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Say what an arbitrage opportunity is and judge whether one is present

CFA® Level II · Portfolio Construction · Using Multifactor Models · L2.PM.4.b

The idea

An arbitrage opportunity is a way to earn a riskless profit with no net investment. Under APT, well-diversified portfolios with the same factor sensitivities must offer the same expected return; if they do not, buy the one with the higher expected return and short the other in amounts that match exposures. With one factor, combine two portfolios to replicate a third's sensitivity: the replicating weights solve w × β1 + (1 − w) × β2 = β3. Compare the replicating portfolio's expected return with the third's and trade the gap; the profit is the return difference times the amount invested. The trap is to call any return gap an arbitrage: portfolios with different sensitivities can rightly earn different returns.

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