Empirical Properties of Straddle Returns

Abstract

An at-the-money (ATM) straddle, i.e., going long an ATM call and an ATM put with the same maturity, is generally thought of as a volatility trade. It is essentially delta-neutral, but a large price move in either direction or an increase in implied volatility will produce a profit. A delta-neutral straddle position also has zero beta, so under the CAPMit should earn the riskless rate. Research has shown, however, that straddles with stock index options tend to lose money, which may be attributed to a volatility risk premium: it is the cost of hedging against a rise in volatility. If buying straddles produces losses, writing straddles should yield excess profits. An important aspect of the trade is that the delta (and beta) of the position change when the underlying index moves away from its initial level, and rebalancing is necessary if one wishes to maintain neutrality.

In this article, Goltz and Lai examine the performance of buying and holding one-month straddles on the DAX index, with and without rebalancing, and find negative returns on average. If investors are entering the trade as a volatility hedge, one might expect the return to vary with other measures on volatility risk and potential hedging demand. They find that a widening credit spread on corporate bonds relative to government bonds, greater stock market turnover, and higher actual volatility all are related to straddle returns. But in considering what position an investor with constant relative risk aversion would take in straddles as part of an optimal portfolio including the underlying stock index and the riskless asset, they show that for risk aversion over a broad range, the optimal position would be to short straddles. That is, the “risk premium” in the market is too big to be consistent with utility maximization by investors with a reasonable level of risk aversion. The effect is most important for daily rebalancing, but that requires bearing heavy transaction costs, to the point that the potential improvement in utility would be largely wiped out in trying to capture it in the market.