Measuring Normality of Fund Performance Data

The next thing investors must determine is how predicable past performance will be going forward. An investor wants to know if a fund's expected return, given a beta measure and a change in the S&P 500 or a factor exposure to interest rates and a change in market yields, will change or if the average returns per month over the past three years will look like the next three years, given a similar set of market conditions.

To do this, an investor must understand if the reported fund data pattern is normally distributed. The ability to rely on an estimate of performance based on a sample of historical returns requires an investor to accept or reject certain assumptions about the reported returns. Is the fund or investment data being evaluated normally distributed? If yes, then an investor can make some assumptions about future returns with a certain degree of statistical confidence. If not, the actual performance may deviate from the historical performance in ways that have adverse implications for the investor.

Skewness measures the asymmetry of a distribution of investment returns. Normal distributions are perfectly symmetrical and have a skewness of zero. Negative skewness implies that the data have some extremely low-value data points below the mean. Negative skewness visually implies a long tail to the left of the mean. In this case, the mean has a value lower than the median value of the distribution due to the adverse effect on the ...

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