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

arXiv:2411.19444v5 Announce Type: replace-cross 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. For some size-based stock portfolios, dividing their returns by the Volatility Index makes them closer to 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.