Semi-equilibrium Pricing: The CAPM Formula

Abstract

We present a new type of pricing method, the semi-equilibrium pricing method, which solves the optimal portfolios of investors first. This stage is consistent with the equilibrium pricing method, but the second stage of the semi-equilibrium pricing method uses only a part of the market clearing conditions rather than the entirety. Based on this, we show that the pricing formula by capital asset pricing model (CAPM) is not an equilibrium pricing formula but a semi-equilibrium pricing formula: When the CAPM formula is valid, the market may not be cleared. Only when the total market value of risky securities is given can the CAPM formula completely determine the price vector of the risky securities. Additionally, we point out that the stochastic discount factor (SDF) pricing formula is the result of investors' portfolio optimization, and the market clearing conditions are not involved at all. The SDF pricing formula is presented in the form of a linear pricing function and can be used as a foundation template to establish pricing functions.

Keywords: Semi-equilibrium Pricing, Law of Asset Portfolio, CAPM, SDF, Mimicking Portfolio

JEL Classification: G12