Finance and Credit

Abstracting and Indexing

Referativny Zhurnal VINITI RAS
LCCN Permalink
Google Scholar

Online available



Cyberleninka (12 month OA embargo)

Securities portfolio selection using the risk margin

Vol. 24, Iss. 12, DECEMBER 2018

Received: 13 September 2018

Received in revised form: 27 September 2018

Accepted: 11 October 2018

Available online: 24 December 2018

Subject Heading: Securities market

JEL Classification: G11, G32

Pages: 2708–2720

Maleeva E.A. National Research Tomsk Polytechnic University (TPU), Tomsk, Russian Federation

ORCID id: not available

Bel'sner O.A. National Research Tomsk Polytechnic University (TPU), Tomsk, Russian Federation

ORCID id: not available

Kritskii O.L. National Research Tomsk Polytechnic University (TPU), Tomsk, Russian Federation

Subject The article considers the issues of securities portfolio building, using the risk margin value, or Value-at-Risk (VaR) measure.
Objectives The article aims to study the impact of risk margin on the amount of total capital and the optimal portfolio allocation. It is necessary to update the classical approach of Markowitz and adapt it to the current requirements in the banking and financial spheres.
Methods For the study, we used the Benati–Rizzi methodology and the mixed-integer linear programming algorithm.
Results We offer our own portfolio selection model taking into account the risk margin value. The article shows the portfolios selected according to the classical algorithm of Markowitz and taking into account the VaR constraints, as well as the results of comparison of the yield and value of two portfolios composed of the shares included in the MICEX 10 Index. The article also shows the results of calculating the risk and yield of passive portfolio investments.
Conclusions and Relevance The presented model of portfolio selection taking into account the margin risk value helps reduce initial investments, weaken the influence of stock market slump on the portfolio value, and increase the investment ex post return at the risk level comparable to the classical methodology of Markowitz. The use of the Benati-Rizzi method is convenient for creating a wide range of investment portfolios for unsophisticated investors with different risk aversion attitude.

Keywords: risk margin, portfolio management, Benati-Rizzi method, Markowitz method


  1. Artzner Ph., Delbaen F., Eber J.-M., Heath D. Coherent Measures of Risk. Mathematical Finance, 1999, vol. 9, iss. 3, pp. 203–228. URL: Link
  2. Kritskii O.L., Ul'yanova M.K. [Assessment of Multivariate Financial Risks of a Stock Share Portfolio]. Prikladnaya ekonometrika = Applied Econometrics, 2007, no. 4, pp. 3–17. URL: Link (In Russ.)
  3. McNeil A.J., Frey R., Embrechts P. Quantitative Risk Management. Concepts, Techniques and Tools. Princeton University Press, 2015, 720 p.
  4. Bronshtein E.M., Tulupova E.V. [The parameters of the complex quantile risk measures in the forming of portfolios of the securities]. Sovremennaya ekonomika: problemy i resheniya = Modern Economics: Problems and Solutions, 2014, no. 5, pp. 16–30. URL: Link (In Russ.)
  5. Engle R.F., Manganelli S. CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. Journal of Business and Economic Statistics, 2004, vol. 22, iss. 4, pp. 367–381. URL: Link
  6. Benati S., Rizzi R. A Mixed Integer Linear Programming Formulation of the Optimal Mean/Value-at-Risk Portfolio Problem. European Journal of Operational Research, 2007, vol. 176, iss. 1, pp. 423–434. URL: Link
  7. Babat O., Vera J.C., Zuluaga L.F. Computing Near-Optimal Value-at-Risk Portfolios Using Integer Programming Techniques. European Journal of Operational Research, 2018, vol. 266, iss. 1, pp. 304–315. URL: Link
  8. Pang T., Karan C. A Closed-form Solution of the Black–Litterman Model with Conditional Value at Risk. Operations Research Letters, 2018, vol. 46, iss. 1, pp. 103–108. URL: Link
  9. Yoshida Y. An Optimal Process for Average Value-at-Risk Portfolios in Financial Management. In: Applied Physics, System Science and Computers. APSAC 2017, Lecture Notes in Electrical Engineering, 2018, vol. 428, pp. 101–107. URL: Link
  10. Zhang T., Liu Z. Fireworks Algorithm for Mean-VaR/CVaR Models. Physica A: Statistical Mechanics and Its Applications, 2017, vol. 483, pp. 1–8. URL: Link
  11. Sahamkhadam M., Stephan A., Östermark R. Portfolio Optimization Based on GARCH-EVT-Copula Forecasting Models. International Journal of Forecasting, 2018, vol. 34, iss. 3, pp. 497–506. URL: Link
  12. Kakouris I., Rustem B. Robust Portfolio Optimization with Copulas. European Journal of Operational Research, 2014, vol. 235, iss. 1, pp. 28–37. URL: Link
  13. Krzemienowski A., Szymczyk S. Portfolio Optimization with a Copula-Based Extension of Conditional Value-at-Risk. Annals of Operations Research, 2016, vol. 237, iss. 1-2, pp. 219–236. URL: Link
  14. Pavlou A., Doumpos M., Zopounidis C. The Robustness of Portfolio Efficient Frontiers: A Comparative Analysis of Bi-objective and Multi-objective Approaches. Management Decision, 2018. URL: Link
  15. Najafi A.A., Mushakhian S. Multi-stage Stochastic Mean–Semivariance–CVaR Portfolio Optimization under Transaction Costs. Applied Mathematics and Computation, 2015, vol. 256, pp. 445–458. URL: Link
  16. Lwin K.T., Qu R., MacCarthy B.L. Mean-VaR Portfolio Optimization: A Nonparametric Approach. European Journal of Operational Research, 2017, vol. 260, iss. 2, pp. 751–766. URL: Link
  17. Lotfi S., Zenios S.A. Robust VaR and CVaR Optimization under Joint Ambiguity in Distributions, Means, and Covariances. European Journal of Operational Research, 2018, vol. 269, iss. 2, pp. 556–576. URL: Link

View all articles of issue


ISSN 2311-8709 (Online)
ISSN 2071-4688 (Print)

Journal current issue

Vol. 25, Iss. 5
May 2019