Can Noise Create Size and Value Effects?

Abstract:     
The price of a stock may differ from its fundamental value by a random noise. In this case, small-capitalization and value stocks are more likely to have negative noise, while large-capitalization and growth stocks are likely to have positive noise. Negative price noise implies that small-capitalization and value stocks are more likely undervalued and thus have higher expected return than justified by risk, while the large-capitalization and growth stocks are more likely overvalued. We formally verify and explore this intuition by using a standard noise-in-price model.

We compute in closed form the cross-sectional variations of the expected stock return. Our model is parsimonious with essentially only one adjustable parameter the volatility of the price noise.

With a moderate volatility of price noise, the cross-section of the expected stock return matches quantitatively the empirical counterpart in Fama and French (1992). Our study suggests that a modest amount of noise in prices can create size and value effects.

Number of Pages in PDF File: 32

Keywords: noise, size effect, value effect

JEL Classification: G12, G14

working papers series