Abstract
It has been widely studied how investors will allocate their assets to an investment when the return of assets is normally distributed. In this context usually, the problem of portfolio optimization is analyzed using mean-variance. When asset returns are not normally distributed, the mean-variance analysis may not be appropriate for selecting the optimum portfolio. This paper will examine the consequences of abnormalities in the process of allocating investment portfolio assets. Here will be shown how to adjust the mean-variance standard as a basic framework for asset allocation in cases where asset returns are not normally distributed. We will also discuss the application of the optimum strategies for this problem. Based on the results of literature studies, it can be concluded that the expected utility approximation involves averages, variances, skewness, and kurtosis, and can be extended to even higher moments.
Highlights
How investors will allocate capital when income is not normally distributed
Various solutions have been introduced, the discussion in this paper focuses on Taylor's expansion of the utility function, which naturally produces utility expectations that depend on the high moment linearity of portfolio income (Batuparan, 2001)
In the case of the CARA and CRRA utility functions, skewness weights and high moments in the expected utility are estimated depending on the risk-avoidance parameters. this is a preference for skewness and risk-avoidance for kurtosis
Summary
How investors will allocate capital when income (return) is not normally distributed. The first approach is based on the direct maximization of utility expectations, under alternative assumptions of distribution for capital income (assets). The advantage of this approach is that it provides a real evaluation of the utility of expectations, that the optimal portfolio is the actual resolution of the original problem (Ruppert, 2004). The second approach is based on the optimization of a problem that does not require numerical integration. This approximation includes the moment of income-portfolio distribution. Various solutions have been introduced, the discussion in this paper focuses on Taylor's expansion of the utility function, which naturally produces utility expectations that depend on the high moment linearity of portfolio income (Batuparan, 2001)
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