Hedging GNMA Mortgage-Backed Securities with T-Note Futures: Dynamic versus Static Hedging
Koutmos, Gregory, Pericli, Andreas, Real Estate Economics
Hedging the interest-rate risk of mortgage-backed securities (MBSs henceforth) is an extremely difficult endeavor. The difficulty is due to the homeowner's prepayment option, which renders the duration and therefore the price sensitivity of MBSs to changes in interest rates highly uncertain. An intuitive understanding of this type of uncertainty can be gained by realizing that the value of a MBS is equal to the value of a riskless fully amortizing bond minus the value of a call option (i.e., the prepayment option). The two components of the MBSs react differently to changes in interest rates. When interest rates rise above the MBS coupon rate, the prepayment option becomes out of the money and the price of the MBS is a strictly convex function with respect to further increases in interest rates. When interest rates fall, however, the prepayment option becomes in the money and it prevents the value of the MBS from rising, a phenomenon that has been called negative convexity. To make matters worse, direct hedging instruments, such as futures on MBSs, are no longer available. The Government National Mortgage Association collateralized depository receipt (GNMA CDR) futures contract introduced by the Chicago Board of Trade (CBOT) in 1975 was withdrawn in 1987 due to investors' lack of interest. Johnson and McConnell (1989) find that the flexible delivery options of the contract reduced its hedging effectiveness. The fate of the mortgage-backed futures contract (MBF), introduced in 1989, was no different. After an initial period of success, trading volume declined continuously until the contract was withdrawn in 1992. According to Nothaft, Lekkas and Wang (1995) the failure was due to the contract's decreasing market liquidity and the existence of more liquid cross-hedging substitutes such as the Treasury-bond and the Treasury-note futures contracts. By most accounts, the 10-year Treasury-note futures contract is the most popular among MBS investors and mortgage originators. The popularity of this hedging instrument is due to the fact that, after allowing for prepayments, the average duration of a typical 30-year MBS is closer to the 10-year Treasury note than any other government fixed-income security for which a futures contract exists. Consequently, changes in MBS prices should be highly correlated with changes in 10-year Treasury-note prices. Evidence on the popularity of the T-note futures contract is provided by Fernald, Keane and Mosser (1994), who find that the hedging of MBSs with Treasury-note futures has essentially changed the short-run dynamics of the term structure of interest rates.
MBS risk hedging has been commonly based on (1) valuation methods and (2) regression methods. The former involves matching the effective duration of the MBS to that of a Treasury bond for which a futures contract exists. Subsequently, the hedger shorts a number of futures contracts equal to the ratio of the durations. Effective durations are derived from option-adjusted spread (OAS) models. Despite its wide acceptance in recent years, effective duration based on OAS suffers from some serious problems. These problems are linked to the sensitivity of duration estimates to the specific prepayment model used. To make matters worse, prepayment rates are extremely sensitive to changes in the term structure. Consequently, modeling prepayments requires explicit modeling of the term structure. Due to differences in prepayment and term-structure modeling, estimated duration measures vary widely across broker-dealer firms. Such wide variations have raised questions regarding the accuracy of OAS effective durations. Choi (1996) compares median broker OAS durations and empirical durations for MBS with nine different coupons for the period February 1992 to March 1994. He finds that the root-mean-square forecast error (RMSE) of OAS durations based on median broker forecasts is 1.13 when averaging across the nine coupons. The average RMSE based on empirical-duration forecasts was 0. …