Discounting earnings with stochastic discount rates

Abstract

This paper presents new equity valuation formulae in closed form that extend the abnormal earnings growth (AEG) valuation of Ohlson and Juettner-Nauroth (2005) to the cases of time-varying or stochastic cost of capital as in Ang and Liu (2004) or to cases of stochastic interest rates as in Ang and Liu (2001). Interest rates are modeled by quadratic term structure models, which are not hindered by restrictions to factors correlation or by other shortcomings of a¢ ne term structure models in discounting long term earnings. This is crucial since valuation can be very sensitive to the correlation between the factors driving earnings and interest rates. Positive correlation reduces price-earnings ratios according to US data. Valuation is also sensitive to the "volatility" of abnormal earnings growth. The residual earnings risk-neutral valuation of Ang and Liu (2001) is adapted to quadratic term structure models.