The time series of risk regimes

The VIX index has been used as a fear index, but we believe the best way to view it is to define risk regimes. There are periods of normal, high, and low risk and the behavior of markets during periods of high risk will differ from periods of low risk. Before we start examining the market response to different risk regimes, we should examine the time series of risk regimes and determine when high- and low-risk regimes occur. 

A good null hypothesis is that market returns are independent of the regime. We assume there is no relationship. However, we do expect there is a trade-off between risk and return. The market will react to risk, and the reaction should be stronger for high-risk regimes.  

We take a long time series of monthly VIX returns and divide the series into quantiles, with the low risk being the lowest quantile, the middle range being the next three quantiles, and the high risk representing the highest VIX value quantile 

We find that high equity risk will coincide with turning points in the stock market. Specifically, a high-risk regime will be associated with recession and drawdowns in equities. There will also be low-risk clusters, and these are associated with higher return periods.

Returns respond differently to high-risk periods than to low-risk periods. This is a piece of ongoing research we are focusing on.