Academic journal article Revue Canadienne des Sciences de l'Administration

Naive versus Conditional Hedging Strategies: The Case of Canadian Stock Index Futures

Academic journal article Revue Canadienne des Sciences de l'Administration

Naive versus Conditional Hedging Strategies: The Case of Canadian Stock Index Futures

Article excerpt

Stock index futures have enjoyed great success since their inception in 1982. In large part this success has been due to the satisfaction of a demand on the part of hedgers for a low transaction cost vehicle for the purpose of adjusting market exposure. The proper determination of hedge ratios and the efficacy of hedging based on these ratios have been a central concern for practitioners as well researchers. For example, it is well known that contract "maturity" has an impact on optimal hedge ratios (e.g., Lee, Bubyns, & Lin, 1987; Merrick, 1988).

In addition, Merrick (1988) has shown that hedge efficacy is diminished by futures mispricing, where the latter is defined to be the difference between the observed futures price and that implied by strict adherence to the carry cost pricing model. Indeed the carry cost model only serves to provide a range of (arbitrage-efficient) prices (for the U.S., see Merrick, 1988; Modest & Sundaresan, 1983; Peters, 1985; for Japan, see Bailey, 1989; Brenner, Subrahmaayam, & Uno, 1989; for Canada, see Beyer, 1985; Deaves, 1990b). This is so, principally because the arbitrage mechanism required to enforce carry cost entails no significant costs and risk.(1)

The purpose of this paper is to investigate the hedging performance of Canadian stock index futures contracts, and to investigate to what extent performance is enhanced by employing subtle procedures over naive ones. Though hedging using U.S. index contracts has been extensively researched (e.g., Figlewski, 1984; Graham & Jennings, 1987; Junkus, 1987; Junkus & Lee, 1985; Lee, Bubyns, & Lin, 1987; Merrick, 1988), the hedging performance of Canadian index futures contracts traded on the Toronto Futures Exchange is as yet unexplored. The TSE 300 contract traded from January 1984 to June 1987, at which time it was phased out in favor of a contract on the more narrowly based TSE 35.(2) These contracts provide a new data set for testing the relative efficacy of various hedging methodologies. Of particular interest is a conditional hedging strategy, since such an approach is theoretically appropriate, as shown below. Since a conditional approach entails a movement towards complexity and additional analysis costs, it is useful to investigate the associated value added. Myers (1991) has shown, in the context of commodity futures, that a time-variant strategy leads to little improvement. Merrick (1988), using a somewhat different methodology from that employed here, also found little improvement for U.S. stock index futures.

The next section provides the appropriate theoretical background. The hedging methodologies and the empirical results are then described. Finally, the main findings of the paper are summarized.

Theoretical Background

The common practice of considering the minimum-variance hedge will be employed here. As shown by Fortin and Khoury (1988), such an approach is only strictly valid when a hedger has strong risk aversion. Thus, hedging should be properly viewed in a mean-variance context. Still, the minimum-variance hedge can serve as a good benchmark for the efficacy of partial (or aver-) hedging strategies.

An investor wishing to hedge market risk in an arbitrary portfolio, whose market value at t is V sub t , over a hedge horizon from t to t+T sells futures contracts with specification for final cash settlement at t+T+r where tau >=0. Let m equal the futures contract multiplier; n sub t equal the number of contracts sold at t; and I sub t equal the level of the cash market index at t. Define the hedge ratio (h sub t,tau as

(Equation 1 omitted)

The hedge ratio is simply the ratio of futures "value" to cash market value.

Next, using (1), the hedged portfolio return (R sup ph sub t ) can be written as

(Equation 2 omitted)

The minimum-variance hedge ratio is calculated by taking the variance of R sup ph sub t in (2), and minimizing with respect to h sub t,tau . …

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