Value Matters: Predictability of Stock Index Returns
The aim of
this paper is twofold: to provide a theoretical framework and to give further
empirical support to Shiller's test of the appropriateness of prices in the
stock market based on the Cyclically Adjusted Price Earnings (CAPE) ratio. We
devote the first part of the paper to the empirical analysis and we show that
the CAPE is a powerful predictor of future long run performances of the market
not only for the U.S. but also for countries such us Belgium, France, Germany,
Japan, the Netherlands, Norway, Sweden and Switzerland. We show four relevant
empirical facts: i) the striking ability of the logarithmic averaged earning
over price ratio to predict returns of the index, with an R squared which
increases with the time horizon, ii) how this evidence increases switching from
returns to gross returns, iii) moving over different time horizons, the
regression coefficients are constant in a statistically robust way, and iv) the
poorness of the prediction when the precursor is adjusted with long term
interest rate. In the second part we provide a theoretical justification of the
empirical observations. Indeed 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.
Ultimately this means that, in our model, the stock prices dynamics may
generate bubbles and crashes in the short and medium run, whereas for future
long-term returns the valuation ratio remains a good predictor.
