Capital Asset Pricing Model with Size Factor and Normalizing by Volatility Index

TL;DR

This paper extends the CAPM by incorporating size effects and normalizing returns with the Volatility Index, resulting in a new model that captures additional risk factors and demonstrates stability with real data.

Contribution

It introduces a novel discrete-time CAPM variant including size and volatility normalization, filling gaps in prior research and linking to Stochastic Portfolio Theory.

Findings

Model fits real-world data effectively

Proves long-term stability of the new model

Connects to Stochastic Portfolio Theory

Abstract

The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on average. Dividing stock index returns by the Volatility Index makes them independent and normal. In this article, we combine these ideas to create a new discrete-time model, which includes volatility, relative size, and CAPM. We fit this model using real-world data, prove the long-term stability, and connect this research to Stochastic Portfolio Theory. We fill important gaps in our previous article on CAPM with the size factor.