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The Arbitrage Pricing Model. Lecture XXVI. A Single Factor Model. Abstracting away from the specific form of the CAPM model, we posit a single factor model written as

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A Single Factor Model

  • Abstracting away from the specific form of the CAPM model, we posit a single factor model written as

    • In this model, the random return on an investment zi is a linear function of some random factor fi and an idiosyncratic term i.


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  • Abstracting away from the idiosyncratic risk

    • If the bis of two assets are the same, then the ais must be the same for an arbitrage free model.

    • Suppose we are interested in forming a portfolio of two assets with different bis, bi  bj , bi  0, bj  0




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Multifactor Models:

  • Suppose that asset returns are generated by a two factor linear model:

    • A portfolio of these assets then yields


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  • The matrix

    must be singular, or the first row must be a linear combination of the last two rows