Alpha Found: The Mathematical Structure of CAPM, EMH, and the Volatility Effect

Abstract

With the volatility effect as a gateway, this paper constructs a new single-factor return model for capital asset prices. The model is built using only elementary techniques. To accomplish this, a new risk measure is introduced such that the volatility effect becomes not an economic or behavioral anomaly, but a mathematical expectation. Consequently, common performance evaluation measures come under new scrutiny. CAPM is shown to be a special case of a more general single-factor model. The ex-ante model and methods have strong explanatory value at the level of analytical expression and simulation. The ex-post estimation techniques give a range of possible ex-ante conditions that lead to market outcomes.

Keywords: Alpha CAPM Volatility

JEL Classification: G