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1 March 1981 Financial Analysts Journal Volume 37, Issue 2

How to Hedge a Bond Investment

  1. Charles H. Gushee

Suppose that, when you buy a bond, you want to keep fully invested at a known yield. If your bond is a zero coupon bond that matures at the end of the period for which you want to keep fully invested, you can lock in the bond’s initial yield simply by holding it to maturity. If your bond has a positive coupon rate, however, you must reinvest the coupon each six months as you receive it. But if you don’t know what the market yield will be at those future reinvestment dates, how can you know exactly what your bond fund will amount to?

A five-year coupon bond may be thought of as a portfolio of 11 zero coupon bonds—10 pieces being the semiannual coupon payments and the eleventh being the principal payment at maturity. The average of the maturities on these 11 zero coupon bonds, weighted by their present worths, is called the duration. With a zero coupon bond, the maturity of the bond equals its duration. On more complicated bonds, duration is less than maturity. The initial yield can still be locked in, but for a period equal to the bond’s duration, rather than its term to maturity. This creates certain complications in practice.

For example, a five-year, seven per cent bond priced to yield eight per cent has a duration of 4.3 years. If the investor’s bond portfolio is to behave like a zero coupon bond with a maturity of 4.3 years, then six months hence its duration must be one-half year less, or 3.787 years. A seven per cent, 4½-year bond yielding eight per cent has a duration, however, of 3.924 years. Obviously, adjustments must be made from time to time to maintain the desired duration. The author provides examples of how these adjustments can lock in initial yields.

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