<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">msuecon</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Московского университета. Серия 6. Экономика</journal-title><trans-title-group xml:lang="en"><trans-title>Lomonosov Economics Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0130-0105</issn><publisher><publisher-name>MSUPRESS</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.38050/01300105201754</article-id><article-id custom-type="elpub" pub-id-type="custom">msuecon-435</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИНАНСОВАЯ ЭКОНОМИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>FINANCIAL STUDIES</subject></subj-group></article-categories><title-group><article-title>Оптимизация инвестиционного портфеля с декомпозицией риска</article-title><trans-title-group xml:lang="en"><trans-title>Portfolio Optimization with Risk Decomposition</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Асатуров</surname><given-names>К. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Asaturov</surname><given-names>K. G.</given-names></name></name-alternatives><email xlink:type="simple">kgasaturov@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный исследовательский университет «Высшая школа экономики»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>National research University "Higher school of Economics"</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>07</day><month>04</month><year>2021</year></pub-date><volume>0</volume><issue>5</issue><fpage>61</fpage><lpage>85</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Асатуров К.Г., 2021</copyright-statement><copyright-year>2021</copyright-year><copyright-holder xml:lang="ru">Асатуров К.Г.</copyright-holder><copyright-holder xml:lang="en">Asaturov K.G.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://msuecon.elpub.ru/jour/article/view/435">https://msuecon.elpub.ru/jour/article/view/435</self-uri><abstract><p>В работе была предложена модификация стандартной оптимизационной задачи для построения портфеля с возможностью контролировать систематический и специфический риск (портфель с декомпозицией риска). С помощью современных эконометрических моделей были оценены и спрогнозированы динамические альфа и бета акций из модели CAPM, которые затем использовались в портфельной оптимизации. В качестве данных применялись недельные цены закрытия 10 австралийских акций и индекса ASX в качестве рыночного портфеля в период с июля 2000 г. по июль 2016 г. В рамках рассматриваемой выборки с помощью построения рыночно нейтрального портфеля было выявлено отсутствие арбитража на австралийском рынке акций. Анализ показал, что портфели с декомпозицией риска превосходят портфель по Марковицу согласно различным показателям эффективности.</p></abstract><trans-abstract xml:lang="en"><p>The paper offers the modification of traditional portfolio optimization approach to construct the portfolio with possibility to control both systematic and specific risk (portfolio with risk decomposition). Built on modern econometric tools, the author estimates and forecasts the dynamics of alphas and betas of stocks in the frame of CAPM model , which are further applied for portfolio optimization. The closing weekly prices of 10 Australian stocks and ASX Index as the market index during the period from July 2000 to July 2016 were used. Within the sample there is no evidence of arbitrage on the Australian equity market employing neutral beta portfolio. The study confirms that portfolios with risk decomposition outperform Markowitz’s one according to various performance indicators. </p></trans-abstract><kwd-group xml:lang="ru"><kwd>оптимизация портфеля</kwd><kwd>бета-нейтральность</kwd><kwd>декомпозиция инвестиционного риска</kwd></kwd-group><kwd-group xml:lang="en"><kwd>portfolio optimization</kwd><kwd>beta-neutrality</kwd><kwd>investment risk decomposition</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Асатуров К. Г. Детерминанты систематического риска: анализ на основе российского фондового рынка // Финансы и кредит. - 2017. - Т. 23. -№ 23. - С. 1343-1363.</mixed-citation><mixed-citation xml:lang="en">Асатуров К. Г. Детерминанты систематического риска: анализ на основе российского фондового рынка // Финансы и кредит. - 2017. - Т. 23. -№ 23. - С. 1343-1363.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Ang A., Kristensen D. Testing Conditional Factor Models // Journal of Financial Economics. - 2012. - Vol. 106. - P. 132-156.</mixed-citation><mixed-citation xml:lang="en">Ang A., Kristensen D. Testing Conditional Factor Models // Journal of Financial Economics. - 2012. - Vol. 106. - P. 132-156.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Bakshi G., Kapadia N., Madan D. Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options // Review of Financial Studies. - 2003. - Vol. 16. - No. 1. - P. 101-143.</mixed-citation><mixed-citation xml:lang="en">Bakshi G., Kapadia N., Madan D. Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options // Review of Financial Studies. - 2003. - Vol. 16. - No. 1. - P. 101-143.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Chen S.-W., Huang N. C. Estimates of the ICAPM with Regime-Switching Betas: Evidence from Four Pacific Rim Economies // Applied Financial Economics. - 2007. - Vol. 17. - P. 313-327.</mixed-citation><mixed-citation xml:lang="en">Chen S.-W., Huang N. C. Estimates of the ICAPM with Regime-Switching Betas: Evidence from Four Pacific Rim Economies // Applied Financial Economics. - 2007. - Vol. 17. - P. 313-327.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Collins D. W., Ledolter J., Rayburn J. Some Further Evidenceon the Stochastic Properties of Systematic risk // Journal of Business. - 1987. - Vol. 60. - No. 3. - P. 425-448.</mixed-citation><mixed-citation xml:lang="en">Collins D. W., Ledolter J., Rayburn J. Some Further Evidenceon the Stochastic Properties of Systematic risk // Journal of Business. - 1987. - Vol. 60. - No. 3. - P. 425-448.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Eisenbeiss M., Kauermann G., Semmler W. Estimating Beta-Coefficients of German Stock Data: A Non-Parametric Approach // The European Journal of Finance. - 2007. - Vol. 13. - No. 6. - P. 503-522.</mixed-citation><mixed-citation xml:lang="en">Eisenbeiss M., Kauermann G., Semmler W. Estimating Beta-Coefficients of German Stock Data: A Non-Parametric Approach // The European Journal of Finance. - 2007. - Vol. 13. - No. 6. - P. 503-522.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Ephraim Y., Merhav N. Hidden Markov Processes // IEEE Transactions on Information Theory. - 2002. - Vol. 48. - No. 6. - P. 1518-1569.</mixed-citation><mixed-citation xml:lang="en">Ephraim Y., Merhav N. Hidden Markov Processes // IEEE Transactions on Information Theory. - 2002. - Vol. 48. - No. 6. - P. 1518-1569.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Esteban M. V., Orbe-Manadaluniz S. A Nonparametric Approach for Estimating Betas: the Smoothed Rolling Estimator // Applied Economics. - 2010. - Vol. 42. - P. 1269-1279.</mixed-citation><mixed-citation xml:lang="en">Esteban M. V., Orbe-Manadaluniz S. A Nonparametric Approach for Estimating Betas: the Smoothed Rolling Estimator // Applied Economics. - 2010. - Vol. 42. - P. 1269-1279.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Fabozzi F., Francis J. Beta as a Random Coefficient // Journal of Financial and Quantative Analysis. - 1978. - Vol. 13. - P. 101-116.</mixed-citation><mixed-citation xml:lang="en">Fabozzi F., Francis J. Beta as a Random Coefficient // Journal of Financial and Quantative Analysis. - 1978. - Vol. 13. - P. 101-116.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Faff R. W., Lee J. H. H., Fry T. R. L. Time stationarity of systematic risk: Some Australian evidence // Journal of Business and Accounting. - 1992. - Vol. 19. - No. 2. - P. 253-270.</mixed-citation><mixed-citation xml:lang="en">Faff R. W., Lee J. H. H., Fry T. R. L. Time stationarity of systematic risk: Some Australian evidence // Journal of Business and Accounting. - 1992. - Vol. 19. - No. 2. - P. 253-270.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Faff R. W., Hillier D., Hillier J. Time-Varying Beta Risk: An Analysis of Alternative Modeling Techniques // Journal of Business Finance and Accounting. - 2000. - Vol. 27. - P. 523-554.</mixed-citation><mixed-citation xml:lang="en">Faff R. W., Hillier D., Hillier J. Time-Varying Beta Risk: An Analysis of Alternative Modeling Techniques // Journal of Business Finance and Accounting. - 2000. - Vol. 27. - P. 523-554.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Fama E. F. Market Efficiency, Long-Term Returns, and Behavioral Finance // Journal of Financial Economics. - 1998. - Vol. 49. - P. 283-306.</mixed-citation><mixed-citation xml:lang="en">Fama E. F. Market Efficiency, Long-Term Returns, and Behavioral Finance // Journal of Financial Economics. - 1998. - Vol. 49. - P. 283-306.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Fama E. F., French K. R. Common Risk Factors in the Returns on Stocks and Bonds // Journal of Financial Economics. - 1993. - Vol. 33. - No. 1. - P. 3-56.</mixed-citation><mixed-citation xml:lang="en">Fama E. F., French K. R. Common Risk Factors in the Returns on Stocks and Bonds // Journal of Financial Economics. - 1993. - Vol. 33. - No. 1. - P. 3-56.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Groenewold N. Share Market Efficiency: Tests Using Daily Data for Australia and New Zealand // Applied Financial Economics. - 1997. - Vol. 7. - P. 645-657.</mixed-citation><mixed-citation xml:lang="en">Groenewold N. Share Market Efficiency: Tests Using Daily Data for Australia and New Zealand // Applied Financial Economics. - 1997. - Vol. 7. - P. 645-657.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Groenewold N., Fraser P. Time-Varying Estimates of CAPM Betas // Mathematics and Computers in Simulations. - 1999. - Vol. 48. - P. 531-539.</mixed-citation><mixed-citation xml:lang="en">Groenewold N., Fraser P. Time-Varying Estimates of CAPM Betas // Mathematics and Computers in Simulations. - 1999. - Vol. 48. - P. 531-539.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Hamilton J. D. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle // Econometrica. - 1989. - Vol. 57. - No. 2. - P. 357-384.</mixed-citation><mixed-citation xml:lang="en">Hamilton J. D. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle // Econometrica. - 1989. - Vol. 57. - No. 2. - P. 357-384.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Hastie T., Tibshirani R. Varying-Coefficient Models // Journal of the Royal Statistic Society, Series B (Methodology). - 1993. - Vol. 55. - No. 4. - P. 757-796.</mixed-citation><mixed-citation xml:lang="en">Hastie T., Tibshirani R. Varying-Coefficient Models // Journal of the Royal Statistic Society, Series B (Methodology). - 1993. - Vol. 55. - No. 4. - P. 757-796.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">He Z., Kryzanowski L. Dynamic Betas for Canadian Sector Portfolios // International Review of Financial Analysis.- 2008. - Vol. 17. - P. 1110-1122.</mixed-citation><mixed-citation xml:lang="en">He Z., Kryzanowski L. Dynamic Betas for Canadian Sector Portfolios // International Review of Financial Analysis.- 2008. - Vol. 17. - P. 1110-1122.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Huang R. H. C. Tests of Regime-Switching CAPM // Applied Financial Economics. - 2000. - Vol. 10. - P. 573-578.</mixed-citation><mixed-citation xml:lang="en">Huang R. H. C. Tests of Regime-Switching CAPM // Applied Financial Economics. - 2000. - Vol. 10. - P. 573-578.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Jacobs B. L., Levy K. N., Markowitz H. M. Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions // Operations Research. - 2005. - Vol. 53. - No. 4. - P. 586-599.</mixed-citation><mixed-citation xml:lang="en">Jacobs B. L., Levy K. N., Markowitz H. M. Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions // Operations Research. - 2005. - Vol. 53. - No. 4. - P. 586-599.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Jacobs B. L., Levy K. N., Starter D. On the Optimality of Long-Short Strategies // Financial Analysts Journal. - 1998. - Vol. 54. - No. 2. - P. 40-51.</mixed-citation><mixed-citation xml:lang="en">Jacobs B. L., Levy K. N., Starter D. On the Optimality of Long-Short Strategies // Financial Analysts Journal. - 1998. - Vol. 54. - No. 2. - P. 40-51.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Kalman R. E. A New Approach to Linear Filtering and Prediction Problems // Journal of Basic Engineering. - 1960. - Vol. 82. - No. 1. - P. 35-45.</mixed-citation><mixed-citation xml:lang="en">Kalman R. E. A New Approach to Linear Filtering and Prediction Problems // Journal of Basic Engineering. - 1960. - Vol. 82. - No. 1. - P. 35-45.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Keating C., Shadwick W. F. A Universal Performance Measure. - UK: The Finance Development Centre Limited, 2002. - P. 1-33.</mixed-citation><mixed-citation xml:lang="en">Keating C., Shadwick W. F. A Universal Performance Measure. - UK: The Finance Development Centre Limited, 2002. - P. 1-33.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Kim D. The Extent of Nonstationarity of Beta // Review of Quantitative Finance and Accounting. - 1993. - Vol. 3. - P. 241-254.</mixed-citation><mixed-citation xml:lang="en">Kim D. The Extent of Nonstationarity of Beta // Review of Quantitative Finance and Accounting. - 1993. - Vol. 3. - P. 241-254.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Klaassen P. Financial Asset Pricing Theory and Stochastic Programming Models for Asset / Liability Management: A Synthesis // Management Science. - 1998. - Vol. 44. - P. 31-48.</mixed-citation><mixed-citation xml:lang="en">Klaassen P. Financial Asset Pricing Theory and Stochastic Programming Models for Asset / Liability Management: A Synthesis // Management Science. - 1998. - Vol. 44. - P. 31-48.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Li Q., Racine J. S. Smooth Varying-Coefficient Estimation and Inference for Qualitative and Quantitative Data // Econometric Theory. - 2010. - Vol. 26. - P. 1607-1637.</mixed-citation><mixed-citation xml:lang="en">Li Q., Racine J. S. Smooth Varying-Coefficient Estimation and Inference for Qualitative and Quantitative Data // Econometric Theory. - 2010. - Vol. 26. - P. 1607-1637.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Li Y., Yang L. Testing Conditional Factor Models: A Nonparametric Approach // Journal of Empirical Finance. - 2011. - Vol. 18. - P. 972-992.</mixed-citation><mixed-citation xml:lang="en">Li Y., Yang L. Testing Conditional Factor Models: A Nonparametric Approach // Journal of Empirical Finance. - 2011. - Vol. 18. - P. 972-992.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Lie F., Brooks R., Fama R. Modelling the Equity Beta Risk of Australian Financial Sector Companies // Australian Economic Papers. - 2000. - Vol. 39. - P. 301-311.</mixed-citation><mixed-citation xml:lang="en">Lie F., Brooks R., Fama R. Modelling the Equity Beta Risk of Australian Financial Sector Companies // Australian Economic Papers. - 2000. - Vol. 39. - P. 301-311.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Markowitz H. M. Portfolio Selection // Journal of Finance. - 1952. - Vol. 12. - P. 77-91.</mixed-citation><mixed-citation xml:lang="en">Markowitz H. M. Portfolio Selection // Journal of Finance. - 1952. - Vol. 12. - P. 77-91.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Markowitz H. M. Portfolio Selection: Efficient Diversification of Investments. - New York: John Wiley and Sons, 1959.</mixed-citation><mixed-citation xml:lang="en">Markowitz H. M. Portfolio Selection: Efficient Diversification of Investments. - New York: John Wiley and Sons, 1959.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Marshall A., Maulana T., Tang L. The Estimation and Determinants of Emerging Market Country Risk and the Dynamic Conditional GARCH Model // International Review of Financial Analysis. - 2009. - Vol. 18. - No. 5. - P. 250-259.</mixed-citation><mixed-citation xml:lang="en">Marshall A., Maulana T., Tang L. The Estimation and Determinants of Emerging Market Country Risk and the Dynamic Conditional GARCH Model // International Review of Financial Analysis. - 2009. - Vol. 18. - No. 5. - P. 250-259.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Mergner S., Bulla J. Time-Varying Beta Risk of Pan-European Industry Portfolios: A Comparison of Alternative Modeling Techniques // European Journal of Finance. - 2008. - Vol. 14. - No. 8. - P. 771-802.</mixed-citation><mixed-citation xml:lang="en">Mergner S., Bulla J. Time-Varying Beta Risk of Pan-European Industry Portfolios: A Comparison of Alternative Modeling Techniques // European Journal of Finance. - 2008. - Vol. 14. - No. 8. - P. 771-802.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Merton R. C. Optimum Consumption and Portfolio Rules in a Continuous Time Model // Journal of Economic Theory. - 1971. - Vol. 3. - No. 4. - P. 373- 413.</mixed-citation><mixed-citation xml:lang="en">Merton R. C. Optimum Consumption and Portfolio Rules in a Continuous Time Model // Journal of Economic Theory. - 1971. - Vol. 3. - No. 4. - P. 373- 413.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Morgan J. P. RiskMetrics (TM): Technical Document (4thed). - New York: Morgan Guaranty Trust Company, 1996.</mixed-citation><mixed-citation xml:lang="en">Morgan J. P. RiskMetrics (TM): Technical Document (4thed). - New York: Morgan Guaranty Trust Company, 1996.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Mulvey J., Shetty B. Financial Planning via Multi-Stage Stochastic Optimization // Computers &amp; Operations Research. - 2004. - Vol. 31. - No. 1. - P. 1-20.</mixed-citation><mixed-citation xml:lang="en">Mulvey J., Shetty B. Financial Planning via Multi-Stage Stochastic Optimization // Computers &amp; Operations Research. - 2004. - Vol. 31. - No. 1. - P. 1-20.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Rabiner L. A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition // IEEE Transactions on Information Theory. - 1989. - Vol. 77. - No. 2. - P. 257-284.</mixed-citation><mixed-citation xml:lang="en">Rabiner L. A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition // IEEE Transactions on Information Theory. - 1989. - Vol. 77. - No. 2. - P. 257-284.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Rockafellar R. T., Uryasev S. Optimization of Conditional Value-at-Risk // Journal of Risk. - 2000. - Vol. 2. - P. 21-42.</mixed-citation><mixed-citation xml:lang="en">Rockafellar R. T., Uryasev S. Optimization of Conditional Value-at-Risk // Journal of Risk. - 2000. - Vol. 2. - P. 21-42.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Samuelson P. Lifetime Portfolio Selection by Dynamic Stochastic Programming // Review of Economic Statistics. - 1969. - Vol. 51. - No. 3. - P. 239-246.</mixed-citation><mixed-citation xml:lang="en">Samuelson P. Lifetime Portfolio Selection by Dynamic Stochastic Programming // Review of Economic Statistics. - 1969. - Vol. 51. - No. 3. - P. 239-246.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Sharpe W. F. Capital Asset Prices: a Theory of Market Equilibrium under Conditions of Risk // Journal of Finance. - 1964. - Vol. 45. - P. 425-442.</mixed-citation><mixed-citation xml:lang="en">Sharpe W. F. Capital Asset Prices: a Theory of Market Equilibrium under Conditions of Risk // Journal of Finance. - 1964. - Vol. 45. - P. 425-442.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Shen C. H. Testing Efficiency of the Taiwan-US Forward Exchange Market - a Markov Switching Model // Asian Economic Journal. - 1994. - Vol. 8. - P. 205-215.</mixed-citation><mixed-citation xml:lang="en">Shen C. H. Testing Efficiency of the Taiwan-US Forward Exchange Market - a Markov Switching Model // Asian Economic Journal. - 1994. - Vol. 8. - P. 205-215.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
