Standard Distribution

Distribution analysis looks at the distribution of returns over a given time period. It is most commonly associated with the bell curve. The x axis shows all the possible returns with the theoretical range of -100% to + infinity. The y axis shows the frequency with which these returns occur.

The purpose of this sort of analysis is to look past the funds average return and determine whether it is the most likely return. This is done by looking the bell curve and measuring the distributions skew and kurtosis.

The measures of skew and kurtosis relate to how the shape of the curve differs from what is regarded, in a statistical sense, as normal. In a normal distribution, the most commonly occurring return (the mode) is also the average (the mean) and the returns are symmetrically distributed on either side of the average return. Therefore when analysing a fund with normally distributed returns we would expect there to be an equal chance of the fund over of underperforming in any single month, and if we were to pick a month at random, there is a high chance that the return will be somewhere close to the average.

It is quite unusual for fund returns to be normally distributed in real life, however. The average return gets distorted by the occasional freak event that either inflates or deflates the mean. The direction in which the average has been dragged is measured with skew.

A normal distribution has zero skew. A fund whose average return is biased downwards by a freak loss exhibits negative skew. In this instance the most commonly occurring return is actually higher than average, the fund is more likely to outperform the average in any given month. A fund whose average has been inflated by a one off large gain exhibits positive skew, in this instance the most commonly occurring returns are below the average and the fund is more likely to underperform in any given month.

The purpose of distribution analysis is to spot those funds which are likely to outperform the average return and avoid those that are likely to underperform.

In order to achieve this we need assess how relevant these freak events affecting the average are, this is done using Kurtosis.

Kurtosis is a measure of how frequently these freak events occur. The lower the kurtosis, the less extreme events have been recorded. This is a good thing as it means we are less likely to be surprised by something completely unexpected i.e. a long way from the average. High kurtosis means freak events have been larger and more frequent. This is undesirable as it makes the expected returns from a fund more unpredictable.

Note: Make sure that you compare your funds to its sector average or benchmark.