Non-Normal Return Distribution of Alternative Investments

Non-normal Returns of Alternative Investments 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 of Alternative Investment Return Distributions

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.

Common Sense Must Be Added to Quantitative Analysis

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

Related pages

intrinsic value of a call optionnotional value futuresvxx optionssample median calculatorexponential moving average excelharmonic mean formula exampleform 13f secstrategies of hedge fundsblack scholes volatility calculatoritm callexcel emacalculate std devannualized volatility formuladjia weightingstd deviation formulaannualised return formula excelthe greeks in financeoptions futures and other derivatives 8th editionoptions trading booktrading the vixnotepad languagesaverage inventory cost formulaonline black scholes calculatordaily volatility formulahow to calculate variance using excelwhat happens when you square a negative numberinterpreting kurtosishow to calculate 95 percentile in excelvxzkurtosis calculatornegative sharpe ratiovar value at risk calculationannualised return formula excelhow to calculate historical volatilitymacd bullish divergenceformula for calculating variance in excelproshares productsdow jones industrial average weightingshort uvxyvxx optionstandard error of skewnesswhat is straddle positionblack scholes xlsstock price volatility calculationstandard deviation in excel 2007mean and variance calculatorhedge fund macro strategyinverse etfs listhow to create excel formulasacceptable skewness and kurtosismacd crossoversvxx optionhow to read rsi chartpayoff put optionforecast variance formulavix sp500cot reportsmeasures of skewness and kurtosiscalculating covariance in exceluses of arithmetic mean in daily lifeaugen the bookhow to read macd indicatoroptions volatility calculatorstandard deviation defdow jones vixvaluing a call optioncumulative distribution function excelstraddle payoff diagramrsi formulaexcel simple formulascboe option calculator