Following the major breakthroughs of Cochrane (1991, 1996) and Berk, Green, and Naik (1999), investment-based asset pricing has experienced rapid growth. Cochrane lays the foundation for adapting the dynamic investment framework of Jorgenson (1963), Tobin (1969), and Lucas and Prescott (1971) to study asset pricing issues. Berk et al. construct a real options model to reproduce the size and book-to-market effects in cross-sectional returns. One strand of the literature has followed Berk et al. in constructing quantitative, dynamic models. Another strand has followed Cochrane in conducting econometric evaluation of the dynamic investment framework in explaining the cross-section of expected stock returns. In particular, Liu, Whited, and Zhang (2009) show that expected stock returns predicted from a dynamic investment model can match the average stock returns of portfolios formed on earnings surprises, book-to-market, and capital investment.
We criticize this burgeoning literature. We quantify a major shortcoming of the dynamic investment framework. The framework has implications not only for the cross-section of expected stock returns, but also for the cross-section of equity valuation ratios. Under constant returns to scale, the market value of equity-to-capital ratio should equal the present value of marginal benefit of investment minus the debt-to-capital ratio. We use generalized method of moments (GMM) to estimate this valuation equation along with investment Euler equation at the portfolio level.
Our key finding is that the standard dynamic investment model fails miserably to explain the value spread, which we define as the equity-to-capital ratio of the high book-to-market decile minus the equity-to-capital ratio of the low book-to-market decile. The value spread is ?5.61 in the data. Albeit going in the right direction, the model only generates a value spread of ?1.94. The error of ?3.67, which is more than 2.5 standard errors from zero, accounts for more than 65% of the value spread in the data. Figure 1 plots the average predicted valuation ratios against the average realized valuation ratios for the book-to-market deciles. If the model’s performance is perfect, all the observations should exactly lie on the 45-degree line. However, the model systematically underpredicts the valuation ratio of the low decile but overpredicts the valuation ratio of the high decile. Both extreme deciles have economically large errors that are also statistically significant.
We emphasize the need to match valuation ratios and expected returns simultaneously. The model parameters are in principle “deep” structural parameters, which should be invariant to changes in optimizing behavior and economic policy in the sense of Lucas (1976). The parameters should in turn be invariant to whichever moments we choose to fit. However, tension exists between matching valuation ratios and matching expected returns. For example, the model captures the valuation ratios across the asset growth deciles, but the resulting expected return errors are even larger in magnitude than those from the CAPM and the Fama-French (1993) three-factor model.
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The Value Spread: A Puzzle
