A simplified Capital Asset Pricing Model

TL;DR

This paper introduces a simplified version of the CAPM within a Black-Scholes market, linking index appreciation to volatility and interest rate, and establishes a fundamental performance dichotomy.

Contribution

It proposes a mathematically simpler formulation of the CAPM and proves a key performance dichotomy in market behavior.

Findings

Either outperform the index or the simplified CAPM holds.

The model simplifies the mathematical expression of the CAPM.

Provides a new perspective on market efficiency and asset pricing.

Abstract

We consider a Black-Scholes market in which a number of stocks and an index are traded. The simplified Capital Asset Pricing Model is the conjunction of the usual Capital Asset Pricing Model, or CAPM, and the statement that the appreciation rate of the index is equal to its squared volatility plus the interest rate. (The mathematical statement of the conjunction is simpler than that of the usual CAPM.) Our main result is that either we can outperform the index or the simplified CAPM holds.