Multiperiod forecasting in stock markets: a paradox solved

摘要

One of the most striking results on asset pricing in the last 20 years is the better forecastability of long-horizon returns over one-step return forecasts. This could seem a paradox, given that the further our forecast horizon the greater the uncertainty we are bound to face. This point can been found in Campbell and Shiller [Journal of Finance 43 (1988) 661; Jpurnal of Finance 40 (1985) 793; American Economic Review 76 (1986) 1142] among others. In this paper, we offer an alternative explanation to this "forecast paradox " that is in agreement with Kim et al. [Review of Economic Studies 30 (1992) 25], who found that the negative serial correlation in long-horizon returns depends very much on the sample choice. Our explanation is based on the existence of simultaneous shifts in the time series of the equilibrium stock price and dividends. This explanation relies on the concept of co-breaking [D.F. Hendry, A theory of co-breaking, Mimeo, Nuffield College, Oxford, 1995.]. We put forward a stochastic present value model, in which we are able to show how shifts in the process for dividends lead to shifts in the equilibrium stock price. This has important implications for multiperiod forecasting, as we demonstrate in this paper. An empirical application supports our results. In our empirical application, we model earning, dividends, stock prices, and the risk-free interest in the United States from 1926 to 1985. We can distinguish three different historical periods where the process for dividends and the equilibrium stock prices are characterized by different properties in terms of their means and variances. Our empirical model is extended to a forecasting exercise where the "forecast paradox" is solved.