• Title/Summary/Keyword: markowitz

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Optimization Methodology for Sales and Operations Planning by Stochastic Programming under Uncertainty : A Case Study in Service Industry (불확실성하에서의 확률적 기법에 의한 판매 및 실행 계획 최적화 방법론 : 서비스 산업)

  • Hwang, Seon Min;Song, Sang Hwa
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.39 no.4
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    • pp.137-146
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    • 2016
  • In recent years, business environment is faced with multi uncertainty that have not been suffered in the past. As supply chain is getting expanded and longer, the flow of information, material and production is also being complicated. It is well known that development service industry using application software has various uncertainty in random events such as supply and demand fluctuation of developer's capcity, project effective date after winning a contract, manpower cost (or revenue), subcontract cost (or purchase), and overrun due to developer's skill-level. This study intends to social contribution through attempts to optimize enterprise's goal by supply chain management platform to balance demand and supply and stochastic programming which is basically applied in order to solve uncertainty considering economical and operational risk at solution supplier. In Particular, this study emphasizes to determine allocation of internal and external manpower of developers using S&OP (Sales & Operations Planning) as monthly resource input has constraint on resource's capability that shared in industry or task. This study is to verify how Stochastic Programming such as Markowitz's MV (Mean Variance) model or 2-Stage Recourse Model is flexible and efficient than Deterministic Programming in software enterprise field by experiment with process and data from service industry which is manufacturing software and performing projects. In addition, this study is also to analysis how profit and labor input plan according to scope of uncertainty is changed based on Pareto Optimal, then lastly it is to enumerate limitation of the study extracted drawback which can be happened in real business environment and to contribute direction in future research considering another applicable methodology.

A Study on Construction of an Optimal Fossil Fuel Mix: A Portfolio-Based Approach (평균-분산 모형을 이용한 화석에너지원 소비조합 구성에 관한 연구)

  • Cha, Kyungsoo
    • Environmental and Resource Economics Review
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    • v.20 no.2
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    • pp.335-356
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    • 2011
  • In this paper, we attempted to suggest a way to evaluate appropriateness and efficiency for the energy consumption structure. For this, based on Markowitz (1952)' mean-variance portfolio model, we constructed an optimal fossil fuel mix. In constructing the optimal mix, we first defined returns on fossil fuels (oil, coal and natural gas) as TOE (Ton of Oil Equivalent) per $1. Then, by using the dynamic latent common factor model, we decomposed the growth rates of the returns on each fossil fuel into two parts : the common part and the idiosyncratic part. Finally, based on the results from the dynamic latent common factor model, we constructed the optimal fossil fuel mix implied by the mean-variance portfolio model. Our results indicate that for the fossil fuel mix to be on the efficient frontier, it is crucial to reduce oil consumption as low as possible. Moreover, our results imply that it is more efficient to increase natural gas consumption rather than coal consumption in reducing oil consumption. These results are in line with the strategies for the future energy consumption structure pursued by Korea and indicate that reduction in oil use can improve overall efficiency in energy consumption.

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Conditional Value-at-Risk Optimization for Conversion of Convertible Bonds (전환사채 주식전환을 위한 조건부 VaR 최적화)

  • Park, Koo-Hyun;Shim, Eun-Tak
    • Korean Management Science Review
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    • v.28 no.2
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    • pp.1-16
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    • 2011
  • In this study we suggested two optimization models to answer a question from an investor standpoint : how many convertible bonds should one convert, and how many keep? One model minimizes certain risk to the minimum required expected return, the other maximizes the expected return subject to the maximum acceptable risk. In comparison with Markowitz portfolio models, which use the variance of return, our models used Conditional Value-at-Risk(CVaR) for risk measurement. As a coherent measurement, CVaR overcomes the shortcomings of Value-at-Risk(VaR). But there are still difficulties in solving CVaR including optimization models. For this reason, we adopted Rockafellar and Uryasev's[18, 19] approach. Then we could approximate the models as linear programming problems with scenarios. We also suggested to extend the models with credit risk, and applied examples of our models to Hynix 207CB, a convertible bond issued by the global semiconductor company Hynix.

Development of LPAKO : Software of Simplex Method for Liner Programming (단체법 프로그램 LPAKO 개발에 관한 연구)

  • 박순달;김우제;박찬규;임성묵
    • Korean Management Science Review
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    • v.15 no.1
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    • pp.49-62
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    • 1998
  • The purpose of this paper is to develope a large-scale simplex method program LPAKO. Various up-to-date techniques are argued and implemented. In LPAKO, basis matrices are stored in a LU factorized form, and Reid's method is used to update LU maintaining high sparsity and numerical stability, and further Markowitz's ordering is used in factorizing a basis matrix into a sparse LU form. As the data structures of basis matrix, Gustavson's data structure and row-column linked list structure are considered. The various criteria for reinversion are also discussed. The dynamic steepest-edge simplex algorithm is used for selection of an entering variable, and a new variation of the MINOS' perturbation technique is suggested for the resolution of degeneracy. Many preprocessing and scaling techniques are implemented. In addition, a new, effective initial basis construction method are suggested, and the criteria for optimality and infeasibility are suggested respectively. Finally, LPAKO is compared with MINOS by test results.

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상하분해 단체법에서 수정 Forrest-Tomlin 방법의 효율적인 구현

  • 김우제;임성묵;박순달
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1998.10a
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    • pp.63-66
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    • 1998
  • In the implementation of the simplex method program, the representation and the maintenance of basis matrix is very important, In the experimental study, we investigates Suhl's idea in the LU factorization and LU update of basis matrix. First, the triangularization of basis matrix is implemented and its efficiency is shown. Second, various technique in the dynamic Markowitz's ordering and threshold pivoting are presented. Third, modified Forrest-Tomlin LU update method exploiting sparsity is presented. Fourth, as a storage scheme of LU factors, Gustavson data structure is explained. Fifth, efficient timing of reinversion is developed. Finally, we show that modified Forrest-Tomlin method with Gustavson data structure is superior more than 30% to the Reid method with linked list data structure.

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Risk-based Optimal Transmission Expansion Planning (위험도기반 최적송전확장계획)

  • Son, Min-Kyun;Kim, Dong-Min;Kim, Jin-O
    • Proceedings of the KIEE Conference
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    • 2006.11a
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    • pp.393-395
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    • 2006
  • In competitive market, it is important to establish a plan of transmission expansion considering uncertainty of future generation and load behavior. For this reason, revised transmission expansion model is proposed in this paper. In the proposed model, information of predictable future condition are included in a cost function of transmission expansion investment. Also, to reduce risk of the investment, mean-variance Markowitz approach is added to the objective function of cost. By optimization programming, the most robust and the minimum cost plan can be obtained.

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The Optimal Mean-Variance Portfolio Formulation by Mathematical Planning (Mean-Variance 수리 계획을 이용한 최적 포트폴리오 투자안 도출)

  • Kim, Tai-Young
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.32 no.4
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    • pp.63-71
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    • 2009
  • The traditional portfolio optimization problem is to find an investment plan for securities with reasonable trade-off between the rate of return and the risk. The seminal work in this field is the mean-variance model by Markowitz, which is a quadratic programming problem. Since it is now computationally practical to solve the model, a number of alternative models to overcome this complexity have been proposed. In this paper, among the alternatives, we focus on the Mean Absolute Deviation (MAD) model. More specifically, we developed an algorithm to obtain an optimal portfolio from the MAD model. We showed mathematically that the algorithm can solve the problem to optimality. We tested it using the real data from the Korean Stock Market. The results coincide with our expectation that the method can solve a variety of problems in a reasonable computational time.

Stock Trading Model using Portfolio Optimization and Forecasting Stock Price Movement (포트폴리오 최적화와 주가예측을 이용한 투자 모형)

  • Park, Kanghee;Shin, Hyunjung
    • Journal of Korean Institute of Industrial Engineers
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    • v.39 no.6
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    • pp.535-545
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    • 2013
  • The goal of stock investment is earning high rate or return with stability. To accomplish this goal, using a portfolio that distributes stocks with high rate of return with less variability and a stock price prediction model with high accuracy is required. In this paper, three methods are suggested to require these conditions. First of all, in portfolio re-balance part, Max-Return and Min-Risk (MRMR) model is suggested to earn the largest rate of return with stability. Secondly, Entering/Leaving Rule (E/L) is suggested to upgrade portfolio when particular stock's rate of return is low. Finally, to use outstanding stock price prediction model, a model based on Semi-Supervised Learning (SSL) which was suggested in last research was applied. The suggested methods were validated and applied on stocks which are listed in KOSPI200 from January 2007 to August 2008.

Robo-Advisor Algorithm with Intelligent View Model (지능형 전망모형을 결합한 로보어드바이저 알고리즘)

  • Kim, Sunwoong
    • Journal of Intelligence and Information Systems
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    • v.25 no.2
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    • pp.39-55
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    • 2019
  • Recently banks and large financial institutions have introduced lots of Robo-Advisor products. Robo-Advisor is a Robot to produce the optimal asset allocation portfolio for investors by using the financial engineering algorithms without any human intervention. Since the first introduction in Wall Street in 2008, the market size has grown to 60 billion dollars and is expected to expand to 2,000 billion dollars by 2020. Since Robo-Advisor algorithms suggest asset allocation output to investors, mathematical or statistical asset allocation strategies are applied. Mean variance optimization model developed by Markowitz is the typical asset allocation model. The model is a simple but quite intuitive portfolio strategy. For example, assets are allocated in order to minimize the risk on the portfolio while maximizing the expected return on the portfolio using optimization techniques. Despite its theoretical background, both academics and practitioners find that the standard mean variance optimization portfolio is very sensitive to the expected returns calculated by past price data. Corner solutions are often found to be allocated only to a few assets. The Black-Litterman Optimization model overcomes these problems by choosing a neutral Capital Asset Pricing Model equilibrium point. Implied equilibrium returns of each asset are derived from equilibrium market portfolio through reverse optimization. The Black-Litterman model uses a Bayesian approach to combine the subjective views on the price forecast of one or more assets with implied equilibrium returns, resulting a new estimates of risk and expected returns. These new estimates can produce optimal portfolio by the well-known Markowitz mean-variance optimization algorithm. If the investor does not have any views on his asset classes, the Black-Litterman optimization model produce the same portfolio as the market portfolio. What if the subjective views are incorrect? A survey on reports of stocks performance recommended by securities analysts show very poor results. Therefore the incorrect views combined with implied equilibrium returns may produce very poor portfolio output to the Black-Litterman model users. This paper suggests an objective investor views model based on Support Vector Machines(SVM), which have showed good performance results in stock price forecasting. SVM is a discriminative classifier defined by a separating hyper plane. The linear, radial basis and polynomial kernel functions are used to learn the hyper planes. Input variables for the SVM are returns, standard deviations, Stochastics %K and price parity degree for each asset class. SVM output returns expected stock price movements and their probabilities, which are used as input variables in the intelligent views model. The stock price movements are categorized by three phases; down, neutral and up. The expected stock returns make P matrix and their probability results are used in Q matrix. Implied equilibrium returns vector is combined with the intelligent views matrix, resulting the Black-Litterman optimal portfolio. For comparisons, Markowitz mean-variance optimization model and risk parity model are used. The value weighted market portfolio and equal weighted market portfolio are used as benchmark indexes. We collect the 8 KOSPI 200 sector indexes from January 2008 to December 2018 including 132 monthly index values. Training period is from 2008 to 2015 and testing period is from 2016 to 2018. Our suggested intelligent view model combined with implied equilibrium returns produced the optimal Black-Litterman portfolio. The out of sample period portfolio showed better performance compared with the well-known Markowitz mean-variance optimization portfolio, risk parity portfolio and market portfolio. The total return from 3 year-period Black-Litterman portfolio records 6.4%, which is the highest value. The maximum draw down is -20.8%, which is also the lowest value. Sharpe Ratio shows the highest value, 0.17. It measures the return to risk ratio. Overall, our suggested view model shows the possibility of replacing subjective analysts's views with objective view model for practitioners to apply the Robo-Advisor asset allocation algorithms in the real trading fields.

Diversified Investment of Commercial Real Estate Assets - Focused on Office Building and Retail Real Estate Markets in Seoul - (상업용 부동산 시장의 분산투자에 관한 연구 - 서울지역의 오피스 빌딩 및 소매용 부동산 시장을 중심으로 -)

  • Park, Jongkwon;Jun, Jaebum
    • Korean Journal of Construction Engineering and Management
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    • v.16 no.6
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    • pp.144-155
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    • 2015
  • This paper is to understand investment's efficiency and performance of commercial real estate assets diversified by use and district. To do so, this paper divides two different commercial real estate markets(office build market and retail real estate market) in Seoul city by district into "GBD(Gangnam Business District), YBD(Yeouido Business District), and CBD(Central Business District)" and "GBD(Gangnam Business District), SBD(Shinchon Business District), and CBD(Central Business District)" respectively, configures these districts each other to structure portfolios as its portion varies based on Markowitz's Mean-Variance principle, and looks at risk-return relationship of portfolios to find out efficiency, performance, and optimal investment chosen based upon Sharpe's Performance Index. As a result, the portfolio configured by "10 to 30% of office building asset at CBD" and "70 to 90% of retail real estate asset at CBD" is shown to be the most optimal, suggesting the highest quarterly Sharpe's performance index of 2.7118~2.7776 with quarterly rate of return of 1.826%~1.838% and quarterly standard deviation of 0.573~0.589. Furthermore, it is obvious that diversified portfolio configured by use(office-retail) shows better investment performance than that by district with same type of asset(office-office or retail-retail). Finally, results driven from this research will play an important role to stimulate real estate and construction markets through enlarging ideas as to diversified investment by use and district on real estate indirect investment products.