Ацканов_резюме_ENG (Динамическая оптимизация стилизованных портфелей акций с применением копул), страница 2

Another important aspect of this study is the construction of amultidimensional copula using a Vine - copula (or construction of pair copulas - PCC). Thisapproach has been used in a number of works, including Joe (1996), Bedford & Cooke (2001,2002) and Kurowicka & Cooke (2006), Penicas (2014), Travkin (2013) and others. Vine copulas significantly simplifies the calculations when constructing a multidimensional copula.Object and subject of researchEquities and depositary receipts of issuers, domiciled in the Russian Federation, as well asstylized investment portfolios, made up of them under the restrictions imposed on the equitymutual funds in Russia, are the main objects of the studyThe subject of the study is stylized portfolio optimization under given restraints and withimplementation of copula to measure a portfolio risk.Purpose and objectives of the studyThe main purpose of the study is the solution to the problem of stylized portfolio optimizationwith development of the necessary procedure and utility functions, as well as assessing thefeasibility of using copulas for this.

At the same time, optimization is based on the characteristicsof equities, which reflect each the aforementioned styles. In this case, optimization is understoodas maximizing the ratio of the style characteristic (which, if one would draw analogy with theportfolio theory of Markowitz, can be interpreted as a proxy for the expected return) to measureof portfolio’s risk.The main objectives of the study:• Build ratings for equities based on investment style characteristics• Develop utility functions that take into account the risk and correspondence of equities to aparticular investment style• Justify the applicability of copulas to optimizing investment portfolios• Justify the advantages of the developed optimization procedure in comparison with the market,using various coefficients of risk and expected return of the portfolios.• Justify the advantage of using copulas in portfolio optimization versus the more traditionaloptimization approach – Markowitz portfolio.• Present results and comparative analysis of stylized portfolios of domestic issuers, as well asjustify the practicality of applying suggested methods.Main HypothesesIn the framework of this research, a number of hypotheses are tested:H1: The hypothesis of the advantage of stylized portfolio optimization over the naive approachof building a portfolio with equal weightsH2: The hypothesis of the advantage of stylized portfolio optimization over the market,represented by stock index.H3: The hypothesis of the advantage of using copula to assess the joint asset risk with stylizedportfolio optimization over the more traditional optimization approach of using covariance andmean return (Markowitz portfolio).Degree of elaboration of the problem.The problem of this research stands at the junction of three areas - the portfolio theory,investment styles and the application of copulas in finance.

Separately, each of these fields ofstudy is quite developed, as indicated by the quantity and quality of the relevant literature.Copulas were proposed by Sklar (1959) back in the last century, but the main papers on the useof copulas in finance began to appear much later - after 2000. It is important to note that thework by Sklar (1959) did not take into account the possibility of changing the structure of thejoint distribution over time.

Meanwhile, a number of research papers in the field of financeshowed that the parameters of joint distribution can change with time, as some significant eventsmay occur. So, Embrechts & Dias (2004) showed the inconsistency of the joint distribution(copula) parameter for the returns of currency pairs; Hu (2008) and Ning (2009) compared staticand dynamic copulas using data on several national stock indices. Although static copulas aresimpler in computation and may even have sometimes more explanatory power than dynamicones, researchers come to the conclusion that dynamic copulas offer greater flexibility tochanging conditions, which is quite important in the field of finance.

Most modern works usingcopulas to assess the relationship of assets or portfolio risk involve the use of a dynamic copula(Ning (2009), Hu (2008), Patton (2013), Deng et al (2011), Bai M. & Sun (2007)). The first mostsignificant paper presenting conversion from a static copula to a dynamic copula is Patton(2006). It also shows the structural shifts in the level of the relationship between currency pairsat the time of introduction of the euro, which was tracked by conditional SJC-copula. Theconditional copula by Patton (2006) has been widely used by researchers for assessing the risksand the level of interdependence between asset returns (Chen & Fan (2006), Genest & Remilard(2008), Remilard (2010), Palaro & Hotta (2004), Huang et al 2009), Brechmann et al (2013) andHu (2010) among others).As noted in Patton (2012), the early studies on copulas were mostly related to the construction ofa two-dimensional joint distributions.

Although most modern works still consider twodimensional or relatively small multidimensional joint distributions (for less than 10 randomvariables), there are also works that consider relatively larger dimensions for joint distributions.The most common approach for construction of multidimensional distributions is the Vinecopulas (also known PCC copulas (Travkin (2013)) or hierarchical copulas (Penicas (2014)), inwhich a multidimensional copula is divided into a combination of conditional pair copulas andmarginal distributions.

The first findings on Vine-copulas can be found in Joe (1996), Bedford &Cooke (2001, 2002), and Kurowicka & Cooke (2006), while the later works study largerdimensions – Aas et al (2009), Heinen & Valdesogo (2009), Min & Czado (2010).Considering portfolio optimization, the key paper is Markowitz (1952), which offers proceduresfor optimizing the investment portfolio of assets based on their statistical indicators. Variousmodifications based on Markowitz (1952) have been proposed, allowing the optimization of aninvestment portfolio with short positions, which was omitted in the original work (Jacobs et al(1999), Jacobs et al (2005), Konno et al. (2005), Jacobs et al (2006), Davidsson (2012)). Anumber of researchers also considered optimizing an investment portfolio under constraints Cvitanić & KaratzasI (1992), Korn & Trautmann (1994), Chekhlov et al. (2000), Krokhmal et al(2001), Wu (2012), Cesarone et al (2013).The convenience of using copulas in assessing risk of a portfolio and an interdependence of assetreturns has become one of the reasons for the emergence of studies relating to the application ofcopulas in the optimization of an investment portfolio.

The significant amount of research hasbeen written on the subject (Patton (2004), Bartram et al. (2006), Hong et al (2007), Bay & Sun(2007), Ortobelly et al (2010), Deng et al. (2011), Michiels & De Schepper (2012), Ortobelly etal. (2012), Christoffersen & Langlois (2013), Kakouris & Rustem (2014), Han et al (2016)among others). Nevertheless, it is possible to identify several problems that have not yet beenfully resolved, and are addressed in this study.

First, there is no research on optimization of aninvestment portfolio of Russian equities. Second, there is no full-fledged study on portfoliooptimization under constraints (for example, a restriction on the weight of a single issuer in aportfolio, such as in mutual investment funds) for optimization with copulas. It is worth notingthe lack of full-fledged work, exploring various aspects of optimizing the investment portfoliowith the use of copulas.Style investing classification is quite firmly entrenched in the world of finance, and researchersoften try to compare different approaches to investing in order to choose the best one by somecriteria (Graham & Dodd (1934), Basu (1977), Barberis & Shleifer (2003), Black & McMillian(2004), Wahal & Yavuz (2013)).

Normally such studies consider the profitability of the so-calledmarket neutral portfolio, in which equities of one style are taken into the portfolio with positiveweights (long position), while equities of a different style are taken into the portfolio withnegative weights (short position). The profitability of such market neutral portfolio should reflectthe existence of the statistically proven advantage of one investment style over another. It isworth mentioning that distribution of weights between individual equities of the same style is notconsidered in such works. Instead so-called naive approach is implemented, when each of theequities has the same weight as others, without additional rules.

Such studies do not take intoaccount liquidity of shares, which may make the research results inapplicable in actual assetmanagement. Even if one ignores liquidity, as its assessment is not always trivial, at least theweight in the portfolio can be distributed taking into account the market capitalization of theportfolio, which may partly be a liquidity proxy. In addition, most of the stock indices arecalculated that way (for example, the whole group of MICEX indices). Thirdly, the balancedportfolio essentially gives all the assets in it equal weights, while individual stocks can be morevivid representatives of one or another investment style and, accordingly, should receive moreweight in the final portfolio. In this study, the last of these problems is solved.One of the most common breakdowns is stocks of growth versus stocks of value. As noted in anumber of researches (Bourguignon & De Jong (2003) and Bird & Casavvechia (2007), Cahine(2008), Athanassakos (2009)) these are the two most well-known investment styles.