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

This paper proposes a dynamic risk-based model that captures 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. 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 have high price ratios, while firms with cash flows weighted more to the present have low price ratios. We model how investors perceive the risks of these cash flows by specifying a stochastic discount factor for the economy. The stochastic discount factor implies that shocks to aggregate dividends are priced, but that shocks to the time-varying price of risk are not. As long-horizon equity, growth stocks co-vary more with this time-varying price of risk than value stocks, which co-vary more with shocks to cash flows. When the model is calibrated to explain aggregate stock market behaviour, we find that it can also account for the observed value premium, the high Sharpe ratios on value stocks relative to growth stocks, and the out-performance of value (and underperformance of growth) relative to the CAPM.