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

ArXiv ID: 2411.19444 “View on arXiv”

Authors: Unknown

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.

Keywords: Capital Asset Pricing Model (CAPM), Size Effect, Volatility Index, Stochastic Portfolio Theory, Discrete-time Model, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical modeling, stochastic processes, and theoretical proofs (e.g., ergodicity, normal order statistics) fitting the ‘Lab Rats’ profile, but it is tempered by real-world data fitting from established financial libraries and explicit stability proofs, pushing it toward ‘Holy Grail’.

  flowchart TD
    A["Research Goal:<br>Create new CAPM model<br>including Size & Volatility"] --> B["Data Sources<br>Stock Indices & Volatility Index VIX"]
    B --> C["Methodology Steps<br>Integrate Size Factor &<br>Normalize by Volatility Index"]
    C --> D["Computational Process<br>Discrete-time Model Fitting<br>& Stability Analysis"]
    D --> E["Key Findings/Outcomes<br>Validated Model<br>Long-term Stability<br>Link to Stochastic Portfolio Theory"]