With the VIX picking up, you might be wondering if it’s time to reduce your exposure to risky assets a bit until the market calms down. According to new research from First Quadrant Analytics that might not be a bad idea because the chance of a sharp, two or three sigma, drop is a lot higher during high volatility regimes.

“While ‘tail risk’ has always existed in the markets, it is mostly since the financial crisis of 2008 and the resulting bear market that investors have become accepting of its persistence,” write First Quadrant partner Ed Peters and associate director Bruno Miranda. “This paper shows that the probability of a large drop in the market varies over the market cycle.”

Traditional stats both over and under-state tail risk: FQ

It’s well known that the normal distribution (or bell curve) isn’t a great approximation of market returns, but without that simplification many analytical problems would just become intractable (a good reason to treat theoretical results with some skepticism). Market results are skewed negative (there are more large, sudden drops than large, sudden jumps) and have a high kurtosis (there’s more tail risk than the normal approximation implies). The chance of a 13% drop is 0.7%, an order of magnitude higher odds than the 0.03% predicted by the normal distribution.

FQ msci v normal 0115 VIX Volatility

That still probably sounds remote, but Peters and Miranda found that using a single number for tail risk is incredibly misleading because the situation is so dramatically difference when volatility changes.

“Traditional statistics both understate and overstate tail risk. The actual methodology for calculating conditional kurtosis and skewness is simple and intuitive though it has not appeared in the literature as far as we know.”

High VIX turns market returns bi-modal

To get a better look, they separate market returns into high and low volatility regimes using a composite VIX: the S&P 500 VIX, EuroStoxx VIX, and WTI oil VIX in a 60/30/10 split (oil is used as a proxy for EM). They found that tail risk falls when volatility is low, the negative skewness is reduced, and the curve looks close to normal if a bit steep. When the composite VIX is high, the shape of the distribution is completely different.

FQ msci high low regime 0115 VIX Volatility

The bi-modal nature of the high composite VIX makes sense. Sometimes the market gets spooked, not much happens, and everything returns to normal in due time. Sometimes the floor falls out from under you. Then the chances of a three-sigma drop isn’t 0.03% or even 0.7%, but 1.36%, thirty times higher than traditional theory tells you. The odds of a two-sigma event are 8.20%, at which point ‘tail risk’ starts to sounds like a misnomer.