Jan 24, 2009

S&P 500 returns and the normal distribution

One of the fundamental assumptions in modern finance's asset pricing models is that returns follow a normal (Gaussian) distribution. The histogram below shows the annual percentage returns on the S&P 500 from 1926-2008, grouped by 5% increments, overlaid with the normal distribution curve. Note the fat tail on the left that includes the two worst years, 1931 and 1937.

Until last year, many assumed that these data points could be ignored because "things were different" after WWII, so they proceeded to fill their VaR models with mean returns and standard deviations calculated post-1945. My finance textbook, published in 2006, discusses the differences between 40-year returns and 80-year returns and decides that the 40-year returns, (which exclude the 1930s) are more appropriate for our purposes. The book states that "it appears that observed fat tails are largely due to older history" and "we have more confidence that the more recent averages better estimate expected returns for the near future." Then 2008 dropped a -37% return on us. It will be interesting to see how they address this issue in the next edition.

No comments: