Risk For Portfolio Selection Research Articles

Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

Abstract In this paper, we propose a modification that improves efficiency, robustness and reliability of the famous HS conjugate gradient method. In particular, we propose a hybrid of the HS and DHS methods, where DHS is another recent modification of the HS method. Irrespective of the line search, the search direction of the proposed method is sufficiently descent. Moreover, the new approach guarantees global convergence for general functions under the strong Wolfe line search. Numerical results and performance profiles are reported, and indicate that the new approach outperforms three similar methods in the literature. We also give a practical application of the new approach in minimizing risk in portfolio selection.

Modeling Tail Risk in Portfolio Selection: Selected Iranian Food Industry Companies

This study extends the extreme downside hedge (EDH) methodology to model the tail risk Co-movement of financial assets in terms of systemic risk as constraint to select an optimal Portfolio among the Food Industry (FI)Companies of Tehran Stock Exchange (TSE). The empirical application investigates: 1) is the optimal portfolio by considering tail risk different from the model without risk in terms of diversification. 2) Is the optimal portfolio by considering tail risk better the model without risk in covering the risk? At the end, the efficiency of the models was examined by a short-term forecast based on the real data of the stock market. We sampled the time series of 11 manufacturing companies in the FI which are publicly listed on the TSE. The data covers daily close prices from October, 2015 to December, 2020. The result shows in all periods and for all degrees of risk Aversion coefficient, portfolio by considering the downside risk has less risk than Markowitz model and which can indicate the superiority of this model over Markowitz model. According to the result, AZP has the higher mean, lower risk, lower kurtosis and also negative total effect, so, the shares of it increase as the risk aversion goes up.

A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection

In this paper, we present a new hybrid conjugate gradient (CG) approach for solving unconstrained optimization problem. The search direction is a hybrid form of the Fletcher-Reeves (FR) and the Dai-Yuan (DY) CG parameters and is close to the direction of the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton approach. Independent of the line search, the search direction of the new approach satisfies the descent condition and possess the trust region. We establish the global convergence of the approach for general functions under the Wolfe-type and Armijo-type line search. Using the CUTEr library, numerical results show that the propose approach is more efficient than some existing approaches. Furthermore, we give a practical application of the new approach in optimizing risk in portfolio selection.

Forecasting systemic risk in portfolio selection: The role of technical trading rules

AbstractThis paper proposes and implements methods for determining whether incorporating technical trading rules accurately forecasts systemic risk and improves the performance of out‐of‐sample portfolios. The proposed methodology considers various trading rules for forecasting and addressing potential systemic risk in portfolio selection problems. The method incorporates major trading rules as early warning systems or alarm rules to detect market failure within diverse reward–risk measures. Methodologically, the alarm rules are integrated into portfolio selection strategies that predict returns using multifactor models. Therefore, the portfolio strategies combine the predictive ability of both technical trading rules and multifactor models. Empirical analyses validate the suggested approaches and evaluate the impacts of different technical trading rules on portfolio selection problems. This paper compares the ex ante sample paths of several portfolio strategies aiming to maximize portfolio wealth using either reward–risk or drawdown‐based performance measures. The results show that the proposed methodologies outperform the classic approach in terms of out‐of‐sample performance.

Optimal trade-off portfolio selection between total risk and maximum relative marginal risk

In this paper, we first introduce the concept of maximum relative marginal risk (MRMR) to measure the effect of risk diversification under the mean–variance portfolio selection. Then we develop an optimal trade-off model between the total risk and the MRMR. Since the MRMR is described as a maximum fractional quadratic functions, we convert it into a quadratic function in terms of auxiliary variables and transform it as a constraint. Then it turns to a non-convex quadratically constrained quadratic problems (QCQP). To solve this non-convex QCQP, we relax and approximate the optimal trade-off model, respectively, and obtain both second-order cone relaxation and inner approximation. Both of them provide a lower bound and an upper bound for the original non-convex QCQP. Furthermore, we solve the QCQP by using an efficient and globally convergence branch-and-bound solution algorithm proposed by Li et al. [Active allocation of systematic risk and control of risk sensitivity in portfolio optimization, Eur. J. Oper. Res. 228 (2013), pp. 556–570]. In the process of solution we only branch the variables related to the MRMR and reduce the numbers of branch largely. Finally, our model is illustrated and demonstrated by empirical analysis. The numerical results show that our model outperforms the existing models to deal with the risks between the total risk and the relative marginal risk in portfolio selection.

Limited Downside Risk In Portfolio Selection Among U.S. and Pacific Basin Equities

In this paper we domostrate safety first portfolio selection using extreme value theory.We show that Roy's safety first criterion can be improved on by exploiting the fat tail property of asset returns. Using daily data for a set of international stock indices for the period 1986-May 2000, we calculate the so-called tail indexes, which are accurate measures of the fat-tailedness of the stock return distributions, and use these to calculate minimum threshold return levels given very low exceedence probabilities for investors. This example is but one way that the theory of extremes can be utilized in economics and finance. [G11]