خلاصة:
In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of return distribution. The proposed TMV model is based on two risk measures the Tail Condition Expectation (TCE) and Tail Variance (TV) under Generalized Skew-Elliptical (GSE) distribution. We first apply a convex optimization approach and obtain an explicit and easy solution for the TMV optimization problem, and then derive the TMV efficient frontier. Finally, we provide a practical example of implementing a TMV optimal portfolio selection in the Tehran Stock Exchange and show TCE-TV efficient frontier.
ملخص الجهاز:
For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of return distribution.
The proposed TMV model is based on two risk measures the Tail Condition Expectation (TCE) and Tail Variance (TV) under Generalized Skew- Elliptical (GSE) distribution.
: Keywords Tail Mean-Variance criterion Optimal portfolio selection Efficient FrontierSkew-Elliptical Distributions 1 Introduction Investment decision making is one of the key issues in financial management.
The Tail Mean- Variance (TMV) model for portfolio selection was introduced by Landsman [19], and is defined as follows: )VIew the image of this page) where > 0 and is a random loss with an elliptical distribution at a portfolio.
We use the explicit formula of the tail variance measure for the GSE distributions, which is introduced by Jamshidi and Khaloozadeh [15] and is equal to: )VIew the image of this page) where )VIew the image of this page) Now, we use these two risk measures to form the TMV model and derive the extended efficient fron- tier under the GSE distribution for optimal portfolio selection.
The tail mean-variance risk measure of the portfolio, introduced by Landsman [19], is defined as )VIew the image of this page) and corresponds to the TMV criterion for portfolio selection.