Two managers can run identical market betas for a decade and still post very different returns. A single-factor model calls that luck. A multifactor model gives the gap a name, a sensitivity, and a price.
A factor is a variable or characteristic with which individual asset returns are correlated. The capital asset pricing model (CAPM) recognizes exactly one: the market portfolio. Decades of equity evidence show that description is incomplete. Multifactor models add explanatory power and flexibility, and they dominate practice because they let you replicate an index, express a macro view, attribute return and risk in detail, and size active decisions against a benchmark.
The logic that survives from the CAPM is the split between risk types. Risk that vanishes inside a diversified portfolio, asset-specific risk, earns no reward. Risk that cannot be diversified away, systematic risk, is priced risk, meaning investors demand extra expected return for bearing it. Multifactor models simply allow more than one dimension of priced risk.
Common mistakes
- Comparing returns at unmatched sensitivities. An arbitrage claim requires a replicating combination with the identical factor sensitivity. Z at 1.30 must be tested against a 1.30-sensitivity blend, not against X's 0.80.
- Reversing the buy and sell legs. An expected return above the pricing line (13.00% versus 11.50%) means undervalued, so you go long it and short the replicate.
- Feeding predicted macro values into a macro model. The independent variables are surprises, actual minus predicted. Predicted inflation of 0.4% against actual 0.5% gives a factor value of 0.1%, not 0.5%.
Bottom line
- APT assumptions: returns follow a factor model, asset-specific risk is diversifiable, no arbitrage among well-diversified portfolios
- APT pricing: E(Rp) = RF + sum of factor risk premium times factor sensitivity; number and identity of factors unspecified
- Arbitrage: no net investment, no risk, expected positive profit; test by replicating the exact factor sensitivity and comparing expected returns
- Higher expected return than the model line means undervalued, so buy it and short the replicate
Exam shortcut
Two portfolios and one factor determine the whole APT line: subtract the equations, divide the return gap by the sensitivity gap for λ, back-solve for RF. Then price every other portfolio off that line before you touch the answers.
The full lesson (about 3,052 words, 20 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- multifactor models
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