You want to invest in a bond and your banker shows you two issued by the same company and that have exactly the same credit risk. They both mature five years from now. One is trading at $129 per share and provides a 12% coupon, while the other trades at $95 and provides a 4% coupon. You look at each bond’s yield-to-maturity (YTM) percentage and see the two are fairly close. Your banker suggests you buy Bond A because it offers the slightly higher YTM (see Table 1).
You have heard about another measure for evaluating bonds with different coupon rates called "duration," but you are not sure what it means and whether you should consider it in making this investment selection. You decide to consult with your financial planner.
Why the Yield-to-Maturity Metric Is Insufficient
Your planner confirms for you that YTM, while an often-used metric, is an incomplete and insufficient measure for your decision-making. She explains it is calculated under the implicit assumption that the interest income (coupons) you will receive can be reinvested at the same YTM rate throughout the entire life of the bond. Since current short-term interest rates are well below the YTM of both bonds, their realized return is likely to be below the promised YTM of 5.25% and 5.16%.
Using the current short-term interest rate of 2%, your planner calculates an expected realized return for both bonds based on their coupon payments being reinvested at the 2% rate. Under these conditions, she shows that Bond B would produce an annualized return of 4.93%, while Bond A would result in an annualized return of 4.72%—a full 21 basis points lower.
Your planner explains this difference between the YTM and the realized return for the bonds is due to their differing sensitivities to interest rate changes. To demonstrate more clearly, she introduces a zero-coupon bond from the same company, Bond C. It matures in 4.6 years and trades at $80 (See Table 2).
Use Duration to Determine Bond's Sensitivity to Interest Rates
The “Interest Rate Sensitivity” columns in Table 2 show how the value of each of the bonds is affected if market interest rates rise or fall by 100 basis points. You can see that the zero-coupon bond behaves more like Bond B than Bond A when interest rates change. This information about sensitivity to interest rates is communicated through the bond’s duration (or modified duration) metric. As shown in Table 2, Bond C and Bond B have the same duration, therefore their values shift similarly for any given change in interest rates. (For related reading, see: Use Duration and Convexity to Measure Bond Risk.)
Duration1 is simply defined as the time-weighted average of a stream of cash flows. As such, it measures the sensitivity of the bond’s present value (or price) to changes in interest rates. A higher duration means a greater sensitivity to interest rate changes, a lower duration means less sensitivity. Therefore, when choosing between bonds with different coupon rates, we should be more concerned with their duration than with their respective maturities.
In the example above, you will certainly favor Bond B over Bond C (same duration but higher yield). Bond A is more difficult to compare because its duration is different. Clearly you will choose it instead of B or C if you expect an interest rate increase. (It experiences less of a drop in price for any given increase in yield.) However, if interest rates fall, because of that same lower sensitivity, A will rise in value less than B or C. To properly evaluate Bond A you have to compare it to other bonds with the same duration.
(For related reading, see: Common Bond-Buying Mistakes.)
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Where: D=duration, t=period: 1,2,…n; Ct=coupon or cash flow at time “t”, & r=YTM.