Jan 30, 2012
What is the best way to describe the distribution of stock returns—a normal distribution, lognormal, or something else? What should investors do with this information?

EFF/KRF: Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions. (This topic takes up half of Gene's 1964 PhD thesis.) In the old literature on this issue, the popular alternatives to the normal distributions were non-normal symmetric stable distributions (which are fat-tailed relative to the normal) and t-distributions with low degrees of freedom (which are also fat-tailed). The message for investors is: expect extreme returns, negative as well as positive.

Eugene F. Fama
The Robert R. McCormick Distinguished Service Professor of Finance at the University of Chicago Booth School of Business
Kenneth R. French
The Roth Family Distinguished Professor of Finance at the Tuck School of Business at Dartmouth College
This information is distributed for educational purposes and should not be considered investment advice or an offer of any security for sale. This article contains the opinions of the author but not necessarily Dimensional Fund Advisors and does not represent a recommendation of any particular security, strategy or investment product. Dimensional Fund Advisors is an investment advisor registered with the Securities and Exchange Commission. Information contained herein has been obtained from sources believed to be reliable, but is not guaranteed. Past performance is not indicative of future results and no representation is made that the stated results will be replicated.

Eugene Fama and Ken French are members of the Board of Directors for and provide consulting services to Dimensional Fund Advisors LP.