Question: EXERCISE 3.21 (Approximate portfolio selection). Assume that the adjusted returns R = (R'; i E I) are very close to zero; think, for example, of

EXERCISE 3.21 (Approximate portfolio selection). Assume that the adjusted returns R = (R'; i E I) are very close to zero; think, for example, of rather short horizon investment. In this case, for portfolio weights T = (7'; i E I) and a > 0, note the first-order approximation Ri (1 + LjeI Ti Ri) iEl Using the above approximation, show that the optimal portfolio for the power (and, when a = 1, logarithmic) utility maximization problem of Exercise 3.9 is approximately TT* ~( ak ) -1b, where the matrix K and vector b are defined via Kil = EP [R'R'], (i.j) EIXI; b' = EP [R'], iEl

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