![]() The idea is to choose the portfolio weights such that the portfolio variance is minimal for a given value of the portfolio return. ![]() developed the mean-variance principle for portfolio selection. Paramater Gamma 2 in the Power Utility function. Many procedures have been proposed in literature how to construct an optimal portfolio, i.e., how to choose the optimal portfolio weights. If W denotes the wealth of the investor, then the power utility is given by \(U\left( W\right) =\frac\) is assumed to be positive definite. The focus of this paper lies on the power and the logarithmic utility functions. In these cases, no closed-form solutions can be derived without information on the distribution of the return process. However, there are many other ways to choose the utility function like e.g., the power and the exponential utility function. ![]() Similarly, a quadratic utility provides a closed-form solution under very general conditions. This result is valid without any distributional assumptions imposed on the returns. The mean-variance approach of turns out to be fully consistent with the expected utility maximization (see ). A widely made approach is based on the maximization of an investor’s utility function, where the investor chooses a portfolio for which its utility reaches a maximum possible value. In the meantime, many further proposals for a portfolio selection have been made. The power utility function is with positive or negative, but non-zero, parameter a < 1. All of these so-called efficient portfolios lie on the efficient frontier which is a parabola in the mean-variance space. He recommended choosing the portfolio weights in such a way that the portfolio variance is minimal for a given level of the expected portfolio return. Markowitz used the variance as a measure of the risk of a portfolio return. ![]() The theory of optimal portfolio choice started with the pioneering contribution of. ![]()
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