This page explains properties of alternative investment return distributions, particularly skewness and kurtosis. It identifies some of the trading style specific sources of non-normality and discusses implications it has on the investment management process.

## Non-Normal Returns and Skewness

Non-normal return distribution is one of the most common features of alternative investments. With alternative investments we mainly look at skewness of the return distribution, which compares probabilities and sizes of profits to those of losses. A positively skewed return distribution shows small frequency of very big profits, while a negatively skewed trading strategy will lead to a lot of small gains and a few large losses.

## Excess Kurtosis

Besides skewness, alternative investment return distributions often show positive excess kurtosis, which means that the frequency of outliers (extra high profits or extra big losses) is higher than what normal distribution would suggest.

Various types of alternative assets show non-normal return distributions: *hedge funds*, *private equity*, *distressed securities*, or *commodities*. A few examples follow.

## Non-Normal Returns of Distressed Securities

When you buy a distressed high yield bond or shares in a company facing the prospect of bankruptcy, you have high probability that your investment will go to zero and you lose virtually all. On the other hand, if things turn around well, you may earn multiples of the initial investment. Such return distribution is far from normal – high frequency of big losses and big profits indicates high kurtosis of the return distribution.

## Negatively Skewed Returns of Relative Value Hedge Funds

When you invest in a hedge fund that identifies little mispricings and places highly leveraged bets on spreads between related securities, you will also most likely see non-normal returns. 37 times out of 38, the bet will work out perfectly and the fund will make money on a consistent basis. But then one trade may prove unsuccessful and wipe out the profit from the previous 10 or 20 trades.

The fund still makes money in the long run, but the return distribution has a sharp negative skew, which may be unsuitable for some investors and in any case requires being part of a diversified portfolio rather then being invested on a standalone basis. Among common hedge fund strategies, *fixed income arbitrage* or *merger arbitrage* typically show negative skewness.

## Hedge Funds Using Derivatives

Another example is options and other derivatives which typically have non-linear returns. Multiple options can be combined in order to get asymmetrical risk and return prospects. Options and other derivatives are widely used by hedge funds.

## Non-Normality and Analyzing Alternative Investment Returns

It is important to be aware of the non-normality of alternative investment returns. Analyzing only percentage return and standard deviation is insufficient, as it fails to identify some kinds of risks. Some of the popular tools which *assume normal distribution of returns* (like *Sharpe ratio*) may be misleading when used with alternative investments.

## Adding Common Sense to Quantitative Analysis

By looking also at skewness and kurtosis, you get a better understanding of a trading strategy and its risk exposures. Even with that, quantitative analysis is still only one part of the investment decision making process. Identifying the logic and common sense behind the statistics is another.