It has been well documented both that stock returns have much fatter tails than a normal distribution would generate, and that tail events occur much more frequently than a normal curve would predict.(1) For example, Benoit Mandelbroit and Richard Hudson examined the daily index movements of the Dow Jones Industrial Index from 1916 to 2003. They noted that if stock returns were normally distributed, a single-day price move of more than 3.4 percent would have occurred 58 times. The actual number of occurrences was 1,001, more than 17 times as frequently. They found that a daily price move of more than 4.5 percent would have occurred just six times, yet it occurred 366 times, or 61 times greater than with a normal distribution. They also found that a daily price move of more than 7 percent would have occurred just once in every 300,000 years. Yet, it had occurred 48 times! In other words, markets are risky and returns exhibit excess kurtosis (the tails are much greater than would be expected if returns were normally distributed). The risk of large losses combined with the high-risk aversion of most investors provides us with a logical answer for why stocks as an asset class have provided such a large risk premium—investors demand a large premium to bear risks they dislike.
Supporting evidence for a large tail risk premium was provided by Fousseni Chabi-Yo, Stefan Ruenzi, and Florian Weigert, authors of the study “Crash Sensitivity and the Cross-Section of Expected Stock Returns,” which was published in the June 2018 issue of the Journal of Financial and Quantitative Analysis. They demonstrated that U.S. stocks that are likely to perform badly during market crashes earn significantly higher average returns than stocks that offer protection against market downturns. And Bryan Kelly and Hao Jiang, authors of the 2014 study “Tail Risk and Asset Prices” found that “cross-sectionally, stocks with high loadings on past tail risk earn an annual three-factor alpha 5.4% higher than stocks with low tail risk loadings.”
Clearly, understanding the dynamics of tail risk and its relation to asset returns is of crucial importance in investment decision making and has implications for portfolio management.
Sofiane Aboura and Y. Eser Arisoy contributes to the literature with their study “Can tail risk explain size, book-to-market, momentum, and idiosyncratic volatility anomalies?” published in the October/November 2019 issue of the Journal of Business, Finance & Accounting. They sought to determine whether tail risk helps explain the performance of size (small stocks), book-to-market ratio (value stocks), momentum, and idiosyncratic volatility (IVOL) sorted portfolios. They used a measure of tail risk (TAIL) developed by Bryan Kelly and Hao Jiang, authors of the aforementioned 2014 study “Tail Risk and Asset Prices.” Their hypothesis was that tail risk-averse investors view stocks with negative (positive) exposure to aggregate tail risk as riskier (less risky), because they are expected to lose more (less) in periods of tail events. Thus, stocks with negative (positive) sensitivity to aggregate tail risk should command a higher (lower) risk premium. Aboura and Arisoy’s study covered the period 1963 through 2013.
The following is a summary of their findings:
Tail risk is time-varying. It’s countercyclical and strongly related to good and bad states of the economy.
The tail risk factor was not correlated with the five Fama-French factors (beta, size, value, investment, and profitability) used in their augmented six-factor model, and the six-factor model explains the cross-section of 25 portfolios (5×5) better than the five-factor model.
Portfolios that contain small, value, high idiosyncratic volatility, and low momentum stocks exhibit negative and statistically significant tail risk betas. In particular, small stocks are far more negatively exposed to tail risk than large stocks.
Tail risk helps in explaining the four pricing anomalies, particularly the size, and idiosyncratic volatility anomalies—explaining virtually half of the IVOL premium and almost two-thirds of the size premium.
Extreme size portfolios (containing the smallest and biggest stocks) are more negatively exposed to aggregate tail risk than mid-cap stocks. In particular, the portfolio of small stocks and the arbitrage portfolio that is long in the quintile of smallest stocks and short in the quintile of biggest stocks (Lo-Hi MCAP) exhibit a negative and statistically significant aggregate tail risk exposure, which is much higher in magnitude compared to any other portfolio.
The portfolio of value stocks and the arbitrage portfolio that goes long the quintile of highest B/M stocks and short the quintile of lowest B/M stocks (Hi-Lo B/M) are negatively and significantly exposed to aggregate tail risk.
The portfolio of stocks with high idiosyncratic volatility and the arbitrage portfolio that is long in high IVOL stocks and short in low IVOL stocks (Hi-Lo IVOL) also exhibit negative and significant aggregate tail risk loadings—due to their strong negative exposure to aggregate tail risk, high idiosyncratic volatility stocks should be considered riskier at times of increased tail risk. This explains why high idiosyncratic volatility stocks lose more during bad states of the economy.
The portfolio of low-momentum stocks exhibits a negative and statistically significant aggregate tail risk exposure, and that the arbitrage portfolio that is long in high MOM stocks and short in low MOM stocks (Hi-Lo MOM) exhibit a positive and significant aggregate tail risk loading— due to their strong negative exposure to aggregate tail risk, low momentum stocks should be considered riskier at times of increased tail risk.
“The results obtained for the whole sample are mainly driven by the subsample characterizing bad states of the economy, in which portfolios containing small, value, high idiosyncratic volatility, and low momentum stocks exhibit significantly higher exposures.”
Tail risk is an important determinant of asset prices. As a result, crash-sensitive stocks command a risk premium. Thus, tail risk provides a risk-based explanation for the size and value premiums. Their findings led Aboura and Arisoy to conclude that,
investors are much more averse to holding small, value, high idiosyncratic volatility, and low momentum stocks due to their increased aggregate tail risk exposures and corresponding losses in times of market distress. Therefore, tail risk averse investors will consider such stocks as riskier and will demand compensation for including them in their portfolios.
As Chief Research Officer for Buckingham Strategic Wealth and Buckingham Strategic Partners, Larry Swedroe spends his time, talent and energy educating investors on the benefits of evidence-based investing with enthusiasm few can match. Larry was among the first authors to publish a book that explained the science of investing in layman’s terms, “The Only Guide to a Winning Investment Strategy You’ll Ever Need.” He has since authored seven 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) and “Think, Act, and Invest Like Warren Buffett” (2012). He has also co-authored eight books about investing. His latest work, “Your Complete Guide to a Successful and Secure Retirement was co-authored with Kevin Grogan and published in January 2019. In his role as chief research officer and as a member of Buckingham’s Investment Policy Committee, Larry, who joined the firm in 1996, regularly reviews the findings published in dozens of peer-reviewed financial journals, evaluates the outcomes and uses the result to inform the organization’s formal investment strategy recommendations. He has had his own articles published in the Journal of Accountancy, Journal of Investing, AAII Journal, Personal Financial Planning Monthly, Journal of Indexing, and The Journal of Portfolio Management. Larry’s dedication to helping others has made him a sought-after national speaker. He has made appearances on national television shows airing on NBC, CNBC, CNN, and Bloomberg Personal Finance. Larry is a prolific writer and contributes regularly to multiple outlets, including Advisor Perspective, Evidence Based Investing, and Alpha Architect. Before joining Buckingham Wealth Partners, Larry was vice chairman of Prudential Home Mortgage. He has held positions at Citicorp as senior vice president and regional treasurer, responsible for treasury, foreign exchange and investment banking activities, including risk management strategies. Larry holds an MBA in finance and investment from New York University and a bachelor’s degree in finance from Baruch College in New York.
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