LR Mixed Fuzzy Random Portfolio Choice Based on the Risk Curve

A restricted portfolio is constructed which includes NYSE common stocks, corporate bonds, government bonds, small capitalization common stocks, residential real estate and farmland and returns for each of four different tax brackets (0%, 15%, 30%, 45%). Next, three alternative measures of rates of return for residential real estate and farmland are used. Finally, since some researchers believe that standard risk measures (variance and standard deviation) do not capture the total risk in real estate, the risk for the real estate returns is increased five times while the returns are held constant. The twenty–four optimal portfolios (four tax brackets with two measures of risk and three measure of return for residential real estate and farmland) are then derived. These results are then compared and contrasted to each other to ascertain the change in sensitivity of the optimal portfolios due to different tax rates, different rates–of–return estimates and different risk estimates.

Convex risk measures based on generalized lower deviation and their applications

Portfolio management using lower partial risk (downside risk) measures is attracting more attention of practitioners in recent years. The purpose of this paper is to review important characteristics of these riskmeasures and conduct simulation using four alternative measures, lower semi-variance, lower semi-absolute deviation, first order below targetrisk and conditional value-at-risk.We will show that these risk measures are useful to control downside risk whenthe distribution of assets is non-symmetric. Further, we will propose a computational scheme to resolve the difficultyassociated with solving a large dense linear programming problems resulting from these models. We will demonstrate that this method can in fact solve problems consisting of104 assets and 105 scenarios within a practical amount of CPU time.

Closed-Form Solutions for Worst-Case Law Invariant Risk Measures with Application to Robust Portfolio Optimization

Risk is one of the important parameters in portfolio optimization problem. Since the introduction of the mean-variance model, variance has become the most common risk measure used by practitioners and researchers in portfolio optimization. However, the mean-variance model relies strictly on the assumptions that assets returns are multivariate normally distributed or investors have a quadratic utility function. Many studies have proposed different risk measures to overcome the drawbacks of variance. The purpose of this paper is to discuss and compare the portfolio compositions and performances of four different portfolio optimization models employing different risk measures, specifically the variance, absolute deviation, minimax and semi-variance. Results of this study show that the minimax model outperforms the other models. The minimax model is appropriate for investors who have a strong downside risk aversion.

Portfolio insurance under a risk-measure constraint

Mean-risk models have been widely used in solving portfolio selection problems in the last years. Since the mean-variance theory of Markowitz, an enormous amount of papers have been published extending or modifying the basic model in several directions like the simplification of the type and amount of input data, the introduction of alternative measures of risk, the incorporation of additional criteria or constraints. Recently, risk measures concerned with the left tails of distributions that evaluate the extremely unfavourable outcomes are used. The most used risk measure for such purposes is Value-at-Risk (VaR). In this paper we concentrate on the second direction of incorporating of a new risk measure in portfolio modeling. We define a new risk measure, which take into consideration the values exceeding a certain threshold in the extreme tail of the loss distribution, called Limited Value-at-Risk (LVaR). We study the properties of this risk measure. We build a new model for portfolio selection, named mean-LVaR model, in which risk is evaluated using LVaR risk measure. We study the properties of the new mean-risk model and compare it with the classical mean-VaR model. We derive the analytical form of LVaR risk measure in the case of normal distribution. We provide computational results and analyze the implications of using the mean-LVaR risk model in portfolio optimization problem.

Portfolio optimization is crucial for investors seeking to maximize returns while minimizing risk. This study determines the optimal portfolio composition of IDX High Dividend 20 stocks using two distinct approaches: Single Index Model (SIM) and Multi Index Model (MIM). SIM utilizes only the Jakarta Composite Index (IHSG) as a market factor, while MIM incorporates three factors: IHSG, USD/IDR exchange rate, and Bank Indonesia (BI) Rate. The study analyzes daily closing price data from 20 stocks in the IDX High Dividend 20 index during the period of June 1 to November 28, 2025, obtained from investing.com.The optimal portfolio is constructed by comparing the Excess Return to Beta (ERB) with the cut-off rate (C*) for each model. Risk measurement and volatility testing include stationarity tests, normality tests, heteroskedasticity tests, and volatility estimation using historical volatility and EWMA methods. The optimal portfolio is constructed by comparing the Excess Return to Beta (ERB) with the cut-off rate (C*) for each model. Risk measurement and volatility testing include stationarity tests (Augmented Dickey-Fuller and KPSS), normality tests (Kolmogorov-Smirnov), heteroskedasticity tests (Breusch-Pagan), and volatility estimation using historical volatility and EWMA methods. The results show that SIM outperforms MIM significantly, with the SIM optimal portfolio consisting of 7 stocks (UNTR 32.93%, ASII 30.84%, UNVR 12.80%, GGRM 9.03%, TLKM 5.92%, INTP 4.91%, HMSP 3.57%) yielding an expected return of 60.63% per annum with a portfolio risk of 17.01% and Sharpe Ratio of 0.201. In contrast, MIM produces only 5 stocks with negative expected return (-57.55% p.a.), higher risk (25.14%), and negative Sharpe Ratio (-0.160). This study demonstrates that for the IDX High Dividend 20 index during the observed period, the simpler SIM approach provides superior risk-adjusted returns compared to the more complex MIM approach.

Tren investasi di pasar saham syariah Indonesia mengalami peningkatan dari tahun 2015 sampai dengan 2017. Peningkatan ini juga harus diimbangi dengan sikap investor yang mampu memilih kombinasi saham terbaik dengan tingkat pengembalian dan risiko yang terukur melalui portofolio optimal. Tujuan penelitian ini adalah untuk menghitung portofolio optimal saham syariah Jakarta Islamic Index menggunakan Model Markowitz dengan preferensi risiko terendah, Model Markowitz dengan sharpe ratio optimal, dan Single Index Model. Analisis kemudian dilakukan untuk membandingkan tingkat pengembalian yang diharapkan dan tingkat risiko portofolio yang terbentuk dari model tersebut, dan memberikan rekomendasi portofolio optimal kepada investor yang dapat dijadikan sebagai bahan pertimbangan pengambilan keputusan dalam berinvestasi pada saham syariah Jakarta Islamic Index. Penelitian ini menggunakan data harga saham harian, data dividen, IHSG, dan data sukuk. Pemilihan 18 objek saham diperoleh dengan menggunakan metode purposive sampling. Berdasarkan hasil perhitungan, portofolio optimal diperoleh menggunakan model Markowitz dengan sharpe ratio optimal yang menghasilkan kombinasi saham terbaik dengan tingkat pengembalian yang diharapkan dan tingkat risiko sebesar 33,74 persen dan 22 persen dalam setahun.

The target of statistical analyses for industrial accident occurrence is to provide various basic information for the decision making on the policy of loss prevention or risk management. For this purpose, it is required that the characterizing and evaluating of the potential risk of accident occurrence could be performed from the results of statistical analyses. This paper proposes a new statistical technique which can give a quantitative index to characterize the potential risk of industrial accident occurrence for many engineering systems. An approach taken in this study is based on the concept of the risk curve, in which the relationship between exceedance cumulative0frequencies and their corresponding magnitude of consequence for hazardous events is described in log-log scale. The representation of the risk for accident occurrence has been examined with the definition of risks considered by Kalpan and Garrick, and the result showed that the risk curves have been clarified to be of characterizing the risk of hazardous events. Furthermore, using a lot of collected actual accident data it was found that the risk curve can be essentially expressed with a mathematical form uniquely determined by one distribution parameter. This parameter characterizing the risk curve means the index as a measure of risk for accident occurrences. It was concluded that a possible method for statistically assessing risks of accident occurrence adopts this index (safety index). Finally, the application of the proposed methodolgy to risk evaluation for damages of equipments and materials will be presented

This paper discusses and analyzes risk measure properties in order to understand how a risk measure has to be used to optimize the investor's portfolio choices. In particular, we distinguish between two admissible classes of risk measures proposed in the portfolio literature: safety-risk measures and dispersion measures. We study and describe how the risk could depend on other distributional parameters. Then, we examine and discuss the differences between statistical parametric models and linear fund separation ones. Finally, we propose an empirical comparison among three different portfolio choice models which depend on the mean, on a risk measure, and on a skewness parameter. Thus, we assess and value the impact on the investor's preferences of three different risk measures even considering some derivative assets among the possible choices.

THE ETHICAL DRUG industry has been under continuous study by governmental investigators and academic researchers for some time. The focal point of many of these studies is the industry's relatively high rate of return on investment (ROI). High rates are often cited as an indication, if not proof, of noncompetitive behavior. However, there is little agreement regarding the definition of ROI, the determinants of ROI, and the proper method for making inter-industry ROI comparisons. These issues were examined and a model was developed to study the ethical drug industry's return on investment. Regression techniques were utilized to test the investment and structural characteristics as potential determinants of ROT. The hypothesized association with ROI was supported for the two risk measures and for growth in demand but rejected for the concentration ratio, average company size, and R and D intensity. The three measures of investment characteristics were combined into a cross-sectional, multiple regression equation giving a model of ROI which was used to study the drug industry's rate of return. Data for the industry were introduced into the model to obtain a forecast of rate of return with variance, skewness, and growth held constant. Comparing the forecast with the observed rate showed observed ethical drug industry average ROI to be below the rate that could result given the particular set of investment characteristics exhibited by the drug industry sample. Therefore, the hypothesis was accepted that ethical drug industry average ROI was the same as allmanufacturing industries average ROI after consideration of investment characteristics. There are several possible explanations for why this model can explain statistically the drug industry ROI: First, data were utilized only for firms primarily engaged in the manufacture of ethical drug products rather than data for both ethical and proprietary drug firms. Second, more recent data may reflect changed economic relationships, both within the drug industry and between the drug and other industries. Third, the model formulated included more variables than prior models. Fourth, explicit consideration was made of possible statistical errors in both the regression equation and in the ROI forecast.

In this paper the concept of quantile-based optimal portfolio selection is introduced and a specific portfolio connected to it, the conditional value-of-return (CVoR) portfolio, is proposed. The CVoR is defined as the mean excess return or the conditional value-at-risk (CVaR) of the return distribution. The portfolio selection consists solely of quantile-based risk and return measures. Financial institutions that work in the context of Basel 4 use CVaR as a risk measure. In this regulatory framework sufficient and necessary conditions for optimality of the CVoR portfolio are provided under a general distributional assumption. Moreover, it is shown that the CVoR portfolio is mean-variance efficient when the returns are assumed to follow an elliptically contoured distribution. Under this assumption the closed-form expression for the weights and characteristics of the CVoR portfolio are obtained. Finally, the introduced methods are illustrated in an empirical study based on monthly data of returns on stocks included in the S&P index. It is shown that the new portfolio selection strategy outperforms several alternatives in terms of the final investor wealth.

A new approach in multi-objective evolutionary optimization is decomposition. Decomposition is a basic method in old multi-objective optimization which in evolutionary multiobjective optimization, has not been widely used. Using this method, a multi-objective optimization problem is converted into a number of scalar subproblems, and all the subproblems are simultaneously optimized. In this paper, the performance and efficiency of the algorithm MOEA/D (multi-objective evolutionary algorithm based on decomposition) with the performance of two algorithms NSGA-II and MOPSO (evolution optimization methods based on dominance) for solving constrained portfolio optimization in Tehran Stock Exchange, has been compared. Portfolio return and its risk, has been considered as the optimization objectives and CvaR has been considered as a risk measure. The results indicate the high potential of these algorithms for constrained portfolio optimization. Also, the results indicate that the optimization algorithm based on decomposition has lower computational complexity, and Pareto front is more extensive than the other two methods. (Abstract)

On Dynamic Measures of Risk