Skewness Premium for Short-Term Exposure to Squared Market Returns

Abstract

Following Kraus and Litzenberger, the skewness of stock returns is often modeled as exposure to the square of the market return. We use a trading strategy in S&P 500 options that creates exposure to the square of the S&P 500 return without affecting other characteristics of a direct index investment. This allows us to uniquely identify the skewness premium. We find a significantly negative premium on daily returns, which amounts to a return difference of 5 percentage points per year between a put-based strategy (negative skewness) and a call-based strategy (positive skewness). Our results suggest that short-term exposure to squared market returns is important for investors, even though this exposure declines sharply when returns are aggregated over months or quarters.