Ацканов_резюме_ENG (Динамическая оптимизация стилизованных портфелей акций с применением копул)

National Research University Higher School of EconomicsAtskanov Isuf AlimovichDYNAMIC OPTIMIZATION OF STYLIZED EQUITY PORTFOLIOSUSING COPULASPhD Dissertation Summaryfor the purpose of obtainingPhilosophy Doctor in Economics HSEAcademic supervisor:Teplova T.V., PhD, ProfessorJEL: С14, С15, С58, G11,G23Moscow – 20181. General description of workRelevance of the research topicInvestigation of the basic investment styles on the stock market, as well as tools for optimizationof an investment portfolio under constraints (which can be determined by regulation in RussianFederation) can increase the degree of elaboration of portfolio theory and solve a number ofactual problems in asset management.

Investing by style assumes the division assets into groupsby some criteria. Criteria can be financial indicators of companies (for example, the ratio ofmarket capitalization of the company to its profits), statistical indicators of stock returns (forexample, volatility), etc. Thus, stylized portfolios include stocks that have a specificcharacteristic that allows being attributed to a particular investment style. In addition to the stylecharacteristic, in this study the portfolio is also optimized in terms of joint risk of assets. Takinginto account both the risk and characteristics of the investment style allows one to operate withthe concept of stylized optimization of the investment portfolio.The paper is devoted to the problem of stylized portfolio optimization in relation to mutual fundsin Russia. This on one hand, allows to bring a solution closer to the reality, as the mutual fundsare subjected to certain regulatory restrictions, while on the other hand offers a solution to theproblem in the context of the most common and transparent forms of mutual investment inRussia.

According to the statistics provided by the "National League of Managers" as of June2017 in Russia, there were more than 100 equity mutual funds with total assets undermanagement of about 33 billion rubles.Distinction between different investment styles is one of the logical steps in the development ofthe stock market and portfolio management in Russia. In developed markets such as US or UK,style investing is already quite widespread. There is a wide range of investment funds, includingETFs, with particular investment style (growth, value, momentum, dividends, etc.). Thus, thesolution to the problem of portfolio optimization within specific investment style could be ofpractical importance, since for asset management companies it will allow diversifying the rangeof available investment products, and, consequently, increasing the attractiveness of mutualfunds as a more flexible instrument. On the other hand, indicating particular investment style of afund will add transparency to expected actions of its manager, which will also increase itsattractiveness in comparison to mutual funds, without a particular declared strategy.At present, mutual funds may acquire additional popularity not only due to the appearance ofIndividual Investment Accounts (IIS) offering tax incentives to Russian residents, but alsobecause of reducing rates on bank deposits, which is the main and most preferred alternative tomutual funds in Russia.

Reduction of rates can cause an outflow of money from bank deposits tothe stock and bond markets, which is already happening (see Figure 1 below). In light of this, itis important to note the need for the development of competencies in asset management.

Theresults of this study can become one of the key additions to the toolkit of traders, asset managersand risk managers, both private and professional. The use of the procedures for optimizingstylized investment portfolios within the framework of investment funds management will allowmaking more flexible investment products in terms of investor preferences, thus providing anadditional competitive advantage for mutual funds over other options for financial investments.Considering the relevance of the study from an academic point of view, it is appropriate toemphasize a number of things.

The first one is the problem of optimizing an investmentportfolio, which was solved generally within the framework of the Markowitz portfolio theory(1952). In the paper, it was proposed to compile investment portfolios as a function of expectedreturn at a given level of risk (and vice versa). The study did not specify particular methods forestimation of risk and expected return.

One may find the most famous and simple solution to thisissue in Sharpe (1978). The solution is to use statistical indicators of returns of assets that makeup a portfolio, in particular covariance and mean return. This method for portfolio optimizationis often referred in the literature as the Markowitz portfolio. Individual works have shown theadvantage of this approach to the naive approach, which builds a portfolio of assets with equalweights (Bernartzi & Thaler (2001), DeMiguel et al. (2009) and Windcliff & Boyle (2004)).

Anumber of researchers (Haugen & Baker (1996), Pástor & Stambaugh (2000), Chou et al. (2006),among others) questioned the applicability of other characteristics of stocks (and/or issuers ofstocks) not based on changes in asset prices (for example, market capitalization, multiples,different financial ratios etc.) to portfolio optimization. They also provided comparison of suchmethods with the more common optimization approach based on statistical indicators.Unfortunately, in most of these papers there is no specific methodology that would link theweights in the portfolio to the specific characteristics of the equities. The solution to this problemappeared somewhat later in the studies by Brandt et al (2009), Hjalmarsson & Manchev (2012),Flieberg et al.

(2016), Fletcher (2017). While these works are close enough to the concept of thisresearch, it is important to emphasize advantages of this study in comparison with itspredecessors. First, while the researchers suggested their approaches to building a portfolio withasset weights dependent on the characteristics of companies / stocks, the risk was taken intoaccount only in Flieberg et al.

(2016) and Fletcher (2017). At the same time, the latter two onlyexamine the risk of each asset individually, without taking into account possibleinterrelationships between returns of different assets. This can lead to erroneous estimation of therisk of the whole portfolio. In contrast, this study assesses the joint risk of assets, instead of onlyindividual risks, thus allowing us to more accurately assess the portfolio risk and optimize itaccordingly. Copulas are used in this research to assess the joint risk.

Copulas basically can bedefined as functions of the joint distribution of random variables, which in the case of this studyare daily stock returns. The use of copulas is justified by a number of advantages. First, copulasdo not impose any restrictions on the distribution of random variables, which is important inanalyzing equity returns. Secondly, copulas allow tracking a nonlinear relationship, which makesthem more preferable than linear models. This allows for a better assessment of the joint risk ofstocks and, as a result, more thorough optimization. Thirdly, using the so-called Vine copulas (orpair copula constructions – PCC ), significantly simplifies joint distribution modeling for a largenumber of random variables.

It is important to emphasize that solution to the problems raised inthe study is provided based on only one particular copula model – rotated Gumbel copula. Othermodels are mentioned in the text, but does not discussed in detail, as the main purpose of thestudy in stylized portfolio optimization. The problem of comparison between different copulamodels is left for other studies.Previously mentioned studies do not consider the optimization of the portfolio within theframework of any investment style, but only explore a set of characteristics to use in portfoliooptimization. In light of this, it seems reasonable to adopt a somewhat more systematic approachthat would consider a specific characteristic (or set of characteristics) of equities correspondingto a certain investment style and build an investment portfolio with assets weights dependent onthat particular characteristic.

That results in a stylized investment portfolio, a portfolio thatcorresponds to specific investment style while taking into account assets risk as well, allowingfor optimal balance between style and risk. The concept of optimality in this case will be definedlater. The following styles are considered: value, growth, profitability, momentum anddividends.Fig.

1 Change in net asset value of mutual funds in Russia since 2012 (in billions rubbles)The second aspect of the relevance of this research from an academic point of view is the maininstrument of the research - copulas. The idea of applying copulas to optimize the investmentportfolio can be justified on the one hand by a large number of new papers suggesting variousmodifications of copulas, and on the other hand, by continuing research on its applications infinance. The presence of a large number of modern studies in the field of finance with the use ofcopulas can be justified for a number of reasons.

First, as shown by several studies (Erb et al.(1994), Longin & Solnik (2001), Ang & Bekaert (2002), Ang & Chen (2002), Bae et al. (2003)),time series which represent change in asset prices are generally not elliptically distributed, whichlimits the applicability of some alternative models. On the other hand, in the case of copulas,there are no requirements for the initial distribution of data, which makes them much moreflexible and applicable. Secondly, copulas allow tracking the non-linear relationship betweentime series, which significantly increases their explanatory power in comparison with linearmodels (Patton (2006), Patton (2012), Creal et al. (2013)). In addition, copulas transfer the issueof the relationship of asset returns to the field of probability theory, allowing operating with suchconcepts as Value-at-Risk, which is widely used in assessing the risk of the investment portfolio(Kakouris & Rustem (2014)).