Bridge over ocean
1 July 1984 Financial Analysts Journal Volume 40, Issue 4

Stock Returns, Beta, Variance and Size: An Empirical Analysis

  1. Josef Lakonishok
  2. Alan C. Shapiro

Using a model that expressed stock returns as a linear function of both beta and total risk (variance), the authors examined monthly returns of all stocks traded on the NYSE for at least four years between January 1962 and December 1980. The results indicated that, over the entire period, the stock market outperformed the risk-free rate by 7.7 per cent annually. Despite this significant return to bearing market risk in the aggregate, however, an individual security’s return did not appear to be specifically related to its degree of systematic risk.

Variance proved to be statistically and economically significant. The returns on stocks grouped in the top quintile for variance exceeded the returns on stocks in the bottom quintile by 3.2 per cent a year. Results obtained by dividing the sample into observations obtained during up markets and down markets indicated that high-beta stocks did perform better in up markets and worse in down markets than low-beta stocks, but the same was true of high-variance stocks.

The analysis was extended to incorporate the effect of size, as measured by the market value of a firm’s assets, on security return. Size turned out to be the only statistically significant variable for the overall period, with the difference in returns between the smallest and largest firms in the sample averaging out to 15.5 per cent per year. Whatever factors size measures, it appears to subsume both beta and variance.

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