scholarly journals Evaluating Various Portfolio Optimization Strategies using High-Dimensional Covariance Matrix Estimators

2020 ◽  
Vol 9 (6) ◽  
pp. 64-67
Keyword(s):  
Portfolio Optimization ◽  
Covariance Matrix ◽  
Global Minimum ◽  
Evaluation Studies ◽  
Minimum Variance ◽  
Portfolio Allocation ◽  
New Strategy ◽  
Rotationally Invariant ◽  
Diversified Portfolio ◽  
Allocation Strategies

We compare the performance of multiple covariance matrix estimators for the purpose of portfolio optimization. This evaluation studies the ability of estimators like Sample Based Estimator (SCE), Ledoit-Wolf Estimator (LWE), and Rotationally Invariant Estimators (RIE) to estimate covariance matrix and their competency in fulfilling the objectives of various portfolio allocation strategies. In this paper, we have captured the effectiveness of strategies such as Global Minimum Variance (GMVP) and Most-Diversified Portfolio (MDP) to produce optimal portfolios. Additionally, we also propose a new strategy inspired from MDP: Most-Diversified Portfolio (MMDP), that enables diversification upon minimizing risk. Empirical evaluations show that by and large, MMDP furnishes the maximum returns. LWE are relatively more robust than SCE and RIE but RIE performs better under certain conditions.

scholarly journals Online Portfolio Optimization with Exponential Gradient and Time Varying CAPM

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
João Daniel Madureira Yamim ◽  
Carlos Cristiano Hasenclever Borges ◽  
Yuri Resende Fonseca ◽  
Raul Fonseca Neto
Keyword(s):  
Portfolio Optimization ◽  
Portfolio Allocation ◽  
Optimization Techniques ◽  
Gradient Algorithm ◽  
Time Varying ◽  
Dynamic Learning ◽  
Best Constant ◽  
Dow Jones Industrial Average ◽  
Online Portfolio ◽  
Allocation Strategies

Since Harry Markowitz's seminal work in 1952, which initiated modern portfolio theory, portfolio allocation strategies have been intensely discussed in the literature. With the development of online optimization techniques, dynamic learning algorithms have proven to be an effective approach to build portfolios. The purpose of this paper was to implement a new version of the Exponential Gradient algorithm in which important information about the risk of stocks are considered in the algorithm's projection step. The portfolios built were compared with the Dow Jones Industrial Average Index (DJIA) and Best Constant Rebalanced Portfolio (BCRP). We used DJIA data from January 2000 to December 2017 with daily observations. The EG beta algorithm outperformed the DJIA in all tests performed, and it was very close to BCRP in periods of market upturn and was able to outperform it in downturns.

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.  

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

scholarly journals Shrinking the Variance-Covariance Matrix: Simpler is Better

2016 ◽  
Vol 21 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Muhammad Husnain ◽  
Arshad Hassan ◽  
Eric Lamarque
Keyword(s):  
Root Mean Square Error ◽  
Covariance Matrix ◽  
Mean Square Error ◽  
Minimum Variance ◽  
Factor Models ◽  
The Philippines ◽  
Risk Profile ◽  
Additional Benefit ◽  
Mean Square ◽  
Weighted Portfolio

This study focuses on the estimation of the covariance matrix as an input to portfolio optimization. We compare 12 covariance estimators across four categories – conventional methods, factor models, portfolios of estimators and the shrinkage approach – applied to five emerging Asian economies (India, Indonesia, Pakistan, the Philippines and Thailand). We find that, in terms of the root mean square error and risk profile of minimum variance portfolios, investors gain no additional benefit from using the more complex shrinkage covariance estimators over the simpler, equally weighted portfolio of estimators in the sample countries.

Sign in / Sign up

Export Citation Format

Share Document