Abstract
Mutual funds are important financial institutes. There are several methods for performance evaluation of mutual funds such as portfolio optimization. Portfolio optimization has a basic model that has completed up to now. One of completions is adding cardinality constraint to the model. Considering cardinality in portfolio optimization model makes it an integer programming problem that solving it, is hard and makes the efficient frontier discontinuous. In current study in first stage we rank the mutual funds with VIKOR method and based on 5 characteristics: rate of return, variance, semivariance, Treynor ratio and Sharpe ratio. In second stage according to cardinality level best ranked mutual funds are chosen. A mean-semivariance portfolio optimization model is written using chosen funds. This model is solved using fuzzy technique programming and efficient frontier is obtained. Real data from NASDAQ based on 92 mutual funds are used to illustrate the effectiveness of proposed methodology. Results show that the efficient frontier obtained from our methodology is continuous and near to unconstrained efficient frontier.
Highlights
The role of mutual funds in financial markets is undeniable
In first stage of this study mutual funds are ranked based on VIKOR method using 5 characteristics: rate of return, variance, semivariance, Treynor index and Sharpe index
In Eq (10) i is the number of mutual funds, R, is the rate of return of ith fund at time t and NAV, is the net asset value of ith fund at time t. 2.2.2 Variance
Summary
The role of mutual funds in financial markets is undeniable. Mutual funds are financial institutes that help investors to have an appropriate portfolio. Basso & funari (2001) used DEA method too They defined their model based on Jenson alpha, Treynor, Sharpe and semivariance indices. In first stage of this study mutual funds are ranked based on VIKOR method using 5 characteristics: rate of return, variance, semivariance, Treynor index and Sharpe index. Considering cardinality in portfolio optimization model change it to an integer programming problem with discrete variables. Because solving this type of problems and obtaining efficient frontier is difficult and time-consuming, in this study a two-stage method is used.
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