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Are You Compensated For Your Risk? Thumbnail

Are You Compensated For Your Risk?

Despite the fact that financial theory suggests stocks with high volatility should have higher expected returns—because investors cannot fully diversify away from the firm-specific risk in their portfolios—a growing body of empirical evidence demonstrates a negative return premium in higher-volatility stocks (the low-volatility/low-beta anomaly).

Research also documents that investor preferences for more volatile stocks are directly associated with preferences for stocks that look like lottery tickets (they have positive skewness and excess kurtosis, or fat tails). The negative premium associated with such stocks persists because of limits to arbitrage.

These findings on volatility and kurtosis are important because extreme positive and/or negative returns happen far more regularly than predicted by a normal distribution. For example, the stock market crash of October 1987 is an occurrence that, according to a normal distribution, would happen only once every 150 million years. Events that would be extremely rare under a normal distribution seem to occur empirically far more often than they otherwise should.

If kurtosis represents some sort of risk that is unaccounted for in other, more common, risk measures, then extreme returns should influence asset prices—excess kurtosis should be associated with higher expected returns. However, it’s also possible that the aforementioned investor preference for lottery tickets, combined with limits to arbitrage, could result in these risky stocks having negative premiums. Lottery-like distributions have been found in IPOs, “penny stocks,” extreme high-beta stocks and small growth stocks with low profitability and high investment.

Research On Kurtosis & Expected Returns

Benjamin Blau and Ryan Whitby contribute to the literature on this topic with their study “Idiosyncratic Kurtosis and Expected Returns,” which they last updated in February 2017.

To determine whether kurtosis affects asset prices, Blau and Whitby sorted stocks into portfolios based on a measure of firm-specific (idiosyncratic) kurtosis. For their measure, they used a rolling six-month window. Their dataset covers the period 1980 through 2010.

Following is a brief summary of their findings:

  • There is a reliably negative relationship between idiosyncratic kurtosis and next-month returns that is robust to controls for idiosyncratic volatility and idiosyncratic skewness.
  • The return difference between the first quintile of stocks (with the least idiosyncratic kurtosis) and the fifth quintile (with the most idiosyncratic kurtosis) was 3% per year, with a t-stat of 2.7. Results were similar when measured against the CAPM, the Fama-French three-factor model and the Carhart four-factor model.
  • Returns decreased monotonically as you moved up quintiles.
  • The negative relationship between idiosyncratic kurtosis and expected returns does not appear to be driven by the skewness of the distribution.

These findings led Blau and Whitby to conclude: “To the extent that kurtosis represents additional risk unaccounted for in traditional measures of volatility, investors do not appear to be compensated for this risk. If anything, investors seem to be overpaying for stocks with higher kurtosis.”


The kurtosis of stock returns seems like an intuitive measure of risk—risk-averse investors demand a premium for taking nondiversifiable risks. Yet we have this anomaly, which can only be explained either by investor preferences for lottery tickets or by the buying of high-kurtosis stocks as a substitute for leverage that might be constrained, combined with limits to arbitrage that prevent sophisticated investors from correcting mispricings.

Given findings that show a negative risk premium for such stocks, investors are best served by avoiding them. These findings are why “passively” managed fund families, such as Dimensional Fund Advisors and Bridgeway Capital Management, screen out stocks of this type from their portfolios. Hopefully, now that you are aware of the information, you, or the funds you invest in, will also be screening them out. (Full disclosure: My firm recommends DFA and Bridgeway funds in constructing client portfolios.)

Larry Swedroe is the director of research for The BAM Alliance.   

This commentary originally appeared March 21 on ETF.com

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