= Assume that the adjusted returns (; i = I) are very close to zero;...
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= Assume that the adjusted returns Ř (Ř¹; i = I) are very close to zero; think, for example, of rather short horizon investment. In this case, for portfolio weights π = (7¹; i = I) and a > 0, note the first-order approximation Ři (1 + Ejel T³i Ři)" *(1-a [~R³). Σπ Using the above approximation, show that the optimal portfolio for the power (and, when = 1, logarithmic) utility maximization problem is approximately a = π* ≈ (aK)-¹b, where the matrix K and vector b are defined via K¹ = EP [Ř¹ Ř¹], (i.j) = I x I; b = EP[R], ie I. = Assume that the adjusted returns Ř (Ř¹; i = I) are very close to zero; think, for example, of rather short horizon investment. In this case, for portfolio weights π = (7¹; i = I) and a > 0, note the first-order approximation Ři (1 + Ejel T³i Ři)" *(1-a [~R³). Σπ Using the above approximation, show that the optimal portfolio for the power (and, when = 1, logarithmic) utility maximization problem is approximately a = π* ≈ (aK)-¹b, where the matrix K and vector b are defined via K¹ = EP [Ř¹ Ř¹], (i.j) = I x I; b = EP[R], ie I.
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Related Book For
Statistics For Business And Economics
ISBN: 9780321826237
12th Edition
Authors: James T. McClave, P. George Benson, Terry T Sincich
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