What are the difficulties of following aduration-matched strategy for hedgingthe interest-rate risk of a defined benefitpension plan?

What will be an ideal response?

In practice there are two problems in following a duration-matched strategy for hedging the interest-rate risk of a defined benefit pension plan. First, the duration of the liabilities may be high (e.g., more than 20). In contrast, the duration of Treasury bonds and high-grade corporate bonds is lower (e.g., not close to 20). Thus, it is difficult to obtain the necessary dollar duration to hedge interest-rate risk. So, even in the textbook illustration (with a duration of 12), the duration given is not likely to be accomplished with high-grade bonds. The solution to address this issue is to use interest-rate derivatives such as futures and swaps to "extend" dollar duration. Consequently, a pension plan sponsor seeking to duration match all or part of the interest-rate risk must be prepared to authorize the use of interest-rate derivatives. Second, we have a problem in that the matching of duration provides a hedge against interest-rate risk for a small change in interest rates. This can be dealt with by frequent portfolio rebalancing. If interest rates move substantially between rebalancing periods, duration matching is not sufficient as a condition for hedging. Instead, the convexity of the assets and liabilities must be matched as closely as possible. More details are given below.

To hedge or immunize (at least as a first approximation) against interest-rate risk resultingin adverse change in the funding gap using a bond-only portfolio, the fund's portfoliocan be constructed and rebalanced so as to maintain the dollar-duration match to preventthe funding gap from increasing.Illustrating this with our hypothetical DB pension plan, because the liability dollar durationcannot be changed, to hedge the interest-rate risk the portfolio dollar duration mustbe $72 million. Letting (Dp) denote duration for the portfolio, then for a 100-bp change ininterest rates the portfolio dollar duration is
0.01 × Dp× $500 million
This amount must be equal to the dollar duration of the liabilities of $72 million. That is,
0.01 × Dp× $500 million = $72 million
Solving, we find Dpis equal to 12 . That is, the portfolio duration must be the same as theliability duration to avoid a change in the funding gap as a result of a rise in interest rates.

The above illustration has two problems. First, it is difficult to obtainthe necessary dollar duration to hedge interest-rate risk. In our illustration, aduration of 12 is not likely to be accomplished with high-grade bonds. Second, the matching of duration provides a hedge against interest-rate risk for a small change in interest rates. If interest rates move substantially between portfolio rebalancing periods, the convexity of the assetsand liabilities must be matched as closely as possible.