Mean-variance-skewness model for portfolio selection with transaction costs. (English) Zbl 1074.91533
A form of the classical portfolio selection theory of Markowitz deals with maximizing the average of potential returns while keeping the variance of potential returns bounded by some fixed level. This is the basic approach.
If one starts with a given portfolio, one wants to include into the analysis the transaction costs that arise from transforming the original portfolio into the optimal one.
One would also like to incorporate natural restrictions into the optimisation problem like disallowing short-selling.
The authors claim that investors prefer portfolios whose returns are very skewed to portfolios whose returns are. very symmetrical. And therefore they propose to investigate the problem of obtaining the portfolio which maximizes skewness subject to the following restrictions: 1) the average return (which now incorporates transaction costs) is bounded below by some level, 2) the variance of the return (risk) is bounded above, and 3) the proportion invested in each stock is positive (no short selling).
To solve the resulting nonlinear programming problem, the problem is first approximated and then transformed into a sequence of simpler problems, the final one being a linear programming problem.
If one starts with a given portfolio, one wants to include into the analysis the transaction costs that arise from transforming the original portfolio into the optimal one.
One would also like to incorporate natural restrictions into the optimisation problem like disallowing short-selling.
The authors claim that investors prefer portfolios whose returns are very skewed to portfolios whose returns are. very symmetrical. And therefore they propose to investigate the problem of obtaining the portfolio which maximizes skewness subject to the following restrictions: 1) the average return (which now incorporates transaction costs) is bounded below by some level, 2) the variance of the return (risk) is bounded above, and 3) the proportion invested in each stock is positive (no short selling).
To solve the resulting nonlinear programming problem, the problem is first approximated and then transformed into a sequence of simpler problems, the final one being a linear programming problem.
Reviewer: José Lúis Fernandez Perez (Madrid)
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