Law of Averages

Law of Averages

Law of Averages

Law of Averages

There is another explanation of the low average returns on stocksof low quality and great variability. These stocks may represent akind of lottery ticket to many investors who are willing to accept lowerexpected returns than they would accept for stocks of higher quality in order to have some chance of very large gain. A person who buysa lottery ticket accepts negative expected returns in order to havesome possibility of extremely great rates of returnsay, 1 million percent. Low-quality stocks do not present possibilities of such extremeenrichment, but the possibility of very large gains may be sufficientto explain the low average returns on these stocks.

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There is another form of this explanation. We have already mentioned the fact that the distribution of returns for individual stocksis usually skewed to the right. This positive skewness is to be expectedsince it is possible to make investments which increase in value bymore than 100 percentespecially if the holding period is severalyearswhile it is difficult to make investments which decrease in valueby more than 100 percent. (It is theoretically possible to make suchinvestments if one sells short or buys on margin, but instances of suchextreme losses are rare.) Positive skewness forces us to considerwhether there are attributes of the distributions of returns other thanthe mean and variance which are of importance to investors. Therehas not been any divine revelation that investors care only about meansand variances; it is quite possible that they like or dislike positiveskewness. If they like it, we would expect to find that positive skewness is inversely related to rates of return; if they dislike it, we would expectto find a positive relationship between skewness and the rate of return.It is not absurd to think that there may be a skewness premium (ordiscount) just as there is a risk premium.

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This subject has been studied in a variety of ways. Hosteller andNogee in some experimental studies found that some investors arewilling to pay a high premium for positive skewness.Some of theirexperimental subjects were willing to accept expectations of loss inorder to have some chance of very large gains. The widespread popularity of lotteries attests to the pervasiveness of this attitude. Of moredirect relevance is the work of Arditti who studied the relationshipbetween measures of positive skewness and rates of return on commonstocks.Arditti concluded that rates of return are positively correlated with variance but inversely correlated with skewness.

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