Monday, June 20, 2016

Skew with trend-following - It may not be because they are good traders

Investors love certain shapes in the return distribution. There is a preference for mean and skew, the first and third moments of the return distribution. They hate volatility and kurtosis, the even or second and fourth moments.  Positive skew will give you more probability of an upside gain. Kurtosis is disliked because there is a high probability of returns in the tails of the distribution. It represents surprise risk.

It is relatively easy for a manager to generate more or less volatility. You can add leverage. Skew is much more complicated. A manager would like to tell you that his activities of trading generates positive skew or a lager right tail.  For example, skew could be created by the manager who hangs onto winner and sells losers. Managers can create skew through the use of stop-loss rules to cut negative tails. This is a good story. Similarly, skew can be created by the instruments bought. A non-normal distribution can be generated through buying and selling options around a position. The non-linear pay-off will create skew in the return pay-off. Finally skew can be created by changing volatility to generate a mixed distribution. This could be caused by adding volatility when returns are expected to be good or changing volatility based on some other criteria. 

If you read about the causes of return skew, you will learn deviations from a normal distribution can be generated from a combination of mixed distributions. If a return series sample mixes periods of high and low volatility, you may get a non-normal distribution with skew. This could be caused by skill of learning when to turn on or off volatility, but it could also be random. The skew may not have anything to do with trading skill.

Campbell and Co discusses this issue in their new paper, "The Taming of the Skew". The authors focus on the volatility management and skew. They look at three different methods for managing volatility and their impact on skew. The first is constant volatility target management (CRT) which has been a new darling of many managers. Second, is a signal risk target strategy (SRT) which varies  with the quality of signals for trends. The third is a equity risk target which focuses on matching volatility with the equity market.

Their work shows that the method for managing volatility will have an important impact on skew and the relationship with other markets. The constant volatility approach will not have skew but will have the highest Sharpe ratio for their tests. The equity based volatility adjustment will have positive skew that will be tied to the equity market moves. It will have the highest crisis alpha or negative correlation during "bad times". The signal generated volatility will have the highest skew but the lowest Sharpe ratio.

Their analysis addresses some fundamental issues with trend-following. Conventional wisdom that all trend-follower will have skew is not always correct or may be right for the wrong reasons. The paper assumes that skew can be caused by mixed distributions, but the method that creates the mixture will have different implications for skew. The volatility management will matter. 

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