A left tail event has occurred in the stock market. But the market is smart (we hope) and the left tail event is not in daily returns but in volatility. As it turns out, this tail event comes from a logistic distribution.
Below is a chart of S&P 500 since 1965 with returns from lowest low to highest high of rolling 7-day periods.
The current reading is 0.774, which is the lowest in 23 years and the second lowest since 1965. The lowest reading of 0.7460 occurred January 20, 1994 and it is marked on the chart with small blue circle.
This volatility crash can be due to several causes including indecision, efficient markets, increased transactions in volatility-related derivatives and, of course, manipulation. This last factor can never be eliminated.
Below is the histogram of returns from lowest low to highest high in 7-day rolling periods for S&P 500 from 01/04/1965 to 05/03/2017.
This is a logistic distribution with high kurtosis and positive skew. This leptokurtic distribution usually arises in processes that involve categorical target variables, for example yes/no or up/down. It is not an accident that this distribution applies in this case.
The current left tail event has probability less than 0.05% and it is preferable to a right tail event with same probability, such as those that occurred during the last two bear markets.
Is the market so smart or something else is going on? I will make a hypothesis here that this left tail event is caused by algos. Actually, some of those algos use the logistic regression in making decisions with models that use as targets the categorical variables “Up” and “Down”.
What will happen when emotive humans return to the market? For now most are in passive mode trying to squeeze out the last drop of positive returns from this 8-year uptrend. The reaction will be massive in either direction when information triggers that. Normally a downtrend should follow an uptrend but there are other choices, for example a protracted sideways market. This last scenario is a nightmare for trend-followers due to model failure in choppy markets.
Academics should be happy; this is the random walk they always dreamed of. Enjoy it while it lasts.
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