Measurement Errors of Expected Returns Proxies and the Implied Cost of Capital

by Charles C.Y. Wang

Overview — In accounting and finance the implied cost of equity capital (ICC)—defined as the internal rate of return that equates the current stock price to discounted expected future dividends—is an increasingly popular class of proxies for the expected rate of equity returns. Though ICCs are intuitively appealing and have the potential to help researchers better understand the cross-sectional variation in expected returns, much remain unknown about the sources of their measurement errors and how to correct for them; thus their use in regression settings should be interpreted with caution. This paper studies the measurement errors properties of GLS, a popular implementation of ICCs developed by Gebhardt, Lee, and Swaminathan (2001). The paper finds that ICCs can have persistent measurement errors that are associated with firms' risk or growth characteristics, and thus produce spurious results in regression settings. It also finds that ICC measurement errors are driven by not only analyst forecast biases but also functional form assumptions, suggesting that correcting for the former alone is unlikely to fully resolve these measurement-error issues. Together, these findings emphasize the importance of complementing ICC regressions with realized returns to establish robust inferences on expected returns. Key concepts include:

The common justification for using ICCs for studying expected returns—that ICCs are far less "noisy" than realized returns—is insufficient without a better understanding of the biases embedded in ICC measurement errors.
ICC measurement errors can be persistent, can be associated with firms' risk or growth characteristics, and thus confound regression inferences on expected returns.
Due to the cross-sectional association between ICC measurement errors and firms' risk or growth characteristics, standard methods for addressing measurement errors, namely portfolio grouping and instrumental variables, may have limited effectiveness.
To convincingly establish an association between expected returns and firm characteristics using ICCs, it is necessary for researchers to complement ICC regressions with regressions using realized returns.

Author Abstract

This paper presents a methodology to study implied cost of capital's (ICC) measurement errors, which are relatively unstudied empirically despite ICCs' popularity as proxies of expected returns. By applying it to the popular implementation of ICCs of Gebhardt, Lee, and Swaminathan (2001) (GLS), I show that the methodology is useful for explaining the variation in GLS measurement errors. I document the first direct empirical evidence that ICC measurement errors can be persistent, can be associated with firms' risk or growth characteristics, and thus confound regression inferences on expected returns. I also show that GLS measurement errors and the spurious correlations they produce are driven not only by analysts' systematic forecast errors but also by functional form assumptions. This finding suggests that correcting for the former alone is unlikely to fully resolve these measurement-error issues. To make robust inferences on expected returns, ICC regressions should be complemented by realized-returns regressions.