Assume there exists a return R that is on the mean-variance frontier and is an affine

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Assume there exists a return R˜ ∗ that is on the mean-variance frontier and is an affine function of a vector F˜; that is, R˜ ∗ = a + b

F˜. Assume either (i) there is a risk-free asset and R˜ ∗ = Rf , or (ii) there is no risk-free asset and R˜ ∗ is different from the GMV return. Show that there is a factor model with factors F˜.

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