Review of Accounting Studies, 6, 397–425, 2001
2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
A General Affine Earnings Valuation Model
Columbia University and NBER, 3022 Broadway, 805 Uris, New York, NY 10027
UCLA, Anderson School C509, UCLA, CA 90095
Abstract. We introduce a methodology, with two applications, that incorporates stochastic interest rates, het-
eroskedasticity and risk aversion into the residual income model. In the ﬁrst application, goodwill is an afﬁne
(constant plus linear term) function where the constant and linear coefﬁcients are time-varying. Homoskedastic
risk gives rise to a constant risk premium, while heteroskedastic risk gives rise to linear state-dependent risk pre-
miums. In the second application, we present a class of models where a non-linear function for the price-to-book
ratio can be derived. We show how interest rates, risk, proﬁtability and growth affect the price-to-book ratio.
Keywords: stock valuation, earnings, residual income model, asset-pricing, afﬁne model, linear information
This paper provides a parametric class of models that showshow a ﬁrm’s market value relates
to accounting data under stochastic interest rates, heteroskedasticity and adjustments for
risk aversion. We use the framework of the Residual Income Model (RIM), which expresses
the value of a stock as the ﬁrm’s book value plus the expected future discounted value of
the ﬁrm’s abnormal (or residual) earnings. Our methodology builds on the framework of
Feltham and Ohlson (1999), who extend the RIM to a no-arbitrage setting to accommodate
time-varying interest rates and risk aversion. Feltham and Ohlson give a partial parametric
model of stock valuation using accounting information in this setting. In a heteroskedastic
environment with stochastic interest rates and risk aversion, we extend this analysis in
several ways. First, we apply this methodology to the case where the dynamics of accounting
variables are expressed in dollar amounts as in Feltham and Ohlson (1995). Second, we
derive a solution for the price-to-book ratio of a ﬁrm as a function of stochastic interest
rates, accounting rates of return and growth in book.
Our ﬁrst result extends the Linear Information Model (LIM) developed in Ohlson (1995)
and Feltham and Ohlson (1995). The LIM presents ﬁrm value as a linear function of
current observable accounting information and is derived under constant discount rates. This
assumption leads to a standard simpliﬁcation where a single discount factor can be applied
to all future periods. The discount factor can incorporate an ad hoc adjustment for risk.
There are certain questions, however, which cannot be addressed under this assumption.
For instance, is it always possible to incorporate risk aversion as a spread in a constant
This paper was originally circulated as the working paper, “A Generalized Earnings Model of Stock Valuation.”