Tag: volatility

VIX and Equity Index Returns, Part II

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:
S&P 500 returns

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:
VIX quintiles over S&P 500

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:
S&P 500 returns over changes in VIX

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.

VIX and Equity Index Returns, Part I

The VIX is a measure of implied volatility of the underlying index. For example, the CBOE Volatility Index is a measure of 30-day expected volatility derived from S&P 500 Index call and put option prices, India VIX similarly uses the NIFTY 50 call and put options prices to derive a measure of volatility. The question we will try to address in this series of posts is whether the VIX can be used to time entries and exits on the underlying index.

The VIX time-series

CBOE and India VIX
The VIX on S&P 500 has been around since the 90’s whereas India VIX started out around 2009. Moreover, the US enjoys a much wider and deeper market for volatility products than any other market in the world. VIX futures, VIX options, VIX of VIX, volatility ETFs and their inverse, all trade fairly well. Whereas in India, even though VIX futures have been listed for a while, it rarely trades. Trading activity of a derivative (VIX, in this case) invariably has an effect on the underlying (S&P 500, NIFTY 50…) So we expect the relationship between S&P 500 VIX and the S&P 500 index to be closer than that between India VIX and the NIFTY 50 index.

VIX quintiles

To begin, we will bucket the trailing 1000-day VIX closing prices into quintiles and observe the next 5, 10, 15 and 20-day returns of the underlying index over them.
S&P 500 VIX
SP500 returns over VIX quintiles
And, more recently:
SP500 returns over VIX quintiles

What is striking here, is that subsequent returns off the 5th quintile (when VIX is at its highest) is higher with smaller negative outliers than returns off the 1st quintile (when VIX is a its lowest.) This is counter-intuitive to the notion that “volatility begets volatility” so investors are better off staying away from the market when it is volatile.

India VIX and NIFTY 50 shows a similar pattern*:
NIFTY 50 returns over India VIX quintiles
*Smaller sample compared to the S&P 500 dataset.

A simple back-test

What happens to a long-only portfolio if it is long the index only when the VIX is within a particular quintile?
S&P 500/VIX
S&P 500 returns over different VIX quintiles
The strategy that is long when VIX is in the 5th quintile (L5) out-performs the other quintile strategies. Also, if you ignore the 2008 collapse, L5 has the shallowest of drawdowns.
Something similar happens with NIFTY 50 as well:
NIFTY 50 returns over different VIX quintiles


Cash-only investors can point to the superiority of buy&hold compared to these VIX-based strategies. However, the shallow drawdowns exhibited by the L5 strategy (long index when VIX is in the 5th quintile) is attractive to leveraged traders. For example, NIFTY 50 futures leverage is between 8x and 10x. So even if you play it safe and leverage only 5x, L5 returns would end up at ~100% compared to buy&hold’s 80% over the same period.

We will dig deeper in the next part of this series. Stay tuned!

Code and more charts are on github.

Volatility and VIX Charts

Our Volatility and VIX Collection had some charts that were more than two years old. This post updates some of those charts and will re-create them more often.

Volatility can be measured in a number of ways and its profile changes based on the look-back period. The parameters are selected based on what the volatility estimate is used for. Moreover, no two indices exhibit the same profile – traders need to be vary of transplanting trading strategies that work for one market into another.

Historical volatility density plots

20-day historical volatility density plots

historical volatility density plot

20-day historical volatility plots

US S&P 500
S&P 500 20-day historical volatility
Japanese Nikkei 225
Nikkei 225 20-day historical volatility
Indian NIFTY 50
NIFTY 50 20-day historical volatility

Implied volatility

S&P 500 VIX and NIFTY 50 VIX

Code and a lot more charts are on github.



Historical volatility and implied volatility.
Read: Part I, Part II

Nifty volatility

Density plots of historical volatility over different horizons.
Read: NIFTY Volatility, Historical Perspective
Charts that are updated often: Volatility and VIX Charts

Dollar ETF volatilities

When you convert Indian indices to dollars, their volatility profile changes.
Read: INDA vs. SPY Observed Volatility

VIX – Implied Volatility Index

Do VIX indices across markets have any relationship with each other?
Read: India VIX vs. SPX VIX

Can a simple VIX based trading strategy avoid market losses?
Read: Macro Volatility and the NIFTY 50, VIX and Equity Index Returns, Part I, Part II.

Can VIX be predicted using a simple model?
ARMA + GARCH to Predict VIX

Macro Volatility and the NIFTY 50

This post is a continuation of our exploration of trying to use macro market indicators to time the NIFTY 50. See World Markets and the NIFTY 50 and India VIX vs. SPX VIX.

Perhaps the problem with using price moving averages was that the major moves were already done before we could short the NIFTY. What if we used volatility instead? Here is how the median of 10-day volatility of major world indices looks like:


What if we went long only when volatility was below the median and went short otherwise?


Looks like the strategy works only in avoiding the 2008 crash. Using observed volatility to time trades doesn’t work. One more to the reject pile.