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.