An important, and often ignored, factor of investing in bonds is the dependence of realized returns on market interest rates. Most investors know that bond prices change inversely with changes in market interest rates. Many though, forget that the return they actually earn depends on the reinvestment of the interest cash flows the bond generates. The consequences of reinvesting cash interest payments can be easily examined with the aid of a spreadsheet.
The issue is not limited to fixed-income investments, however. The realized return and the wealth accumulation for any investment depends on the reinvestment of the cash the investment generates. And the impact over time can be substantial. Dividend reinvestment generates a wealth level nearly 20 times greater than that of pure capital appreciation ($518 vs. $26 on $1 invested at the end of 1925).
The differences in wealth accumulation arise from different realized rates of return. The S&P 500 offers a capital gain of about 5% a year, and dividend reinvestment offers nearly another 5%. That extra 5% a year from dividend reinvestment eventually results in a substantially greater accumulated wealth. Of course, this example covers a 65-year time frame, but the results are still quite noticeable over much shorter horizons. With fixed-income investments, an initial 30-year horizon is quite common, and even a 10-year horizon can be long enough to generate a substantial difference in return. Long-term government bonds have actually suffered net capital losses over the period shown. Most of the losses occurred during the highly inflationary period since the 1970s.
Our spreadsheet deals with a bond's realized return, but it can be modified for any other investment. For other investments, we would have to enter the periodic cash flows as well as the estimated returns to determine the realized return. With fixed-income securities, it is possible to estimate the future returns from current market data.
The main question that must be answered in determining the return a bond might generate is what market interest rate is relevant at any given period of time. After the fact, this rate can be determined from a number of sources. The Value Line Investment Survey now has a section on fixed-income securities giving interest rates for different bond rating categories and for Treasury issues of different maturities. The Standard & Poor's Bond Guide carries similar information.
The Yield Curve
For planning purposes, though, an investor will want to examine the effect of potential interest rate changes before they occur. While this estimation is not easy, there are some ways to approach the problem. One of the most common methods of estimating future interest rates uses the yield curve. The yield curve is a graphical view of the relationship between maturity and yield to maturity for Treasury securities. This relationship between yield and maturity is also referred to as the term structure of interest rates. From this data, it is possible to make inferences about the market's perceptions of future interest rates on government securities. To pass from Treasuries to corporate issues, it is necessary to estimate the premium that the riskiness of corporates will command relative to Treasuries.
Risk Premiums and Returns
The risk premium on any security--or for an entire segment of the market, such as AA-rated corporates or junk bonds--is a measure of the extra return that security, or that market segment, is offering in compensation for its risk over and above the risk of a Treasury issue. We usually presume that Treasuries are free of default risk (which seems reasonable), but of course, there is interest rate risk even on Treasuries. Nevertheless, Treasury securities serve as our benchmark, and the base from which yields on other securities are estimated. Estimates of these premiums (or yield spreads) can be derived from the Federal Reserve Bulletin, which most large libraries should carry.
This yield spread is called a default yield spread since it measures the extra return (or risk premium) an investor receives for taking the risk of default from a corporate security. The default yield spread depends on the creditworthiness of the issuer, which can change over time. Various investment information services rate fixed-income securities by credit risk. Perhaps the best known of these companies are Standard & Poor's and Moody's. The top four credit ratings (AAA to BBB for S&P; Aaa to Baa for Moody's) are referred to as investment grade. Securities with these ratings usually carry relatively low risk of default and therefore have a small yield spread. One of the major determinants of a high bond rating is substantial coverage of interest and other fixed outlays. This is called cash flow coverage and it measures the amount by which a company's cash flow can shrink before they cannot meet their fixed obligations.
The 1970s saw a vast growth in the issuance of lesser-rated securities, so called "junk bonds." Barron's tracks the yield spread on junk bonds in its Market Laboratory section each week.
The growth in this market was fueled by research that showed a relatively low rate of default on these securities, especially considering the substantial yield premiums they offered. However, these studies did not examine the effect of a general economic slowdown on this entire segment of the market. Diversification among a range of junk bonds will indeed reduce the risk of default from factors that affect only one company. A recession will affect this entire market segment much more severely than the segment of investment-grade bonds because the cash flow coverage of low-grade bonds is much tighter. Interestingly enough, research on fixed-income securities has shown that yield spreads on high-grade issues tend to get larger as the time to maturity increases, while yield spreads on lower-grade issues tend to shrink as the maturity lengthens. The explanation for this is that longer maturities open up the possibility for more bad things to happen to good companies and more good things to happen to bad companies. In any event, an investor will expect some extra return for taking default risk. Our approach is to add some premium to the imputed Treasury return to account for this risk. The premiums in the spreadsheet are meant to be illustrative and should not be taken as investment rules.
Using the Yield Curve
Estimating (short-term) interest rates from the yield curve is relatively simple. We just assume that the return over a two-year period (which we can determine from the rate on a two-year maturity Treasury bond) is equal to the rate we can earn for one year (from a one year maturity bond) times the return that could be earned by reinvesting after one year in another one-year maturity bond. In other words, the market is telling us, from the two-year return and the one-year return, its judgment of the future one-year return. This analysis can be applied to any future time period.
Economists call this the expectations theory of the term structure, but as investors we simply want to use this information to estimate future interest rates for analyzing our bond portfolio. We do this with the market expectation of future rates. In a formula, the two-year return is the product of the known one-year return times the estimated one year return one year from now.
(1 + 0R2)^t = (1 + 0R1)^t (1 + 1R2)^t
where:
0R2= the return on a two-year maturity Treasury note issued today maturing two years from today
0R1= the return on a one-year maturity Treasury note issued today maturing one year from today
1R2 = the market's implicit (expected) return on a one-year maturity investment starting one year from now--in other words, the return over the year starting one year from now and maturing two years from now
t = years to maturity for each issue from time of investment
The estimated future one-year return is what we want to know, so we rearrange this relationship to get:
(1 + 1R2)^1 = (1 + 0R2)^2 (1 + 0R1)^1
This "forward rate" is the market's expected return on a one-year Treasury investment starting a year from now. As investors, we can infer other forward rates in the same fashion. The market is giving us a kind of consensus forecast of future interest rates.
By matching the maturity of the Treasury issue with the maturity of the bond we own (or are considering investing in), we can infer the reinvestment return over our entire future holding period of the bond. In addition, these expected future levels of interest rates imply market returns that can be used to determine the price at which our bond investment might trade in the future. This allows us to determine our realized return at any future date on the assumption that we might have to sell the bond before maturity.
The expected market yield on a bond with 20 years to maturity in 2001 (10 years from now) is determined by an analogous formula. 10R30 = [(1 + 0R30)^30 / (1 + 0R10)^10]^1/20-1
Duration and the Realized Rate of Return
The duration of the 30-year bond is 11.26 years initially. In addition, the realized return (total return if sold) on the bond is around 8.5% after 11 years. This corresponds to our initial yield to maturity and roughly matches the duration. We know that if we hold a bond to its duration (rather than to its maturity), our realized yield is independent of future changes in rates, and the spreadsheet shows this.
Setting Up the Spreadsheet
The spreadsheet requires only a few major formulas, most of which can be copied to perform the rest of the calculations you need. The first part of the spreadsheet contains the basic input data on the 30-year bond. The second part contains the Treasury yield curve data derived from the implied forward rates. We then enter formulas to determine the accumulated value, the value of the bond if sold prior to maturity, and the realized return at that selling date. In addition, we have added the calculation of the bond's
Duration (in years):
Effect of 1% Market Yield Change:-10.8% duration (a measure of its price sensitivity to interest rate changes) and the approximate percentage change in the bond's value for a one percentage point move in interest rates. For more information on duration, see the September/October 1988 issue of CI.
The data entered are the bond's current market price, its initial yield to maturity, its face value, its coupon rate (to determine the interest payments), the current date and the maturity date. The yield curve data are entered in columns J through L. Estimated default yield spread data is in columns N and T.
To see in detail the changes in future market interest rates, we have created several columns of information from J26 to L87. This information shows the expected future interest rate from each date for a period of time equal to the bond's remaining maturity. Since we have used Treasury bond data at five year increments to estimate future rates, we have averaged these rates to prevent large jumps or declines in the realized return that are simply due to starting with a new market rate at five-year intervals. The calculations perform a weighted average between the new rate and the old rate. These rates are then referred to in calculating the bond's market price and realized rate of return.
