Please read Part I for the introduction.
Holding-period back-test
In Part I, we ran a quick back-test that would go long the equity index if the VIX was in a certain quintile and saw how the 5th quintile produced the lowest draw-down returns. The index was held only for a day. However, our box-plot of VIX quintile vs. subsequent n-day returns begs us to look at alternate holding periods as well. What would the returns be if we held onto the index beyond a day?
Here is how long-only S&P 500 returns when VIX is in the 5th quintile, across different holding periods looks like:
The problem with this strategy is that when there is a steep fall in the index, the VIX keeps going higher and will be in the 5th quintile for an extended period of time. Have a look at the 2008-2009 segment in this chart:
What happens if we used the change in VIX to time the equity index?
VIX returns deciles
If we bucket VIX returns (percentage change over previous close over n-days, 1000 trailing observations) into deciles and observe the next 5, 10, 15 and 20-day returns of the underlying index over them:
There is no determinable pattern here. Perhaps the VIX and the index are co-incident with none holding the power of prediction over the other.
Interested readers can browse the github repo for corresponding Nikkei 225 and NIFTY 50 charts.