Can Noise Create the Size and Value Effects?

If the price of a stock differs from its intrinsic value by a random noise, then value stocks are more likely to have negative noise; they are thus more likely undervalued and have higher expected return than justified by risk. The same intuition applies to small capitalization stocks. We formally verify and explore this intuition by using a standard noise-in-price model. This intuition is different from the Jensen’s inequality effect studied by Blume and Stambaugh [Blume ME, Stambaugh RF (1983) Biases in computed returns: An application to the size effect. J. Financial Econom. 12(3):387–404]. Our model is parsimonious: the value premium as well as size premium are computed in closed form and depend on only four parameters: mean of stock return, volatility of stock return, volatility of the price-to-dividend ratio, and noise volatility. We emphasize that only a moderate volatility of price noise is needed to generate the observed value premium. However, the model cannot generate the observed size premium.

This paper was accepted by Wei Jiang, finance.