Predictable Return Distributions

Abstract

Using quantile regression this paper explores predictability of the stock and bond return distributions as a function of economic state variables. The use of quantile regression allows us to examine specific parts of the return distribution such as the tails and the center, and for a sufficiently fine grid of quantiles we can trace out the entire distribution. A univariate quantile regression model is used to examine the marginal stock and bond return distributions, while a multivariate model is used to capture their joint distribution. An empirical analysis on US data shows that economic state variables predict the stock and bond return distributions in quite different ways in terms of, for example, location-shifts, volatility, and skewness. Comparing the different economic state variables in terms of their out-of-sample forecasting performance, the empirical analysis also shows that the relative accuracy of the state variables varies across the return distribution. Density forecasts based on an assumed normal distribution with forecasted mean and variance is compared to forecasts based on quantiles estimates, and in general the latter yields the best performance.