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.
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
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.)
McNeil A.J., Frey R., Embrechts P. Quantitative Risk Management. Concepts, Techniques and Tools. Princeton University Press, 2015, 720 p.
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.)
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
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
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
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
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
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
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
Kakouris I., Rustem B. Robust Portfolio Optimization with Copulas. European Journal of Operational Research, 2014, vol. 235, iss. 1, pp. 28–37. URL: Link
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
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
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
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
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