Noise, CAPM and the Size and Value Effects

Journal of Investment Management, Vol. 6, No. 1, First Quarter 2008

Posted: 27 Mar 2008

See all articles by Robert D. Arnott

Robert D. Arnott

Research Affiliates, LLC

Jason C. Hsu

Research Affiliates; Rayliant Global Advisors; University of California, Los Angeles - Anderson School of Business

Multiple version iconThere are 2 versions of this paper

Abstract

We model a continuous time one factor economy where stock prices are noisy proxies of the informationally efficient stock values. The pricing error process is modeled as a mean-reverting process, which gives us a well-defined notion of over-pricing (positive pricing error) and under-pricing (negative pricing error) in the market. We show that in this economy, cap-weighting is a sub-optimal portfolio strategy. This is because, in a cap-weighting scheme, portfolio weights are driven by market prices; as such, more weights are allocated to over-valued stocks and less weight to under-valued stocks. More importantly, we show that the CAPM would be rejected in this one factor economy with noise. Regressing portfolio returns against market clearing portfolio returns, non-cap-weighted portfolios exhibit significant alpha on average! Additionally, a value tilted or size tilted portfolio is predicted to outperform(risk-adjusted). By construction, value and size are not risk factors in our one factor economy. However, in the cross-section, large cap stocks and high price-to-book stocks (growth stocks) tend to underperform. This is because higher capitalization stocks and higher price-to books stocks are indeed more likely to be stocks with positive pricing errors. We note that prices are explicitly inefficient in our economy. However, the inefficiency does not lead to arbitrage opportunities. We carefully show conditions which prevent arbitrage in our informationally inefficient economy. The paper contributes to the anomalies literature by showing that mean-reversion in stock returns and the Fama-French size and value effects are driven by the same market defect-pricing noise! This suggests that models, such as disposition effect and information herding, which can generate stock price over-reaction and therefore mean-reversion in stock prices, can also explain the value and size puzzle.

Keywords: Noise, value effect, size effect, CAPM, non-price-weighted portfolios

JEL Classification: G00

Suggested Citation

Arnott, Robert D. and Hsu, Jason C. and Hsu, Jason C., Noise, CAPM and the Size and Value Effects. Journal of Investment Management, Vol. 6, No. 1, First Quarter 2008, Available at SSRN: https://ssrn.com/abstract=1112861

JOIM Editor (Contact Author)

Journal of Investment Management (JOIM) ( email )

3658 Mt. Diablo Blvd.
Suite 200
Lafayette, CA 94549
United States
925-299-7800 (Phone)
925-299-7815 (Fax)

Robert D. Arnott

Research Affiliates, LLC ( email )

620 Newport Center Dr
Ste 900
Newport Beach, CA 92660
United States
949-325-8700 (Phone)
949-325-8901 (Fax)

HOME PAGE: http://www.researchaffiliates.com

Jason C. Hsu

Rayliant Global Advisors ( email )

Hong Kong

Research Affiliates ( email )

620 Newport Center Dr
Suite 900
Newport Beach, CA 92660
United States

HOME PAGE: http://www.jasonhsu.org

University of California, Los Angeles - Anderson School of Business

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Abstract Views
1,319
PlumX Metrics