Power-Log Optimization and Positively Skewed Option Returns Reduce Risk and Raise Portfolio Performance

Abstract

The current low-interest-rate, low-volatility environment demands a more innovative approach to investment management than the allocation to stocks and bonds that is practiced widely today. Options, with their significantly positively skewed returns, offer us the opportunity of boosting returns while controlling downside risk. Power-log optimization gives us the means to incorporate options into the asset allocation process effectively and requires only one input parameter, the downside power, to specify investor preferences. Using data for the last 20 years for a Treasury security, the S&P 500 Index, and a call option on the index, the authors find that optimal power-log portfolios reduce downside risk and the standard deviation of return for both conservative and risky portfolios, which results in positively skewed returns for the portfolios. The authors also deliver higher geometric average returns for riskier portfolios than matched mean–variance-efficient portfolios. In addition, they provide much better downside protection against unanticipated market shocks, such as the down markets in 2002 and 2008, and as a result deliver better performance for both conservative and risky portfolios in bad markets.