Stochastic Portfolio Theory vs. Modern Portfolio Theory and the Implications for the Capital Asset Pricing Model

Abstract

This paper contrasts the perspectives provided by the traditional Modern Portfolio Theory (MPT) analysis, which uses arithmetic returns, and the Stochastic Portfolio Theory (SPT) analysis, which uses continuous returns. The MPT analysis implies that an efficient portfolio’s reward is proportional to its risk and that its information ratio is independent of its risk. The SPT analysis implies that an efficient portfolio’s reward is not proportional to its risk, first rising with risk and then declining with risk, and that its information ratio declines as its risk increases. The analysis also has implications for the Capital Asset Pricing Model (CAPM). According to the MPT analysis, a stock’s expected excess return is equal to its beta times the market’s expected excess return. The SPT analysis shows that a stock’s expected excess arithmetic return is equal to its beta times the market’s expected excess arithmetic return plus one-half the market’s variance of return times the excess of the stock’s beta over 1. Compared to the MPT version of CAPM, the SPT version of CAPM shows that high beta stocks offer more expected excess arithmetic return and low beta stocks offer less expected excess arithmetic return.