Discounting earnings with stochastic discount rates

This paper presents new equity valuation formulae in closed form that extend the abnormal earnings growth (AEG) valuation of Ohlson 2005. “On Accounting-Based Valuation Formulae.” Review of Accounting Studies 10: 323–347] to the cases of time-varying or stochastic cost of capital as in Ang and Liu 2004. “How to Discount Cash Flows with Time-Varying Expected Returns.” Journal of Finance 59 (6): 2745–2783] or to cases of stochastic interest rates as in Ang and Liu 2001. “A General Affine Earnings Valuation Model.” Review of Accounting Studies 6: 397–425]. Interest rates are modelled by quadratic term structure models, which are not hindered by restrictions to factors correlation or by other shortcomings of affine 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.