Bernoulli speculator and trading strategy risk

In a continuous-time model of a complete information economy, we examine th e case of a "pure" speculator who chooses to trade only on forward or futur es contracts written on interest-rate-sensitive instruments. Assuming logar ithmic utility, we assess whether his strategy exhibits the same structure as when he uses primitive assets only. It turns out that when interest rate s follow stochastic processes, as in the model of Heath, Jarrow, and Morton (1992), where the instantaneous forward rate is driven by an arbitrary num ber of factors, the speculative trading strategy involving forwards exhibit s an extra term vis-a-vis the one using futures or primitive assets. This e xtra term, different: from a Merton-Breeden dynamic hedge, is novel and can be interpreted as a hedge against an "endogenous risk," namely the interes t-rate risk brought about by the optimal trading strategy itself. Thus, onl y the strategy using futures (or the cash assets themselves) involves a sin gle speculative term, even for the Bernoulli speculator. This result illust rates another major aspect of the marking to market feature that differenti ates futures and forwards, and thus has some bearing on the issue of the op timal design of financial contracts. Real financial markets being, in fact, incomplete, the additional "endogenous" risk associated with forwards cann ot be hedged perfectly. Since using futures eliminates the latter, risk-ave rse agents will find them attractive in relation to forward contracts, othe r things being equal. (C) 2000 John Wiley & Sons, Inc.