Comment on “Usefulness of Treasury Bill Futures As Hedging Instruments”

✍ Scribed by David H. Goldenberg

• Publisher: John Wiley and Sons
• Year: 1983
• Tongue: English
• Weight: 101 KB
• Volume: 3
• Category: Article
• ISSN: 0270-7314
• DOI: 10.1002/fut.3990030210

✦ Synopsis

The purpose of that article was to present a model in which "when testing the effectiveness of hedging Treasury bills, one must take into account the term to maturity on the deliverable bill and adjust for the constant yield price accumulation."

The Dale et al. analysis is misleading because it focuses unnecessarily on the adjustment of the return on the hedge for the constant yield price accumulation. On the other hand, adjusting (the hedge ratio) for the term to maturity is clearly necessary for effective hedging. The issue is to clarify the mechanism for achieving this adjustment. Consider the following two methods for arriving at the optimal (risk-minimizing) hedge ratio.

Method 1: As in Dale et al. subtract the "constant yield price accumulation" from the return on the portfolio of spot and futures. Then, calculate the variance of that adjusted return and minimize with respect to b, the proportion of spot position to be hedged. Formally this is accomplished by subtracting from the authors' Eq. (3), the rate of return on the portfolio, and then minimizing with respect to b = -X,/Xs to arrive at the optimal hedge ratio:

Here DM2 is the number of days to maturity remaining on the bill being hedged when the hedge is lifted.