Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation

Danı́elsson, Jón; Jørgensen, Bjørn N.; Vries, Casper G. de; Yang, Xiaoguang

doi:10.1007/s10436-007-0081-3

Cited by 25 publications

(15 citation statements)

References 21 publications

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“…Danielsson, J., Jorgensen, B. N., de Vries, C. G. (Da nielsson, Jorgensen, de Vries, 2008) [9] characterized the investor's optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. Fernandes, B., Street, A., Valladao, D., Fernandes, C. (Fernandes, Street, Valladao, Fernandes, 2016) [10] provided a new perspective on robust portfolio optimization where they imposed an intuitive loss constraint for the optimal portfolio considering asset returns in a data-dri ven polyhedral uncertainty set.…”

Section: Brief Literature Reviewmentioning

confidence: 99%

Portfolio optimization using the GO-GARCH model: evidence from Ukrainian Stock Exchange

Lakshina

Zoriana²,

Deari³

2016

EA-XXI

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Abstract. This paper provides an experimental study on optimal portfolio composition. Data on seven stocks, included in Ukrainian Exchange Index, for the period from January to December 2015 are considered. In total, seven big industrial, electric and military companies are selected from the Ukrainian Exchange: Avdiivka Coke Plant, PJSC; Azovstal Iron and Steel Works, PJSC; Raiffeisen Bank Aval, JSC; Centerenergo, PJSC; Donbasenergo, PJSC; Motor Sich, JSC; and Ukrnafta, OPJC. The sample amounts to 226 observations. The analysis covers descriptive statistics, correlation, and, finally, optimal investment weights, which are calculated using Sharpe ratio. Covariance matrix of returns is estimated by means of generalized orthogonal GARCH model with Gaussian and normalinverse Gaussian distributions for errors. Selected stocks during the considered period have on average negative rates of returns. At the same time, these stocks in most of cases are positively correlated with each other, leading hence to a fewer room for the efficient diversification. Both Gaussian and normal-inverse Gaussian portfolios preclude that on average investment weights one should be focused mainly on Centerenergo and Motor Sich stocks. Based on these results, the investor should buy 46% of Centerenergo's stocks and 34% of Motor Sich's stocks. Selected stocks during the considered period have on average negative rates of returns. At the same time, these stocks in most of cases are positively correlated with each other, leading hence to a fewer room for the efficient diversification. Despite this, our results denoted that implementation of multivariate GARCH together with normal-inverse Gaussian distribution for errors enables to reduce the portfolio risk substantially. Comparing optimal GO-GARCH portfolios with naїve portfolio with all weights equal and Ukrainian Exchange Index we demonstrate that the former provide smaller portfolio variance and better VaR than naїve portfolio and the Index. Keywords: Portfolio; GO-GARCH Model; Return; Risk; Optimizations; Stock Exchange; Portfolio JEL Classіfіcatіon: G11; C58 Acknowledgement. This paper has been prepared under financial support of Ukrainian Stock Exchange. DOI: https://doi.org/10.21003/ea.V160-23 Мацук З. А. кандидат економічних наук, доцент, Івано-Франківський національний технічний університет нафти і газу, Івано-Франківськ, Україна Деарі Ф. кандидат економічних наук, доцент, Північно-Східний європейський університет, Тетово, Республіка Македонія Лакшина В. В. аспірант, старший викладач, Національний дослідний університет «Вища школа економіки», Москва, Росія Оптимізація інвестиційного портфеля за допомогою моделі GO-GARCH (на матеріалах Української фондової біржі) Анотація. У статті представлено емпіричне дослідження процесу формування оптимального портфеля на основі даних семи акцій, які включено до індексу Української біржі, за період з січня по грудень 2015 року. Аналіз включає в себе описову статистику, кореляцію та розрахунок оптимальних ваг у портфелі. Варіаційно-коваріаційна матри...

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Section: Brief Literature Reviewmentioning

confidence: 99%

Portfolio optimization using the GO-GARCH model: evidence from Ukrainian Stock Exchange

Lakshina

Zoriana²,

Deari³

2016

EA-XXI

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“…Assume that x * , K, K 1 and I satisfy (19,20). Then, one of the following three possibilities hold:…”

Section: Convergence Of Algorithm 41mentioning

confidence: 99%

“…The optimization problem which yields a portfolio with maximal gain and satisfies constraints on VaR is considered in [20,23], where some algorithms are suggested. The problem is difficult due to the complicated geometry of the feasible set.…”

Section: Introductionmentioning

confidence: 99%

Low order-value approach for solving VaR-constrained optimization problems

et al. 2011

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In Low Order-Value Optimization (LOVO) problems the sum of the r smallest values of a finite sequence of q functions is involved as the objective to be minimized or as a constraint. The latter case is considered in the present paper. Portfolio optimization problems with a constraint on the admissible Value at Risk (VaR) can be modeled in terms of a LOVO problem with constraints given by Low Order-Value functions. Different algorithms for practical solution of this problem will be presented. Using these techniques, portfolio optimization problems with transaction costs will be solved.

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“…Danielsson et al [20] for an exposition in a discrete setting. Note also that the portfolio insurance problem as discussed in Grossman and Vila [21] is related to the VaR restricted portfolio optimization problems of the present paper since it corresponds to the case of the parameter α (see below) set equal to zero, i.e.…”

Section: Introductionmentioning

confidence: 99%

Static and dynamic VaR constrained portfolios with application to delegated portfolio management

Pınar

2013

Optimization

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We give a closed-form solution to the single-period portfolio selection problem with a Value-at-Risk (VaR) constraint in the presence of a set of risky assets with multivariate normally distributed returns and the risk-less account, without short sales restrictions. The result allows to obtain a very simple, myopic dynamic portfolio policy in the multiple period version of the problem. We also consider mean-variance portfolios under a probabilistic chance (VaR) constraint and give an explicit solution. We use this solution to calculate explicitly the bonus of a portfolio manager to include a VaR constraint in his/her portfolio optimization, which we refer to as the price of a VaR constraint.

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Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation

Cited by 25 publications

References 21 publications

Portfolio optimization using the GO-GARCH model: evidence from Ukrainian Stock Exchange

Portfolio optimization using the GO-GARCH model: evidence from Ukrainian Stock Exchange

Low order-value approach for solving VaR-constrained optimization problems

Static and dynamic VaR constrained portfolios with application to delegated portfolio management

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