Production-based Stochastic Discount Factors

Abstract

We recover a stochastic discount factor (SDF) for asset returns from a firm’s investment Euler equation. Given a parametric statistical specification of the SDF and profitability process, we solve for the firms’ optimal investment decision with approximate analytical solutions and provide a dissection of the determinants of real investment. We estimate a specification of the model to discipline the free parameters of the SDF by matching moments of both aggregate real quantities and asset prices. We use the estimated parameters to recover the latent SDF from data on aggregate investment rates, risk-free rates, and profitability growth rates. Innovations in the recovered SDF are driven dominantly by innovations in investment rates and marginally by innovations in risk-free rates and profitability growth rates. The recovered SDF exhibits strong counter-cyclicality with large jumps in recessions and prices standard Fama-French portfolios out of sample reasonably well. Our model allows us to explicitly characterize the risk-free rate, the equity premium, the term structure of interest rates, and the term structure of equity risk premia. The framework we propose here is general and can be extended to accommodate several additional aggregate shocks and frictions that have been proposed in the literature.

Keywords: stochastic discount factor, investment, investment-based asset pricing

JEL Classification: E23, E44, G1, G12