Combination Hedges Applied to U.S. Markets

Financial futures hedges typically use one futures market (e.g., a 10-year-note futures to hedge a position in 10-year U.S. Treasury securities). This article reports tests of combination hedges composed of 10-year-note futures and long-bond futures to hedge 10-year Treasuries and compares combination hedges with the standard one-market hedge. The study applies to the U.S. market an approach developed and tested successfully for the German bond market. Combination hedges are generally found to be superior. Of three methods examined for determining hedge ratios—using yields, option-adjusted modified durations, or non-option-adjusted modified durations—combination hedge ratios derived from option-adjusted modified durations performed best.Futures market practitioners have developed a wide variety of techniques for hedging price and interest rate risk. Typically, the hedge ratios involved are based on the use of one futures instrument. Because the cheapest-to-deliver (CTD) instrument for the futures contract is usually not the issue one hopes to hedge, an inherent mismatch of maturities and durations occurs. This article looks at combination hedges as a solution to the problem. Combination hedges use more than one contract to simulate the duration of the target instrument being hedged. Broadly, the results of the study show that combination hedges are more precise than single-contract hedges.This analysis is based on original work by Heiko Leschhorn reported in the Financial Analysts Journal in 2001 that derived combination hedge ratios based on the relationship between the yields and maturities of the target instrument to be hedged and those of the CTD instruments of the futures contracts used in the combination hedge and then applied the combinations successfully to the German bond market. The current article extends that work to the U.S. Treasury securities market.The futures contracts were chosen so that their maturities or durations bracketed the maturity or duration of the target U.S. Treasury note. In all cases, the hedge ratios of the two combination futures contracts were derived from two things—(1) the ratio of the dollar values of 1 bp of the target instrument and the futures contract and (2) weights that depended on the position of the yield or duration of the target instrument relative to those of the hedge vehicles. For instance, if the duration of the target was two-thirds of the way between the shorter-duration and longer-duration contracts, the longer-duration contract—the one closer to that of the target—would have a larger weight than the shorter-duration contract. The article contains formulas for calculating these weights and hedge ratios.The article reports tests of the efficacy of combination hedges compared with that of single-contract hedges. The hedge target was always the current 10-year U.S. Treasury note (T-note). Single-contract hedges were the 10-year-note, 5-year-note, and long-bond futures contracts. Combination hedges combined 10-year-note and long-bond futures. Notionally, this combination was a long position in the 10-year T-note and short positions in futures markets to hedge its value.The study covered 27 periods in 1998–2005, each three months long, from one futures delivery month to the next. I describe the results of three tests. First, I report the mean absolute value of the changes in the value of the total hedged position (that is, the long cash and short futures positions together); the smaller the mean absolute value, the more precise and successful the hedge. Second, I report standard deviation of the total value of the hedged position; again, the smaller the standard deviation, the better the hedge. Third, I provide rank scores for the various hedges for each period; in this test, the best hedge in a given period was assigned a rank of 1, the next best received a rank of 2, and so on through 12 hedging strategies; the smaller the sum of the ranks for all periods for a given strategy, the better the strategy.Generally, combination hedges outperformed single-contract hedges as measured by all three tests, although results were not absolutely consistent. Also, among the three methods for constructing combinations, using option-adjusted futures’ modified durations tended to be most attractive.In addition, I examined whether there was any relationship between the success of the strategies and market conditions (direction of yield movements and changes in yield curves), but I found no clear correspondence.I conclude that hedgers can expect moderately more effective hedges by using combinations rather than single contracts.