How Investors Set Valuation Ratios Using a Micro-Founded Gordon Asset Pricing Model

Abstract

A Micro-Founded Gordon Asset Pricing Model (MF-GAPM) is developed that allows calculation of the current E/P of an equity using reported data. In the original Gordon Model, the discounting is done assuming constant growth and a constant discount rate, with the simple result E/P = r - g where r is the so-called required yield and g is the growth expectation. The MF-GAPM applies the standard CRRA utility methodology to the real-world problem of investors maximizing their real returns, but in contrast to common practice in academic finance where the growth is subject to stochastic fluctuations, the MF-GAPM assumes constant growth like the original Gordon Model. It is shown that the E/P that maximizes the utility of the investors lifetime return then reduces to E/P = (γ-1)*µ where µ is the growth expectation and γ is the curvature of the investors CRRA utility function. This result can be viewed as a micro-founded Gordon Model with required yield equal r = γ*µ. An Empirical Model (Empirical Model) is developed to identify the data variables that investors use to set the MF-GAPM’s assumed parameters. The Empirical Model identifies two broad classes of variables whose variation about their own stationary means explain the variation of E/P about its mean: a sentiment variable S_N and a trailing earnings growth variable EG_N. The two data variables suggest there are two types of investors: rational investors who trade on observed earnings growth and irrational investors who trade on sentiment. Noting the natural associations, the first-order expansions of the functional relationships µ = µ(EG_N) and γ = γ(S_N) provide direct links between the data variables and the parameters of the MF-GAPM. The direct links allow price forecasts to be made using only expectations for the future values of the data variables themselves – expectations about expectations are not required. The feasibility of forecasting prices considering the Model’s StdError is discussed. The lack of randomness in the observed historical earnings growth record is discussed in an Academic Addendum as the rational for abandoning the i.i.d. lognormal growth assumption. With the inclusion of both rational and irrational agents, the MF-GAPM seeks to integrate the classical and behavioral approaches to finance.