Does Noise Create the Size and Value Effects ? ∗

Does Noise Create the Size and Value Effects? Black (1986) and Summers (1986) suggest that the price of a stock can deviate from its intrinsic value by a random noise. In this paper, we show that a stock with such a noise has a higher expected return when its market capitalization or price-dividend ratio is low, because a low market capitalization or price-dividend ratio is a signal that the noise in price is negative and the stock is thus undervalued. Furthermore, the expected returns for different market-capitalization and price-dividend ratio deciles, implied by our model (using plausible parameters), are similar to the empirical expected returns for different market-capitalization and price-book deciles documented in Fama and French (1992). Thus, our study suggests that noise can create the size and value effect. Our results can be applied to any model in which there is a random difference between the price and the value of a stock due to rational or behaviorial noise trader or any other source. Our model also suggests that the difference in expected returns of stocks can be caused by the difference in independent realization of noise, in addition to the difference in unconditional parameters such as volatility or beta as in Blume and Stambaugh (1983) and Berk (1996, 1997).