Саркисов_резюме_ENG (Формирование портфеля акций на фондовом рынке с использованием непараметрических методов)

National Research University Higher School of EconomicsArtur R. SarkisovConstructing of an Optimal Portfolio on the Stock Market Using aNonparametric MethodPhD Dissertation Summaryfor the purpose of obtainingPhilosophy Doctor in Economics HSEAcademic Supervisor:Elena A. Bujanova,PhD in Physico-Mathematical ScienceJEL: G10, G11, G17Moscow – 2018Problem descriptionForming of an investment portfolio is one of the main subjects ofmodern finance theory. In economic literature there are a lot ofresearches devoted to forming optimal investment portfolio usingtechnical and fundamental analysis of characteristics of issuers byparametric methods.

However, often the application of parametricmethods of analysis leads to ineffectiveness and bias of final estimates.This is due to the fact that in most cases the analyzed data series wereeither too short or had an unstable internal structure. Thus, at themoment, an important issue is the development of algorithms forhandling with short time series and series with a large number ofoutliers. Due to these problems was caused the transition from methodsbased on distribution characteristics of variables to the nonparametricmethods, which don’t impose such requirements.

Therefore, therelevance of dissertation research is caused by the need to improveapproaches of the forming of investment portfolios on the basis ofanalysis of factors of technical and fundamental analysis.Contribution1. For the first time were developed algorithms of forminganinvestment portfolio on Russian stock market (MICEX) using threenonparametric methods: CART, ANN and kernel regression.2.

The effectiveness of nonparametric methods has been proved bycomparing of returns of portfolio formed using nonparametricmethods, market return and return of portfolio formed usingparametric method. The analysis was conducted on time period ofstable market (jan.2016 – dec.2016) and on time of crisis (jan. 2008– dec.2008)3. The unique set of factors determining dynamic of MICEX indexand ,hence,its return was found.

This set of factors provedhypothesis of speculative nature of Russian stock market.4. For the first time was conducted comparative analysis ofeffectiveness nonparametric method on Russian stock marketBrief literature reviewIn the area of constructing an optimal portfolio using nonparametricmethods the following two areas of research should be highlighted.

First: atearly stages of development of this direction, researchers tried to show theeffectiveness of the nonparametric methods, using only standard indicatorsof fundamental analysis. Second: in later studies attempts were made toobtain the optimal combination of factors for both technical andfundamental analysis, which would be most suitable for a specific market.Below is a list of the main works on the use of nonparametric methods infinance.Breiman (1987) formulated the main advantages of nonparametricmethods: Don’t require preselection of parameters; there is no problem ofmisspecification Insensitive to monotonic transformation of independentvariables Results are robust to sample outliersAndriyashin,HardlyandTimofeev(2008),Breiman(1984),Chavarnakul and Enke (2009) described the theoretical basis for using themethod of classification trees to construct an optimal portfolio in the stockmarkets of developed countries.The method of kernel regression was used Shiraishi & Taniguchi(2007) to estimate the variance of stock returns on the Tokyo StockExchange.

The authors showed that by using of thisnonparametricmethod it is possible to effectively predict the behavior of stocks and buildan optimal portfolio. At the same time, the authors note that theeffectiveness of a nonparametric method can be different depending on thedata structure.The so-called I (d) processes (Bierens, 1997) was used in research byAue & Ming (2014), in which the authors built a model of optimaldiversification in the selection of securities to the portfolio.

The authorsfound that US stock markets (Dow Jones 30 and S & P 500) are pairwisecointegrated with the BRICS stock markets.Krizanowski et al. (1992), Jang and Lai (1994), Freitas (2001), Aliceand Wilson (2005), Vanstone (Vanstone et al., 2010) , Fernandez and Gomez(2012) used in their works the method of artificial neural networks to buildthe optimal portfolio.Authors of these researchers have developed atheoretical foundation for the portfolio selection using the ANN methodand the main algorithms for determining the optimal size of a neuralnetwork.

Not only projections of the cost of financial instruments wereconstructed using the ANN method, but also the effectiveness of thismethod was tested by fitting to existing data.Agurar and West (2000), Avramov (2002), Barberis (2000), Brown(1976), Cremers (2002), Frost and Savarino (1986), Crawford and Wood(2016) used different variations of the Bayesian methods to constructeffective trading strategies in stock markets. Moreover, in these studies, ahigh degree of stability of the results was noted even though there werestructural shifts in the data and short data series.Objectives of the researchThe main goal of the research is to evaluate effectiveness ofnonparametric methods as an instrument for portfolio selection on Russianstock market and develop algorithms of portfolio formation and managingusing nonparametric methods.To achieve the goal the following objectives were formulated:1.

Order theoretical and empirical studies devoted to portfolioselection using parametric and nonparametric methods2. Form a system of fundamental, technical and macroeconomicfactors which will be used in portfolio selection by nonparametricmethods3. Develop an algorithm for constructing and rebalancing aninvestment portfolio using CART, ANN, and the method of kernelregression4. Form investment portfolios using developed algorithms, andcompare the obtained results with the market return, as well aswith return of the portfolio formed using the parametric method.Make this check on the period of a stable market and during thecrisis period5.

Identify the main determinants of the changes in the Russian stockindex. Check selected factors on economic interpretation6. Compare the effectiveness of nonparametric methods amongthemselves. Solve the problem of maximizing the investor's utilityfor different levels of risk aversion7.

Test the developed algorithms for false significance on the series ofrandom walksMethodologyIn use of nonparametric methods an important step is selectingthe correct input parameters (for example, for neural networks, thenumber of layers and neurons in each). Within the framework of thisstudy, for each of the three methods (CART, ANN, and the method ofkernel regression) optimal parameters of the architecture wereselected, which allowed constructing effective algorithms for theformation of investment portfolios.• For the classification tree method was used the SE Rule forthe training sample to determine the optimal tree size.

By solving theoptimization problem, the size of the test sample was obtained atlevel 35% of the total number of observations.• For a ANN method were formed artificial neural networkswith 3 hidden layers of 9 neurons in each. The method ofconstructing "learning with the teacher" with the backwardpropagation of the error was used.• For the method of kernel regression was used the NadarayaWatson evaluation function was used, which showed better resultsthan the Priestley-Kao and Gasser-Müller methodsIt should be noted that despite the existence of procedures thatallow selecting architecture parameters for nonparametric methods,the main selection method is the trial and error method.

Theeffectiveness of input set of parameters could be studied onlyempirically on test samples.For two methods (classification trees and artificial neuralnetworks method) to form optimal trading strategy it was necessaryto assign a certain class from a finite set of classes С = {1,2, … , }.For financial assets it is convenient to form classes depending on theirreturn ( ): {buy asst}, {sell asset}, { hold asset}.

The threshold value̅ was used for each asset as a criterion for assigning one of the threeclasses. ̅ was based on the average value of the asset's return overcertain period in the past: > ̅, = {buy asset}[ < −̅, = {sell asset}−̅ ≤ ≤ ̅, = {hold asset},where threshold values −̅ и ̅ were selected basing on the averagereturn of the target market over analyzed period.Stocks of the companies, which are included in MICEXcalculation base, were analyzed in this research, because they are themost liquid instruments on Russian stock market.

Weekly return ofthe stock was analyzed. It was calculated by following formula: =where: (+1 ) − ,(1) −return of share in period , − price of the share in period ,+1 − price of the share in period + 1, (+1 ) − expected from period price of share in period + 1.Thus, the primary formation of portfolios constructed using themethods of classification trees and artificial neural networks consistsof following steps (example of the algorithm used for the test period2016):1. Input matrix was formed for each company included inthe calculation base of the MICEX index and include datafor the period from January 2008 to December 20152.

Class vector was formed for each observation С ={(buy sell), (sell asset), (hold asset)} depending on the ratioof weekly returns and index returns for the period fromJanuary 2008 to December 20153. Shares of companies were selected, which at the time ofDecember 2015 were assigned a class {buy asset} based onthe built classification trees and neural networks4. Determine the weight of shares with class {buy asset} inportfolio by solving the next optimization task to maximizethe Sharpe ratio of the portfolio:max −= ∑=1 = √∑=1 2 2 + 2 ∑−1=1 ∑=+1 (2)∑=1 = 1 ≥ 0,{where: − return of share , − st. dev. of share , − weight of share in portfolio.Risk free rate was determined as monthly average return ofgovernment bonds with tenor 3-5 years.After the initial formation of portfolios they were rebalanced every 3months.