Conditional characteristics of risk-return trade-off : a stochastic discount factor framework

Abstract

Modeling of the stochastic discount factor using state variables to proxy for the marginal utility substituting for the failure of aggregate consumption data to account for the conditional characteristics of asset returns. The focus is on the conditional characteristics of historical stock returns specifically the trade-off between risk and return. The nonlinear least squares method inspired by the inference methodology of Britten-Jones (1999) is applied to estimate the parameters and estimate conditional volatility of the stochastic discount factor with GARCH and stochastic volatility models.

The results indicate that the estimated stochastic discount factor is conditionally heteroskedastic and its conditional volatility captures the conditional variation that coincides with the phases of the business cycle significantly better than consumption-based SDF. However, the proxy for the risk-return trade-off does not capture substantial conditional variation and magnitude relative to the empirically estimated conditional Sharpe ratios that prominent literature reports. The estimated SDF accounts for predictability but cannot account for the high equity premium particularly the long-run equity premium as the conditional volatility appears to be stationary.