Beta and Returns Revisited: Evidence from the German Stock Market

The Capital Asset Pricing Model (CAPM) predicts that the expected return on a stock depends on its systematic risk as measured by its beta. However, recent empirical evidence suggests that the relation between beta and realized returns is weak or even non-existent. The traditional two-step procedure due to Fama / MacBeth (1973) used in most studies implies a test of two joint hypotheses. The hypothesis that there is a positive relationship between beta and realized return is tested jointly with the hypothesis that the average market risk premium is positive. Pettengill / Sundaram / Mathur (1995) proposed a procedure that allows to independently test the hypothesis of a relation between beta and realized returns. The procedure makes use of the fact that the ex-post formulation of the CAPM used in the empirical tests predicts a conditional relation between beta and expected returns. Stocks with a higher beta should have higher [lower] realized returns when the market risk premium is positive [negative]. We perform Monte Carlo simulations that show that the conditional test reliably identifies the relation between beta and return. In an empirical examination for the German stock market we find a positive and statistically significant relation between beta and return in our sample period 1960-1995 as well as in all subperiods we analyze. The reason why previous studies did not identify this relationship is likely to be the fact that the average market risk premium in the sample period was close to zero. Our empirical results provide a justification for the use of betas estimated from historical return data by portfolio managers.

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