Ацканов_резюме_ENG (Динамическая оптимизация стилизованных портфелей акций с применением копул), страница 6

For that the comparison of CVaR stylized portfolios versus Markowitz stylizedportfolios is provided in the table below. As can be seen from the table, in most cases, the newmethod offers better performance (besides the standard deviation of return, which makes it morerisky, although that is justified by higher return). This confirms the H3 hypothesis: copulas doallow for better tracking of the relationship and joint risk of assets, and therefore they allowbuilding a portfolio that is more effective in terms of risk and return than the traditional approachthat uses covariance for risk assessment.

The only style that showed a slightly higher maximumdrawdown for the new portfolio format is profitability stocks, however, this high drawdown isoffset by a higher expected return and new method still has advantage in terms of the return-torisk ratio. Therefore, the advantage of the new method is confirmed for all considered styles andH3 hypothesis is accepted fully.MomentumProfitabilityGrowthValueDividendsGain-To-Pain RatioSortino RationAnnualized standard negativedeviationMaximum DrawdownSharpe RationAnnualized standard deviationAnnualized returnTotal RturnPortfolio methodInvestment StylesTable 3 Comparison of the results of Stylized CVaR-Copula portfolios and Stylized Markowitz portfoliosMarkowitz307.6%13.51%26.12%0.5267.48%-22.4%0.600.20Copula CVaR587.9%19.00%26.80%0.7165.19%-20.8%0.910.29Markowitz285.9%13.0%27.9%0.4667.7%-21.0%0.620.19Copula CVaR492.6%17.4%28.2%0.6268.4%-20.1%Markowitz296.3%13.23%29.17%0.4571.20%-20.4%0.870.650.260.19Copula CVaR678.3%20.34%29.45%0.6968.53%-19.8%1.020.30Markowitz364.5%14.86%35.45%0.4272.88%-22.2%0.670.20Copula CVaR513.7%17.78%36.17%0.4972.06%-22.0%0.810.25Markowitz174.8%9.55%31.05%0.3177.68%-21.5%0.440.12Copula CVaR327.5%14.00%31.96%0.4476.64%-20.9%0.670.18Table 4 below provides comparison of the proposed copula CVaR procedure of stylizedoptimization and the naive method of constructing a stylized portfolio.

A naive method is theconstruction of a portfolio with all assets in it weighted equally. For better comparison naïveportfolios are also stylized in a way that they contain Top-30%, Top-40% or Top 50% or assetsof a particular investment style. As can be seen from the Table 4, almost for all styles, a CopulaCVaR approach with a stylized portfolio optimization gives better results in terms of return torisk ratio than naïve approach.

However, there are 2 caveats:• Naive construction of a growth stocks portfolio gives better results than the stylizedoptimization approach in terms of all coefficients except standard negative deviation andmaximum drawdown. Although the advantage is not significant in order to simplify investmentprocess, it makes sense to choose the naive approach over the Copula CVaR approach• For momentum and dividend styles, stylized Copula CVaR optimization may appear morerisky in terms of the standard deviation, although higher risks are justified by higher return.NaiveMomentumCopula CVaRNaiveProfitabilityCopula CVaRNaiveGrowthCopula CVaRNaiveValueCopula CVaRNaiveDividendsCopula CVaRGain-To-Pain RatioSortino RationAnnualized standard negativedeviationMaximum DrawdownSharpe RationAnnualized standard deviationAnnualized returnTotal RturnPortfolio methodInvestment StylesTable 4 Comparison of the results of portfolios constructed by the naive and the Copula CVaR method proposed in thispaper285%587.9%13%19.00%27%26.80%0.490.7170%65.19%-24%-20.8%0.550.910.180.29391.9%492.6%15.46%17.4%28.49%28.2%0.540.6269.58%68.4%-19.6%-20.1%0.790.220.870.26739.8%678.3%21.16%20.34%29.34%29.45%0.720.6970.84%68.53%-20.2%-19.8%1.051.020.300.30-53.5%513.7%-6.68%17.78%38.72%36.17%-0.170.4989.60%72.06%-28.3%-22.0%-0.240.81-0.070.25173.4%327.5%9.50%14.00%31.17%31.96%0.300.4476.66%76.64%-21.3%-20.9%0.440.670.120.18Thus, the hypothesis H1 about the advantage of stylized optimization over the naive method ofbuilding a portfolio can be accepted, but with the above-mentioned exception for growth stocks3.

Main conclusions of the studyIn this paper, methods for optimizing stylized investment portfolios were developed andanalyzed. The introduced methods allow obtaining effective portfolios corresponding to one ofthe specific investment styles - value, growth, profitability, dividends, and momentum. At thecore of the methods is the optimization with the utility function that uses the ratio ofcharacteristic of a particular investment style to a measure of risk of the portfolio. That way aninvestor can obtain a portfolio that suits particular investment style, yet is also balanced in termsof risk. The introduced procedure was defined as a stylized optimization of the investmentportfolio.

Stylized portfoliosfrom 2006 to 2017, and thennaive stylized portfolios andunder particular restrictions,Federation.were built from stocks of Russian companies during the periodcompared with the benchmarks - the MICEX Total Return Index,stylized Markowitz portfolios. Also, portfolios were constructedcorresponding to the regulation of mutual funds in the RussianThree hypotheses were tested within the framework of the study:H1: The hypothesis of the advantage of stylized portfolio optimization over the naive approachof building a portfolio with equal weights for each of the styles in question - value, growth,profitability, momentum, dividends.H2: The hypothesis of the advantage of stylized portfolio optimization before the market, as theproxy of which is the stock index.H3: The hypothesis of the advantage of using copula to assess the joint asset risk with stylizedportfolio optimization before the more traditional approach using covariance.An advantage of one portfolio over another was defined by higher ratios of expected return torisk.

A number of performance coefficients were used for comparison of the portfolios. Based onthe results of the study, it was proved for all the considered styles the advantage of theintroduced methodology both over market benchmark and over stylized Markowitz investmentportfolio. Therefore the hypotheses H2 and H3 have been fully accepted.

The H1 hypothesis ispartially accepted, since for growth style a naive approach of construction a portfolio yieldedslightly better results than stylized optimization.In addition, the stylized portfolios were compared to each other. In terms of the ratio of expectedreturn to risk, the most efficient in the analyzed period were portfolios of growth momentumstocks, although during the period from 2007 to 2011, value portfolio was the top performer.These results generally coincide with the conclusions of modern studies on the behavior ofinvestment styles during periods of crisis, recovery, growth and slowdown of the economy. Thelong-term advantage of the growth stocks and momentum stocks can be explained not only bysuch factors as overstated expectations and reactionary decision-making by investors on theRussian market, but also by a strong imbalance of liquidity, that is, value stocks can be ignoreddue to the fact that they are not liquid enough.

An analysis of possible costs was carried outseparately. Even if one takes them into account, stylized copula CVaR portfolios showsignificant outperformance over the benchmark.The results of this study may be of practical interest to both professional portfolio managers andrisk managers, as well as to private investors with a mathematical mindset, since managingstylized portfolios according to the proposed methodology requires complex calculations.However, it is important to note that this optimization procedure should rather serve as anadditional tool in the process of making investment decisions. Important issues that cannot besolved solely by the proposed methodology include, but are not limited to: exposuremanagement for individual asset styles/classes, hedging of individual risks, loss limitation,market timing and other.

The solution of these issues should allow, among other things, to limitthe size of the maximum drawdown, which is rather large for the introduced stylized portfolios,although smaller that for benchmark.There are several possible developments of the study. Firstly, it makes sense to consider morestrict criteria for determining a particular investment style; this might improve the overallperformance of a stylized portfolio. Secondly, the problems raised in the previous paragraph arealso worthy of separate and detailed consideration.