Mind the Gap: Using Derivatives Overlays to Hedge Pension Duration

Abstract

Recent legislation and accounting rule changes motivate defined-benefit pension plans to manage the interest rate risk arising from volatility in their liabilities, as measured by either the accumulated benefit obligation (ABO) or the projected benefit obligation (PBO). For either measure, asset portfolios comprising equity and fixed-income bonds usually have much lower average durations than do liabilities. This article discusses how interest rate derivatives overlay strategies can be used to reduce or eliminate the negative duration gap. A theoretical model is developed to show how to calculate the ABO and PBO measures and their duration statistics.

Recent legislation and accounting rule changes—in particular, the U.S. Pension Protection Act of 2006 and Financial Accounting Standard (FAS) No. 158—motivate sponsors of defined-benefit (DB) pension plans to manage the interest rate risk arising from volatility in their plans’ liabilities, as measured by either the accumulated benefit obligation (ABO) or the projected benefit obligation (PBO). ABO, a measure of the sponsor’s current legal liability, is the present value of retirement benefits based on current wages. PBO is a larger amount because it is based on the estimated future wage level at the time of retirement. In the past, the plan sponsor recognized a funding deficit on its balance sheet only if the fair value of plan assets was less than the ABO liability. Now, under FAS No. 158, PBO is used to determine the funding status of the DB pension plan.

In practice, the interest rate risk of an asset or liability is measured by its duration statistic, which is a measure of the change in value given a change in interest rates. The essence of the risk management problem facing the typical DB pension plan is that the average duration of its asset portfolio—which is usually invested about two-thirds in equity and one-third in fixed income—is much less than the estimated duration of either its ABO or PBO liability. Thus, a significant negative duration gap exists: Lower interest rates increase asset values much less than they increase liabilities. In this article, we develop a theoretical model (based on a representative employee) to demonstrate how the ABO and PBO liability durations are estimated.

A promising method to decrease the interest rate risk facing a DB pension plan is a derivatives overlay strategy that reduces or eliminates the negative duration gap without changing the asset portfolio. Derivatives—in particular, interest rate swaps or options on swaps (“swaptions”)—transform the risk profile of the overall plan while leaving the existing asset allocation (i.e., investments in equity and fixed income) intact. For example, we show that a receive-fixed interest rate swap has a positive duration. The plan manager can choose the requisite notional principal on the swap to close the negative duration gap fully or partially. We present numerical examples to illustrate this calculation.

Another derivatives overlay strategy is for the DB pension plan to buy a “receiver swaption.” The plan pays the premium and has the right to enter into an interest rate swap as the receiver of the fixed rate. If interest rates fall, the value of the swaption goes up, thus offsetting the increase in the plan’s liability. A related strategy is for the plan to enter into a “swaption collar” whereby a “payer swaption” is sold to provide the premium to offset the cost of the purchased receiver swaption.