To determine the optimal mean-variance portfolio of an investor, one needs to estimate the moments of asset returns, such as means, volatilities, and correlations. Traditionally, historical data on returns have been used to estimate these moments, but researchers have found that portfolios based on sample estimates perform poorly out of sample. A number of approaches have been proposed for improving the performance of portfolios based on historical data, however one should understand that any estimate based on historical data implicitly assumes that history will repeat, and it is certainly far from obvious!
We use a different idea: when investors come to market to trade options, their opinions, information, and sentiment are incorporated into the current prices of options, so that these prices fully absorb current expectations about the future from all market participants. Thus, instead of trying to improve the quality of the moments estimated from historical data, one can use forward-looking moments of stock-return distributions that are implied by option prices. The main contribution of our work is to evaluate empirically which aspects of option-implied information are particularly useful for improving the out-of-sample performance of portfolios with a large number of stocks. Specifically, we consider option-implied volatility, correlation, skewness, and the risk premium for stochastic volatility.
When option prices are available, an intuitive first step is to use this information to back out implied volatilities and use them to predict volatility, and hence as a first experiment we consider the use of option implied volatilities and correlations to improve out-of-sample performance of mean-variance portfolios invested in only risky stocks. When evaluating the benefits of using option-implied volatilities and correlations, we set expected returns to be the same across all assets so that the results are not confounded by the large errors in estimating expected returns. Consequently, the mean-variance portfolio reduces to the minimum-variance portfolio. In addition to considering the minimum-variance portfolio based on the sample covariance matrix, we consider also the shortsale-constrained minimum-variance portfolio, the minimum-variance portfolio with shrinkage of the covariance matrix, and the minimum-variance portfolio obtained by assuming all correlations are equal to zero or with correlations set equal to the mean correlation across all asset pairs. We find that using risk-premium-corrected option-implied volatilities in minimum-variance portfolios improves the out-of-sample volatility by more than 10% compared to the traditional portfolios based on only historical stock-return data, while the changes in the Sharpe ratio are insignificant. Thus, using option-implied volatility allows one to reduce the out-of-sample portfolio volatility significantly.
Next, we examine the use of risk-premium corrected option-implied correlations to improve the performance of minimum-variance portfolios. We find that in most cases option-implied correlations do not lead to any improvement in performance. Our empirical results indicate that the gains from using implied correlations are not substantial enough to offset the higher turnover resulting from the increased instability over time of the covariance matrix when it is estimated using option-implied correlations.
Finally, to improve the out-of-sample performance of mean-variance portfolios we consider the use of option-implied volatility, risk premium for stochastic volatility, and option-implied skewness. These characteristics have been shown in the literature to help explain the cross section of expected returns. Therefore, it makes sense to explore their effect in the framework of mean-variance portfolios. Using these characteristics to rank stocks and adjusting by a scaling factor the expected returns of the stocks, or using these characteristics with the parametric-portfolio methodology, leads to a substantial improvement in the Sharpe ratio, even after prohibiting shortsales and accounting for transactions costs.
Bottom line: We find that using option-implied volatilities can lead to a significant improvement in portfolio volatility; however, option-implied correlations are less useful in reducing port- folio volatility. We also find that forming portfolios using expected returns that exploit information in option-implied model-free skewness and implied volatility achieve a higher Sharpe ratio than portfolios that ignore option-implied information (the benchmark portfolios are the 1/N portfolio; four types of minimum- variance portfolios and four types of mean-variance portfolios based on historical returns; and, the parametric portfolios of Brandt, Santa-Clara, and Valkanov (2009), based on historical returns and size, value, and momentum characteristics). This improvement in performance is present even after adjusting for transactions costs. Based on our empirical analysis, we conclude that prices of stock options contain information that can be useful for improving the out-of-sample performance of portfolios.