Tail Risk is Not Crash Risk…or Is It?

[This is the second of a new series of editorials by Executive Editor Andrew Karolyi at the Review of Financial Studies featuring forthcoming or recent papers at the journal. This editorial features “Tail Risk and Asset Prices,” by Chicago-Booth’s Bryan Kelly and Michigan State University’s Hao Jiang, lead article in Issue 27(10). It was selected as an Editor’s Choice article on the Oxford University Press web site for RFS.]

stock-exchange-1376107_640-pixabayThe global financial crisis called into question the ability of markets to deal with extreme events. As The Economist magazine put it a few years ago (“Fat-tail attraction,” March 24, 2011), “…tail-risk hedging was the talk of Wall Street in 2008 after global markets nosedived.” The key word here is after. The article points out how anxious investors tried to figure out how they could protect themselves from extreme or “black swan” events that arise outside the mid-range of the distribution of outcomes. The current (2014) unstable global market environment has surely revved up investor interest in uncovering such protections anew.

Excess tail risk is technically defined as a higher-than-expected likelihood of an investment position moving more than two or three standard deviations away from the mean. For many, tail risk simply means any large decline in a portfolio’s value. But a critical first step to hedging tail risk is to measure it. What Kelly and Jiang’s (2014) study proposes is an innovative measure of time-varying tail risk that is implied by the cross-section of stock returns. What they do is assess the magnitude of firm-level price declines every month to come up with a market-wide measure of common fluctuations in tail risk among individual stocks. They demonstrate how their measure is linked to traditional ones of tail risk extracted from equity index options, and how it moves inversely with real economic conditions. But what Kelly and Jiang ultimately seek out–and affirm–is an ability to forecast aggregate stock market returns while also capturing the cross-section of returns. Their back-tested portfolio that spreads U.S. equities on past tail-risk exposures delivers a juicy annual alpha of more than 5%.

Those statistics may capture active investor attention, but allow me to offer a few sobering thoughts the authors shared about their study’s most important findings. “I think it’s important to emphasize that our findings suggest that investors hedge against risk of an aggregate tail event…(and they are) not about stocks with higher crash risk having higher average returns,” states Bryan Kelly. In other words, they interpret their measure as an aggregate crash risk “state variable” contributing to fluctuations in investors’ marginal utility. This is why market participants will sacrifice a big chunk of their return on wealth to insulate themselves against a surge in crash risk. They also caution that their finding is “…not solely about return tails,” and show in their paper a significant correlation between return tails and cash-flow tails, which I think is very interesting. What is the link between tails on asset price returns and tails on the real side of firm behavior? One wonders how these concepts are connected to the surge of recent research on uncertainty shocks and disaster-risk shocks. The authors propose another intriguing connection may be to derivative pricing models that incorporate not only some measure of volatility as an observable state variable, but also build in a dynamic jump intensity. Which could be related to those volatility dynamics…or something else. Indeed, could Kelly-Jiang’s new measure of tail risk represent a useful observational process for jump-risk modeling in derivatives?

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