{"id":2872,"date":"2026-05-14T08:42:08","date_gmt":"2026-05-14T08:42:08","guid":{"rendered":"https:\/\/blogs.mathworks.com\/finance\/?p=2872"},"modified":"2026-05-14T08:42:10","modified_gmt":"2026-05-14T08:42:10","slug":"portfolio-optimization-with-target-factor-exposures","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/finance\/2026\/05\/14\/portfolio-optimization-with-target-factor-exposures\/","title":{"rendered":"Portfolio Optimization with Target Factor Exposures"},"content":{"rendered":"

A practical MATLAB walkthrough comparing tracking error and exact exposure approaches. <\/em><\/p>\n

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When you build a factor-based portfolio, the central design choice is how strictly to enforce your factor views. Do you treat target exposures as soft goals or do you impose them as hard constraints that the portfolio must satisfy exactly? That decision can materially change the diversification, concentration, and feasibility of the resulting portfolio.<\/p>\n

In this blog post, we use data from the Fama-French Data Library, a widely used academic source, to make the comparison practical in a realistic setting. While the example uses the Fama-French three-factor structure\u2014market (Mkt), size (SMB), and value (HML)\u2014the techniques apply to any multi-factor framework.<\/p>\n

We compare two practical optimization approaches using MATLAB\u00ae:<\/p>\n

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  1. Tracking Error Minimization<\/strong>\u2014Targets specific factor exposures while allowing small deviations, which can improve diversification and feasibility.<\/li>\n
  2. Exact Exposure Matching<\/strong>\u2014Enforces target factor exposures exactly using equality constraints, which is useful when strict mandates or regulatory requirements must be met.<\/li>\n<\/ol>\n
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    Explore the example<\/a><\/div>\n
    Watch the demo video<\/a><\/div>\n<\/div>\n
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    1. Load Data and Set Up the Factor Model<\/strong><\/h1>\n

    We start with one year of price data for the 30 stocks in the Dow Jones Industrial Average\u00ae (DJIA), which we convert to returns. Separately, we load the three Fama-French factors: excess market return (Mkt), small minus big (SMB), and high minus low (HML).<\/p>\n

    After synchronizing the stock and factor data, MATLAB estimates the joint covariance structure using a Portfolio<\/span> object. In the tracking error formulation, the factor return series are included in that covariance structure even though they are not investable assets. This setup allows the optimization to reflect both stock-return risk and the portfolio\u2019s relationship to the factor returns.<\/p>\n

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    2. Apply Realistic Constraints<\/strong><\/h1>\n

    Both approaches share the same set of practical constraints:<\/p>\n