Probability Distributions of Bull and Bear Market States

Numerous academic papers have shown that the options markets are not only the place where the supply and demand for options meets. For example, they might point out to the smart money positioning, help to assess risk in the form of implied volatility, or be base of the well-known fear index VIX. Novel research of Bhansali and Holdom (2021), uses information embedded in options markets to construct a probability-weighted mixture of two distributions of bull and bear market states for the S&P 500 index. The results show that the implied return distribution drastically change switching from normal to stressed market states and vice versa. Moreover, the uncertainty in both distributions changes in the same fashion.

An excellent example is the shift of distribution before and after the recent US presidential election, which can be found below. Many have feared that if the democrat candidate Biden wins the elections, it would be a bad signal for the markets. However, after the uncertainty has passed, the fear has seemed to disappear. Additionally, the paper also shows how to use the bimodality in return distributions for the asset allocation using various utility functions. Allocations are made using a risky asset, risk-free and even options. Indeed, this research is worth reading. — The Encyclopedia of Quantitative and Algorithmic Trading Strategies