Building a CAPM Covariance Matrix for Portfolio Optimization

Summary

The document raises a portfolio-construction question about estimating the covariance matrix under the Capital Asset Pricing Model. The author is simulating a portfolio of five assets and comparing optimal weights from a single-index statistical model with weights from CAPM. They ask whether covariance calculations should use each stock’s beta or the portfolio allocation to that stock.

The document contains no answer, formula, calculation, or simulation results. It frames a useful distinction: asset betas are model inputs used to estimate how returns co-move through their shared market exposure, while portfolio weights enter later when calculating portfolio-level risk. The exact covariance estimate also depends on assumptions and any residual or idiosyncratic risk treatment, which the post does not specify.

Key ideas

• The question is how CAPM can be used to construct an asset return covariance matrix.
• It compares a single-index model with CAPM in a portfolio optimization setting.
• Betas describe modeled market exposure, while portfolio weights are used to aggregate asset exposures and risk.
• The document provides no worked example or answer.

Tags

# covariance matrix in the CAPM model


# covariance matrix in the CAPM model












I'm running a simulation for a 5 asset portfolio, calculating the optimal weights of each asset both with the statistical model (i.e. single index) and with the CAPM. my question is: how do you compute the covariance matrix in the CAPM? should I use the beta of each stock or the w% invested in each stock?

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