Removing Biases in Computed Returns

33 Pages Posted: 17 Jun 2009  

Lawrence Fisher

Rutgers University, Newark, School of Business-Newark, Department of Finance & Economics

Daniel G. Weaver

Rutgers Business School

Gwendolyn P. Webb

City University of New York (CUNY) - Baruch College - Zicklin School of Business

Date Written: June 15, 2009

Abstract

This paper presents a straightforward method for asymptotically removing the well-known upward bias in observed returns of equally-weighted portfolios. Our method removes all of the bias due to any random transient errors such as bid-ask bounce and allows for the estimation of short horizon returns. We apply our method to the CRSP equally-weighted monthly return indexes for the NYSE, Amex, and NASDAQ and show that the bias is cumulative. In particular, a NASDAQ index (with a base of 100 in 1973) grows to the level of 17,975 by 2006, but nearly half of the increase is due to cumulative bias. We also conduct a simulation in which we simulate true prices and set spreads according to a discrete pricing grid. True prices are then not necessarily at the midpoint of the spread. In the simulation we compare our method to calculating returns based on observed closing quote midpoints and find that the returns from our method are statistically indistinguishable from the (simulated) true returns. While the mid-quote method results in an improvement over using closing transaction prices, it still results in a statistically significant amount of upward bias. We demonstrate that applying our methodology results in a reversal of the relative performance of NASDAQ stocks versus NYSE stocks over a 25 year window.

Keywords: Unbiased market index, Bias in computed returns, Jensen's inequality, Asset pricing, Index construction

JEL Classification: G10, G12, C43

Suggested Citation

Fisher, Lawrence and Weaver, Daniel G. and Webb, Gwendolyn P., Removing Biases in Computed Returns (June 15, 2009). Available at SSRN: https://ssrn.com/abstract=1420314 or http://dx.doi.org/10.2139/ssrn.1420314

Lawrence Fisher

Rutgers University, Newark, School of Business-Newark, Department of Finance & Economics ( email )

111 Washington Avenue
Newark, NJ 07102
United States

Daniel G. Weaver (Contact Author)

Rutgers Business School ( email )

94 Rockafeller Road
Piscataway, NJ 08854
United States
848.445.5644 (Phone)
732.445.2333 (Fax)

HOME PAGE: http://weaver.rutgers.edu

Gwendolyn P. Webb

City University of New York (CUNY) - Baruch College - Zicklin School of Business ( email )

Department of Economics & Finance
P.O. Box B13-289 1 Bernard Baruch Way
New York, NY 10010
United States
646-312-3485 (Phone)

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