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.

PRACTICAL INVESTMENT CONSEQUENCES OF THE SCALARIZATION PARAMETER FORMULATION IN DYNAMIC MEAN–VARIANCE PORTFOLIO OPTIMIZATION

2021 ◽  
Vol 24 (05) ◽  
pp. 2150029
Author(s):  
PIETER M. VAN STADEN ◽  
DUY-MINH DANG ◽  
PETER A. FORSYTH
Keyword(s):  
Risk Aversion ◽  
Portfolio Optimization ◽  
Optimization Problem ◽  
Jump Diffusion ◽  
Investment Strategies ◽  
Institutional Settings ◽  
Portfolio Optimization Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Theoretical Risk

We consider the practical investment consequences of implementing the two most popular formulations of the scalarization (or risk-aversion) parameter in the time-consistent dynamic mean–variance (MV) portfolio optimization problem. Specifically, we compare results using a scalarization parameter assumed to be (i) constant and (ii) inversely proportional to the investor’s wealth. Since the link between the scalarization parameter formulation and risk preferences is known to be nontrivial (even in the case where a constant scalarization parameter is used), the comparison is viewed from the perspective of an investor who is otherwise agnostic regarding the philosophical motivations underlying the different formulations and their relation to theoretical risk-aversion considerations, and instead simply wishes to compare investment outcomes of the different strategies. In order to consider the investment problem in a realistic setting, we extend some known results to allow for the case where the risky asset follows a jump-diffusion process, and examine multiple sets of plausible investment constraints that are applied simultaneously. We show that the investment strategies obtained using a scalarization parameter that is inversely proportional to wealth, which enjoys widespread popularity in the literature applying MV optimization in institutional settings, can exhibit some undesirable and impractical characteristics.

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.

Exploring the mean-variance portfolio optimization approach for planning wind repowering actions in Spain

2017 ◽  
Vol 106 ◽  
pp. 335-342 ◽  
Author(s):  
F.J. Santos-Alamillos ◽  
N.S. Thomaidis ◽  
J. Usaola-García ◽  
J.A. Ruiz-Arias ◽  
D. Pozo-Vázquez
Keyword(s):  
Portfolio Optimization ◽  
Optimization Approach ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

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.

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