scholarly journals A remark on some extensions of the mean-variance portfolio selection models

2021 ◽  
Vol 16 (3) ◽  
pp. 26-34
Author(s):  
Enrico Moretto ◽  
Keyword(s):  
Portfolio Management ◽  
Proper Time ◽  
Research Question ◽  
The Third ◽  
Management Techniques ◽  
The Common ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
The Right ◽  
Mean Variance

Quantitative risk management techniques should prove their efficacy when financially turbulent periods are about to occur. Along the common saying “who needs an umbrella on a sunny day?”, a theoretical model is really helpful when it carries the right suggestion at the proper time, that is when markets start behaving hecticly. The beginning of the third decade of the 21st century carried along a turmoil that severely affected worldwide economy and changed it, probably for good. A consequent and plausible research question could be this: which financial quantitative approaches can still be considered reliable? This article tries to partially answer this question by testing if the mean-variance selection model (Markowitz [16], [17]) and some of his refinements can provide some useful hints in terms of portfolio management.

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.

PORTFOLIO MODEL UNDER FRACTAL MARKET BASED ON MEAN-DCCA

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050142
Author(s):  
WEIDE CHUN ◽  
HESEN LI ◽  
XU WU
Keyword(s):  
Analytical Solution ◽  
Correlation Analysis ◽  
Capital Market ◽  
Cross Correlation ◽  
Investment Portfolio ◽  
Cross Correlation Analysis ◽  
Risk Criterion ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

Under the realistic background that the capital market nowadays is a fractal market, this paper embeds the detrended cross-correlation analysis (DCCA) into the return-risk criterion to construct a Mean-DCCA portfolio model, and gives an analytical solution. Based on this, the validity of Mean-DCCA portfolio model is verified by empirical analysis. Compared to the mean-variance portfolio model, the Mean-DCCA portfolio model is more conducive for investors to build a sophisticated investment portfolio under multi-time-scale, improve the performance of portfolios, and overcome the defect that the mean-variance portfolio model has not considered the existence of fractal correlation characteristics between assets.

scholarly journals ON TIME CONSISTENCY FOR MEAN-VARIANCE PORTFOLIO SELECTION

2020 ◽  
Vol 23 (06) ◽  
pp. 2050042 ◽  
Author(s):  
ELENA VIGNA
Keyword(s):  
Portfolio Selection ◽  
Optimal Strategy ◽  
Time Consistency ◽  
Time Inconsistency ◽  
Selection Problem ◽  
Portfolio Selection Problem ◽  
The Mean ◽  
Optimal Approach ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper addresses a comparison between different approaches to time inconsistency for the mean-variance portfolio selection problem. We define a suitable intertemporal preferences-driven reward and use it to compare three common approaches to time inconsistency for the mean-variance portfolio selection problem over [Formula: see text]: precommitment approach, consistent planning or game theoretical approach, and dynamically optimal approach. We prove that, while the precommitment strategy beats the other two strategies (that is a well-known obvious result), the consistent planning strategy dominates the dynamically optimal strategy until a time point [Formula: see text] and is dominated by the dynamically optimal strategy from [Formula: see text] onwards. Existence and uniqueness of the break even point [Formula: see text] is proven.

scholarly journals Applying Least Squares Support Vector Machines to Mean-Variance Portfolio Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Wang ◽  
Junseok Kim
Keyword(s):  
Support Vector Machines ◽  
Least Squares ◽  
Portfolio Management ◽  
Stock Exchange ◽  
Efficient Frontier ◽  
Support Vector ◽  
Research Fields ◽  
Vector Machines ◽  
Mean Variance Portfolio ◽  
Mean Variance

Portfolio selection problem introduced by Markowitz has been one of the most important research fields in modern finance. In this paper, we propose a model (least squares support vector machines (LSSVM)-mean-variance) for the portfolio management based on LSSVM. To verify the reliability of LSSVM-mean-variance model, we conduct an empirical research and design an algorithm to illustrate the performance of the model by using the historical data from Shanghai stock exchange. The numerical results show that the proposed model is useful when compared with the traditional Markowitz model. Comparing the efficient frontier and total wealth of both models, our model can provide a more measurable standard of judgment when investors do their investment.

scholarly journals Mean-Variance Portfolio Selection with Tracking Error Penalization

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1915
Author(s):  
William Lefebvre ◽  
Grégoire Loeper ◽  
Huyên Pham
Keyword(s):  
Portfolio Selection ◽  
Tracking Error ◽  
Efficient Frontier ◽  
Minimum Variance ◽  
Sharpe Ratio ◽  
Portfolio Strategy ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Variance Criterion

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the case of misspecified parameters, by “fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean–Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

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.

scholarly journals On new properties of light exhibited in the optical phenomena of mother-of-pearl, and other bodies to which the superficial structure of that substance can be communicated. By David Brewster, LL. D . F. R. S. Edin. and F. S. A. Ed. In a letter addressed to the Right Hon. Sir Joseph Banks, Bart. K. B. P. R. S

1832 ◽  
Vol 1 ◽  
pp. 502-504
Keyword(s):  
Optical Properties ◽  
Angular Distance ◽  
Transmitted Light ◽  
The Third ◽  
The Common ◽  
Optical Phenomena ◽  
The Right

The first section of this paper is devoted to the optical properties peculiar to mother-of-pearl; the second to the communication of these properties to other bodies; the third to the consideration of the cause of these phenomena; and the fourth to the description of the peculiar species of polarization produced by this substance. Dr. Brewster observes, mother-of-pearl is composed of laminae, much resembling in their arrangement those of the agate; that when it is imperfectly polished, a coloured image of a candle is seen in it by reflection in the neighbourhood of the common image, having its blue extremity towards this image, and being always situated, with respect to it, in the direction of an axis of extraordinary reflection, the angular distance varying with the inclination and situation of the rays, and being also different in magnitude in different specimens, but always observing certain laws. There is also a mass of coloured light, crimson at great angles of incidence, and green at smaller, beyond the regular coloured image, its distance varying according to a different law; becoming brighter when the substance is polished, and varying also with its thickness. Similar appearances are observed in a surface obtained by fracture; but a higher polish produces a new coloured image on the opposite side of the common image, and nearly as bright as the former, which is rendered somewhat less brilliant by the operation of polishing. Similar appearances, but somewhat less distinct, are observed when a candle is viewed through a thin piece of mother-of-pearl; and it is remarkable, that the image which is the brighter when seen by reflection, is the less bright when seen by transmission. When the opposite surfaces happen to have different axes of extraordinary reflection, they produce the appearance of four images in the transmitted light.

scholarly journals Comparative anatomical analysis of the transcallosal-transchoroidal and transcallosal-transforniceal-transchoroidal approaches to the third ventricle

2017 ◽  
Vol 127 (1) ◽  
pp. 209-218 ◽  
Author(s):  
João Luiz Vitorino Araujo ◽  
José C. E. Veiga ◽  
Hung Tzu Wen ◽  
Almir F. de Andrade ◽  
Manoel J. Teixeira ◽  
...  
Keyword(s):  
Corpus Callosum ◽  
Third Ventricle ◽  
Anterior Region ◽  
Cerebral Aqueduct ◽  
Tuber Cinereum ◽  
The Third ◽  
Longitudinal Plane ◽  
The Mean ◽  
The Right ◽  
Longitudinal Diameter

OBJECTIVEAccess to the third ventricle is a veritable challenge to neurosurgeons. In this context, anatomical and morphometric studies are useful for establishing the limitations and advantages of a particular surgical approach. The transchoroidal approach is versatile and provides adequate exposure of the middle and posterior regions of the third ventricle. However, the fornix column limits the exposure of the anterior region of the third ventricle. There is evidence that the unilateral section of the fornix column has little effect on cognitive function. This study compared the anatomical exposure afforded by the transforniceal-transchoroidal approach with that of the transchoroidal approach. In addition, a morphometric evaluation of structures that are relevant to and common in the 2 approaches was performed.METHODSThe anatomical exposure provided by the transcallosal-transchoroidal and transcallosal-transforniceal-transchoroidal approaches was compared in 8 fresh cadavers, using a neuronavigation system. The working area, microsurgical exposure area, and angular exposure on the longitudinal and transversal planes of 2 anatomical targets (tuber cinereum and cerebral aqueduct) were compared. Additionally, the thickness of the right frontal lobe parenchyma, thickness of the corpus callosum trunk, and longitudinal diameter of the interventricular foramen were measured. The values obtained were submitted to statistical analysis using the Wilcoxon test.RESULTSIn the quantitative evaluation, compared with the transchoroidal approach, the transforniceal-transchoroidal approach provided a greater mean working area (transforniceal-transchoroidal 150 ± 11 mm2; transchoroidal 121 ± 8 mm2; p < 0.05), larger mean microsurgical exposure area (transforniceal-transchoroidal 101 ± 9 mm2; transchoroidal 80 ± 5 mm2; p < 0.05), larger mean angular exposure area on the longitudinal plane for the tuber cinereum (transforniceal-transchoroidal 71° ± 7°; transchoroidal 64° ± 6°; p < 0.05), and larger mean angular exposure area on the longitudinal plane for the cerebral aqueduct (transforniceal-transchoroidal 62° ± 6°; transchoroidal 55° ± 5°; p < 0.05). No differences were observed in angular exposure along the transverse axis for either anatomical target (tuber cinereum and cerebral aqueduct; p > 0.05). The mean thickness of the right frontal lobe parenchyma was 35 ± 3 mm, the mean thickness of the corpus callosum trunk was 10 ± 1 mm, and the mean longitudinal diameter of the interventricular foramen was 4.6 ± 0.4 mm. In the qualitative assessment, it was noted that the transforniceal-transchoroidal approach led to greater exposure of the third ventricle anterior region structures. There was no difference between approaches in the exposure of the structures of the middle and posterior region.CONCLUSIONSThe transforniceal-transchoroidal approach provides greater surgical exposure of the third ventricle anterior region than that offered by the transchoroidal approach. In the population studied, morphometric analysis established mean values for anatomical structures common to both approaches.

scholarly journals Portfolio Selection Models

2017 ◽  
pp. 43-82
Keyword(s):  
Decision Theory ◽  
Portfolio Selection ◽  
Portfolio Management ◽  
Asset Allocation ◽  
Computer Programs ◽  
Var Analysis ◽  
Widespread Acceptance ◽  
Portfolio Manager ◽  
The Mean ◽  
Mean Variance

The main goal behind the concept of portfolio management is to combine various assets into portfolios and then to manage those portfolios so as to achieve the desired investment objectives. To be more specific, the investors' needs are mostly defined in terms of profit and risk, and the portfolio manager makes a sound decision aimed ether to maximize the return or minimize the risk. The Mean-Variance and Mean-VaR analysis has gained widespread acceptance among practitioners of asset allocation. Although they are the simplest models of investment, sometimes they are sufficiently rich to be directly useful in applied problems and decision theory. Here you will learn how to apply these analyses in practice using computer programs and spreadsheets.

scholarly journals ELECTIONS TO THE KYIV CITY THOUGHT ON JULY, 23 1917: PREPARATION, CONDUCTING AND RESULTS

2016 ◽  
pp. 38-42
Author(s):  
Ya. Kupchik
Keyword(s):  
Political Parties ◽  
Short Review ◽  
Professional Organizations ◽  
Scientific Development ◽  
Social Origin ◽  
Municipal Elections ◽  
The Third ◽  
The Common ◽  
The Right ◽  
Electoral Law

In the article on the basis of analysis of the archived materials and magazine municipal elections are reflected to Kiev city thought, that happened on July, 23 1917. By Author the opinion is expressed, that experience of these elections may need during election in local advices in modern Ukraine. At the same time the short review of scientific development of problem is carried out. It is found out, that the Ukrainian historian until now examined only the separate aspects of elections to Kiev city thought in 1917 the electoral legislation which regulated organization and conducting of city elections is analysed. It is found out, that elections took place on the basis of electoral law common, direct, even and secret. According to the proportional system of elections (slates from political parties, public associations, professional organizations or their blocks) elected 120 vowel, plenary powers of which were to be halted the quantity of electors, their social origin and appearance, is on January, 1 of 1919. Set on elections. It is certain, that in elections 65% from the common amount of the persons conferred the right the choice took part. In the article it is indicated about more political of election company. It is noticed, that candidates accented attention on the "matter of revolution", instead of improvement of city economy. The electorate of political parties and blocks which conducted to city thought of the vowel is explored. It is marked, that a "socialistic block" was supported by poor layers which lived on the outskirts of city. The results of city elections and new composition of Kiev city thought are found out. Won over a "socialistic block" (44 delegates) on elections, the "Ukrainian block" (USDRP-UPSR) which conducted in advice 24 delegates went farther. The third place was occupied by monarchists (18 delegates). Represented bolshevists in advice only 7 delegates.

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