Sparse and robust mean–variance portfolio optimization problems

2019 ◽  
Vol 523 ◽  
pp. 1371-1378 ◽  
Author(s):  
Zhifeng Dai ◽  
Fei Wang
Keyword(s):  
Portfolio Optimization ◽  
Optimization Problems ◽  
Mean Variance Portfolio ◽  
Mean Variance

scholarly journals An Entropy-Based Approach to Portfolio Optimization

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 332 ◽  
Author(s):  
Peter Joseph Mercurio ◽  
Yuehua Wu ◽  
Hong Xie
Keyword(s):  
Objective Function ◽  
Portfolio Optimization ◽  
Historical Data ◽  
Optimization Problems ◽  
Improved Method ◽  
Financial Industry ◽  
New Family ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper presents an improved method of applying entropy as a risk in portfolio optimization. A new family of portfolio optimization problems called the return-entropy portfolio optimization (REPO) is introduced that simplifies the computation of portfolio entropy using a combinatorial approach. REPO addresses five main practical concerns with the mean-variance portfolio optimization (MVPO). Pioneered by Harry Markowitz, MVPO revolutionized the financial industry as the first formal mathematical approach to risk-averse investing. REPO uses a mean-entropy objective function instead of the mean-variance objective function used in MVPO. REPO also simplifies the portfolio entropy calculation by utilizing combinatorial generating functions in the optimization objective function. REPO and MVPO were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases.

HYPER SENSITIVITY ANALYSIS OF PORTFOLIO OPTIMIZATION PROBLEMS

2004 ◽  
Vol 21 (03) ◽  
pp. 297-317 ◽  
Author(s):  
LEONID CHURILOV ◽  
IMMANUEL M. BOMZE ◽  
MOSHE SNIEDOVICH ◽  
DANIEL RALPH
Keyword(s):  
Sensitivity Analysis ◽  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Optimization Problems ◽  
Selection Problem ◽  
Full Size ◽  
Concave Programming ◽  
Hyper Sensitivity ◽  
Mean Variance Portfolio ◽  
Mean Variance

Hyper Sensitivity Analysis (HSA) is an intuitive generalization of conventional sensitivity analysis, where the term "hyper" indicates that the sensitivity analysis is conducted with respect to functions rather than numeric values. In this paper Composite Concave Programming is used to perform HSA in the area of Portfolio Optimization Problems. The concept of HSA is suited for situations where several candidates for the function quantifying the utility of (mean, variance) pairs are available. We discuss the applications of HSA to two types of mean–variance portfolio optimization problems: the classical one and a discrete knapsack-type portfolio selection problem. It is explained why in both cases the methodology can be applied to full size problems.

scholarly journals An Improvement of Stochastic Gradient Descent Approach for Mean-Variance Portfolio Optimization Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Stephanie S. W. Su ◽  
Sie Long Kek
Keyword(s):  
Portfolio Optimization ◽  
Standard Error ◽  
Gradient Descent ◽  
Optimization Problem ◽  
Stochastic Gradient Descent ◽  
Moment Estimation ◽  
The Mean ◽  
Portfolio Optimization Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, the current variant technique of the stochastic gradient descent (SGD) approach, namely, the adaptive moment estimation (Adam) approach, is improved by adding the standard error in the updating rule. The aim is to fasten the convergence rate of the Adam algorithm. This improvement is termed as Adam with standard error (AdamSE) algorithm. On the other hand, the mean-variance portfolio optimization model is formulated from the historical data of the rate of return of the S&P 500 stock, 10-year Treasury bond, and money market. The application of SGD, Adam, adaptive moment estimation with maximum (AdaMax), Nesterov-accelerated adaptive moment estimation (Nadam), AMSGrad, and AdamSE algorithms to solve the mean-variance portfolio optimization problem is further investigated. During the calculation procedure, the iterative solution converges to the optimal portfolio solution. It is noticed that the AdamSE algorithm has the smallest iteration number. The results show that the rate of convergence of the Adam algorithm is significantly enhanced by using the AdamSE algorithm. In conclusion, the efficiency of the improved Adam algorithm using the standard error has been expressed. Furthermore, the applicability of SGD, Adam, AdaMax, Nadam, AMSGrad, and AdamSE algorithms in solving the mean-variance portfolio optimization problem is validated.

scholarly journals Mean-Variance Optimization Is a Good Choice, But for Other Reasons than You Might Think

Risks ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 29 ◽  
Author(s):  
Andrea Rigamonti
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Risk Measures ◽  
Traditional Approach ◽  
Real Data ◽  
Downside Risk ◽  
Good Choice ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Allocation Decisions

Mean-variance portfolio optimization is more popular than optimization procedures that employ downside risk measures such as the semivariance, despite the latter being more in line with the preferences of a rational investor. We describe strengths and weaknesses of semivariance and how to minimize it for asset allocation decisions. We then apply this approach to a variety of simulated and real data and show that the traditional approach based on the variance generally outperforms it. The results hold even if the CVaR is used, because all downside risk measures are difficult to estimate. The popularity of variance as a measure of risk appears therefore to be rationally justified.

scholarly journals Mean–variance portfolio optimization when means and covariances are unknown

2011 ◽  
Vol 5 (2A) ◽  
pp. 798-823 ◽  
Author(s):  
Tze Leung Lai ◽  
Haipeng Xing ◽  
Zehao Chen
Keyword(s):  
Portfolio Optimization ◽  
Mean Variance Portfolio ◽  
Mean Variance
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