• Title/Summary/Keyword: Portfolio Optimization

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OPTIMAL PORTFOLIO SELECTION UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES

  • KIM, MI-HYUN;KIM, JEONG-HOON;YOON, JI-HUN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.4
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    • pp.417-428
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    • 2015
  • Although, in general, the random fluctuation of interest rates gives a limited impact on portfolio optimization, their stochastic nature may exert a significant influence on the process of selecting the proportions of various assets to be held in a given portfolio when the stochastic volatility of risky assets is considered. The stochastic volatility covers a variety of known models to fit in with diverse economic environments. In this paper, an optimal strategy for portfolio selection as well as the smoothness properties of the relevant value function are studied with the dynamic programming method under a market model of both stochastic volatility and stochastic interest rates.

Diversification, performance and optimal business mix of insurance portfolios

  • Kim, Hyun Tae
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.6
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    • pp.1503-1520
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    • 2013
  • For multi-line insurance companies, allocating the risk capital to each line is a widely-accepted risk management exercise. In this article we consider several applications of the Euler capital allocation. First, we propose visual tools to present the diversification and the line-wise performance for a given loss portfolio so that the risk managers can understand the interactions among the lines. Secondly, on theoretical side, we prove that the Euler allocation is the directional derivative of the marginal or incremental allocation method, an alternative capital allocation rule in the literature. Lastly, we establish the equivalence between the mean-shortfall optimization and the RORAC optimization when the risk adjusted capital is the expected shortfall, and show how to construct the optimal insurance business mix that maximizes the portfolio RORAC. An actual loss sample of an insurance portfolio is used for numerical illustrations.

Portfolio optimization strategy based on financial ratios (재무비율을 활용한 포트폴리오 최적화 전략)

  • Choi, Jung Yong;Kim, Jiwoo;Oh, Kyong Joo
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.6
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    • pp.1481-1500
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    • 2017
  • This study examines the stability and excellence of portfolio investment strategies based on the accounting information of the Korean stock market. In the process of constructing the portfolio, various combinations of financial ratios are used to select the stocks with high expected return and to measure their performance. We also tried to improve our investment performance by using genetic algorithm optimization. The results of this study show that portfolio strategies using accounting information are effective for investment decision making and can achieve high investment performance. We also verify that portfolio strategy using genetic algorithms can be effective for investment decision making.

ASYMPTOTIC ANALYSIS FOR PORTFOLIO OPTIMIZATION PROBLEM UNDER TWO-FACTOR HESTON'S STOCHASTIC VOLATILITY MODEL

  • Kim, Jai Heui;Veng, Sotheara
    • East Asian mathematical journal
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    • v.34 no.1
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    • pp.1-16
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    • 2018
  • We study an optimization problem for hyperbolic absolute risk aversion (HARA) utility function under two-factor Heston's stochastic volatility model. It is not possible to obtain an explicit solution because our financial market model is complicated. However, by using asymptotic analysis technique, we find the explicit forms of the approximations of the optimal value function and the optimal strategy for HARA utility function.

An Empirical Study on Statistical Optimization Model for the Portfolio Construction of Sponsored Search Advertising(SSA) (키워드검색광고 포트폴리오 구성을 위한 통계적 최적화 모델에 대한 실증분석)

  • Yang, Hognkyu;Hong, Juneseok;Kim, Wooju
    • Journal of Intelligence and Information Systems
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    • v.25 no.2
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    • pp.167-194
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    • 2019
  • This research starts from the four basic concepts of incentive incompatibility, limited information, myopia and decision variable which are confronted when making decisions in keyword bidding. In order to make these concept concrete, four framework approaches are designed as follows; Strategic approach for the incentive incompatibility, Statistical approach for the limited information, Alternative optimization for myopia, and New model approach for decision variable. The purpose of this research is to propose the statistical optimization model in constructing the portfolio of Sponsored Search Advertising (SSA) in the Sponsor's perspective through empirical tests which can be used in portfolio decision making. Previous research up to date formulates the CTR estimation model using CPC, Rank, Impression, CVR, etc., individually or collectively as the independent variables. However, many of the variables are not controllable in keyword bidding. Only CPC and Rank can be used as decision variables in the bidding system. Classical SSA model is designed on the basic assumption that the CPC is the decision variable and CTR is the response variable. However, this classical model has so many huddles in the estimation of CTR. The main problem is the uncertainty between CPC and Rank. In keyword bid, CPC is continuously fluctuating even at the same Rank. This uncertainty usually raises questions about the credibility of CTR, along with the practical management problems. Sponsors make decisions in keyword bids under the limited information, and the strategic portfolio approach based on statistical models is necessary. In order to solve the problem in Classical SSA model, the New SSA model frame is designed on the basic assumption that Rank is the decision variable. Rank is proposed as the best decision variable in predicting the CTR in many papers. Further, most of the search engine platforms provide the options and algorithms to make it possible to bid with Rank. Sponsors can participate in the keyword bidding with Rank. Therefore, this paper tries to test the validity of this new SSA model and the applicability to construct the optimal portfolio in keyword bidding. Research process is as follows; In order to perform the optimization analysis in constructing the keyword portfolio under the New SSA model, this study proposes the criteria for categorizing the keywords, selects the representing keywords for each category, shows the non-linearity relationship, screens the scenarios for CTR and CPC estimation, selects the best fit model through Goodness-of-Fit (GOF) test, formulates the optimization models, confirms the Spillover effects, and suggests the modified optimization model reflecting Spillover and some strategic recommendations. Tests of Optimization models using these CTR/CPC estimation models are empirically performed with the objective functions of (1) maximizing CTR (CTR optimization model) and of (2) maximizing expected profit reflecting CVR (namely, CVR optimization model). Both of the CTR and CVR optimization test result show that the suggested SSA model confirms the significant improvements and this model is valid in constructing the keyword portfolio using the CTR/CPC estimation models suggested in this study. However, one critical problem is found in the CVR optimization model. Important keywords are excluded from the keyword portfolio due to the myopia of the immediate low profit at present. In order to solve this problem, Markov Chain analysis is carried out and the concept of Core Transit Keyword (CTK) and Expected Opportunity Profit (EOP) are introduced. The Revised CVR Optimization model is proposed and is tested and shows validity in constructing the portfolio. Strategic guidelines and insights are as follows; Brand keywords are usually dominant in almost every aspects of CTR, CVR, the expected profit, etc. Now, it is found that the Generic keywords are the CTK and have the spillover potentials which might increase consumers awareness and lead them to Brand keyword. That's why the Generic keyword should be focused in the keyword bidding. The contribution of the thesis is to propose the novel SSA model based on Rank as decision variable, to propose to manage the keyword portfolio by categories according to the characteristics of keywords, to propose the statistical modelling and managing based on the Rank in constructing the keyword portfolio, and to perform empirical tests and propose a new strategic guidelines to focus on the CTK and to propose the modified CVR optimization objective function reflecting the spillover effect in stead of the previous expected profit models.

Linear programming models using a Dantzig type risk for portfolio optimization (Dantzig 위험을 사용한 포트폴리오 최적화 선형계획법 모형)

  • Ahn, Dayoung;Park, Seyoung
    • The Korean Journal of Applied Statistics
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    • v.35 no.2
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    • pp.229-250
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    • 2022
  • Since the publication of Markowitz's (1952) mean-variance portfolio model, research on portfolio optimization has been conducted in many fields. The existing mean-variance portfolio model forms a nonlinear convex problem. Applying Dantzig's linear programming method, it was converted to a linear form, which can effectively reduce the algorithm computation time. In this paper, we proposed a Dantzig perturbation portfolio model that can reduce management costs and transaction costs by constructing a portfolio with stable and small (sparse) assets. The average return and risk were adjusted according to the purpose by applying a perturbation method in which a certain part is invested in the existing benchmark and the rest is invested in the assets proposed as a portfolio optimization model. For a covariance estimation, we proposed a Gaussian kernel weight covariance that considers time-dependent weights by reflecting time-series data characteristics. The performance of the proposed model was evaluated by comparing it with the benchmark portfolio with 5 real data sets. Empirical results show that the proposed portfolios provide higher expected returns or lower risks than the benchmark. Further, sparse and stable asset selection was obtained in the proposed portfolios.

A LINE SEARCH TRUST REGION ALGORITHM AND ITS APPLICATION TO NONLINEAR PORTFOLIO PROBLEMS

  • Gu, Nengzhu;Zhao, Yan;Gao, Yan
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.233-243
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    • 2009
  • This paper concerns an algorithm that combines line search and trust region step for nonlinear optimization problems. Unlike traditional trust region methods, we incorporate the Armijo line search technique into trust region method to solve the subproblem. In addition, the subproblem is solved accurately, but instead solved by inaccurate method. If a trial step is not accepted, our algorithm performs the Armijo line search from the failed point to find a suitable steplength. At each iteration, the subproblem is solved only one time. In contrast to interior methods, the optimal solution is derived by iterating from outside of the feasible region. In numerical experiment, we apply the algorithm to nonlinear portfolio optimization problems, primary numerical results are presented.

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A NEW CLASS OF NONLINEAR CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION MODELS AND ITS APPLICATION IN PORTFOLIO SELECTION

  • Malik, Maulana;Sulaiman, Ibrahim Mohammed;Mamat, Mustafa;Abas, Siti Sabariah;Sukono, Sukono
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.4
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    • pp.811-837
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    • 2021
  • In this paper, we propose a new conjugate gradient method for solving unconstrained optimization models. By using exact and strong Wolfe line searches, the proposed method possesses the sufficient descent condition and global convergence properties. Numerical results show that the proposed method is efficient at small, medium, and large dimensions for the given test functions. In addition, the proposed method was applied to solve practical application problems in portfolio selection.

Optimum Risk-Adjusted Islamic Stock Portfolio Using the Quadratic Programming Model: An Empirical Study in Indonesia

  • MUSSAFI, Noor Saif Muhammad;ISMAIL, Zuhaimy
    • The Journal of Asian Finance, Economics and Business
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    • v.8 no.5
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    • pp.839-850
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    • 2021
  • Risk-adjusted return is believed to be one of the optimal parameters to determine an optimum portfolio. A risk-adjusted return is a calculation of the profit or potential profit from an investment that takes into account the degree of risk that must be accepted to achieve it. This paper presents a new procedure in portfolio selection and utilizes these results to optimize the risk level of risk-adjusted Islamic stock portfolios. It deals with the weekly close price of active issuers listed on Jakarta Islamic Index Indonesia for a certain time interval. Overall, this paper highlights portfolio selection, which includes determining the number of stocks, grouping the issuers via technical analysis, and selecting the best risk-adjusted return of portfolios. The nominated portfolio is modeled using Quadratic Programming (QP). The result of this study shows that the portfolio built using the lowest Value at Risk (VaR) outperforms the market proxy on a risk-adjusted basis of M-squared and was chosen as the best portfolio that can be optimized using QP with a minimum risk of 2.86%. The portfolio with the lowest beta, on the other hand, will produce a minimum risk that is nearly 60% lower than the optimal risk-adjusted return portfolio. The results of QP are well verified by a heuristic optimizer of fmincon.

Shrinkage Model Selection for Portfolio Optimization on Vietnam Stock Market

  • NGUYEN, Nhat;NGUYEN, Trung;TRAN, Tuan;MAI, An
    • The Journal of Asian Finance, Economics and Business
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    • v.7 no.9
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    • pp.135-145
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    • 2020
  • This paper provides the practical application of a linear shrinkage framework on Vietnam stock market. The cumulative data points observed in this analysis are 468 weeks from January 2011 to December 2019. All the companies listed on Ho Chi Minh City Stock Exchange (HOSE), except the companies under two years period from Initial Public Offering (IPO), are considered. The cumulative number of stocks picked is therefore 350 companies. The VNINDEX, which is the Vietnam Stock Index, is used as a reference index for shrinking to a single-index model. The empirical results show that the shrinkage of covariance matrix for portfolio optimization gives the promising results for the investors on Vietnam stock market. The shrinkage method helps the investors to produce the optimal portfolio in the sense of having higher profit with lower levels of risk compared to the portfolio of the traditional SCM method. Moreover, the portfolio turnover of shrinkage method is always kept at low magnitudes, and this makes the shrinkage portfolios save much transaction costs and reduce the liquidity risks in the trading process. In addition, the ability of shrinkage method in making profit is once again confirmed by the Alpha coefficient that achieves a high positive value.