### Skewness in Equity Curve

the Skewness in the Equity Curve of a strategy- whether backtested or real- is an important indicator of the stability of the strategy.

Would you like to trade a strategy with 99% profitability? This is not very hard to accomplish. As an example, assume a pair trading strategy in which you buy one pair and short another and wait for a simple 0.20% profit opportunity. Assume that both stocks have high level of correlation coefficient. In such case it will be easy to achieve a 99% winning trade streak. The stocks may occasionally diverge an show negative market return of 1-2%, but will eventually come in your favor to book the regular profit.

Now assume that an event occurs which triggers a fundamental rift in both stock prices. This will push the trade into mounting loss and hundreds of small losses may be offset by a single losing trade. This is classical example of a negatively skewed strategy. Most arbitrage strategies have a negative skew.

Skewed strategies exhibit an asymmetric distribution of the probability curve of gains and losses.

A negatively skewed strategy may have the same profit probability curve as a symmetric strategy, but the overall probability of outperforming the expected profitability increases. Such “feeling” of profitability will soon be offset by few large losses.

The diagram above shows a strategy with 60% chances of making money and 40% chances of losing money. Whether a strategy makes or loses money in long-term depends upon its competitive advantage. Even if the mean returns are zero, a negative skewed strategy will exhibit a high probability of making small profits; and a low probability of encountering few large losses.

A positively skewed strategy, on the other hand, may be losing most of the time; but such small losses will be offset by few large winning trades. Trend Following strategies tend to be positively skewed in contrast to arbitrage/pair strategies which are negatively skewed.

The majority of hedge funds are fat tailed with symmetric distribution or negatively skewness. No doubt when the returns of hedge funds are adjusted with all fees and costs, they may just underperform the market index.

The below exhibits are courtesy “Trend Following with Managed Futures”, Alex Greyserman, Kathryn Kaminsk.