The Conditional Distribution of Excess Returns: An Empirical Analysis

Abstract

In this paper we describe the cumulative distribution function of excess returns conditional on a broad set of predictors that summarize the state of the economy. We do so by estimating a sequence of conditional logit models over a grid of values of the response variable. Our method uncovers higher-order multidimensional structure that cannot be found by modeling only the first two moments of the distribution.

We compare two approaches to modeling: one based on a conventional linear logit model, the other an additive logit. The second approach avoids the “curse of dimensionality” problem of fully nonparametric methods while retaining both interpretability and the ability to let the data determine the shape of the relationship between the response variable and the predictors.

We find that additive logit fits better and reveals aspects of the data that remain undetected by the linear logit. The additive model retains its superiority even in out-of-sample prediction and portfolio selection performance, suggesting that this model captures genuine features of the data which seem to be important to guide investors’ optimal portfolio choices.