Value Matters: The Long-run Behavior of Stock Index Returns

We present a simple dynamical model of stock index returns grounded on the ability of the Cyclically Adjusted Price Earning valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. Specifically, within the model returns are driven by a fundamental term and an autoregressive component perturbed by external random disturbances. The autoregressive component arises from the agents’ belief that expected returns are higher in bullish markets than in bearish ones. The fundamental value, towards which fundamentalists expect that the current price should revert, varies in time and depends on the initial averaged Price-to- Earnings ratio. We demonstrate both analytically and by means of numerical experiments that the long-run behavior of the stylized dynamics agrees with empirical evidences reported in literature