Selecting hedge ratio maximizing utility or adjusting portfolio's beta

To hedge a portfolio of risky assets against market risk, the prevalent view consists of selecting the hedge ratio minimizing the variance of a position combining a long position on the portfolio and a short position on a futures contract. A more general approach amounts to select a hedge ratio maximizing the expected utility of some specific function. The portfolio approach so defined takes simultaneously into account the expected return and variance of the combined position. Nevertheless, for several reasons, one usually prefers to restrain the choice of a hedge ratio to a simple risk-minimizing position. We intend to show here that the choice of a hedge ratio maximizing utility corresponds essentially to an adjustment of portfolio beta to some expected value. Empirical estimations are based on a futures contract relative to the CAC 40 Index, traded on the MATIF (Marche international de France, Paris). They show that the two approaches are equivalent. Incidentally, if the decision not to hedge is generally a rational solution, it appears that, during some periods (such as the year 1994) it is irrational.