Sigma Stigma

Just as we each are redefining boundaries in the new reality of “social distancing”, the events of the past month have reset what investors consider “normal” for markets. Blown to bits are expected ranges that had previously been precisely defined by statistical analysis, and the overly generous (mis)use of the Gaussian distribution. Analysts and commentators have casually thrown around “sigmas” that are of decreasing relevance as asset return distributions are being rapidly redrawn. I, too, have referenced sigma moves and levels as short-hand to describe outsized moves. The fact is that asset price returns do not easily conform to statistical models (just ask the quants after this month's performance). This is particularly true in credit where the return profile is asymmetric. Credit returns are left-skewed; prone to severe negative outcomes that register as extreme on the scale of normality. 

   As with credit, which has a higher probability density in the left tail, investors are finding that other asset classes that are known to have leptokurtic return distributions are also exhibiting left skew. The unwind of the previous herding into different investment vehicles pursuing essentially the same strategies is one reason we are now experiencing more extreme outcomes. Structurally impaired market trading liquidity is another cause, while volatility clustering is yet a third reason. Amplified volatility has moved portfolio loss attachment points faster than parametric VaR models have been able to adjust to the new reality. The rapid asset price moves should cause many investors to reassess the probability-weighted expected return prospects of positions across all asset classes. Probabilities derived from the normal distribution will prove misleading in the new market paradigm. In thinking of a range of possible outcomes, the use of a simple rule of thumb may be of some help. Around 170 years ago, a Russian mathematician named Chebyshev developed a simple formula for determining the probabilistic boundaries for return distributions of unknown shape. The calculation informs the maximum probability density of any distribution that could lie within a given number of standard deviations. The result is that one can identify the outer goal post probability of an “X” sigma move. The rub is that it implies extreme outcomes are much more common than the normal distribution would suggest. The analysis helps put into perspective the alternative reality we all now seem to be living. Abnormal is becoming the new normal.

A sense of how the recent market moves stack up:

Data Source: Bloomberg

"Abby Normal" is the new normal: