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

Abraham Atsiwo and Andrey Sarantsev

Papers from arXiv.org

Abstract: The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in the CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on average. Our goal is to make the resulting linear regressions have independent identically distributed Gaussian residuals. In some cases, we find that including the Volatility Index as a multiplicative factor by these residuals makes them closer to that ideal. In this article, we combine these ideas to create a new discrete-time model, which includes volatility, relative size, and the CAPM. We fit this model using real-world data, prove the long-term stability, and connect this research to Stochastic Portfolio Theory.

Date: 2024-11, Revised 2026-06
New Economics Papers: this item is included in nep-fmk and nep-rmg
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