The purpose of this paper is to introduce a non‐normality premium (NNP) to identify the extra return that will compensate an investor for a non‐normal return distribution. The NNP quantifies the economic significance of non‐normality to complement a statistical significance test of non‐normality, such as the Jarque‐Bera test.
The NNP is patterned after the risk premium, the amount that compensates an investor for the risk of an investment. The theoretical NNP is examined on the margins with Taylor series approximation and applied to hedge fund data.
An increase of 1 in the skewness has the same effect on an investor as an increase in the mean of 2.5 basis points per month. An increase of 1 in the kurtosis has the same effect on an investor as a decrease in the mean of 0.15 basis points per month. A sample of 716 hedge funds revealed that while 72 per cent statistically reject normality, only 29 per cent require more than a single basis point per month difference in the mean to compenscate an investor for the non‐normality.
The NNP allows for a valuation on the higher moments (skewness and kurtosis) of an investor's return distribution. The evaluation is tailored to the individual through use of a utility function. Once applied to an alternative investment vehicle, it is learned that rejecting normality is not sufficient grounds to suspect that the non‐normality is important to investors.
