Measuring the Asymmetry of Stock Market Risk

Portfolio and asset pricing theory use symmetric volatility measures to evaluate risk. We propose a method to isolate the risk that the portfolio suffers a loss, separate from the risk that the portfolio reaps uncommon gains. Specifically we take advantage of the one-sided nature of option payments and show how downside risk will only affect the value of a put option (with correctly specified strike prices). An important advantage is that we have a forward-looking measure, as opposed to beta or other risk factors that use historical variation. We use implied volatility of put for about 100 stocks. We also assemble return data, some competing measures of asymmetry including downside standard deviation and downside beta. We find that our forward-looking option market measure performs better than competing measures of downside risk in predicting out-of-sample future returns.