Value matters: Predictability of Stock Index Returns

We test the ability of the Cyclically Adjusted Price Earnings (CAPE) ratio introduced by Robert Shiller to predict the future long run performances of international stock markets. We devote the first part of the seminar to the empirical analysis of numerous equity indices. We question if the striking ability of CAPE to predict returns of the index is a genuine effect or if it is a spurious consequence of the persistence and endogeneity of the regressor. The evidence rooted on a bootstrap analysis of the regression plays in favour of statistically significant predictability of long run yields for the US market (Standard & Poor and NYSE monthly data are available since 1870 and 1926, respectively). The same analysis extended to ten different countries is less conclusive. We believe that this is largely due to fact that the time series employed in the analysis are quite short (MSCI data are recorded since January 1970). In the second part, we provide a theoretical justification of the empirical observations from the US market. We propose a simple model of the price dynamics in which the return growth depends on three components: a) a momentum component, naturally justified in terms of agents' belief that expected returns are higher in bullish markets than in bearish ones; b) a fundamental component proportional to the log earnings over price ratio at time zero. The initial value of the ratio determines the reference growth level, from which the actual stock price may deviate as an effect of random external disturbances, and c) a driving component ensuring the diffusive behaviour of stock prices. Under these assumptions, we are able to prove that, if we consider a sufficiently large number of periods, the expected rate of return and the expected gross return are linear in the initial time value of the log earnings over price ratio, and their variance goes to zero with rate of convergence equal to minus one.