A Model for Convexity-Based Cross-Hedges with Treasury Futures

Abstract

Even when Treasury future’s convexity becomes negative, a convexity-based hedge that does not require an option-theoretic solution is still possible because near the delivery month, a linear, arbitrage-free relationship should hold between Treasury futures and the cheapest-to-deliver (CTD) Treasury. Using this hedging implication and Rendleman’s [1999] framework for duration hedge, a model is developed for forward-looking, convexity-based cross-hedges. The numerical analysis of hedge cost performance indicates the following: 1) the forward-looking hedge is cheaper in most scenarios that involve different term structures of interest rates, hedge horizons, pairs of Treasury futures, and duration levels of both bond portfolio and CTD Treasuries, and 2) the cost saving is large when the convexity-based hedge is most needed; that is, when high-duration bonds are hedged, the term structure of interest rates is steep and the CTD pays high coupons.