Why is Long-Horizon Equity Less Risky? A Duration-Based Explanation of the Value Premium

We propose a dynamic risk-based model that captures the value premium. Firms are modeled as long-lived assets distinguished by the timing of cash flows. The stochastic discount factor is specified so that shocks to aggregate dividends are priced, but shocks to the discount rate are not. The model implies that growth firms covary more with the discount rate than do value firms, which covary more with cash flows. When calibrated to explain aggregate stock market behavior, the model accounts for the observed value premium, the high Sharpe ratios on value firms, and the poor performance of the CAPM. THIS PAPER PROPOSES A DYNAMIC RISK-BASED MODEL that captures both the high expected returns on value stocks relative to growth stocks, and the failure of the capital asset pricing model to explain these expected returns. The value premium, first noted by Graham and Dodd (1934), is the finding that assets with a high ratio of price to fundamentals (growth stocks) have low expected returns relative to assets with a low ratio of price to fundamentals (value stocks). This finding by itself is not necessarily surprising, as it is possible that the premium on value stocks represents compensation for bearing systematic risk. However, Fama and French (1992) and others show that the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) cannot account for the value premium: While the CAPM predicts that expected returns should rise with the beta on the market portfolio, value stocks have higher expected returns yet do not have higher betas than growth stocks. To model the difference between value and growth stocks, we introduce a cross-section of long-lived firms distinguished by the timing of their cash flows. Firms with cash flows weighted more to the future endogenously have high price ratios, while firms with cash flows weighted more to the present have low price ratios. Analogous to long-term bonds, growth firms are high-duration ∗ Lettau is at the Stern School of Business at New York University. Wachter is at the Wharton