The Perils of Relying on Return Data When Testing Asset Pricing Models

John F Pinfold

doi:10.4236/jmf.2022.121004

Abstract

Asset pricing models are almost always tested using stock returns over multiple time periods, and the returns of portfolios over the investment horizon determined using the arithmetic average of these portfolio returns. The arithmetic average returns of portfolios selected using the model’s parameters are calculated and compared. However, investors’ returns are derived from changes in the value of their portfolios. This paper shows how the use of arithmetic returns creates large biases in the magnitude and statistical significance of asset pricing models’ outcomes. It argues only evaluations using the values of portfolios produce reliable results. The identified bias is created because a positive return and its equal but negative return, represent different sized price movements, and this becomes obscured when returns are analysed and averaged over multiple periods. Most existing pricing models are potentially invalid because of the biases generated by the methodology used in their development.

Highlights

The problems associated with using arithmetic returns in place of geometric returns when calculating stock returns and portfolio returns over multiple periods are well known
Asset pricing models are almost always tested using stock returns over multiple time periods, and the returns of portfolios over the investment horizon determined using the arithmetic average of these portfolio returns
This paper shows how the use of arithmetic returns creates large biases in the magnitude and statistical significance of asset pricing models’ outcomes

Summary

Introduction

The problems associated with using arithmetic returns in place of geometric returns when calculating stock returns and portfolio returns over multiple periods are well known. Almost all research on asset pricing models and stock performance uses arithmetic stock returns to evaluate the returns of an investment strategy This seems to be based on the idea that while the magnitude of the effect may be overstated, the differences in portfolio performance of the strategies are real, and the statistical significance tests are valid. If price movements are normally distributed, returns will inevitable be skewed in the positive direction, creating problems with statistical tests, which may not be properly rectified by the methods adopted This explanation of the problem does not persuasively establish the nature and magnitude of the problem, so a simulation will be used to show how random price movements can generate errors which have the potential to accumulate and invalidate a pricing model’s claims as to the economic and statistical significance. The use of stock return data instead of prices can allow researchers to find statistically significant relationships in random data and this will be demonstrated

Testing a Random Simulation

Are the Relationships in the Simulation Statistically Significant?

Findings

Discussion