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Review of Quantitative Finance and Accounting

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01-02-2015 | Original Research

On the use of the market model R-square as a measure of stock price efficiency

Authors: Riccardo Bramante, Giovanni Petrella, Diego Zappa

Published in: Review of Quantitative Finance and Accounting | Issue 2/2015

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Abstract

The R-square of the market model is a very popular measure of stock price efficiency. However, its interpretation is far from being unambiguous. Some scholars argue that the R-square is a direct measure of efficiency, others argue that the R-square is an indirect measure of efficiency. This paper contributes to the literature in two ways. First, we model the relationship between the market model R-square and the delay in the price discovery process and, second, we find that the correlation between R-square and delay is consistently negative. We conclude that the R-square is a direct measure of price efficiency.

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In the literature several authors (e.g., Hou and Moskowitz 2005) use the normalized definition of $delay\equiv \delta^{*} = 1 - \frac{{R^{2} }}{{R_{U}^{2} }}$. Previous conclusions do not change.

We point out that the aim of this paper is not to test whether the delay is significant. Nevertheless we have computed for all the stocks the p value of the hypothesis.

$$H_{0} : \beta_{1}^{U} = \beta_{2}^{U} = 0$$

By ANOVA and assuming the error component of models (1) and (2) normally distributed, the equivalent test statistics is $\frac{{(R_{U}^{2} - R^{2} )/2}}{{(1 - R^{2} )/(n - 2)}}\sim F_{2,n - 2}$, where $F_{2,n - 2}$ is the Fisher distribution with 2 and n − 2 degrees of freedom (d.f.). As expected, in almost all the cases the test was not significant.

We set B = 10,000.

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Title: On the use of the market model R-square as a measure of stock price efficiency
Authors: Riccardo Bramante
Giovanni Petrella
Diego Zappa
Publication date: 01-02-2015
Publisher: Springer US
Published in: Review of Quantitative Finance and Accounting / Issue 2/2015
Print ISSN: 0924-865X
Electronic ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-013-0410-8

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