Bridge over ocean
1 May 1989 Financial Analysts Journal Volume 45, Issue 3

Forecasting the Size Effect

  1. Bruce I. Jacobs
  2. Kenneth N. Levy

It has been known for some time that the returns of small firms often differ from those of large firms, and that asset pricing theories, including the Capital Asset Pricing Model and Arbitrage Pricing Theory, cannot account for the difference. Small-capitalization stocks have provided higher average returns than large-capitalization stocks, and the outperformance has been strongest in the month of January. Various researchers have sought to explain this size effect as the result of differential transaction costs, liquidity, informational uncertainty and year-end tax-loss selling. Others have suggested that small stocks outperform because they tend to have lower P/E ratios.

A multifactor analysis “disentangles” the effect of firm size from related factors that may influence return. These factors include cross-sectional effects, such as firm neglect and low P/E, and calendar effects, such as tax-loss selling. Disentangling provides “pure” returns to size that avoid the confounding associated with proxy effects. For instance, disentangling reveals the January small-firm seasonal to be a mere surrogate for the rebound that follows the abatement of tax-loss selling.

An analysis of pure returns reveals that the size effect is buffeted by economic forces. There are times when small stocks outperform the market, and other times when they lag. But while the payoffs to the size effect are not at all regular to the naked eye, they are predictable in a broader empirical framework that incorporates macroeconomic drivers such as interest rates and industrial production. An examination of various forecasting models, including univariate and multivariate time-series techniques, indicates that one that imposes a Bayesian random-walk prior belief on the coefficients of a vector autoregressive model provides the best results.

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