Friday, June 10, 2016

On a source for a mean-variance portfolio optimization result


In the context of a mean_variance framework consider an optimizing investor who chooses at time T portfolio weights w so as to maximize the quadratic objective function:


U(w)=E[Rp]γ2Var[Rp]=wμγ2wVw


Where E and Var denote the mean and variance of the uncertain portfolio rate of return Rp=wRT+1 to be realized in time T+1 and γ is the relative risk aversion coefficient. The optimal portfolio weights will be:


w=1γV1μ



Could I have a reference that proves this result? preferably a textbook that builds up to it.




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