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BAM Intelligence

Predictable & Skewed Returns

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 (VRPU) and downside (VRPD) 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:

  • The downside-variance-risk premium is the main component of the overall variance-risk premium. On average, more than 80% of the VRP is compensation for bearing changes in downside risk.
  • The skewness-risk premium is a priced factor with significant predictive power for aggregate excess returns.
  • There’s a positive and significant link between the downside-variance-risk premium and the equity premium, as well as a positive and significant relationship between the skewness-risk premium and the equity premium.
  • The predictive power of VRPD and SRP increases over the term structure of equity returns. This result is robust to the inclusion of a wide variety of common pricing factors, meaning it is independent from other common pricing ratios, such as the price-dividend ratio, price-earnings ratio or default spread.
  • The asymmetries are observed in “normal times.” However, the model is capable of addressing regularities that emerge from the occurrence of a rare disaster, such as the Great Recession of 2007-2009.
  • The VRP and its components are predictors of risk in financial markets. An increase in VRP or VRPD implies expectations of elevated risk levels in the future, and hence compensation for bearing that risk.
  • The “most striking outcome” was related to Federal Reserve Board announcements. For all variance-risk components, policy announcements that resolve financial or monetary uncertainty also reduce the premia.


Feunou, Jahan-Parvar and Okou contribute to the literature by providing a model that provides simple consumption and risk-based—yet insightful—economic intuitions. They show that investors are more concerned with market downturns and demand a premium for bearing that risk. In contrast, investors like upward uncertainty in the markets, and thus accept lower returns.

Furthermore, the authors’ results show that the downside-variance-risk premium (the difference between option-implied, risk-neutral expectations of market downside volatility and historical, realized downside variances) demonstrates significant predictive power (which is at least as powerful as the variance-risk premium, and often stronger) for excess returns.

Finally, the authors also show that the difference between upside- and downside-variance-risk premia—a proposed measure of the skewness-risk premium—is both a priced factor in equity markets and a powerful predictor of excess returns.

This commentary originally appeared December 2 on ETF.com

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The opinions expressed by featured authors are their own and may not accurately reflect those of the BAM ALLIANCE. This article is for general information only and is not intended to serve as specific financial, accounting or tax advice.

© 2015, The BAM ALLIANCE

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Chief Research Officer

Larry Swedroe is Chief Research Officer for the BAM ALLIANCE.

Previously, Larry was vice chairman of Prudential Home Mortgage. Larry holds an MBA in finance and investment from NYU, and a bachelor’s degree in finance from Baruch College.

To help inform investors about the evidence-based investing approach, he was among the first authors to publish a book that explained evidence-based investing in layman’s terms — The Only Guide to a Winning Investment Strategy You’ll Ever Need. He has authored 15 more books:

What Wall Street Doesn’t Want You to Know (2001)
Rational Investing in Irrational Times (2002)
The Successful Investor Today (2003)
Wise Investing Made Simple (2007)
Wise Investing Made Simpler (2010)
The Quest for Alpha (2011)
Think, Act and Invest Like Warren Buffett (2012)
The Incredible Shrinking Alpha (2015)
Your Complete Guide to Factor-Based Investing (2016)
Reducing the Risk of Black Swans (2018)
Your Complete Guide to a Successful & Secure Retirement (2019)

He also co-authored four books: The Only Guide to a Winning Bond Strategy You’ll Ever Need (2006), The Only Guide to Alternative Investments You’ll Ever Need (2008), The Only Guide You’ll Ever Need for the Right Financial Plan (2010) and Investment Mistakes Even Smart Investors Make and How to Avoid Them (2012). Larry also writes blogs for MutualFunds.com and Index Investor Corner on ETF.com.

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