Irreversible Investment and the Cross-Section of Stock Returns in General Equilibrium

A general equilibrium production economy with heterogeneous firms and irreversible investment generates the value premium. Investment irreversibility prevents unprofitable value firms from optimally scaling down their capital stock. In contrast, profitable and fast growing growth firms can optimally use investment to provide consumption insurance. Value firms are riskier and have higher expected returns than growth firms, especially in bad times when consumption volatility is high. The value premium is larger for small stocks as small value firms are more severely affected by irreversibility. Firms’ investment and capital predict the cross-section of stock returns much like book-to-market and market equity both in the model and data. The model can replicate the failure of the unconditional CAPM. Multifactor models, including the Fama and French (1993) factor model, and to a lesser extent, conditional versions of the CAPM, outperform the unconditional CAPM. Value stocks with high book-to-market ratios have earned higher average returns than growth stocks with low book-to-market ratios as documented in Fama and French (1992). While it seems natural to interpret this di¤erence in average stock returns namely, the value premium as compensation for fundamental risk, the well-known Capital Asset Pricing Model (CAPM) fails to explain this pattern in average returns, as market betas have, if anything, the opposite pattern. These facts have motivated a large number of empirically successful asset-pricing models that extend the CAPM in various ways (Cochrane (2006) contains a detailed survey). Despite their empirical success, however, little is known about whether and how di¤erences in rm fundamentals and exposure to fundamental risk can account for such cross-sectional heterogeneity in stock returns. I develop a general equilibrium model that produces value and size e¤ects. Firms are subject to aggregate and rm-speci c productivity shocks. Through optimal capital investment, these shocks generate endogenous cross-sectional variation in rm characteristics such as market equity, book-to-market, investment and capital. Firms face adjustment costs and irreversibility in investment. Adjustment costs are lower for rms with low capital relative to the average rm capital. Small rms invest more and grow faster than otherwise identical rms, a model implication I verify empirically. The adjustment-cost speci cation makes a rm marginal q di¤erent from Tobins (average) Q, thus generating expected pro tability and size e¤ects in both a rms investment and its stock returns. Investorspreferences are power utility. The model aggregates so that a single moment of the joint cross-sectional distribution of rm-speci c productivity and capital, along with aggregate productivity, are su¢ cient state variables for aggregate quantities and prices. I investigate the properties of the model through its analytic solution, and I simulate a calibrated version to study the models ability to match empirical facts quantitatively. While with power utility the model cannot satisfactorily address the equity premium and risk-free rate puzzles (Mehra and Prescott (1985), Weil (1989)), it does capture several familiar features of the data. First, value rms with high book-to-market ratios and small rms with low market equity have higher average stock returns, and the value e¤ect relating book-to-market ratios with returns is weaker for large rms. Second, the unconditional CAPM fails to capture this variation in average returns. Third, multifactor models, such