% |
Only if the rate on a 1-year T-bill rises from 5% this year to 7% next year will investors be indifferent between these 2 strategies. Thus, according to the expectations hypothesis, an upward-sloping yield curve means that investors expect interest rates to rise, and a downward-sloping yield curve means that investors expect interest rates to fall.
Example
Suppose the yield curve is inverted, and 1-year bonds offer a 5% yield while 2-year bonds pay a 4.5% yield. According to the expectations hypothesis, what do investors expect the 1-year bond yield to be 1 year from now? Remember that the expectations hypothesis says today’s short-term and long-term interest rates are set at a level which makes investors indifferent between short-term and long-term bonds, given their beliefs about where interest rates are headed. Therefore, to determine the expected 1-year bond yield next year, you must determine what return in the second year would make investors just as happy to buy two 1-year bonds as they are to buy one 2-year bond.
· Return on a 2-year bond = 4.5% + 4.5%Return on a 2-year bond = 4.5% + 4.5%
· Return on two 1-year bonds = 5.0% + xReturn on two 1-year bonds = 5.0% + x
The x in the second equation represents the expected rate on the 1-year bond next year. The top equation shows that an investor earns 9% over 2 years by purchasing a 2-year bond, so to achieve the same return on a series of two 1-year bonds, the return in the second year must be 4%.
Liquidity Preference Theory
More often than not, yield curves have an upward slope. The expectations hypothesis would interpret this as a sign that investors usually expect rates to rise. That seems somewhat illogical. Why would investors expect interest rates to rise more often than they expect rates to fall? Put differently, why would investors expect interest rates to trend up over time? There is certainly no historical pattern to lead one to hold that view. One explanation for the frequency of upward-sloping yield curves is the liquidity preference theory . This theory states that long-term bond rates should be higher than short-term rates because of the added risks involved with the longer maturities. In other words, because of the risk differential between long- and short-term debt securities, rational investors will prefer the less risky, short-term obligations unless they can be motivated, via higher interest rates, to invest in longer-term bonds. Even if investors do not expect short-term rates to rise, long-term bonds will still have to offer higher yields to attract investors.
Actually, there are a number of reasons why rational investors should prefer short-term securities. To begin with, they are more liquid (more easily converted to cash) and less sensitive to changing market rates, which means there is less price volatility. For a given change in market rates, the prices of longer-term bonds will show considerably more movement than the prices of short-term bonds. In addition, just as investors tend to require a premium for tying up funds for longer periods, borrowers will also pay a premium in order to obtain long-term funds. Borrowers thus assure themselves that funds will be available, and they avoid having to roll over short-term debt at unknown and possibly unfavorable rates. All of these preferences explain why higher rates of interest should be associated with longer maturities and why it’s perfectly rational to expect upward-sloping yield curves.
Market Segmentation Theory
Another often-cited theory, the market segmentation theory , suggests that the market for debt is segmented on the basis of the maturity preferences of different financial institutions and investors. According to this theory, the yield curve changes as the supply and demand for funds within each maturity segment determines its prevailing interest rate. The equilibrium between the financial institutions that supply the funds for short-term maturities (e.g., banks) and the borrowers of those short-term funds (e.g., businesses with seasonal loan requirements) establishes interest rates in the short-term markets. Similarly, the equilibrium between suppliers and demanders in such long-term markets as life insurance and real estate determines the prevailing long-term interest rates.
An Advisor’s Perspective
Ryan McKeown Senior VP-Financial Advisor, Wealth Enhancement Group
“I pay very close attention to the yield curve.”
MyFinanceLab
The shape of the yield curve can slope either upward or downward, as determined by the general relationship between rates in each market segment. When supply outstrips demand for short-term loans, short-term rates are relatively low. If, at the same time, the demand for long-term loans is higher than the available supply of funds, then long-term rates will move up, and the yield curve will have an upward slope. If supply and demand conditions are reversed—with excess demand for borrowing in the short-term market and an excess supply of funds in the long-term market—the yield curve could slope down.
Which Theory Is Right?
All three theories of the term structure have at least some merit in explaining the shape of the yield curve. These theories tell us that, at any time, the slope of the yield curve is affected by the interaction of (1) expectations regarding future interest rates, (2) liquidity preferences, and (3) the supply and demand conditions in the short- and long-term market segments. Upward-sloping yield curves result from expectations of rising interest rates, lender preferences for shorter-maturity loans, and a greater supply of short- than of long-term loans relative to the respective demand in each market segment. The opposite conditions lead to a downward-sloping yield curve.
More about the Yield Curve
Using the Yield Curve in Investment Decisions
Bond investors often use yield curves in making investment decisions. Analyzing the changes in yield curves provides investors with information about future interest rate movements, which in turn affect the prices and returns on different types of bonds. For example, if the entire yield curve begins to move upward, it usually means that inflation is starting to heat up or is expected to do so in the near future. In that case, investors can expect that interest rates, too, will rise. Under these conditions, most seasoned bond investors will turn to short or intermediate (three to five years) maturities, which provide reasonable returns and at the same time minimize exposure to capital loss when interest rates go up. A downward-sloping yield curve signals that rates have peaked and are about to fall and that the economy is slowing down.
Another factor to consider is the difference in yields on different maturities—the “steepness” of the curve. For example, a steep yield curve is one where long-term rates are much higher than short-term rates. This shape is often seen as an indication that the spread between long-term and short-term rates is about to fall, either because long-term rates will fall or short-term rates will rise. Steep yield curves are generally viewed as a bullish sign. For aggressive bond investors, they could be the signal to start moving into long-term securities. Flatter yield curves, on the other hand, sharply reduce the incentive for going long-term since the difference in yield between the 5- and 30-year maturities can be quite small. Under these conditions, investors would be well advised to just stick with the 5- to 10-year maturities, which will generate about the same yield as long bonds but without the risks.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 11.1 Is there a single market rate of interest applicable to all segments of the bond market, or is there a series of market yields? Explain and note the investment implications of such a market environment.
2. 11.2 Explain why interest rates are important to both conservative and aggressive bond investors. What causes interest rates to move, and how can you monitor such movements?
3. 11.3 What is the term structure of interest rates and how is it related to the yield curve? What information is required to plot a yield curve? Describe an upward-sloping yield curve and explain what it has to say about the behavior of interest rates. Do the same for a flat yield curve.
4. 11.4 How might you, as a bond investor, use information about the term structure of interest rates and yield curves when making investment decisions?
The Pricing of Bonds
1. LG 3
No matter who the issuer is, what kind of bond it is, or whether it’s fully taxable or tax-free, all bonds are priced using similar principles. That is, all bonds (including notes with maturities of more than one year) are priced according to the present value of their future cash flow streams. Indeed, once the prevailing or expected market yield is known, the whole process becomes rather mechanical.
Market yields largely determine bond prices. That’s because in the marketplace, investors first decide what yield is appropriate for a particular bond, given its risk, and then they use that yield to find the bond’s price (or market value). As we saw earlier, the appropriate yield on a bond is a function of certain market and economic forces (e.g., the risk-free rate of return and inflation), as well as key issue and issuer characteristics (like years to maturity and the issue’s bond rating). Together these forces combine to form the required rate of return, which is the rate of return the investor would like to earn in order to justify an investment in a given fixed-income security. The required return defines the yield at which the bond should be trading and serves as the discount rate in the bond valuation process.
Investor Facts
Prices Go Up, Prices Go Down We all know that when market rates go up, bond prices go down (and vice versa). But bond prices don’t move up and down at the same speed because they don’t move in a straight line. Rather, the relationship between market yields and bond prices is convex, meaning bond prices will rise at an increasing rate when yields fall and decline at a decreasing rate when yields rise. That is, bond prices go up faster than they go down. This is known as positive convexity, and it’s a property of all noncallable bonds. Thus, for a given change in yield, you stand to make more money when prices go up than you’ll lose when prices move down!
The Basic Bond Valuation Model
Generally speaking, when you buy a bond you receive two distinct types of cash flow: (1) periodic interest income (i.e., coupon payments) and (2) the principal (or par value) at the end of the bond’s life. Thus, in valuing a bond, you’re dealing with an annuity of coupon payments for a specified number of periods plus a large single cash flow at maturity. You can use these cash flows, along with the required rate of return on the investment, in a present value-based bond valuation model to find the dollar value, or price, of a bond. Using annual compounding, you can calculate the price of a particular bond (BPi) using the following equation:
BPi=N∑t=1C(1+ri)t+PVN(1+ri)N=Present value of coupon payments + Present value of bond’s par valueBPi=∑t=1NC(1+ri)t+PVN(1+ri)N=Present value of coupon payments + Present value of bond’s par valueEquation11.2
where
· BPi = current price (or value) of a particular bond i
· C = annual coupon (interest) payment
· PVN = par value of the bond, at maturity
· N = number of years to maturity
· ri = prevailing market yield, or required annual return on bonds similar to bond i
In this form, you can compute the bond’s current value, or what you would be willing to pay for it, given that you want to generate a certain rate of return, as defined by ri. Alternatively, if you already know the bond’s price, you can solve for ri in the equation, in which case you’d be looking for the yield to maturity embedded in the current market price of the bond.
In the discussion that follows, we will demonstrate the bond valuation process in two ways. First, we’ll use annual compounding—that is, because of its computational simplicity, we’ll assume we are dealing with coupons that are paid once a year. Second, we’ll examine bond valuation under conditions of semiannual compounding, which is the way most bonds actually pay their interest.
Annual Compounding
You need the following information to value a bond: (1) the annual coupon payment, (2) the par value (usually $1,000), and (3) the number of years (i.e., time periods) remaining to maturity. You then use the prevailing market yield, ri, as the discount rate to compute the bond’s price, as follows:
Bond price=Present value of coupon payments + Present value ofbond’s par valueBond price = Present value of coupon payments + Present value of bond’s par valueEquation11.3
BPi=C(1+ri)1+C(1+ri)2+…+C(1+ri)N+$1,000(1+ri)NBPi=C(1+ri)1+C(1+ri)2+…+C(1+ri)N+$1,000(1+ri)NEquation11.3a
where again
· C = annual coupon payment
· N = number of years to maturity
Example
A 20-year, 4.5% bond is priced to yield 5%. That is, the bond pays an annual coupon of 4.5% (or $45), has 20 years left to maturity, and has a yield to maturity of 5%, which is the current market rate on bonds of this type. We can use Equation 11.3 to find the bond’s price.
BPi=$45(1+0.05)1+$45(1+0.05)2+…+$45(1+0.05)20+$1,000(1+0.05)20=$937.69BPi=$45(1+0.05)1+$45(1+0.05)2+…+$45(1+0.05)20+$1,000(1+0.05)20=$937.69
Note that because this is a coupon-bearing bond, we have an annuity of coupon payments of $45 a year for 20 years, plus a single cash flow of $1,000 that occurs at the end of year 20. Thus, we find the present value of the coupon annuity and then add that amount to the present value of the recovery of principal at maturity. In this particular case, you should be willing to pay almost $938 for this bond, as long as you’re satisfied with earning 5% on your money.
Notice that this bond trades at a discount of $62.31 ($1,000 − $937.69)($1,000 − $937.69). It trades at a discount because its coupon rate (4.5%) is below the market’s required return (5%). You can directly link the size of the discount on this bond to the present value of the difference between the coupons that it pays ($45) and the coupons that would be required if the bond matched the market’s 5% required return ($50). In other words, this bond’s coupon payment is $5 less than what the market requires, so if you take the present value of that difference over the bond’s life, you will calculate the size of the bond’s discount:
$5(1+0.05)1+$5(1+0.05)2+…+$5(1+0.05)20=$62.31$5(1+0.05)1+$5(1+0.05)2+…+$5(1+0.05)20=$62.31
In a similar vein, for a bond that trades at a premium, the size of that premium equals the present value of the difference between the coupon that the bond pays and the (lower) coupon that the market requires.
Bonds initially sell for a price close to par value because bond issuers generally set the bond’s coupon rate equal or close to the market’s required return at the time the bonds are issued. If market interest rates change during the life of the bond, then the bond’s price will adjust up or down to reflect any differences between the bond’s coupon rate and the market interest rate. Although bonds can sell at premiums or discounts over their lives, as the maturity date arrives, bond prices will converge to par value. This happens because as time passes and a bond’s maturity date approaches, there are fewer interest payments remaining (so any premium or discount is diminishing) and the principal to be repaid at maturity is becoming an ever bigger portion of the bond’s price since the periods over which it is being discounted are disappearing.
Calculator Use
For annual compounding, to price a 20-year, 4.5% bond to yield 5%, use the keystrokes shown in the margin, where:
· N = number of years to maturity
· I = required annual return on the bond (what the bond is being priced to yield)
· PMT = annual coupon payment
· FV = par value of the bond
· PV = computed price of the bond
Recall that the calculator result shows the bond’s price as a negative value, which indicates that the price is a cash outflow for an investor when buying the bond’s cash flows.
Financial Calculator Tutorials
Spreadsheet Use
The bond’s price can also be calculated as shown on the following Excel spreadsheet.
Semiannual Compounding
Although using annual compounding simplifies the valuation process a bit, it’s not the way most bonds are actually valued in the marketplace. In practice, most bonds pay interest every six months, so it is appropriate to use semiannual compounding to value bonds. Fortunately, it’s relatively easy to go from annual to semiannual compounding: All you need to do is cut the annual interest income and the required rate of return in half and double the number of periods until maturity. In other words, rather than one compounding and payment interval per year, there are two (i.e., two 6-month periods per year). Given these changes, finding the price of a bond under conditions of semiannual compounding is much like pricing a bond using annual compounding. That is:
Bond price (with semiannual compounding)=Present value of the annuity ofsemiannual coupon payments+Present value of thebond’s par valueBond price (with semiannual compounding) = Present value of the annuity of semiannual coupon payments + Present value of the bond’s par valueEquation11.4
BPi=C/2(1+ri2)1+C/2(1+ri2)2+…+C/2(1+ri2)2N+$1,000(1+ri2)2NBPi=C/2(1+ri2)1+C/2(1+ri2)2+…+C/2(1+ri2)2N+$1,000(1+ri2)2NEquation11.4a
where, in this case,
· C/2 = semiannual coupon payment, or the amount of interest paid every 6 months
· ri = the required rate of return per 6-month period
Example
In the previous bond-pricing example, you priced a 20-year bond to yield 5%, assuming annual interest payments of $45. Suppose the bond makes semiannual interest payments instead. With semiannual payments of $22.50, you adjust the semiannual return to 2.5% and the number of periods to 40. Using Equation 11.4 , you’d have:
BPi=$45/2(1+0.052)1+$45/2(1+0.052)2+…+$45/2(1+0.052)40+1,000(1+0.052)40=$937.24BPi=$45/2(1+0.052)1+$45/2(1+0.052)2+…+$45/2(1+0.052)40+1,000(1+0.052)40=$937.24
The price of the bond in this case ($937.24) is slightly less than the price we obtained with annual compounding ($937.69).
Calculator Use
For semiannual compounding, to price a 20-year, 4.5% semiannual-pay bond to yield 5%, use the keystrokes shown in the margin, where:
· N = number of 6-month periods to maturity (20×2=40)(20×2=40)
· I = yield on the bond, adjusted for semiannual compounding (5%÷2=2.5%)(5%÷2=2.5%)
· PMT = semiannual coupon payment ($45.00÷2=$22.50)($45.00÷2=$22.50)
· FV = par value of the bond
· PV = computed price of the bond
Spreadsheet Use
You can calculate the bond’s price with semiannual coupon payments as shown on the following Excel spreadsheet. Notice that in cell B8 the required annual return is divided by coupon payment frequency to find the required rate of return per 6-month period, and the number of years to maturity is multiplied times the coupon payment frequency to find the total number of 6-month periods remaining until maturity.
Accrued Interest
Most bonds pay interest every six months, but you can trade them any time that the market is open. Suppose you own a bond that makes interest payments on January 15 and July 15 each year. What happens if you sell this bond at some time between the scheduled coupon payment dates? For example, suppose you sell the bond on October 15, a date that is roughly halfway between two payment dates. Fortunately, interest accrues on bonds between coupon payments, so selling the bond prior to a coupon payment does not mean that you sacrifice any interest that you earned. Accrued interest is the amount of interest earned on a bond since the last coupon payment. When you sell a bond in between coupon dates, the bond buyer adds accrued interest to the bond’s price (the price calculated using Equation 11.3 or 11.4 depending on whether coupons arrive annually or semiannually).
Example
Suppose you purchase a $1,000 par value bond that pays a 6% coupon in semiannual installments of $30. You received a coupon payment two months ago, and now you are ready to sell the bond. Contacting a broker, you learn that the bond’s current market price is $1,010. If you sell the bond, you will receive not only the market price, but also accrued interest. Because you are about one-third of the way between the last coupon payment and the next one, you receive accrued interest of $10 (i.e., 1/3 × $30)$10 (i.e., 1/3 × $30), so the total cash that you receive in exchange for your bond is $1,020.
Traders in the bond market sometimes refer to the price of a bond as being either clean or dirty. The clean price of a bond equals the present value of its cash flows, as in Equations 11.3 and 11.4 . As a matter of practice, bond price quotations that you may find in financial periodicals or online are nearly always clean prices. The dirty price of a bond is the clean price plus accrued interest. In the example above, the clean price is $1,010, and the dirty price is $1,020.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 11.5 Explain how market yield affects the price of a bond. Could you price a bond without knowing its market yield? Explain.
2. 11.6 Why are bonds generally priced using semiannual compounding? Does it make much difference if you use annual compounding?
Measures of Yield and Return
1. LG 4
In the bond market, investors focus as much on a bond’s yield to maturity as on its price. As you have seen, the yield to maturity helps determine the price at which a bond trades, but it also measures the rate of return on the bond. When you can observe the price of a bond that is trading in the market, you can simply reverse the bond valuation process described above to solve for the bond’s yield to maturity rather than its price. That gives you a pretty good idea of the return that you might earn if you purchased the bond at its current market price. Actually, there are three widely used metrics to assess the return on a bond: the current yield, the yield to maturity, and the yield to call (for bonds that are callable). We’ll look at all three measures here, along with a concept known as the expected return, which measures the expected (or actual) rate of return earned over a specific holding period.
Current Yield
The current yield is the simplest of all bond return measures, but it also has the most limited application. This measure looks at just one source of return: a bond’s annual interest income. In particular, it indicates the amount of current income a bond provides relative to its prevailing market price. The current yield equals:
Current yield=Annual interest incomeCurrent market price of the bondCurrent yield = Annual interest incomeCurrent market price of the bondEquation11.5
Example
An 8% bond would pay $80 per year in interest for every $1,000 of principal. However, if the bond was currently priced at $800, it would have a current yield of $80÷$800 = 0.10 = 10%$80÷$800 = 0.10 = 10%. The current yield measures a bond’s annual interest income, so it is of interest primarily to investors seeking high levels of current income, such as endowments or retirees.
Yield to Maturity
The yield to maturity (YTM) is the most important and most widely used measure of the return provided by a bond. It evaluates the bond’s interest income and any gain or loss that results from differences between the price that an investor pays for a bond and the par value that the investor receives at maturity. The YTM takes into account all of the cash flow received over a bond’s life. Also known as the promised yield , the YTM shows the rate of return earned by an investor, given that the bond is held to maturity and all principal and interest payments are made in a prompt and timely fashion. In addition, the YTM calculation implicitly assumes that the investor can reinvest all the coupon payments at an interest rate equal to the bond’s yield to maturity. This “reinvestment assumption” plays a vital role in the YTM, which we will discuss in more detail later in this chapter (see the section entitled Yield Properties).
The yield to maturity is used not only to gauge the return on a single issue but also to track the behavior of the market in general. In other words, market interest rates are basically a reflection of the average promised yields that exist in a given segment of the market. The yield to maturity provides valuable insights into an issue’s investment merits that investors can use to assess the attractiveness of different bonds. Other things being equal, the higher the promised yield of an issue, the more attractive it is.
Although there are a couple of ways to compute the YTM, the best and most accurate procedure is derived directly from the bond valuation model described above. That is, you can use Equations 11.3 and 11.4 to determine the YTM for a bond. The difference is that now instead of trying to determine the price of the bond, you know its price and are trying to find the discount rate that will equate the present value of the bond’s cash flow (coupon and principal payments) to its current market price. This procedure may sound familiar. It’s just like the internal rate of return measure described earlier in the text. Indeed, the YTM is basically the internal rate of return on a bond. When you find that, you have the bond’s yield to maturity.
Using Annual Compounding
Finding yield to maturity is a matter of trial and error. In other words, you try different values for YTM until you find the one that solves the equation. Let’s say you want to find the YTM for a 7.5% ($1,000 par value) annual-coupon-paying bond that has 15 years remaining to maturity and is currently trading in the market at $809.50. From Equation 11.3 , we know that
BPi=$809.50=$75(1+ri)1+$75(1+ri)2+…+$75(1+ri)15+$1,000(1+ri)15BPi=$809.50=$75(1+ri)1+$75(1+ri)2+…+$75(1+ri)15+$1,000(1+ri)15
Notice that this bond sells below par (i.e., it sells at a discount). What do we know about the relationship between the required return on a bond and its coupon rate when the bond sells at a discount? Bonds sell at a discount when the required return (or yield to maturity) is higher than the coupon rate, so the yield to maturity on this bond must be higher than 7.5%.
Through trial and error, we might initially try a discount rate of 8% or 9% (or, since it sells at a discount, any value above the bond’s coupon). Sooner or later, we’ll try a discount rate of 10%, and at that discount rate, the present value of the bond’s cash flows is $809.85 (use Equation 11.3 to verify this), which is very close to the bond’s market price.
Because the computed price of $809.85 is reasonably close to the bond’s current market price of $809.50, we can say that 10% represents the approximate yield to maturity on this bond. That is, 10% is the discount rate that leads to a computed bond price that’s equal (or very close) to the bond’s current market price. In this case, if you were to pay $809.50 for the bond and hold it to maturity, you would expect to earn a YTM very close to 10.0%. Doing trial and error by hand can be time consuming, so you can use a handheld calculator or computer software to calculate the YTM.
Calculator Use
For annual compounding, to find the YTM of a 15-year, 7.5% bond that is currently priced in the market at $809.50, use the keystrokes shown in the margin. The present value (PV) key represents the current market price of the bond, and all other keystrokes are as defined earlier.
Spreadsheet Use
The bond’s YTM can also be calculated as shown on the following Excel spreadsheet.
Using Semiannual Compounding
Given some fairly simple modifications, it’s also possible to find the YTM using semiannual compounding. To do so, we cut the annual coupon and discount rate in half and double the number of periods to maturity. Returning to the 7.5%, 15-year bond, let’s see what happens when you use Equation 11.4 and try an initial discount rate of 10%.
BPi=$75.00/2(1+0.102)1$75.00/2(1+0.102)2+…+$75.00/2(1+0.102)30+$1,000(1+0.102)30=$807.85BPi=$75.00/2(1+0.102)1$75.00/2(1+0.102)2+…+$75.00/2(1+0.102)30+$1,000(1+0.102)30=$807.85
As you can see, a semiannual discount rate of 5% results in a computed bond value that’s well short of the market price of $809.50. Given the inverse relationship between price and yield, it follows that if you need a higher price, you have to try a lower YTM (discount rate). Therefore, you know the semiannual yield on this bond has to be something less than 5%. By trial and error, you would determine that the yield to maturity on this bond is just a shade under 5% per half year—approximately 4.99%. Remember that this is the yield expressed over a 6-month period. The market convention is to simply state the annual yield as twice the semiannual yield. This practice produces what the market refers to as the bond equivalent yield . Returning to the YTM problem started above, you know that the issue has a semiannual yield of about 4.99%. According to the bond equivalent yield convention, you double the semiannual rate to obtain the annual rate of return on this bond. Doing this results in an annualized yield to maturity (or promised yield) of approximately 4.99%×2=9.98%4.99%×2=9.98%. This is the annual rate of return you will earn on the bond if you hold it to maturity.
Calculator Use
For semiannual compounding, to find the YTM of a 15-year, 7.5% bond that is currently priced in the market at $809.50, use the keystrokes shown here. As before, the PV key is the current market price of the bond, and all other keystrokes are as defined earlier. Remember that to find the bond equivalent yield, you must double the computed value of I, 4.987%. That is 4.987%×2=9.97%4.987%×2=9.97%. The difference between our answer here, 9.97%, and the 9.98% figure in the previous paragraph is simply due to the calculator’s more precise rounding.
Spreadsheet Use
A semiannual bond’s YTM and bond equivalent yield can also be calculated as shown on the following Excel spreadsheet.
Yield Properties
Actually, in addition to holding the bond to maturity, there are several other critical assumptions embedded in any yield to maturity figure. The promised yield measure—whether computed with annual or semiannual compounding—is based on present value concepts and therefore contains important reinvestment assumptions. To be specific, the YTM calculation assumes that when each coupon payment arrives, you can reinvest it for the remainder of the bond’s life at a rate that is equal to the YTM. When this assumption holds, the return that you earn over a bond’s life is in fact equal to the YTM. In essence, the calculated yield to maturity figure is the return “promised” only as long as the issuer meets all interest and principal obligations on a timely basis and the investor reinvests all interest income at a rate equal to the computed promised yield. In our example above, you would need to reinvest each of the coupon payments and earn a 10% return on those reinvested funds. Failure to do so would result in a realized yield of less than the 10% YTM. If you made no attempt to reinvest the coupons, you would earn a realized yield over the 15-year investment horizon of just over 6.5%—far short of the 10% promised return. On the other hand, if you could reinvest coupons at a rate that exceeded 10%, the actual yield on your bond over the 15 years would be higher than its 10% YTM. The bottom line is that unless you are dealing with a zero-coupon bond, a significant portion of the bond’s total return over time comes from reinvested coupons.
When we use present value-based measures of return, such as the YTM, there are actually three components of return: (1) coupon/interest income, (2) capital gains (or losses), and (3) interest on interest. Whereas current income and capital gains make up the profits from an investment, interest on interest is a measure of what you do with those profits. In the context of a bond’s yield to maturity, the computed YTM defines the required, or minimum, reinvestment rate. Put your investment profits (i.e., interest income) to work at this rate and you’ll earn a rate of return equal to YTM. This rule applies to any coupon-bearing bond—as long as there’s an annual or semiannual flow of interest income, the reinvestment of that income and interest on interest are matters that you must deal with. Also, keep in mind that the bigger the coupon and/or the longer the maturity, the more important the reinvestment assumption. Indeed, for many long-term, high-coupon bond investments, interest on interest alone can account for well over half the cash flow.
Finding the Yield on a Zero
You can also use the procedures described above ( Equation 11.3 with annual compounding or Equation 11.4 with semiannual compounding) to find the yield to maturity on a zero-coupon bond. The only difference is that you can ignore the coupon portion of the equation because it will, of course, equal zero. All you need to do to find the promised yield on a zero-coupon bond is to solve the following expression:
Yield=($1,000Price)1N−1Yield = ($1,000Price)1N−1
Example
Suppose that today you could buy a 15-year zero-coupon bond for $315. If you purchase the bond at that price and hold it to maturity, what is your YTM?
Yield=($1,000$315)115−1=0.08=8%Yield = ($1,000$315)115−1=0.08=8%
The zero-coupon bond pays an annual compound return of 8%. Had we been using semiannual compounding, we’d use the same equation except we’d substitute 30 for 15 (because there are 30 semiannual periods in 15 years). The yield would change to 3.93% per half year, or 7.86% per year.
Calculator Use
For semiannual compounding, to find the YTM of a 15-year zero-coupon bond that is currently priced in the market at $315, use the keystrokes shown in the margin. PV is the current market price of the bond, and all other keystrokes are as defined earlier. To find the bond equivalent yield, double the computed value of I, 3.926%. That is, 3.926%×2 = 7.85%3.926%×2 = 7.85%.
Spreadsheet Use
A semiannual bond’s YTM and bond equivalent yield can also be calculated as shown on the following Excel spreadsheet. Notice that the spreadsheet also shows 7.85% for the bond equivalent yield.
Yield to Call
Bonds can be either noncallable or callable. Recall that a noncallable bond prohibits the issuer from calling the bond prior to maturity. Because such issues will remain outstanding to maturity, you can value them by using the standard yield to maturity measure. In contrast, a callable bond gives the issuer the right to retire the bond before its maturity date, so the issue may not remain outstanding to maturity. As a result, the YTM may not always provide a good measure of the return that you can expect if you purchase a callable bond. Instead, you should consider the impact of the bond being called away prior to maturity. A common way to do that is to use a measure known as the yield to call (YTC) , which shows the yield on a bond if the issue remains outstanding not to maturity but rather until its first (or some other specified) call date.
The YTC is commonly used with bonds that carry deferred-call provisions. Remember that such issues start out as noncallable bonds and then, after a call deferment period (of 5 to 10 years), become freely callable. Under these conditions, the YTC would measure the expected yield on a deferred-call bond assuming that the issue is retired at the end of the call deferment period (that is, when the bond first becomes freely callable). You can find the YTC by making two simple modifications to the standard YTM equation ( Equation 11.3 or 11.4 ). First, define the length of the investment horizon (N) as the number of years to the first call date, not the number of years to maturity. Second, instead of using the bond’s par value ($1,000), use the bond’s call price (which is stated in the indenture and is frequently greater than the bond’s par value).
For example, assume you want to find the YTC on a 20-year, 10.5% deferred-call bond that is currently trading in the market at $1,204 but has five years to go to first call (that is, before it becomes freely callable), at which time it can be called in at a price of $1,085. Rather than using the bond’s maturity of 20 years in the valuation equation ( Equation 11.3 or 11.4 ), you use the number of years to first call (five years), and rather than the bond’s par value, $1,000, you use the issue’s call price, $1,085. Note, however, you still use the bond’s coupon (10.5%) and its current market price ($1,204). Thus, for annual compounding, you would have:
BPi=$1,204=$105(1+ri)1+$105(1+ri)2+$105(1+ri)3+$105(1+ri)4+$105(1+ri)5+$1,085(1+ri)5BPi=$1,204=$105(1+ri)1+$105(1+ri)2+$105(1+ri)3+$105(1+ri)4+$105(1+ri)5+$1,085(1+ri)5Equation11.6
Through trial and error, you could determine that at a discount rate of 7%, the present value of the future cash flows (coupons over the next five years, plus call price) will exactly (or very nearly) equal the bond’s current market price of $1,204.
Thus, the YTC on this bond is 7%. In contrast, the bond’s YTM is 8.37%. In practice, bond investors normally compute both YTM and YTC for deferred-call bonds that are trading at a premium. They do this to find which yield is lower; the market convention is to use the lower, more conservative measure of yield (YTM or YTC) as the appropriate indicator of the bond’s return. As a result, the premium bond in our example would be valued relative to its yield to call. The assumption is that because interest rates have dropped so much (the YTM is two percentage points below the coupon rate), it will be called in the first chance the issuer gets. However, the situation is totally different when this or any bond trades at a discount. Why? Because the YTM on any discount bond, whether callable or not, will always be less than the YTC. Thus, the YTC is a totally irrelevant measure for discount bonds—it’s used only with premium bonds.
Calculator Use
For annual compounding, to find the YTC of a 20-year, 10.5% bond that is currently trading at $1,204 but can be called in five years at a call price of $1,085, use the keystrokes shown in the margin. In this computation, N is the number of years to first call date, and FV represents the bond’s call price. All other keystrokes are as defined earlier.
Spreadsheet Use
A callable bond’s YTC can also be calculated as shown on the following Excel spreadsheet.
Expected Return
Rather than just buying and holding bonds, some investors prefer to actively trade in and out of these securities over fairly short investment horizons. As a result, measures such as yield to maturity and yield to call have relatively little meaning, other than as indicators of the rate of return used to price the bond. These investors obviously need an alternative measure of return that they can use to assess the investment appeal of those bonds they intend to trade. Such an alternative measure is the expected return . It indicates the rate of return an investor can expect to earn by holding a bond over a period of time that’s less than the life of the issue. (Expected return is also known as realized yield because it shows the return an investor would realize by trading in and out of bonds over short holding periods.)
The expected return lacks the precision of the yield to maturity (and YTC) because the major cash flow variables are largely the product of investor estimates. In particular, going into the investment, both the length of the holding period and the future selling price of the bond are pure estimates and therefore subject to uncertainty. Even so, you can use essentially the same procedure to find a bond’s realized yield as you did to find the promised yield. That is, with some simple modifications to the standard bond-pricing formula, you can use the following equation to find the expected return on a bond.
Bond price=Present value of the bond'sannual coupon paymentsover the holding period+Present value of the bond'sfuture price at the endof the holding periodBond price = Present value of the bond's annual coupon payments over the holding period+Present value of the bond's future price at the end of the holding periodEquation11.7
BPi=C(1+ri)1+C(1+ri)2+…+C(1+ri)N+FV(1+ri)NBPi=C(1+ri)1+C(1+ri)2+…+C(1+ri)N+FV(1+ri)NEquation11.7a
where this time N represents the length of the holding period (not years to maturity), and FV is the expected future price of the bond.
As indicated above, you must determine the future price of the bond when computing its expected return. This is done by using the standard bond price formula, as described earlier. The most difficult part of deriving a reliable future price is, of course, coming up with future market interest rates that you feel will exist when the bond is sold. By evaluating current and expected market interest rate conditions, you can estimate the YTM that you expect the issue to provide at the date of sale and then use that yield to calculate the bond’s future price.
To illustrate, take one more look at our 7.5%, 15-year bond. This time, let’s assume that you feel the price of the bond, which is now trading at a discount, will rise sharply as interest rates fall over the next few years. In particular, assume the bond is currently priced at $809.50 (to yield 10%) and you anticipate holding the bond for three years. Over that time, you expect market rates to drop to 8%. With that assumption in place, and recognizing that three years from now the bond will have 12 remaining coupon payments, you can use Equation 11.3 to estimate that the bond’s price will be approximately $960 in three years. Thus, you are assuming that you will buy the bond today at a market price of $809.50 and sell it three years later—after interest rates have declined to 8%—at a price of $960. Given these assumptions, the expected return (realized yield) on this bond is 14.6%, which is the discount rate in the following equation that will produce a current market price of $809.50.
BPi=$809.50=$75(1+ri)1+$75(1+ri)2+$75(1+ri)3+$960(1+ri)3BPi=$809.50=$75(1+ri)1+$75(1+ri)2+$75(1+ri)3+$960(1+ri)3
where
ri=0.146=14.6%.ri=0.146=14.6%.
The return on this investment is fairly substantial, but keep in mind that this is only an estimate. It is, of course, subject to variation if things do not turn out as anticipated, particularly with regard to the market yield expected at the end of the holding period. This example uses annual compounding, but you could just as easily have used semiannual compounding, which, everything else being the same, would have resulted in an expected yield of 14.4% rather than the 14.6% found with annual compounding.
Calculator Use
For semiannual compounding, to find the expected return on a 7.5% bond that is currently priced in the market at $809.50 but is expected to rise to $960 within a three-year holding period, use the keystrokes shown in the margin. In this computation, PV is the current price of the bond, and FV is the expected price of the bond at the end of the (three-year) holding period. All other keystrokes are as defined earlier. To find the bond equivalent yield, double the computed value of I, 7.217%. That is 7.217%×2=14.43%7.217%×2=14.43%.
Spreadsheet Use
The expected return for semiannual compounding can also be calculated as shown on the following Excel spreadsheet. Notice that the spreadsheet shows 14.43% for the bond equivalent yield.
Valuing a Bond
Depending on their objectives, investors can estimate the return that they will earn on a bond by calculating either its yield to maturity or its expected return. Conservative, income-oriented investors focus on the YTM. Earning interest income over extended periods of time is their primary objective, above earning a quick capital gain if interest rates fall. Because these investors intend to hold most of the bonds that they buy to maturity, the YTM (or the YTC) is a reliable measure of the returns that they can expect over time—assuming, of course, the reinvestment assumptions embedded in the yield measure are reasonable. More aggressive bond traders, who hope to profit from swings in market interest rates, calculate the expected return to estimate the return that they will earn on a bond. Earning capital gains by purchasing and selling bonds over relatively short holding periods is their chief concern, so the expected return is more important to them than the YTM.
In either case, the promised or expected yield provides a measure of return that investors can use to determine the relative attractiveness of fixed-income securities. But to evaluate the merits of different bonds, we must evaluate their returns and their risks. Bonds are no different from stocks in that the return (promised or expected) that they provide should be sufficient to compensate investors for the risks that they take. Thus, the greater the risk, the greater the return the bond should generate.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 11.7 What’s the difference between current yield and yield to maturity? Between promised yield and realized yield? How does YTC differ from YTM?
2. 11.8 Briefly describe the term bond equivalent yield. Is there any difference between promised yield and bond equivalent yield? Explain.
3. 11.9 Why is the reinvestment of interest income so important to bond investors?
Duration and Immunization
1. LG 5
One of the problems with the yield to maturity is that it assumes you can reinvest the bond’s periodic coupon payments at the same rate over time. If you reinvest this interest income at a lower rate (or if you spend it), your actual return will be lower than the YTM. Another flaw is that YTM assumes the investor will hold the bond to maturity. If you sell a bond prior to its maturity, the price that you receive will reflect prevailing interest rates, which means that the return that you will earn will probably differ from the YTM. If rates have moved up since you purchased the bond, the bond will sell at a discount, and your return will be less than the YTM. If interest rates have dropped, the opposite will happen.
The problem with yield to maturity, then, is that it fails to take into account the effects of reinvestment risk and price (or market) risk. To see how reinvestment and price risks behave relative to one another, consider a situation in which market interest rates have undergone a sharp decline. Under such conditions, bond prices will rise. You might be tempted to cash out your holdings and take some gains (i.e., do a little “profit taking”). Indeed, selling before maturity is the only way to take advantage of falling interest rates because a bond will pay its par value at maturity, regardless of prevailing interest rates. That’s the good news about falling rates, but there is a downside. When interest rates fall, so do the opportunities to reinvest at high rates. Therefore, although you gain on the price side, you lose on the reinvestment side. Even if you don’t sell out, you are faced with decreased reinvestment opportunities. To earn the YTM promised on your bonds, you must reinvest each coupon payment at the same YTM rate. Obviously, as rates fall, you’ll find it increasingly difficult to reinvest the stream of coupon payments at that rate. When market rates rise, just the opposite happens. The price of the bond falls, but your reinvestment opportunities improve.
Bond investors need a measure that helps them judge just how significant these risks are for a particular bond. Such a yardstick is provided by something called duration . It captures in a single measure the extent to which the price of a bond will react to different interest rate environments. Because duration gauges the price volatility of a bond, it gives you a better idea of how likely you are to earn the return (YTM) you expect. That, in turn, will help you tailor your holdings to your expectations of interest rate movements.
The Concept of Duration
The concept of duration was first developed in 1938 by actuary Frederick Macaulay to help insurance companies match their cash inflows with payments. When applied to bonds, duration recognizes that the amount and frequency of interest payments, the yield to maturity, and the term to maturity all affect the interest rate risk of a particular bond. Term to maturity is important because it influences how much a bond’s price will rise or fall as interest rates change. In general, when rates move, bonds with longer maturities fluctuate more than shorter issues. On the other hand, while the amount of price risk embedded in a bond is related to the issue’s term to maturity, the amount of reinvestment risk is directly related to the size of a bond’s coupon. Bonds that pay high coupons have greater reinvestment risk simply because there’s more to reinvest.
As it turns out, both price and reinvestment risk are related in one way or another to interest rates, and therein lies the conflict. Any change in interest rates (whether up or down) will cause price risk and reinvestment risk to push and pull bonds in opposite directions. An increase in rates will produce a drop in price but will increase reinvestment opportunities. Declining rates, in contrast, will boost prices but decrease reinvestment opportunities. At some point in time, these two forces should exactly offset each other. That point in time is a bond’s duration.
In general, bond duration possesses the following properties:
· Higher coupons result in shorter durations.
· Longer maturities mean longer durations.
· Higher yields (YTMs) lead to shorter durations.
Together these variables—coupon, maturity, and yield—interact to determine an issue’s duration. Knowing a bond’s duration is helpful because it captures the bond’s underlying price volatility. That is, since a bond’s duration and volatility are directly related, it follows that the shorter the duration, the less volatility in bond prices—and vice versa, of course.
Measuring Duration
Duration is a measure of the average maturity of a fixed-income security. The term average maturity may be confusing because bonds have only one final maturity date. An alternative definition of average maturity might be that it captures the average timing of the bond’s cash payments. For a zero-coupon bond that makes only one cash payment on the final maturity date, the bond’s duration equals its maturity. But because coupon-paying bonds make periodic interest payments, the average timing of these payments (i.e., the average maturity) is different from the actual maturity date. For instance, a 10-year bond that pays a 5% coupon each year distributes a small cash flow in year 1, in year 2, and so on up until the last and largest cash flow in year 10. Duration is a measure that puts some weight on these intermediate payments, so that the “average maturity” is a little less than 10 years.
You can think of duration as the weighted-average life of a bond, where the weights are the fractions of the bond’s total value accounted for by each cash payment that the bond makes over its life. Mathematically, we can find the duration of a bond as follows:
Duration=N∑t=1[PV(Ct)BP×t]Duration = ∑t=1N[PV(Ct)BP×t]Equation11.8
where
· PV(Ct) = present value of a future coupon or principal payment
· BP = current market price of the bond
· t = year in which the cash flow (coupon or principal) payment is received
· N = number of years to maturity
The duration measure obtained from Equation 11.8 is commonly referred to as Macaulay duration—named after the actuary who developed the concept.
Although duration is often computed using semiannual compounding, Equation 11.8 uses annual coupons and annual compounding to keep the ensuing discussion and calculations as simple as possible. Even so, the formula looks more formidable than it really is. If you follow the basic steps noted below, you’ll find that duration is not tough to calculate.
1. Step 1. Find the present value of each annual coupon or principal payment [PV(Ct)]. Use the prevailing YTM on the bond as the discount rate.
2. Step 2. Divide this present value by the current market price of the bond (BP). This is the weight, or the fraction of the bond’s total value accounted for by each individual payment. Because a bond’s value is just the sum of the present values of its cash payments, these weights must sum to 1.0.
3. Step 3. Multiply this weight by the year in which the cash flow is to be received (t).
4. Step 4. Repeat steps 1 through 3 for each year in the life of the bond, and then add up the values computed in step 3.
Table 11.1 Duration Calculation for a 7.5%, 15-Year Bond Priced to Yield 8%
|
(1) |
(2) |
(3) |
(4) |
(5) |
|
Year t |
Annual Cash Flow Ct |
Present Value at 8% of Annual Cash Flow (2)÷(1.08)t(2)÷(1.08)t |
Present Value of Annual Cash Flow Divided by Price of the Bond (3)÷$957.20(3)÷$957.20 |
Time-Weighted Relative Cash Flow (1)×(4)(1)×(4) |
|
1 |
$ 75 |
$ 69.44 |
0.0725 |
0.0725 |
|
2 |
$ 75 |
$ 64.30 |
0.0672 |
0.1344 |
|
3 |
$ 75 |
$ 59.54 |
0.0622 |
0.1866 |
|
4 |
$ 75 |
$ 55.13 |
0.0576 |
0.2304 |
|
5 |
$ 75 |
$ 51.04 |
0.0533 |
0.2666 |
|
6 |
$ 75 |
$ 47.26 |
0.0494 |
0.2963 |
|
7 |
$ 75 |
$ 43.76 |
0.0457 |
0.3200 |
|
8 |
$ 75 |
$ 40.52 |
0.0423 |
0.3387 |
|
9 |
$ 75 |
$ 37.52 |
0.0392 |
0.3528 |
|
10 |
$ 75 |
$ 34.74 |
0.0363 |
0.3629 |
|
11 |
$ 75 |
$ 32.17 |
0.0336 |
0.3696 |
|
12 |
$ 75 |
$ 29.78 |
0.0311 |
0.3734 |
|
13 |
$ 75 |
$ 27.58 |
0.0288 |
0.3745 |
|
14 |
$ 75 |
$ 25.53 |
0.0267 |
0.3735 |
|
15 |
$1,075 |
$338.88 |
0.3540 |
5.3106 |
|
|
|
Price of Bond: $957.20 |
1.00 |
Duration: 9.36 yr |
Excel@Investing
Duration for a Single Bond
Table 11.1 illustrates the four-step procedure for calculating the duration of a 7.5%, 15-year bond priced at $957.20 to yield 8%. Table 11.1 provides the basic input data: Column (1) shows the year t in which each cash flow arrives. Column (2) provides the dollar amount of each annual cash flow (Ct) (coupons and principal) made by the bond. Column (3) lists the present value of each annual cash flow in year t at an 8% discount rate (which is equal to the prevailing YTM on the bond). For example, in row 1 of Table 11.1 , we see that in year 1 the bond makes a $75 coupon payment, and discounting that to the present at 8% reveals that the first coupon payment has a present value of $69.44. If we sum the present value of the annual cash flows in column (3), we find that the current market price of the bond is $957.20.
Investor Facts
Different Bonds, Same Durations Sometimes, you really can’t judge a book—or a bond, for that matter—by its cover. Here are three bonds that, on the surface, appear to be totally different:
· An 8-year, zero-coupon bond priced to yield 6%
· A 12-year, 8.5% bond that trades at a yield of 8%
· An 18-year, 10.5% bond priced to yield 13%
Although these bonds have different coupons and different maturities, they have one thing in common: they all have identical durations of eight years. Thus, if interest rates went up or down by 50 to 100 basis points, the market prices of these bonds would all behave pretty much the same!
Next, in column 4 we divide the present value in column 3 by the current market price of the bond. If the present value of this bond’s first coupon payment is $69.45 and the total price of the bond is $957.20, then that first payment accounts for 7.25% of the bond’s total value (i.e., $69.45÷$957.20 = 0.0725)(i.e., $69.45÷$957.20 = 0.0725) Therefore, 7.25% is the “weight” given to the cash payment made in year 1. If you sum the weights in column 4, you will see that they add to 1.0. Multiplying the weights from column 4 by the year t in which the cash flow arrives results in a time-weighted value for each of the annual cash flow streams shown in column 5. Adding up all the values in column 5 yields the duration of the bond. As you can see, the duration of this bond is a lot less than its maturity. In addition, keep in mind that the duration on any bond will change over time as YTM and term to maturity change. For example, the duration on this 7.5%, 15-year bond will fall as the bond nears maturity and/or as the market yield (YTM) on the bond increases.
Duration for a Portfolio of Bonds
The concept of duration is not confined to individual bonds only. It can also be applied to whole portfolios of fixed-income securities. The duration of an entire portfolio is fairly easy to calculate. All we need are the durations of the individual securities in the portfolio and their weights (i.e., the proportion that each security contributes to the overall value of the portfolio). Given this, the duration of a portfolio is the weighted average of the durations of the individual securities in the portfolio. Actually, this weighted-average approach provides only an approximate measure of duration. But it is a reasonably close approximation and, as such, is widely used in practice—so we’ll use it, too.
To see how to measure duration using this approach, consider the following five-bond portfolio:
|
Bond |
Amount Invested * |
Weight |
× |
Bond Duration |
= |
Portfolio Duration |
|
* Amount invested = Current market price × Par value of the bonds. That is, if the government bonds are quoted at 90 and the investor holds $300,000 in these bonds, then 0.90 × $300,000 = $270,000. |
||||||
|
Government bonds |
$ 270,000 |
0.15 |
|
6.25 |
|
0.9375 |
|
Aaa corporates |
$ 180,000 |
0.10 |
|
8.90 |
|
0.8900 |
|
Aa utilities |
$ 450,000 |
0.25 |
|
10.61 |
|
2.6525 |
|
Agency issues |
$ 360,000 |
0.20 |
|
11.03 |
|
2.2060 |
|
Baa industrials |
$ 540,000 |
0.30 |
|
12.55 |
|
3.7650 |
|
|
$1,800.000 |
1.00 |
|
|
|
10.4510 |
In this case, the $1.8 million bond portfolio has an average duration of approximately 10.5 years.
If you want to change the duration of the portfolio, you can do so by (1) changing the asset mix of the portfolio (shift the weight of the portfolio to longer- or shorter-duration bonds, as desired) and/or (2) adding new bonds to the portfolio with the desired duration characteristics. As we will see below, this approach is often used in a bond portfolio strategy known as bond immunization.
Bond Duration and Price Volatility
A bond’s price volatility is, in part, a function of its term to maturity and, in part, a function of its coupon. Unfortunately, there is no exact relationship between bond maturities and bond price volatilities with respect to interest rate changes. There is, however, a fairly close relationship between bond duration and price volatility—as long as the market doesn’t experience wide swings in interest rates. A bond’s duration can be used as a viable predictor of its price volatility only as long as the yield swings are relatively small (no more than 50 to 100 basis points or so). That’s because as interest rates change, bond prices change in a nonlinear (convex) fashion. For example, when interest rates fall, bond prices rise at an increasing rate. When interest rates rise, bond prices fall at a decreasing rate. The duration measure essentially predicts that as interest rates change, bond prices will move in the opposite direction in a linear fashion. This means that when interest rates fall, bond prices will rise a bit faster than the duration measure would predict, and when interest rates rise, bond prices will fall at a slightly slower rate than the duration measure would predict. The bottom line is that the duration measure helps investors understand how bond prices will respond to changes in market rates, as long as those changes are not too large.
The mathematical link between changes in interest rates and changes in bond prices involves the concept of modified duration. To find modified duration, we simply take the (Macaulay) duration for a bond (as found from Equation 11.8 ) and divide it by the bond’s yield to maturity.
Modified duration=(Macaulay) Duration in years1+Yield to maturityModified duration = (Macaulay) Duration in years1+Yield to maturityEquation11.9
Thus, the modified duration for the 15-year bond discussed above is
Modified duration=9.361+0.08=8.67––––––––––Modified duration = 9.361+0.08=8.67__
Note that here we use the bond’s computed (Macaulay) duration of 9.36 years and the same YTM we used to compute duration in Equation 11.8 ; in this case, the bond was priced to yield 8%, so we use a yield to maturity of 8%.
To determine, in percentage terms, how much the price of this bond would change as market interest rates increased by 50 basis points from 8% to 8.5%, we multiply the modified duration value calculated above first by − (because of the inverse relationship between bond prices and interest rates) and then by the change in market interest rates. That is,
Percent changein bond price=−1×Modified duration×Change in interest rates=−1×8.67×0.5% =−4.33––––––––––Percent change in bond price=−1×Modified duration×Change in interest rates= −1×8.67×0.5% =−4.33__Equation11.10
Thus, a 50-basis-point (or ½ of 1%) increase in market interest rates will lead to an approximate 4.33% drop in the price of this 15-year bond. Such information is useful to bond investors seeking—or trying to avoid—price volatility.
Effective Duration
One problem with the duration measures that we’ve studied so far is that they do not always work well for bonds that may be called or converted before they mature. That is, the duration measures we’ve been using assume that the bond’s future cash flows are paid as originally scheduled through maturity, but that may not be the case with callable or convertible bonds. An alternative duration measure that is used for these types of bonds is the effective duration. To calculate effective duration (ED), you use Equation 11.11 :
ED=BP(ri⏐↓)−BP(ri↑⏐)2×BP×ΔriED = BP(ri↓)−BP(ri↑)2×BP×ΔriEquation11.11
where
· BP(ri↑) = the new price of the bond if market interest rates go up
· BP(ri↓) = the new price of the bond if market interest rates go down
· BP = the original price of the bond
· Δri = the change in market interest rates
Example
Suppose you want to know the effective duration of a 25-year bond that pays a 6% coupon semiannually. The bond is currently priced at $882.72 for a yield of 7%. Now suppose the bond’s yield goes up by 0.5% to 7.5%. At that yield the new price would be $831.74 (using a calculator, N = 50, I = 3.75, PMT = 30, and PV = 1,000). What if the yield drops by 0.5% to 6.5%? In that case, the price rises to $938.62 (N = 50, I = 3.25, PMT = 30, PV = 1,000). Now we can use Equation 11.11 to calculate the bond’s effective duration.
Effective duration = ($938.62−$831.74)÷(2×$882.72×0.005) = 12.11Effective duration = ($938.62−$831.74)÷(2×$882.72×0.005) = 12.11
This means that if interest rates rise or fall by a full percentage point, the price of the bond would fall or rise by approximately 12.11%. Note that you can use effective duration in place of modified duration in Equation 11.10 to find the percent change in the price of a bond when interest rates move by more or less than 1.0%. When calculating the effective duration of a callable bond, one modification may be necessary. If the calculated price of the bond when interest rates fall is greater than the bond’s call price, then use the call price in the equation rather than BP(ri↓) and proceed as before.
Uses of Bond Duration Measures
You can use duration analysis in many ways to guide your decisions about investing in bonds. For example, as we saw earlier, you can use modified duration or effective duration to measure the potential price volatility of a particular issue. Another equally important use of duration is in the structuring of bond portfolios. That is, if you thought that interest rates were about to increase, you could reduce the overall duration of the portfolio by selling higher-duration bonds and buying shorter-duration bonds. Such a strategy could prove useful because shorter-duration bonds do not decline in value to the same degree as longer-duration bonds. On the other hand, if you felt that interest rates were about to decline, the opposite strategy would be appropriate.
Active, short-term investors frequently use duration analysis in their day-to-day operations. Longer-term investors also employ it in planning their investment decisions. Indeed, a strategy known as bond portfolio immunization represents one of the most important uses of duration.
Bond Immunization
Some investors hold portfolios of bonds not for the purpose of “beating the market,” but rather to accumulate a specified level of wealth by the end of a given investment horizon. For these investors, bond portfolio immunization often proves to be of great value. Immunization allows you to derive a specified rate of return from bond investments over a given investment interval regardless of what happens to market interest rates over the course of the holding period. In essence, you are able to “immunize” your portfolio from the effects of changes in market interest rates over a given investment horizon.
To understand how and why bond portfolio immunization is possible, you will recall from our earlier discussion that changes in market interest rates will lead to two distinct and opposite changes in bond valuation. The first effect is known as the price effect, and the second is known as the reinvestment effect. Whereas an increase in rates has a negative effect on a bond’s price, it has a positive effect on the reinvestment of coupons. Therefore, when interest rate changes do occur, the price and reinvestment effects work against each other from the standpoint of the investor’s wealth.
Excel@Investing
Table 11.2 Bond Immunization
|
Year t |
Cash Flow from Bond |
|
|
|
|
|
Terminal Value of Reinvested Cash Flow |
|
1 |
$ 80 |
× |
(1.08)4 |
× |
(1.06)3 |
= |
$ 129.63 |
|
2 |
$ 80 |
× |
(1.08)3 |
× |
(1.06)3 |
= |
$ 120.03 |
|
3 |
$ 80 |
× |
(1.08)2 |
× |
(1.06)3 |
= |
$ 111.14 |
|
4 |
$ 80 |
× |
(1.08) |
× |
(1.06)3 |
= |
$ 102.90 |
|
5 |
$ 80 |
× |
(1.06)3 |
|
|
= |
$ 95.28 |
|
6 |
$ 80 |
× |
(1.06)2 |
|
|
= |
$ 89.89 |
|
7 |
$ 80 |
× |
(1.06) |
|
|
= |
$ 84.80 |
|
8 |
$ 80 |
|
|
|
|
= |
$ 80.00 |
|
8 |
$1,036.67 |
|
|
|
|
|
$1,036.67 |
|
|
|
|
Total |
$1,850.33 |
|||
|
|
|
|
Investor’s required wealth at 8% |
$1,850.93 |
|||
|
|
|
|
Difference |
$ 0.60 |
When the average duration of the portfolio just equals the investment horizon, these counteracting effects offset each other and leave your position unchanged. This should not come as much of a surprise because such a property is already embedded in the duration measure. If that relationship applies to a single bond, it should also apply to the weighted-average duration of a whole bond portfolio. When such a condition (of offsetting price and reinvestment effects) exists, a bond portfolio is immunized. More specifically, your wealth is immunized from the effects of interest rate changes when the weighted-average duration of the bond portfolio exactly equals your desired investment horizon. Table 11.2 provides an example of bond immunization using a 10-year, 8% coupon bond with a duration of 8 years. Here, we assume that your desired investment horizon is also 8 years.
The example in Table 11.2 assumes that you originally purchased the 8% coupon bond at par. It further assumes that market interest rates for bonds of this quality drop from 8% to 6% at the end of the fifth year. Because you had an investment horizon of exactly 8 years and desire to lock in an interest rate return of exactly 8%, it follows that you expect to accumulate cash totaling $1,850.93 [i.e., $1,000 invested at 8% for 8 years = $1,000×(1.08)8 = $1,850.93]8 years = $1,000×(1.08)8 = $1,850.93], regardless of interest rate changes in the interim. As you can see from the results in Table 11.2 , the immunization strategy netted you a total of $1,850.33—just 60 cents short of your desired goal. Note that in this case, although reinvestment opportunities declined in years 5, 6, and 7 (when market interest rates dropped to 6%), that same lower rate led to a higher market price for the bond. That higher price, in turn, provided enough capital gains to offset the loss in reinvested income. This remarkable result clearly demonstrates the power of bond immunization and the versatility of bond duration. And note that even though the table uses a single bond for purposes of illustration, the same results can be obtained from a bond portfolio that is maintained at the proper weighted-average duration.
Maintaining a fully immunized portfolio (of more than one bond) requires continual portfolio rebalancing. Indeed, every time interest rates change, the duration of a portfolio changes. Because effective immunization requires that the portfolio have a duration value equal in length to the remaining investment horizon, the composition of the portfolio must be rebalanced each time interest rates change. Further, even in the absence of interest rate changes, a bond’s duration declines more slowly than its term to maturity. This, of course, means that the mere passage of time will dictate changes in portfolio composition. Such changes will ensure that the duration of the portfolio continues to match the remaining time in the investment horizon. In summary, portfolio immunization strategies can be extremely effective, but immunization is not a passive strategy and is not without potential problems, the most notable of which are associated with portfolio rebalancing.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 11.10 What does the term duration mean to bond investors and how does the duration of a bond differ from its maturity? What is modified duration, and how is it used? What is effective duration, and how does it differ from modified duration?
2. 11.11 Describe the process of bond portfolio immunization, and explain why an investor would want to immunize a portfolio. Would you consider portfolio immunization a passive investment strategy comparable to, say, a buy-and-hold approach? Explain.
Bond Investment Strategies
1. LG 6
Generally speaking, bond investors tend to follow one of three kinds of investment programs. First, there are those who live off the income. They are conservative, quality-conscious, income-oriented investors who seek to maximize current income. Second, there are the speculators (bond traders). Their investment objective is to maximize capital gains, often within a short time span. Finally, there are the long-term investors. Their objective is to maximize total return—from both current income and capital gains—over fairly long holding periods.
In order to achieve the objectives of any of these programs, you need to adopt a strategy that is compatible with your goals. Professional money managers use a variety of techniques to manage the multimillion- (or multibillion-) dollar bond portfolios under their direction. These range from passive approaches, to semiactive strategies, to active, fully managed strategies using interest rate forecasting and yield spread analysis. Most of these strategies are fairly complex and require substantial computer support. Even so, we can look briefly at some of the more basic strategies to gain an appreciation of the different ways in which you can use fixed-income securities to reach different investment objectives.
Passive Strategies
The bond immunization strategies we discussed earlier are considered to be primarily passive in nature. Investors using these tools typically are not attempting to beat the market but to lock in specified rates of return that they deem acceptable, given the risks involved. As a rule, passive investment strategies are characterized by a lack of input regarding investor expectations of changes in interest rates and/or bond prices. Further, these strategies typically do not generate significant transaction costs. A buy-and-hold strategy is perhaps the most passive of all investment strategies. All that is required is that the investor replace bonds that have deteriorating credit ratings, have matured, or have been called. Although buy-and-hold investors restrict their ability to earn above-average returns, they also minimize the losses that transaction costs represent.
One popular approach that is a bit more active than buy-and-hold is the use of bond ladders . In this strategy, equal amounts are invested in a series of bonds with staggered maturities. Here’s how a bond ladder works. Suppose you want to confine your investing to fixed-income securities with maturities of 10 years or less. Given that maturity constraint, you could set up a ladder by investing (roughly) equal amounts in, say, 3-, 5-, 7-, and 10-year issues. When the 3-year issue matures, you would put the money from it (along with any new capital) into a new 10-year note. You would continue this rolling-over process so that eventually you would hold a full ladder of staggered 10-year notes. By rolling into new 10-year issues every 2 or 3 years, the interest income on your portfolio will be an average of the rates available over time. The laddered approach is a safe, simple, and almost automatic way of investing for the long haul. A key ingredient of this or any other passive strategy is, of course, the use of high-quality investments that possess attractive features, maturities, and yields.
Trading on Forecasted Interest Rate Behavior
In contrast to passive strategies, a more risky approach to bond investing is the forecasted interest rate approach. Here, investors seek attractive capital gains when they expect interest rates to decline and preservation of capital when they anticipate an increase in interest rates. This strategy is risky because it relies on the imperfect forecast of future interest rates. The idea is to increase the return on a bond portfolio by making strategic moves in anticipation of interest rate changes. Such a strategy is essentially market timing. An unusual feature of this tactic is that most of the trading is done with investment-grade securities because these securities are the most sensitive to interest rate movements, and that sensitivity is what active traders hope to profit from.
This strategy brings together interest rate forecasts and the concept of duration. For example, when a decline in rates is anticipated, aggressive bond investors often seek to lengthen the duration of their bonds (or bond portfolios) because bonds with longer durations (e.g., long-term bonds) rise more in price than do bonds with shorter durations. At the same time, investors look for low-coupon and/or moderately discounted bonds because these bonds have higher durations, and their prices will rise more when interest rates fall. Interest rate swings may be short-lived, so bond traders try to earn as much as possible in as short a time as possible. When rates start to level off and move up, these investors begin to shift their money out of long, discounted bonds and into high-yielding issues with short maturities. In other words, they do a complete reversal and look for bonds with shorter durations. During those periods when bond prices are dropping, investors are more concerned about preservation of capital, so they take steps to protect their money from capital losses. Thus, they tend to use such short-term obligations as Treasury bills, money funds, short-term (two- to five-year) notes, or even variable-rate notes.
Bond Swaps
In a bond swap , an investor simultaneously liquidates one position and buys a different issue to take its place. Swaps can be executed to increase current yield or yield to maturity, to take advantage of shifts in interest rates, to improve the quality of a portfolio, or for tax purposes. Although some swaps are highly sophisticated, most are fairly simple transactions. They go by a variety of colorful names, such as “profit takeout,” “substitution swap,” and “tax swap,” but they are all used for one basic reason: portfolio improvement. We will briefly review two types of bond swaps that are fairly simple and hold considerable appeal: the yield pickup swap and the tax swap.
In a yield pickup swap , an investor switches out of a low-coupon bond into a comparable higher-coupon issue in order to realize an instantaneous pickup of current yield and yield to maturity. For example, you would be executing a yield pickup swap if you sold 20-year, A-rated, 6.5% bonds (which were yielding 8% at the time) and replaced them with an equal amount of 20-year, A-rated, 7% bonds that were priced to yield 8.5%. By executing the swap, you would improve your current yield (your interest income would increase from $65 a year to $70 a year) as well as your yield to maturity (from 8% to 8.5%). Such swap opportunities arise because of the yield spreads that normally exist between different types of bonds. You can execute such swaps simply by watching for swap candidates and asking your broker to do so. In fact, the only thing you must be careful of is that transaction costs do not eat up all the profits.
Another popular type of swap is the tax swap , which is also relatively simple and involves few risks. You can use this technique whenever you have a substantial tax liability as a result of selling some security holdings at a profit. The objective is to execute a swap to eliminate or substantially reduce the tax liability accompanying the capital gains. This is done by selling an issue that has undergone a capital loss and replacing it with a comparable obligation.
For example, assume that you had $10,000 worth of corporate bonds that you sold (in the current year) for $15,000, resulting in a capital gain of $5,000. You can eliminate the tax liability accompanying the capital gain by selling securities that have capital losses of $5,000. Let’s assume you find you hold a 20-year, 4.75% municipal bond that has undergone a $5,000 drop in value. Thus, you have the required tax shield in your portfolio. Now you need to find a viable swap candidate. Suppose you find a comparable 20-year, 5% municipal issue currently trading at about the same price as the issue being sold. By selling the 4.75s and simultaneously buying a comparable amount of the 5s, you will not only increase your tax-free yields (from 4.75% to 5%) but will also eliminate the capital gains tax liability.
The only precaution in doing tax swaps is that you cannot use identical issues in the swap transactions. The IRS would consider that a “wash sale” and disallow the loss. Moreover, the capital loss must occur in the same taxable year as the capital gain. Typically, at year-end, tax loss sales and tax swaps multiply as knowledgeable investors hurry to establish capital losses.
Concepts in Review
Answers available at http://www.pearsonhighered.com/smart
1. 11.12 Briefly describe a bond ladder and note how and why an investor would use this investment strategy. What is a tax swap and why would it be used?
2. 11.13 What strategy would you expect an aggressive bond investor (someone who’s looking for capital gains) to employ?
3. 11.14 Why is interest sensitivity important to bond speculators? Does the need for interest sensitivity explain why active bond traders tend to use high-grade issues? Explain.
Case Problem 10.2 The Case of the Missing Bond Ratings
1. LG 2
It’s probably safe to say that there’s nothing more important in determining a bond’s rating than the underlying financial condition and operating results of the company issuing the bond. Just as financial ratios can be used in the analysis of common stocks, they can also be used in the analysis of bonds—a process we refer to as credit analysis. In credit analysis, attention is directed toward the basic liquidity and profitability of the firm, the extent to which the firm employs debt, and the ability of the firm to service its debt.
|
Financial Ratio |
Company 1 |
Company 2 |
Company 3 |
Company 4 |
Company 5 |
Company 6 |
|
1. Current ratio |
1.13 |
1.39 |
1.78 |
1.32 |
1.03 |
1.41 |
|
2. Quick ratio |
0.48 |
0.84 |
0.93 |
0.33 |
0.50 |
0.75 |
|
3. Net profit margin |
4.6% |
12.9% |
14.5% |
2.8% |
5.9% |
10.0% |
|
4. Return on total capital |
15.0% |
25.9% |
29.4% |
11.5% |
16.8% |
28.4% |
|
5. Long-term debt to total capital |
63.3% |
52.7% |
23.9% |
97.0% |
88.6% |
42.1% |
|
6. Owners’ equity ratio |
18.6% |
18.9% |
44.1% |
1.5% |
5.1% |
21.2% |
|
7. Pretax interest coverage |
2.3 |
4.5 |
8.9 |
1.7 |
2.4 |
6.4 |
|
8. Cash flow to total debt |
34.7% |
48.8% |
71.2% |
20.4% |
30.2% |
42.7% |
|
Notes: 1. Current ratio = current assets / current liabilities 2. Quick ratio = (current assets – inventory) / current liabilities 3. Net profit margin = net profit / sales 4. Return on total capital = pretax income / (equity + long-term debt) 5. Long-term debt to total capital = long-term debt / (long-term debt + equity) 6. Owner’s equity ratio = stockholders’ equity / total assets 7. Pretax interest coverage = earnings before interest and taxes / interest expense 8. Cash flow to total debt = (net profit + depreciation) / total liabilities |
||||||
|
A Table Of Financial Ratios (All ratios are real and pertain to real companies.) |
The financial ratios shown in the preceding table are often helpful in carrying out such analysis. The first two ratios measure the liquidity of the firm; the next two, its profitability; the following two, the debt load; and the final two, the ability of the firm to service its debt load. (For ratio 5, the lower the ratio, the better. For all the others, the higher the ratio, the better.) The table lists each of these ratios for six companies.
Questions
a. Three of these companies have bonds that carry investment-grade ratings. The other three companies carry junk-bond ratings. Judging by the information in the table, which three companies have the investment-grade bonds and which three have the junk bonds? Briefly explain your selections.
b. One of these six companies is an AAA-rated firm and one is B-rated. Identify those companies. Briefly explain your selections.
c. Of the remaining four companies, one carries an AA rating, one carries an A rating, and two have BB ratings. Which companies are they?
Case Problem 11.1 The Bond Investment Decisions of Dave and Marlene Carter
1. LG 3
2. LG 4
3. LG 6
Dave and Marlene Carter live in the Boston area, where Dave has a successful orthodontics practice. Dave and Marlene have built up a sizable investment portfolio and have always had a major portion of their investments in fixed-income securities. They adhere to a fairly aggressive investment posture and actively go after both attractive current income and substantial capital gains. Assume that it is now 2016 and Marlene is currently evaluating two investment decisions: one involves an addition to their portfolio, the other a revision to it.
The Carters’ first investment decision involves a short-term trading opportunity. In particular, Marlene has a chance to buy a 7.5%, 25-year bond that is currently priced at $852 to yield 9%; she feels that in two years the promised yield of the issue should drop to 8%.
The second is a bond swap. The Carters hold some Beta Corporation 7%, 2029 bonds that are currently priced at $785. They want to improve both current income and yield to maturity and are considering one of three issues as a possible swap candidate: (a) Dental Floss, Inc., 7.5%, 2041, currently priced at $780; (b) Root Canal Products of America, 6.5%, 2029, selling at $885; and (c) Kansas City Dental Insurance, 8%, 2030, priced at $950. All of the swap candidates are of comparable quality and have comparable issue characteristics.
Questions
a. Regarding the short-term trading opportunity:
1. What basic trading principle is involved in this situation?
2. If Marlene’s expectations are correct, what will the price of this bond be in two years?
3. What is the expected return on this investment?
4. Should this investment be made? Why?
b. Regarding the bond swap opportunity:
1. Compute the current yield and the promised yield (use semiannual compounding) for the bond the Carters currently hold and for each of the three swap candidates.
2. Do any of the swap candidates provide better current income and/or current yield than the Beta Corporation bonds the Carters now hold? If so, which one(s)?
3. Do you see any reason why Marlene should switch from her present bond holding into one of the other issues? If so, which swap candidate would be the best choice? Why?
Case Problem 10.1 Max and Veronica Develop a Bond Investment Program
1. LG 1
2. LG 4
Max and Veronica Shuman, along with their teenage sons, Terry and Thomas, live in Portland, Oregon. Max is a sales rep for a major medical firm, and Veronica is a personnel officer at a local bank. Together they earn an annual income of around $100,000. Max has just learned that his recently departed rich uncle has named him in his will to the tune of some $250,000 after taxes. Needless to say, the family is elated. Max intends to spend $50,000 of his inheritance on a number of long-overdue family items (like some badly needed remodeling of their kitchen and family room, the down payment on a new Porsche Boxster, and braces to correct Tom’s overbite). Max wants to invest the remaining $200,000 in various types of fixed-income securities.
Max and Veronica have no unusual income requirements or health problems. Their only investment objectives are that they want to achieve some capital appreciation, and they want to keep their funds fully invested for at least 20 years. They would rather not have to rely on their investments as a source of current income but want to maintain some liquidity in their portfolio just in case.
Questions
a. Describe the type of bond investment program you think the Shuman family should follow. In answering this question, give appropriate consideration to both return and risk factors.
b. List several types of bonds that you would recommend for their portfolio and briefly indicate why you would recommend each.
c. Using a recent issue of the Wall Street Journal, Barron’s, or an online source, construct a $200,000 bond portfolio for the Shuman family. Use real securities and select any bonds (or notes) you like, given the following ground rules:
1. The portfolio must include at least one Treasury, one agency, and one corporate bond; also, in total, the portfolio must hold at least five but no more than eight bonds or notes.
2. No more than 5% of the portfolio can be in short-term U.S. Treasury bills (but note that if you hold a T-bill, that limits your selections to just seven other notes/bonds).
3. Ignore all transaction costs (i.e., invest the full $200,000) and assume all securities have par values of $1,000 (although they can be trading in the market at something other than par).
4. Use the latest available quotes to determine how many bonds/notes/bills you can buy.
d. Prepare a schedule listing all the securities in your recommended portfolio. Use a form like the one shown below and include the information it calls for on each security in the portfolio.
e. In one brief paragraph, note the key investment attributes of your recommended portfolio and the investment objectives you hope to achieve with it.
|
Security |
Latest Quoted Price |
Number of Bonds Purchased |
Amount Invested |
Annual Coupon Income |
Current Yield |
|
Issuer-Coupon-Maturity |
|
|
|
|
|
|
Example: U.S. Treas - 8½%-’18 |
1468/32 |
15 |
$21,937.50 |
$1,275 |
5.81% |
|
1. |
|
|
|
|
|
|
2. |
|
|
|
|
|
|
3. |
|
|
|
|
|
|
4. |
|
|
|
|
|
|
5. |
|
|
|
|
|
|
6. |
|
|
|
|
|
|
7. |
|
|
|
|
|
|
8. |
|
|
|
|
|
|
Totals |
— |
|
$200,000.00 |
$ |
% |
Case Problem 11.2 Grace Decides to Immunize Her Portfolio
1. LG 4
2. LG 5
3. LG 6
Grace Hesketh is the owner of an extremely successful dress boutique in downtown Chicago. Although high fashion is Grace’s first love, she’s also interested in investments, particularly bonds and other fixed-income securities. She actively manages her own investments and over time has built up a substantial portfolio of securities. She’s well versed on the latest investment techniques and is not afraid to apply those procedures to her own investments.
Grace has been playing with the idea of trying to immunize a big chunk of her bond portfolio. She’d like to cash out this part of her portfolio in seven years and use the proceeds to buy a vacation home in her home state of Oregon. To do this, she intends to use the $200,000 she now has invested in the following four corporate bonds (she currently has $50,000 invested in each one).
1. A 12-year, 7.5% bond that’s currently priced at $895
2. A 10-year, zero-coupon bond priced at $405
3. A 10-year, 10% bond priced at $1,080
4. A 15-year, 9.25% bond priced at $980
(Note: These are all noncallable, investment-grade, nonconvertible/straight bonds.)
Questions
a. Given the information provided, find the current yield and the promised yield for each bond in the portfolio. (Use annual compounding.)
b. Calculate the Macaulay and modified durations of each bond in the portfolio and indicate how the price of each bond would change if interest rates were to rise by 75 basis points. How would the price change if interest rates were to fall by 75 basis points?
c. Find the duration of the current four-bond portfolio. Given the seven-year target that Grace has set, would you consider this an immunized portfolio? Explain.
d. How could you lengthen or shorten the duration of this portfolio? What’s the shortest portfolio duration you can achieve? What’s the longest?
e. Using one or more of the four bonds described above, is it possible to come up with a $200,000 bond portfolio that will exhibit the duration characteristics Grace is looking for? Explain.
f. Using one or more of the four bonds, put together a $200,000 immunized portfolio for Grace. Because this portfolio will now be immunized, will Grace be able to treat it as a buy-and-hold portfolio-one she can put away and forget about? Explain.
|
Levels/Criteria |
200-180 |
179-160 |
159-150 |
Below 150 |
|
Demonstration of Reading Comprehension (In-Class Essay Only) |
Writing demonstrates strong comprehension of reading through apt summarizing, paraphrasing, and quoting. |
Writing demonstrates sufficient comprehension of reading through clear summarizing, paraphrasing, and quoting. |
Writing demonstrates superficial or inaccurate comprehension of reading through insufficient or inaccurate summarizing, paraphrasing, and quoting. |
Writing does not demonstrate comprehension of reading. MLA format not in place |
|
Thesis/Main Idea |
The writing asserts a precise, thoughtful position in its thesis or main idea. |
The writing presents a clear, specific position in its thesis or main idea. |
The writing does not present a clear, specific position in its thesis or main idea. |
The writing has no apparent thesis. |
|
Organization |
- Writing demonstrates an effective pattern of organization that facilitates the reader's understanding of the thesis. - Main points are clearly, precisely stated. - Paragraphs are appropriately organized and avoid redundancy. |
- Writing follows an appropriate pattern of organization. - Main points are sufficiently clear - Paragraphs have sufficient internal organization. - Writing is only occasionally redundant. -Uses the writer’s name in analysis |
- Writing is not well organized. - Main points are not clearly stated. - Paragraphs do not have sufficient internal organization - Writing is sometimes redundant. -Writer’s name is in the points and analysis |
- Writing lacks coherent structure. - There do not seem to be main points. - Paragraphs do not have coherent internal organization. - Writing is redundant throughout. |
|
Development/ Illustration |
Statements are substantially supported Illustration (a) is the only place in the body with the writer’s name. |
Statements are sufficiently supported with relevant illustration. |
Statements are insufficiently illustrated or illustration is irrelevant. |
Statements are not illustrated. Lacks Summary |
|
Use of Textual Evidence |
Writing adeptly uses appropriate and convincing passages from texts. 4 lines or 5lines or more a block quotation. |
Writing sufficiently uses appropriate passages from texts. |
Writing does not sufficiently incorporate appropriate passages from texts. 5 or more lines |
Writing does not incorporate passages from texts. |
|
Analysis |
- Analysis is insightful and well articulated - Ideas are logically connected. - Writing duly considers more than one viewpoint/position and provides concessions where appropriate. Don’t include the writer’s name in analysis |
- Analysis is cogent and clear - Ideas are logically connected. - Writing accounts for more than one perspective and provides some concession. |
- Analysis is superficial and/or poorly articulated. - Writing does not connect ideas logically. - Writing provides only superficial discussion of more than one viewpoint. |
- Analysis is nonexistent or illogical. - Writing provides no discussion of more than one viewpoint. |
|
Clarity/Style |
- Writing engages reader. - Vocabulary and sentence structure are appropriate for the topic and intended audience. - Writing is clear and precise. |
- Writing enables reader to understand with little or no rereading. - Vocabulary and sentence structure are sufficiently appropriate and clear. |
- Writing requires reader to reread in order to understand ideas. - Vocabulary and sentence structure are ineffective or unclear. |
Writing is not comprehensible. |
|
Mechanics/ Usage |
Writing is virtually free from errors that distract from meaning and readability. |
Occasional errors distract from meaning and readability. |
Grammatical errors are noticeably distracting. Title is punctuated incorrectly, header not in place. |
Grammatical errors are consistently distracting and make writing difficult to follow. |
3
1st Essay Prompt, February 15th
1st Essay Due March 15th on Canvas before Midnight. 200 Points. I don’t accept late papers.
Choose one essay in Rereading America that you have read that writes about the challenges of being a human being in the world. Your assignment is to establish not only what the challenges are but why they exist.
In order to write this essay, you must consider themes associated with the readings such as education, indoctrination, race, class, gender, sexual orientation, religion, police brutality, violence, social norms, fear, knowledge, philosophy, cultural leadership, dominance, power, resistance, dehumanization, marginalization, power, structural racism, assimilation, condition, cognitive dissonance and many more presented in class and in the reading.
This assignment is an argumentative essay, which is in third person. You will not use the words, “we, our, us, you or I.” You will use words like society, people, individuals, and persons.
This essay is not a summary of the reading, so don’t write the author’s name in the points or the explanations sections. Do write the author’s name at the beginning of the summaries of the quotes in Illustration A of each body paragraph (look below).
You will also implement the MLA format. Here is the link to make sure you are clear about the form https://www.youtube.com/watch?v=oP0js5gFkfY If you don’t have the MLA format, points will be deducted for each error. Make sure to watch the video and apply the steps to your essay before writing.
To establish your thesis, answer the question: What are the problems that exist in society because of social constructs of power? The thesis is a combination of any three points you choose from the homework assignments.
Introduction and Thesis
1st paragraph:
1. Write a summary of one of the essays from Rereading America. Include the
writer’s name and title of the book; the book is either underlined or italicized. (5 sentences)
2. Answer the question above to get your thesis. The answer is the last sentence(s) of the first paragraph. No more than 2 sentences.
Body of the Essay
2nd paragraph:
1. Point: What is the first problem that exist because of a social construct? (no more than 2 sentences)
2. Illustration (A): Write a summary of the quotation; begin with Coates’
name. (Must be 5 sentences)
3. Illustration (B): Insert a quotation that reflects the summary. Include page inside the parenthesis. Don’t pp. pg, or p inside the
parenthesis.
4. Explanation: Why is this social construct a problem in society?
(4-7 sentences)
3rd paragraph:
1. Point: What is the second problem that exist because of a social construct? (no more than 2 sentences)
2. Illustration (A): Write a summary of the quotation; begin with Coates’
name. (Must be 5 sentences)
3. Illustration (B): Insert a quotation that reflects the summary. Include page inside the parenthesis. Don’t pp. pg, or p inside the
parenthesis.
4. Explanation: Why is this social construct a problem in society?
(4-7 sentences)
4th paragraph:
1. Point: What is the third problem that exist because of a social construct? (no more than 2 sentences)
2. Illustration (A): Write a summary of the quotation; begin with Coates’
name. (Must be 5 sentences)
3. Illustration (B): Insert a quotation that reflects the summary. Include page inside the parenthesis. Don’t pp. pg, or p inside the
parenthesis.
Only include the page number. For example: (45).
4. Explanation: Why is this social construct a problem in society?
(4-7 sentences)
CONCLUSION
5th Paragraph:
1. Reintroduce the introduction with the writer’s name. Do not include the title of
the book. (4-5 sentences)
2. Reintroduce the thesis. (1-2 sentences)
Get help from top-rated tutors in any subject.
Efficiently complete your homework and academic assignments by getting help from the experts at homeworkarchive.com