Optimal Option Portfolio Strategies

Options should play an important role in asset allocation. They allow for kernel spanning and provide access to additional (priced) risk factors such as stochastic volatility and negative jumps. Unfortunately, traditional methods of asset allocation (e.g. mean-variance optimization) are not adequate for options because the distribution of returns is non-normal and the short sample of option returns available makes it difficult to estimate the distribution. We propose a method to optimize option portfolios that solves these limitations. An out-of-sample exercise is performed and we show that, even when transaction costs are incorporated, our portfolio strategy delivers an annualized Sharpe ratio of 0.59 between January 1996 and September 2008.We offer a simple portfolio optimization method that solves simultaneously these problems. Instead of a mean-variance objective, we maximize an expected utility function, such as power utility, which accounts for all the moments of the portfolio return distribution and, in particular, penalizes negative skewness and high kurtosis. We deal with the small sample of option returns by relying on data for the underlying asset instead. In our application, we use returns of the S&P 500 index since 1950 to simulate returns of the underlying asset going forward and, from the definition of option payoffs, generate simulated option returns. Plugging the simulated option returns into the utility function and averaging across simulations gives us an approximation of the expected utility which can be maximized to obtain optimal portfolio weights. Note that only current option prices are needed in our procedure, since the payoff is determined by the simulations of the underlying asset. We study the performance of our optimal option portfolio strategies, which we denote by OOPS, in an out-of-sample (OOS) exercise. We find the optimal option portfolios one month before option maturity and examine the return that they would have had at maturity. The resulting time series of returns could have been obtained by an investor following our method in real time. We can then compute measures of performance such as Sharpe ratios or alphas to assess the interest of the method. It should be stressed that for the each OOS observation, only one month of option observations is needed. For the entire period of 153 monthly observations, 99% of the sample is OOS. This per se is significantly different from previous studies. OOPS have large Sharpe ratios in our sample period between January 1996 and September 2008. The best strategy yields a Sharpe ratio of 0.59. This compares well with the Sharpe ratio of the market in the same period of 0.20, or even in the full sample since 1950 of 0.40. In addition, several strategies present positive skewness and low excess kurtosis. We find that our strategies load significantly on all four options, and that the optimal weights vary over time. Finally, our optimal strategies are almost delta-neutral albeit with significant elasticity.