Abstract
In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter λ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ).
Highlights
The portfolio selection problem is of both theoretical and of practical interest (Castellano and Cerqueti 2014; Li and Hoi 2014; Shen et al 2014; Fletcher 2015; Fulga 2016; Ray and Jenamani 2016)
As for the efficient frontier, we conclude from (21) that the efficient frontier corresponding to the generalized and classical Sharpe ratios belongs to the efficient frontier corresponding to the mean-variance model (See proof of Corollary 1), with the following set showing the relation between the mean variance (MV) risk aversion parameter, λ, and the generalized Sharpe ratio risk aversion parameter, β, b2 ( β − 21 )
We suggested a novel generalized optimal portfolio selection utility measure which incorporates many popular portfolio selection utility measures as special cases
Summary
The portfolio selection problem is of both theoretical and of practical interest (Castellano and Cerqueti 2014; Li and Hoi 2014; Shen et al 2014; Fletcher 2015; Fulga 2016; Ray and Jenamani 2016). Let us notice that the mean-variance model is the balanced difference between the expectation of returns, which measures an average asset profit, and the variance of returns, which measures the associated risk. Let us notice that in the case when short selling is possible, the mean-variance OPS problem has an analytic explicit-form solution, because it reduces to a classical quadratic programming problem. Another key approach in the OPS theory is the maximization of the Sharpe ratio (see, for instance, Sharpe 1998), which was introduced in Sharpe (1966), and has the form. The maximization of the Sharpe ratio is motivated by maximization of expected profit and minimization of risk.
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