Assets performance evaluation with the use of returns distribution characteristics

Portfolio optimization is a selection of assets with the lowest risk and highest return. Asset performance evaluation is a useful way to choose assets and construct a profitable portfolio. For this purpose, the non-parametric Data Envelopment Analysis (DEA) method is used, which is a suitable tool for measuring performance. By the fact that stock returns are not normally distributed and usually exhibit skewness, kurtosis and heavy-tails, which definitely affects the assets performance, we have to consider the characteristics of the returns distribution. In the proposed model, we apply the Variance Gamma (VG) process, which covers the skewness and kurtosis of returns. As a result, we construct a portfolio by selecting assets which their performance is more realistic.

In the introduced model, the only input of the model is Conditional Value at Risk (CVaR), and the mean return and Sharpe index are the model’s outputs. Since the outputs can be negative, the model is inspired by VRM in the output-oriented DEA model, which deals with negative values. As the returns on stock are VG distributed, its parameters are simulated by the method of moments estimation, and then the process factors are simulated by the Monte Carlo technique. Finally, the scenarios of returns are obtained, and the assets performance is evaluated.

The correctness of the model is investigated by evaluating the relative efficiency of 7 companies from different industries in Iran Stock market. The results show that by considering the returns distribution characteristics, the input and outputs values of the model are estimated more realistically and more reliable results can be obtained; thus a profitable portfolio can be constructed.

Originality/Value: 

Evaluation of the assets performance by taking into account the returns distribution characteristics leads to realistic results.