READING 62: MULTI-FACTOR RISK METRICS AND HEDGES

Weaknesses of Single-Factor Approaches

        The single-factor approach to hedging risk of fixed-income portfolios is limiting because it assumes that all future rate changes are driven by a single factor.

Key Rate Exposures

        Key rate exposures hedge risk by using rates from a small number of available liquid bonds. Partial ‘01s are used with swaps, and use a greater number of securities. Forward-bucket ‘01s are also used with swaps and use predefined regions to determine changes due to shifts in forward rates. Forward-bucket ‘01s enable us to understand a portfolio’s yield curve risk.

Key Rate Shift Technique

        The key rate shift technique is a multi-factor approach to nonparallel shifts in the yield curve that allows for changes in all rates to be determined by changes in key rates. Choices have to be made regarding which key rates shift and how the key rate movements relate to prior or subsequent maturity key rates.

Key Rate ‘01 and Key Rate Duration

        Key rate ‘01s are calculated as follows:

         Key rate durations are calculated as follows:

Hedging Applications

        For every basis point shift in a key rate, the corresponding key rate ‘01 provides the dollar change in the value of the bond. Similarly, key rate duration provides the approximate percentage change in the value of the bond.
        Hedging positions can be created in response to shifts in key rates by equating individual key rate exposures adjacent to key rate shifts to the overall key rate exposure for that particular key rate change. The resulting positions indicate either long or short positions in securities to protect against interest rate changes surrounding key rate shifts.

Partial ‘01s And Forward-Bucket ‘01s

        A partial ‘01 is the change in the value of the portfolio from a one basis point decrease in the fitted rate and subsequent refitting of the curve. Forward-bucket ‘01s are computed by shifting the forward rate over several regions of the term structure, one region at a time, after the term structure is divided into various buckets.

Hedging Across Forward-Bucket Exposures

        In order to set up a proper hedge for a swap position across an entire range of forward-bucket exposures, the hedger will determine the various forward-bucket exposures for several different swaps and select the hedge that contains the lowest forward-bucket exposures in net position.

Estimating Portfolio Volatility

        Multifactor approaches to hedging, such as key rate and bucket shift approaches, can be used to estimate portfolio volatility effects because they incorporate correlations across a variety of interest rate effects.