There has been a lot of research recently that investigates the link between stock returns and higher moments of the return distribution, specifically the skewness of returns. This link, unfortunately, is frequently ignored by more standard measures of market risk and volatility.

Skewness, if you’ll recall, measures the asymmetry of a distribution. In terms of the stock market, the asymmetric pattern of historical returns doesn’t resemble a normal distribution, also known as the familiar bell curve. Negative skewness occurs when the values to the left of (less than) the mean are fewer but farther from it than values to the right of (greater than) the mean.

For example, the return series of -30%, 5%, 10% and 15% has a mean of 0%. There is only one return less than zero, and three that are higher. The single negative return is much farther from zero than the positive ones, so the return series has negative skewness. Positive skewness, on the other hand, occurs when values to the right of (greater than) the mean are fewer but farther from it than values to the left of (less than) the mean.

**The Value-Risk Premium**

Bruno Feunou, Mohammad Jahan-Parvar and Cedric Okou—authors of the January 2015 working paper titled “Downside Variance Risk Premium”—contribute to the literature by decomposing the variance risk premium (VRP) in terms of upside (VRP^{U}) and downside (VRP^{D}) variance risk premia.

The VRP can be interpreted as the premium a market participant is willing to pay to hedge against variation in future realized volatilities. It proxies the premium associated with the volatility of volatility, which not only reflects how future random returns vary, but also assesses fluctuations in the tail thickness of the future returns distribution.

The VRP is intuitively expected to be positive because of the assumption that risk-averse investors dislike large swings in volatility, especially in “bad times.” The difference between upside- and downside-variance-risk premia is a measure of the skewness-risk premium (SRP).

The authors’ working hypothesis is that “investors like good uncertainty—as it increases the potential of substantial gains—but dislike bad uncertainty—as it increases the likelihood of severe losses.” In other words, risk-averse investors ask for a premium to face risk they don’t like while they are more willing to pay for exposure to favorable uncertainties (risk they like). Thus, upside- and downside-variance-risk premia tend to have opposite signs.

The authors write: “Thus, the (total) variance risk premium that sums these two components essentially mixes together market participants’ (asymmetric) views about good and bad uncertainties.”

**Study Results**

Because the study required reliable high-frequency data, as well as option-implied volatilities, the authors’ data sample spans the period September 1996 to December 2010. Following is a summary of their findings: