Sharpe ratio

Portfolio selection is one of the most important financial and investment issues. Portfolio selection seeks to allocate a predetermined capital (wealth) over one or multiple time periods between assets and stocks in a such way that the wealth of investor (portfolio owner) is maximized the risks are minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount Sharpe ratios of portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a robust possibilistic programming model (based on necessity theory) has been developed, which is capable of adjusting the robust degree of output decisions to the uncertainty of the parameters. The proposed model has been tested on 27 companies active in the Tehran stock market. At the end, the results of the model demonestrate the good performance of the robust possibilistic programming model.

one of the most important financial and investment issues is Portfolio selection, that seeks to allocate a predetermined capital (wealth) over one or multiple periods between assets and stocks in such a way that the wealth of investor (portfolio owner) is maximized and, Simultaneously, its risk minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount of Sharpe ratios of the portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a robust possibilistic programming model (based on necessity theory) has been developed, which is capable of adjusting the robust degree of output decisions to the uncertainty of the parameters. The proposed model was tested on 27 companies active in the Tehran stock market. In the end, the results of the model demonstrated the good performance of the robust possibilistic programming model. 

This study aims at getting a better performance for optimal stock portfolios by modeling stocks prices dynamics through a continuous paths Levy process. To this end, the share prices are simulated using a multi-dimensional geometric Brownian motion model. Then, we use the results to form the optimal portfolio by maximizing the Sharpe ratio and comparing the findings with the outputs of the conventional model. To examine the robustness of the results, we have evaluated its performance for different investment horizons and various volumes of price information over a long period (approximately twenty years) in the Tehran Stock Exchange (TSE). Findings indicate that within the trading dates spanning the interval 24-Mar-2001 to 19-Sep-2020, the return of the portfolios obtained from applying this simulation scheme for maximization of Sharpe ratio is (244% on average) higher and their risk (standard deviation) are lower (1227% on average) than those realized by the conventional methods. Additionally, a comparison of the simulation approach with a performance of the actual market portfolios indicates that the Sharpe ratios of the simulation method are higher (0.055% on average) than those resulting from the total market performances. The results of the stochastic dominance test show that our proposed strategy has a first-order stochastic dominance (FSD) over the conventional one and market portfolios, that means at each level of cumulative distribution, the Sharpe ratio of our method is higher, and as FSD test makes no assumptions about the curvature of investors' utility functions, these results do not depend on the degree of risk aversion of investors, and as long as investors prefer a higher Sharpe ratio, they would be better off if they follow our proposed strategy.

Risk parity is perceived as one of the stock portfolio selection models that have received a lot of attention since the US financial crisis in 2008. The philosophy of this model is to allocate the same amount of portfolio risk between the constituent assets. In the present study, the combined portfolio selection model of relative robust risk parity is introduced, which uses the worst-case scenario approach on the covariance matrix parameter appearing in the robust risk model in portfolio robustness. According to historical data, several scenarios are considered for the covariance matrix. The objective function value of the hybrid model for each portfolio (feasible point) is the worst result (with most volatility) among the set of scenarios.  Finally, the model selects a portfolio for which the worst possible result has the least relative volatility. The research portfolio consists of 8 industries from Tehran Stock Exchange in the period 2011 to 2020. This portfolio has a higher Sharpe ratio than conventional models of mean-variance and weight parity, and is more resilient to market declines than the two models and produces less loss. Therefore, risk-averse investors are advised to use this stock portfolio selection model as a cover to face severe market declines.

As a trading strategy, pairs trading is performed based on the arbitrage opportunities extracted from statistical models. It is an outcome of the distance between an asset pair and the equilibrium state. Consequently, selecting a pair with the potential to form long-term relationships and reverting to the mean is the main challenge associated with pair trading. Cointegration is one of the most famous statistical tests for selecting a pair's trading. The present study uses Empirical Mode Decomposition (EMD) to decompose the time series of an asset pair price into its constituent elements (intrinsic mode functions). This study examined the property of cointegration across different levels and the corresponding levels of 2- time series to find the cointegration pairs in different decomposition levels and finally examine the resulting profitability. To this end, the profitability of the pairs trading system related to 14 stocks of the Tehran Stock Exchange throughout 2012-2021 was investigated based on EMD. The results showed that the outputs are pretty noticeable for the first level of decomposition (the first intrinsic mode function), and the number of trading opportunities increased by more than two times compared to the normal pair trading with cointegration; the daily returns increased by four times; and the Sharpe ratio increased by about two times compared to the normal pairs trading. The system formed based on the second mode function also outperformed the normal cointegration, and the performance of the third intrinsic mode function is almost on par with that of cointegration. Moreover, the mean transaction duration decreased remarkably in the first and second mode functions.