Abstract
The downside risk measure methods have gained in popularity within the frame of the Post-Modern Portfolio theory. Many studies have suggested different cosemivariance formulas with the downside risk measures. The purpose of this study is to compare the performances of the portfolio optimization models that apply different risk measures such as variance, semi-variance, and lower partial moment (LPM) with the different cosemivariance formulas. In the study, the Estrada (2007) and Nawrocki (1991) approaches were chosen to demonstrate the differences between different cosemivariance statistics used in the semi-variance risk measures. The results of the models are also compared with the mean-variance results. Sharpe and Sortino ratios are used as a comparison measure. In the study, efficient portfolios are created for investors having different risk attitudes with the LPM approach. Additionally, portfolio optimization is conducted by using the LPM approach with the stochastic modeling to avoid the uncertainty of portfolio returns. It was concluded that the Nawrocki model is beneficial to control the downside risk and it is a better choice as it includes the calculation of correlations between the assets and that the stochastic return model produces more conservative results compared to the deterministic model.
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