Nonparametric Estimation of the Time-varying Sharpe Ratio in Dynamic Asset Pricing Models

Economic research of the last decade linking macroeconomic fundamentals to asset prices has revealed evidence that standard intertemporal asset pricing theory is not successful in explaining (unconditional) ¯rst moments of asset market characteristics such as the risk-free interest rate, equity premium and the Sharpe-ratio. Subsequent empirical research has pursued the question whether those characteristics of asset markets are time varying and, in particular, varying over the business cycle. Recently intertemporal asset pricing models have been employed to replicate those time varying characteristics. The aim of our contribution is (1) to relax some of the assumptions that previous work has imposed on underlying economic and ¯nancial vari- ables, (2) to extend the solution technique of Marcet and Den Haan (1990) for those models by nonparametric expectations and (3) to propose a new estimation procedure based on the above solution technique. To allow for nonparametric expectations in the expectations approach for numerically solving the intertemporal economic model we employ the Local Linear Maps (LLMs) of Ritter, Martinetz and Schulten (1992) to approximate conditional expectations in the Euler equation. In our estimation approach based on non-parametric expectations we are able to use full structural information and, consequently, Monte Carlo simulations show that our estimations are less biased than the widely applied GMM procedure. Based on quarterly U.S. data we also empirically estimate structural parameters of the model and explore its time varying asset price characteristics for two types of preferences, power utility and habit persistence.