Empirical research has shown that return premium may be captured in equity markets if we base our investments on certain factors, included in which are: equity size, value or momentum. The nowadays-popular low-volatility (low-beta) factor may also be include. This (to a certain point) is the basis of this post.

Following this factor approach, we are going to test a new factor: the **volatility of volatility**. The use of the volatility of the implied volatility in the option market is well known. However, what I would like to test here is not related with the option market. My interest is in the *premium* we may achieve, when focusing on the stocks with the lowest volatility of volatility.

There are studies (Baltusen, Bekkum, Grient, 2013) suggesting that the volatility of a stock option’s implied volatility, can be seen as a way to measure the uncertainty of the stock’s future returns: the higher the uncertainty, the less the future returns.

## Testing the theory

In this post, I am going to capture this idea by testing a universe made up of the S&P 500 components from 1/1/2007 to 31/12/2013, using exclusively the index components of each moment, to avoid any potential survivorship bias.

My tests calculate the volatility of the historical volatility of the daily returns, with 6 months rolling windows. From this point on, the volatility of volatility will be referred to as VoV.

There is no clear pattern if we analyse what happens when selecting weekly deciles from the ranking on VoV. However, we see that the first two deciles have sharpe ratios higher than the ones of the upper deciles.

Likewise, we can see that the maximum draw down grows as we move to the upper deciles.

These statistics resemble those seen in the studies related with the** low volatility anomaly**. The same type of graphs based on the simple volatility ranking can be seen below.

Can this resemblance be attributed to a very similar ranking in volatility and VoV? In the following chart, we can see that the stocks in the first decile of the VoV fall greatly in the first decile of the volatility ranking. In addition, the first decile VoV is also distributed mostly in the first 4-5 volatility deciles.

The method I used to calculate the VoV explains this result: the calculus of the VoV have not been normalised. For example, dividing by the mean VoV makes it probable that the stocks with lower VoV correspond to some extent with the stocks with lower volatility. Thus, there’s a high coincidence between the first deciles of the low VoV and the low volatility strategies.

Then, if VoV is apparently taking advantage of the low volatility anomaly, why should we base our strategy in the volatility of volatily? Does VoV contribute anything?

## Precedence in Volatility Strategies

Previous history shows that low volatility strategies can fall behind with their references under very **bullish markets**. On the other hand, low volatility strategies show very good behavior in **bearish situations**. Can we expect this same behavior in a Low VoV strategy?

In the following picture of annual returns, Low VoV clearly surpasses Low Volatility strategy in 2009 and 2013, which are very bullish years. However, during the terrible draw down of 2008, low Volatility beats both the market *and* the low VoV portfolio (although low VoV also achieves a great spread with the market).

The table of statistics presents very similar annualized returns for both strategies, with lower maximum draw down and volatility in Low Volatility, but higher maximum rolling run up for low VoV.

* 1/1/2007 – 31/12/2013

In terms of 1 year rolling spreads with the S&P 500 Index, low VoV is higher above the index and keeps spreads less extreme than the ones of the Low Vol strategy.

## In Summary

The results displayed in this post suggest that a low volatility of volatility strategy could be an alternative to the Low Volatility strategies, keeping the pros of the former and improving the results in “boosting” markets.

To obtain more reliable conclusions, we would need to lengthen the period and to broaden the markets of study.