Can Noise Create the Size and Value Effects?

Can Noise Create the Size and Value Effects? Small-capitalization and value stocks are likely to predominantly have negative noise, while large-capitalization and growth stocks are likely to have positive noise, if prices contain random 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 ∗Jun Liu is from University of California, San Diego, and is affiliated with Cheung-Kong Graduate School of Business (CKGSB). We are grateful for comments from Andrew Ang, Phil Dybvig, Harrison Hong, Ming Huang, John Hughes, Feifei Li, Jing Liu, Jun Pan, Allan Timmermann, and Rossen Valkanov and from seminar participants at the 2007 Chinese International Conference in Finance, 2007 Financial Management Association Meeting, 2008 American Finance Association Meeting, Central University of Finance and Economics of China, Cheung-Kong Graduate School of Business, Chinese University of Hong Kong, Georgia Tech, Southwestern University of Finance and Economics, Shandong University, Peking University, Shanghai University of Finance and Economics, TsingHua University, and UCSD. We would like to thank Vitali Kalesnik for helpful technical assistance. overvalued. We formally verify and explore this intuition by using a standard noise-inprice model. We compute in closed form and match quantitatively the level of and the crosssectional variations in the expected stock return documented in Fama and French (1992). Our model is parsimonious with essentially only one adjustable parameter, the volatility of the price noise. Our study suggests that a modest amount of noise in prices can create size and value effects. Blume and Stambaugh (1983) assume small-cap stocks have higher noise volatility and show that they have higher expected return because of Jensen’s inequality. This channel is shut off in our paper because we assume all stocks have the identical return distribution thus the same noise volatility. Small-cap stocks in our paper are defined to be ones with low market capitalization and they generate higher expected returns because of the negative realization of random price noise.