"I can immunize a portfolio simply by investingin zero-coupon Treasury bonds." Comment on this statement

Question

What will be an ideal response?

Answer 1

If all the cash flows are received at the liability due date, the immunization risk measure is zero. In such a case the portfolio is equivalent to a pure discount security (zero-coupon security) that matures on the liability due date. If a portfolio can be constructed that replicates a pure discount security maturing on the liability due date, that portfolio will be the one with the lowest immunization risk. Typically, however, it is not possible to construct such an ideal portfolio. More details are given below.

An alternative approach to immunizing a portfolio against changes in the market yield is to invest in zero-coupon bonds with a maturity equal to the investment horizon. This is consistent with the basic principle of immunization, because the duration of a zero-coupon bond equals the liability's duration. However, in practice, the yield on zero-coupon bonds is typically lower than the yield on coupon bonds. Thus using zero-coupon bonds to fund a bullet liability requires more funds, because a lower target yield (e.g., yield on the zero-coupon bond) is being locked in.

Suppose, for example, that a portfolio manager must invest funds to satisfy a known liability of $20 million five years from now. If a target yield of 10% on a bond-equivalent basis (5% every six months) can be locked in using zero-coupon Treasury bonds, the funds necessary to satisfy the $20 million liability will be $12,278,260, the present value of $20 million using a discount rate of 10% (5% semiannually).

Suppose, instead, that by using coupon Treasury securities, a target yield of 10.3% on a bond-equivalent basis (5.15% every six months) is possible. Then the funds needed to satisfy the $20 million liability will be $12,104,240, the present value of $20 million discounted at 10.3% (5.15% semiannually). Thus a target yield higher by 30 basis points would reduce the cost of funding the $20 million by $12,278,260 – $12,104,240 = $174,020 . But the reduced cost comes at a price—the risk that the target yield will not be achieved.