A State-Space Model Approach to the Return Decomposition

Abstract

We test the implications of the return decomposition of Campbell (1991), in which the unexpected market return is decomposed into cash-flow and discount-rate news. Unlike most of the previous literature, which uses VAR models to implement the return decomposition, we propose a state-space model with parameter restrictions, which is a more systematic and direct than the VAR approach on two aspects. First, the state-space model approach simultaneously models returns, cash-flow news, and discount-rate news, whereas the VAR approach models discount-rate news and uses the return decomposition to back out cash flow news. Second, the state-space model allows us to use information directly related to market and portfolio returns to study the return decomposition, whereas the VAR approach utilizes different predictive variables. We find that discount-rate news has larger variance than does cash-flow news and that the two types of news are nearly perfectly correlated, which can be economically intuitive. We also find that small stocks have higher cash-flow betas than do large stocks, but do not find that value stocks have higher ashflow betas than do growth stocks.