scholarly journals Técnicas Quantitativas de Otimização de Carteiras Aplicadas ao Mercado de Ações Brasileiro

2012 ◽  
Vol 10 (3) ◽  
pp. 369
Author(s):  
André Alves Portela Santos ◽  
Cristina Tessari
Keyword(s):  
Covariance Matrix ◽  
Minimum Variance ◽  
Short Selling ◽  
Optimization Techniques ◽  
Market Portfolio ◽  
Sample Covariance ◽  
Out Of Sample ◽  
Weighted Portfolio ◽  
Performance Statistics ◽  
Mean Variance

In this paper we assess the out-of-sample performance of two alternative quantitative portfolio optimization techniques - mean-variance and minimum variance optimization – and compare their performance with respect to a naive 1/N (or equally-weighted) portfolio and also to the market portfolio given by the Ibovespa. We focus on short selling-constrained portfolios and consider alternative estimators for the covariance matrices: sample covariance matrix, RiskMetrics, and three covariance estimators proposed by Ledoit and Wolf (2003), Ledoit and Wolf (2004a) and Ledoit and Wolf (2004b). Taking into account alternative portfolio re-balancing frequencies, we compute out-of-sample performance statistics which indicate that the quantitative approaches delivered improved results in terms of lower portfolio volatility and better risk-adjusted returns. Moreover, the use of more sophisticated estimators for the covariance matrix generated optimal portfolios with lower turnover over time.

Improving Minimum-Variance Portfolios by Alleviating Overdispersion of Eigenvalues

2019 ◽  
Vol 55 (8) ◽  
pp. 2700-2731
Author(s):  
Fangquan Shi ◽  
Lianjie Shu ◽  
Aijun Yang ◽  
Fangyi He
Keyword(s):  
Covariance Matrix ◽  
General Framework ◽  
Minimum Variance ◽  
Risk Minimization ◽  
Portfolio Risk ◽  
Computationally Efficient ◽  
Estimation Errors ◽  
Inverse Covariance Matrix ◽  
Sample Covariance ◽  
Out Of Sample

In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. Yet the eigenvalues of the sample covariance matrix are often overdispersed, leading to severe estimation errors in the inverse covariance matrix. To deal with this problem, we propose a general framework by shrinking the sample eigenvalues based on the Schatten norm. The proposed framework has the advantage of being computationally efficient as well as structure-free. The comparative studies show that our approach behaves reasonably well in terms of reducing out-of-sample portfolio risk and turnover.

scholarly journals Does GMVP Strategy Reduce Risk? A Global Asset Approach

2014 ◽  
Vol 30 (6) ◽  
pp. 1873
Author(s):  
Arben Zibri ◽  
Agim Kukeli
Keyword(s):  
Risk Reduction ◽  
Covariance Matrix ◽  
Minimum Variance ◽  
Portfolio Constraints ◽  
Stock Portfolios ◽  
Sample Covariance ◽  
Out Of Sample ◽  
Bond Portfolios ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio

<p>This paper studies the out of sample risk reduction of global minimum variance portfolio. The analysis are drown from the discussions of Jagannathan and Ma (2003) regarding the risk reduction in US stock portfolios using portfolio constraints. We estimate the covariance matrix using the sample covariance matrix approach and derive optimal minimum variance portfolios considering upper/lower bounds and no restrictions. Results are shown under different revision frequency and transaction costs assumed. The data used are monthly indices of stocks, bonds, gold oil and spreads from 1996 until 2013. Unconstrained GMVPs result in the lowest out of sample variance, while unconstrained GMVPs of global bond portfolios performs the best in terms of risk reduction. Diversification through global asset classes result in a better strategy than international stock diversification regarding risk, as suggested by the literature.</p>

FAST METHODS FOR LARGE-SCALE NON-ELLIPTICAL PORTFOLIO OPTIMIZATION

2014 ◽  
Vol 09 (02) ◽  
pp. 1440001 ◽  
Author(s):  
MARC S. PAOLELLA
Keyword(s):  
Portfolio Optimization ◽  
Large Scale ◽  
Asset Returns ◽  
Short Selling ◽  
Sharpe Ratio ◽  
Mixture Of Normals ◽  
Optimization Via Simulation ◽  
Fast Methods ◽  
Out Of Sample ◽  
Weighted Portfolio

Simple, fast methods for modeling the portfolio distribution corresponding to a non-elliptical, leptokurtic, asymmetric, and conditionally heteroskedastic set of asset returns are entertained. Portfolio optimization via simulation is demonstrated, and its benefits are discussed. An augmented mixture of normals model is shown to be superior to both standard (no short selling) Markowitz and the equally weighted portfolio in terms of out of sample returns and Sharpe ratio performance.

Improving Mean Variance Optimization through Sparse Hedging Restrictions

2015 ◽  
Vol 50 (6) ◽  
pp. 1415-1441 ◽  
Author(s):  
Shingo Goto ◽  
Yan Xu
Keyword(s):  
Covariance Matrix ◽  
Factor Model ◽  
Risk Minimization ◽  
Portfolio Risk ◽  
Finite Samples ◽  
Inverse Covariance Matrix ◽  
Out Of Sample ◽  
Nonnegativity Constraints ◽  
Mean Variance ◽  
Equal Weighting

AbstractIn portfolio risk minimization, the inverse covariance matrix prescribes the hedge trades in which a stock is hedged by all the other stocks in the portfolio. In practice with finite samples, however, multicollinearity makes the hedge trades too unstable and unreliable. By shrinking trade sizes and reducing the number of stocks in each hedge trade, we propose a “sparse” estimator of the inverse covariance matrix. Comparing favorably with other methods (equal weighting, shrunk covariance matrix, industry factor model, nonnegativity constraints), a portfolio formed on the proposed estimator achieves significant out-of-sample risk reduction and improves certainty equivalent returns after transaction costs.

A comparison of minimum variance and maximum Sharpe ratio portfolios for mainstream investors

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anja Vinzelberg ◽  
Benjamin Rainer Auer
Keyword(s):  
Minimum Variance ◽  
Sharpe Ratio ◽  
Optimization Techniques ◽  
Estimation Methods ◽  
Content Type ◽  
Single Index ◽  
Index Model ◽  
Single Index Model ◽  
Out Of Sample ◽  
Asset Classes

PurposeMotivated by the recent theoretical rehabilitation of mean-variance analysis, the authors revisit the question of whether minimum variance (MinVar) or maximum Sharpe ratio (MaxSR) investment weights are preferable in practical portfolio formation.Design/methodology/approachThe authors answer this question with a focus on mainstream investors which can be modeled by a preference for simple portfolio optimization techniques, a tendency to cling to past asset characteristics and a strong interest in index products. Specifically, in a rolling-window approach, the study compares the out-of-sample performance of MinVar and MaxSR portfolios in two asset universes covering multiple asset classes (via investable indices and their subindices) and for two popular input estimation methods (full covariance and single-index model).FindingsThe authors find that, regardless of the setting, there is no statistically significant difference between MinVar and MaxSR portfolio performance. Thus, the choice of approach does not matter for mainstream investors. In addition, the analysis reveals that, contrary to previous research, using a single-index model does not necessarily improve out-of-sample Sharpe ratios.Originality/valueThe study is the first to provide an in-depth comparison of MinVar and MaxSR returns which considers (1) multiple asset classes, (2) a single-index model and (3) state-of-the-art bootstrap performance tests.

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.

scholarly journals Seleção de carteiras ótimas sob restrições nas normas dos vetores de alocação: uma avaliação empírica com dados da BM&FBOVESPA

2015 ◽  
Vol 13 (3) ◽  
pp. 504
Author(s):  
Paulo Ferreira Naibert ◽  
João Caldeira
Keyword(s):  
Stock Market ◽  
Covariance Matrix ◽  
Portfolio Selection ◽  
Stock Exchange ◽  
Minimum Variance ◽  
Average Risk ◽  
Short Sale ◽  
Performance Indexes ◽  
Out Of Sample ◽  
Minimum Variance Portfolio

In this paper, we study the problem of minimum variance portfolio selection based on a recent methodology for portfolio optimization restricting the allocation vector proposed by Fan et al. (2012). To achieve this, we consider different conditional and unconditional covariance matrix estimators. The main contribution of this paper is one of empirical nature for the brazilian stock market. We evaluate out of sample performance indexes of the portfolios constructed for a set of 61 different stocks traded in the São Paulo stock exchange (BM&FBovespa). The results show that the restrictions on the norms of the allocation vector generate substantial gains in relation to the no short-sale portfolio, increasing the average risk-adjusted return (larger Sharpe Ratio) and lowering the portfolio turnover.

scholarly journals Desempenho Fora-da-Amostra da Otimização Robusta de Carteiras

2010 ◽  
Vol 8 (2) ◽  
pp. 141 ◽  
Author(s):  
André Alves Portela Santos
Keyword(s):  
Robust Optimization ◽  
Portfolio Optimization ◽  
Estimation Error ◽  
Simulated Data ◽  
Minimum Variance ◽  
Optimization Techniques ◽  
Practical Implementation ◽  
Out Of Sample ◽  
Portfolio Optimization Problem ◽  
Over Time

Robust optimization has been receiving increased attention in the recent few years due to the possibility of considering the problem of estimation error in the portfolio optimization problem. A question addressed so far by very few works is whether this approach is able to outperform traditional portfolio optimization techniques in terms of out-of-sample performance. Moreover, it is important to know whether this approach is able to deliver stable portfolio compositions over time, thus reducing management costs and facilitating practical implementation. We provide empirical evidence by assessing the out-of-sample performance and the stability of optimal portfolio compositions obtained with robust optimization and with traditional optimization techniques. The results indicated that, for simulated data, robust optimization performed better (both in terms of Sharpe ratios and portfolio turnover) than Markowitz's mean-variance portfolios and similarly to minimum-variance portfolios. The results for real market data indicated that the differences in risk-adjusted performance were not statistically different, but the portfolio compositions associated to robust optimization were more stable over time than traditional portfolio selection techniques.

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 Stable Portfolio Selection Strategy for Mean-Variance-CVaR Model under High-Dimensional Scenarios

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yu Shi ◽  
Xia Zhao ◽  
Fengwei Jiang ◽  
Yipin Zhu
Keyword(s):  
Optimization Problems ◽  
Short Selling ◽  
Computational Method ◽  
High Dimensional ◽  
Selection Strategy ◽  
Covariance Estimator ◽  
Out Of Sample ◽  
Sparse Portfolio ◽  
Mean Variance ◽  
Progressive Optimization

This paper aims to study stable portfolios with mean-variance-CVaR criteria for high-dimensional data. Combining different estimators of covariance matrix, computational methods of CVaR, and regularization methods, we construct five progressive optimization problems with short selling allowed. The impacts of different methods on out-of-sample performance of portfolios are compared. Results show that the optimization model with well-conditioned and sparse covariance estimator, quantile regression computational method for CVaR, and reweighted L1 norm performs best, which serves for stabilizing the out-of-sample performance of the solution and also encourages a sparse portfolio.

Sign in / Sign up

Export Citation Format

Share Document