Discounting earnings with stochastic discount rates

摘要

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 USdata. Valuation is also sensitive to the volatility' ofabnormal earnings growth. The residual earnings risk-neutral valuation of Ang and Liu(2001) is adapted to quadratic term structure models.