C12 MODELING NON PARALLEL TERM STRUCTURE

WEAKNESS OF SINGLE FACTOR APPROACHES #

• A single-factor approach to measuring and hedging risk in fixed income markets is quite limiting because it assumes that within the term structure of interest rates, all rate changes are driven by a single factor.
• The single-factor approach does not protect against yield curve risk.

KEY RATE EXPOSURES #

Key rate exposures are utilized for measuring and hedging risk in bond portfolios using rates from the most liquid bonds available, which are generally government bonds that have been issued recently and are selling at or near par.

Partial ‘01s are utilized for measuring and hedging risk in swap portfolios. These partial ‘01s are derived from the most liquid money market and swap instruments for which a swap curve is usually constructed.

Forward-bucket ‘01s are also used in swap and combination bond/swap contexts, but instead of measuring risk based on other securities, they measure risk based on changes in the shape of the yield curve.

KEY RATE SHIFT TECHNIQUE #

Key rate shift analysis makes the simplifying assumption that all rates can be determined as a function of a few “key rates.”

The most common key rates used for the U.S. Treasury and related markets are par yield bonds—2-, 5-, 10- and 30-year par yields. If one of these key rates shifts by one basis point, it is called a key rate shift.

The key rate shift technique is an approach to nonparallel shifts in the yield curve, which allows for changes in all rates to be determined by changes from selected key rates.

KEY RATE SHIFT TECHNIQUE #

• Key rate ‘01 are calculated as follows:

DV01^K = (-1/10000) (ΔBV/Δy^K)

• Key rate durations are calculated as follows:

D^k = (-1/BV)(ΔBV/Δy^k)

HEDGING APPLICATIONS #

Key rate shifts allow for better hedging of a bond position, and when summed across all key rates, assume a parallel shift across all maturities in the maturity spectrum.

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 #

Partial ‘01s and forward-bucket ‘01s are often used with more complex portfolios that contains swaps. These approaches are similar to the key rate approach, but instead divide the term structure into more parts. Risk along the yield curve is thus measured more frequently, in fact daily.

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.

The forward-bucket ‘01 approach is a more direct and mechanical approach for looking at exposures. 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 #

Key rates and bucket analysis allow a manager to use more than a single factor to manage interest rate risk effects on a portfolio. These multi-factor approaches work well not only in estimating changes in the level of the portfolio, but also in the estimation of portfolio volatility because it incorporates correlation effects between various interest rate assumptions.