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The Size Effect in Up and Down Markets

March 28, 2007 • Posted in Size Effect

Does the size effect, the tendency of small capitalization stocks to outperform, hold in both advancing and declining markets? In their March 2007 paper entitled “Stock Market Returns and Size Premium”, Jungshik Hur and Vivek Sharma explore how the size premium differs when the overall stock market is moving up and down. Using monthly return data for a sample of NYSE/AMEX stocks for July 1931 through December 2004 and NASDAQ stocks for June 1975 through December 2004, they conclude that:

  • In the entire sample period, there are 522 (360) months in which the stock market outperforms (underperforms) the risk-free rate. Across all months, the tenth of stocks with the smallest (largest) market capitalizations produce an average monthly equally-weighted excess return of 1.91% (0.64%) with an average relative volatility, or beta, of 1.40 (0.64).
  • During the 522 up months, the tenth of stocks with the smallest market capitalizations produce an average monthly equally-weighted excess return of 6.66%, nearly twice the 3.36% of the largest. The difference in average volatilities adequately explains the difference in average returns (reward for beta risk). In other words, for up markets, there is no size effect.
  • During the 360 down months, the tenth of stocks with the smallest market capitalizations produce an average monthly equally-weighted excess return of -4.97%, compared to -3.31% for the largest. The stocks of small firms in this case do not lose as much as indicated by their average volatility. In other words, the size effect is a down market anomaly.
  • The average buy-and-hold return for the tenth of stocks with the smallest (largest) market capitalizations over the previous five years is 41.0% (127%), suggesting that long-term mean reversion of earnings and stock returns may explain part of the size effect.
  • The inconsistent relationship between market capitalization and beta suggests that market inefficiency or investor irrationality may drive the size effect.
  • Conclusions are robust to choice of sample period, market index, definition of up/down market and beta calculation method.

The following charts, taken from the paper, relate market capitalization and stock returns in up and down markets, after controlling for beta. The chart on the left (right) shows the beta risk-adjusted returns in up (down) markets for ten portfolios sorted by market capitalization. The chart on the left shows that there is no relationship between size and returns beyond that indicated by portfolio beta. The chart on the right shows that, after accounting for portfolio beta, returns are higher for the stocks of smaller firms. Less than expected declines in small stocks when the overall market goes down thus drive the size effect.

In summary, a small-stock buy-and-hold approach benefits fully from upside volatility (beta) but does not suffer the entire penalty of downside volatility.

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