scholarly journals Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan Dengan Keterbatasan Manusia Dalam Memprediksi Masa Depan Dalam Perspektif Al-Qur`an

2012 ◽  
Vol 1 (1) ◽  
pp. 27
Author(s):  
Noor Saif Muhammad Mussafi
Keyword(s):  
Quadratic Programming ◽  
Geometric Mean ◽  
Minimum Variance ◽  
Arithmetic Mean ◽  
Theoretical Frameworks ◽  
Expected Return ◽  
Research And Practice ◽  
Graphic Analysis ◽  
Minimum Variance Portfolio ◽  
Mean Variance

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio  produces a convex quadratic programming, that is minimizing the objective function  𝑄𝑥with constraints𝜇 𝑇 𝑥 ≥ 𝑅and𝐴𝑥 = 𝑏. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis.

Mean-Variance Analysis

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Global Minimum ◽  
Minimum Variance ◽  
Variance Analysis ◽  
Affine Function ◽  
Market Portfolio ◽  
Minimum Variance Portfolio ◽  
The Mean ◽  
Global Minimum Variance Portfolio ◽  
Mean Variance

The mean‐variance frontier is characterized with and without a risk‐free asset. The global minimum variance portfolio and tangency portfolio are defined, and two‐fund spanning is explained. The frontier is characterized in terms of the return defined from the SDF that is in the span of the assets. This is related to the Hansen‐Jagannathan bound. There is an SDF that is an affine function of a return if and only if the return is on the mean‐variance frontier. Separating distributions are defined and shown to imply two‐fund separation and mean‐variance efficiency of the market portfolio.

scholarly journals An analysis of a mean-variance enhanced index tracking problem with weights constraints

2018 ◽  
Vol 15 (4) ◽  
pp. 183-192
Author(s):  
Wanderlei Lima de Paulo ◽  
Marta Ines Velazco Fontova ◽  
Renato Canil de Souza
Keyword(s):  
Asset Allocation ◽  
Global Minimum ◽  
Minimum Variance ◽  
Index Tracking ◽  
Tracking Problem ◽  
Market Index ◽  
Satisfactory Performance ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Mean Variance

In this paper, the authors deal with a mean-variance enhanced index tracking (EIT) problem with weights constraints. Using a shrinkage approach, they show that constructing the constrained EIT portfolio is equivalent to constructing the unconstrained EIT portfolio. This equivalence allows to study the effect of weights constraints on the covariance matrix and on the EIT portfolio. In general, the effects of weights constraints on the EIT portfolio are different from those observed in the case of global minimum variance portfolio. Finally, the authors present a numerical asset allocation example, where the S&P 500 index is used as the market index to be tracked using a portfolio composed of ten stocks, in which the constrained EIT portfolio shows a satisfactory performance when compared to the unconstrained case.

Markowitz Theory in Portfolio Optimization for Heavy Tailed Assets

2019 ◽  
Vol 1 (3) ◽  
pp. 1-14
Author(s):  
Wong Ghee Ching ◽  
Che Mohd Imran Che Taib
Keyword(s):  
Portfolio Optimization ◽  
Composite Index ◽  
Minimum Variance ◽  
Optimization Techniques ◽  
Expected Return ◽  
Markowitz Model ◽  
The Mean ◽  
Heavy Tailed ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper aims at solving an optimization problem in the presence of heavy tail behavior of financial assets. The question of minimizing risk subjected to a certain expected return or maximizing return for a given expected risk are two objective functions to be solved using Markowitz model. The Markowitz based strategies namely the mean variance portfolio, minimum variance portfolio and equally weighted portfolio are proposed in conjunction with mean and variance analysis of the portfolio. The historical prices of stocks traded at Bursa Malaysia are used for empirical analysis. We employed CAPM in order to investigate the performance of the Markowitz model which was benchmarked with risk adjusted KLSE Composite Index. We performed a backtesting study of portfolio optimization techniques defined under modern portfolio theory in order to find the optimal portfolio. Our findings showed that the mean variance portfolio outperformed the other two strategies in terms of performance of investment for heavy tailed assets.

MEAN-VARIANCE APPROXIMATIONS TO THE GEOMETRIC MEAN

2012 ◽  
Vol 07 (01) ◽  
pp. 1250001 ◽  
Author(s):  
HARRY MARKOWITZ
Keyword(s):  
Geometric Mean ◽  
Equity Markets ◽  
Arithmetic Mean ◽  
The Other ◽  
Mean And Variance ◽  
Asset Classes ◽  
Real Returns ◽  
Mean Variance

This paper uses two databases to test the ability of six functions of arithmetic mean and variance to approximate geometric mean return or, equivalently, Bernoulli's expected log utility. The two databases are: (1) a database of returns on frequently used asset classes, and (2) that of real returns on the equity markets of sixteen countries, 1900–2000. Three of the functions of arithmetic mean and variance do quite well, even for return series with large losses. The other three do less well.

Study of the Portfolio Sensitivity of Combined Assets of Real Estate Indirect Investment Products

2019 ◽  
Vol 118 (8) ◽  
pp. 356-365
Author(s):  
Suk-Hyun Choi ◽  
Jong-Jin Kim
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Analysis ◽  
Real Estate ◽  
Price Index ◽  
Minimum Variance ◽  
Asset Portfolio ◽  
Minimum Variance Portfolio ◽  
Mean Variance ◽  
Input Ratio

This study constructed combined REITs and real estate funds in traditional portfolios and analyzed the inclusion ratio of efficient real estate indirect investment products through sensitivity analysis of profits and risks by input ratio. Methods/Statistical analysis: To measure the rate of profits and risks of the composite asset portfolio, Minimum Variance Portfolio and Optimal Risky Portfolio were drawn through mean-variance and sensitivity analysis was conducted on changes in the rates of risks and profits by the increase of the weight of real estate indirect investment products. Concrete variables consisted of KRX BOND, KOSPI, and Office (Seoul) Price Index; REITs TRUS Y7 in operation was used as the products; and real estate funds were set by combining HanwhaLasal Global Real Estate Funds.

scholarly journals Analisis Portofolio Investasi dengan Metode Multi Objektif

Jurnal Varian ◽  
2019 ◽  
Vol 3 (1) ◽  
pp. 6-12
Author(s):  
Gilang Primajati ◽  
Ahmad Zuli Amrullah ◽  
Ahmad Ahmad
Keyword(s):  
Minimum Variance ◽  
Optimal Portfolio ◽  
Risk Level ◽  
Risk Averse ◽  
Expected Return ◽  
Risky Assets ◽  
Variant Method ◽  
The Mean ◽  
Mean Variance ◽  
Constraint Method

In the formation of an efficient portfolio, many methods can be used. Of course with its own assumptions and advantages. In the process, reasonable investor assumptions tend to be risk averse. Investors who are risk averse are investors who, when faced with two investments with the same expected return, will choose an investment with a lower risk level. If an investor has several efficient portfolio choices, then the most optimal portfolio will be chosen. Optimal portfolio with mean-variance efficient portfolio criteria, investors only invest in risky assets. Investors do not include risk free assets in their portfolios. Mean-variance efficient portfolio is defined as a portfolio that has a minimum variance among all possible portfolio that can be formed, at the mean level of the same expected return. The mean variant method of the two constraints can be used as a basis in determining the optimal portfolio weight by minimizing the risk of portfolio return with two constraints. In this article the problem referred to is symbolized by lamda and beta. With this two-constraint method, the results obtained are more detailed so that they can describe the results of a sharper analysis for an investor.

Study of the Portfolio Sensitivity of Combined Assets of Real Estate Indirect Investment Products

2019 ◽  
Vol 118 (2) ◽  
pp. 27-34
Author(s):  
Suk-Hyun Choi ◽  
Jong-Jin Kim
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Analysis ◽  
Real Estate ◽  
Price Index ◽  
Minimum Variance ◽  
Asset Portfolio ◽  
Minimum Variance Portfolio ◽  
Mean Variance ◽  
Input Ratio

Background/Objectives: This study constructed combined REITs and real estate funds in traditional portfolios and analyzed the inclusion ratio of efficient real estate indirect investment products through sensitivity analysis of profits and risks by input ratio. Methods/Statistical analysis: To measure the rate of profits and risks of the composite asset portfolio, Minimum Variance Portfolio and Optimal Risky Portfolio were drawn through mean-variance and sensitivity analysis was conducted on changes in the rates of risks and profits by the increase of the weight of real estate indirect investment products. Concrete variables consisted of KRX BOND, KOSPI, and Office (Seoul) Price Index; REITs TRUS Y7 in operation was used as the products; and real estate funds were set by combining HanwhaLasal Global Real Estate Funds.

scholarly journals QUADRATIC PROGRAMMING: AN OPTIMIZATION TOOL FOR BUILDING GLOBAL MINIMUM VARIANCE PORTFOLIO WITH NO SHORT SALE

2021 ◽  
Vol 15 (2) ◽  
pp. 305-314
Author(s):  
Nurwahidah Nurwahidah
Keyword(s):  
Quadratic Programming ◽  
Portfolio Optimization ◽  
Global Minimum ◽  
Minimum Variance ◽  
Stock Market Index ◽  
Positive Weight ◽  
Short Sale ◽  
Markowitz Portfolio ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio

Quantitative method in portfolio selection is a fascinating issue to make a decision in investment. Portfolio optimization is a very important to manage investment risk. There are many papers dealing with the Markowitz portfolio model, but not all of the papers studied about positive weight portfolio or no short sale constrained portfolio. Positive weight portfolio describes that short sale is allowed for the investor. While, short sale is banned in a certain economic condition due to its ability in decreasing stock market index. Besides, Islamic capital market does not allow speculative transaction such as short selling. Hence, portfolio with no short sale constraint is needed. This study aims to build Global Minimum Variance Portfolio (GMVP) with no short sale constraint. The GMVP with positive asset allocation based on Markowitz model can be built by using quadratic programming with interior point method. The main theory applied in this research is Markowitz portfolio optimization model. Mean and variance of stocks closing price are two things that should be considered in this model. The result shows that the positive weight of GMVP includes 0% of ADRO shares; 2, 65% of ANTM shares; 0% of CTRA shares; 30,27% of EXCL shares; 37,21% of ICBP shares; 3,37% of INCO shares; 13,89% of KLBF shares; 0% of PGAS shares; and 12,61% of PTBA shares.  

On Statistics of Log-Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power

2012 ◽  
Vol E95-B (2) ◽  
pp. 647-650
Author(s):  
Ning WANG ◽  
Julian CHENG ◽  
Chintha TELLAMBURA
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Log Ratio
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