Logica

# Negative Skew - A Hidden Killer

Fresh off a decent, quick correction to markets around the world (and one in which many unfortunate investors fell prey to the allure of the crowded short volatility trade), it might be insightful to again consider the role negative skew can play in our investment decisions. As you can see from the date ranges of the analyses below, this text was written (on another forum) well before recent events occurred. It just goes to show: there is nothing new under the sun. Markets have always acted this way, and likely always will.

To put it simply, it took about two weeks for those passively invested in the S&P 500 index to lose more than two months worth of gains. Why does this is happen? Is it the exception, or the rule?

A primary issue with using summary statistics to evaluate performance is that most distributions of daily returns are not normal. That is, metrics like mean and standard deviation are only accurate portrayals of expected returns if the distribution is normal. When distributions exhibit characteristics such as skew or kurtosis, outcomes are no longer predictable using these metrics. In fact, by introducing a third parameter like skew, i.e. return behavior that has rare, or larger, events either on the positive or negative side of the mean, there is nothing “standard” about the deviations from the mean. To make matters worse, most hedge funds and mutual funds are negatively skewed. In layman’s terms, we are saying that an investor in these products is likely to greatly underestimate their true risk of capital loss if they only look at conventional metrics like average annualized return, standard deviation, and of course the resulting Sharpe Ratio.

Now, negative skew may not matter so much in the long run insofar as a strategy can eventually recoup losses. For example, a strategy that has a day of -3%, followed by 2 days of +1.6% each would have a positive mean with very negative skew, and so we may say there is “nothing to worry about.” What we find, though, in the hedge fund universe is the existence of auto correlation. Translation: these outsized negative days tend to cluster together, forming large drawdowns.

My favorite ways to measure this are simply by conventional drawdown information that include the length (# days) and depth (%) of the drawdown, as well as the time it takes the strategy to recover. Another way to approximate this information is to look at a distribution’s skew over multiple day periods. That is, we slice the daily time series in different ways, and consider 2 days to be a single observation, then 3 days, then 4, etc...The result is a grid that tells us the level of skew over all e.g. 1-10 day periods. In our example above, if a strategy always recouped its losses 2 days after the negative day, we would see that the “3 day skew” calculation would be non-negative. What we actually find, though, as expected, is that most hedge funds and mutual funds exhibit worsening skew when we look at multiple days in a row. This means that multi-day drawdowns are not recouped in a similar amount of time on the upside. For an individual that may require use of investment funds at exactly the worst time, we can see the problem, here. Further, for an investor that is charged incentive fees before the inevitable drawdown occurs, this is unacceptable.

The evidence is clear. Below we see the grid of a few different assets and the resulting n day skews (remember, for e.g. n=2, we would look at all 2 day interval periods in a time series and calculate the skewness of this distribution of observations). What we’re looking for in the results are general trends. If, for example, the skew values were drastically different from n=2 to n=3 to n=4, with some positive, and some negative, we might conclude that this metric doesn’t have much reliability. But, we see that it’s a fairly consistent result across n = 1 to 21. In fact, for most assets, the skew gets more negative which is precisely what all the fuss is (or should be) about.

The conclusion is, again, that it takes magnitudes longer to make your money back than it does to lose it – the ugly byproduct of negative skew. Consequently, the questions we should be asking when evaluating a manager’s skill, or analyzing a passive investment, go much further than average return and standard deviation.