Ацканов_резюме_ENG (1137943), страница 5
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This study examines momentum for 3, 6 and 12 months’ timeframes. For each periodicity aportfolio is built. The utility function for momentum portfolio is as follows:/Whereis the weighted average return on the portfolio with weights W during previousperiod of time.Dividend stocks in this study are defined as stocks with the highest dividend yield. Stylizedoptimization in this case results in a portfolio that is balanced by risk and dividend yield.
Utilityfunction in this case can be written as:/Whereis the weighted average dividend yield of the portfolio with weights W.Since the correspondence of a stock to a particular investment style is determined relatively to allother stocks in the sample, it seems reasonable to consider several rankings - Top-30%, Top40% and Top-50% of stocks that best suit a particular investment style. In this case, for eachstyle, except for "momentum" there are 3 portfolios, optimized based on the each of the ranks. Inthe case of momentum stocks, 3 periodicities (3, 6 and 12 months) are also considered, making 9different stylized momentum portfolios. Based on the performance of each portfolio the topportfolio for each style is selected for further study. The criteria for ranking of each style are asfollows:1) Growth stocks are ranked in descending order by multiple Price-To-Book2) Value stocks are ranked in ascending order by multiple Price-To-Book.3) Momentum stocks are ranked in descending order by return for the previous period (which ischosen variably 3, 6, 12 months)4) Profitability stocks are ranked in descending order by ROE coefficient5) Dividend stocks are ranked in descending order by annualized dividend yieldTo test the H3 hypothesis, one also needs to determine the stylized Markowitz portfolio.
Stocksare selected similarly to stylized groups as described above, still the utility function is the samefor all stylized Markowitz portfolios:Whereis the mean portfolio return:=,is the standard deviation of the portfolio return:=×,×,Where is the mean return on stock i, is the standard deviation of returns of stock i,correlation between returns of stocks i and j,is the weight of stocks i in the portfolio.is theFor naïve portfolio construction, which is required to test H1 hypothesis, stocks are also selectedvia ratings, mentioned above, but weights in the portfolio are assigned equally.In order to compare resulting portfolios a number of ratios is used. Some of them are describedbelow in detail.The simplest and most common indicator is total return of a portfolio over the whole period(TR):=Whereand−1 %are the portfolio values at the beginning and at the end of the period.From total return one may also calculate average annual return of the portfolio (AR):=(+ 1)−1 %Where T is the total number of days when portfolio was managed, including weekends andholidays.A number of coefficients are used to assess the risk of a portfolio as well.
Basing on Sharpe(1978), one may find it enough to use only the standard deviation of return, but there are moreinformative indicators that might be useful. For example, the maximum drawdown shows thesize of the maximum loss that an investor could suffer if investing in a particular investmentportfolio at certain periods in the past. The maximum drawdown is determined on the basis ofhistorical data. The formula can be written as follows:=−1 %Whereis the portfolio price at time ∈ [1, ],for the entire time before moment t.is the maximum portfolio priceIn fact, comparing portfolios by coefficients that take into account only risk or only expectedreturn is not advisable, since there can be different combinations of risk and return that aresuitable for one investor and do not for the others. Therefore, it is appropriate to consider thecoefficients combining risk and expected return in one.
In addition to the standard performanceratios of Sharpe and Sortino, the coefficient Gain-to-Pain, which was proposed in Fitshen (2013),is used:=Based on the results of optimization of various types of stylized portfolios, most effective oneswere chosen for each of the styles. Next, selected 5 portfolios corresponding to each of the fivestyles (growth, cost, profitability, dividends and "momentum") were compared with MICEXTotal Return Index, naive stylized portfolios and stylized Markowitz portfolios. Also 5 portfolioswere compared and among themselves.The dynamics of the stylized portfolios total return are shown in Figure 2.600%500%400%Value Stocks, top-30%Growth Stocks, top-40%Dividend Stocks, top-30%Profitability Stocks, top-30%1Y Momentum Stocks, top-50%300%Micex Total Return Index200%100%-100%-200%31-Jul-200730-Nov-200731-Mar-200831-Jul-200830-Nov-200831-Mar-200931-Jul-200930-Nov-200931-Mar-201031-Jul-201030-Nov-201031-Mar-201131-Jul-201130-Nov-201131-Mar-201231-Jul-201230-Nov-201231-Mar-201331-Jul-201330-Nov-201331-Mar-201431-Jul-201430-Nov-201431-Mar-201531-Jul-201530-Nov-201531-Mar-201631-Jul-201630-Nov-20160%Fig.
2 Stylized CVaR portfolios performance versus Micex Total Return IndexAs can be seen from the figure, the proposed procedure for optimizing the investment portfolioallows obtaining results that exceed the benchmark (MICEX Total Return Index) for each style.The most profitable in the domestic stock market are stylized portfolios of Top-30% growthstocks and Top-50% 12 month momentum stocks. However, in the first half of the analyzedperiod the leading style was value stocks. From the figure above one may also draw twointeresting conclusions regarding the financial crisis in 2007-2008:• Investment style that first began to decline before the global financial crisis was growth stocks.• Investment style, which started to recover after the global financial crisis of 2008 faster than therest, was profitability stocks and value stocks.Table 1 shows performance indicators for each of the stylized portfolios and the benchmark MICEX Total Return Index.
As can be seen from the table, portfolios of growth and momentumstocks are close to each other not only in terms of total return, but also in terms of risk. They alsohave quite similar Gain-To-Pain, Sharpe and Sortino ratios, yet momentum stocks are slightlybetter. MICEX Total Return Index is the least risky, but the higher risk of stylized portfolios isjustified by higher return ratio.
Thus, H2 hypothesis about the advantage of stylized portfoliosagainst the market, which is represented by MICEX Total Return Index, is accepted.Table 1 Performance indicators of optimized portfolios of different styles vs MICEX Total Return IndexTotal ReturnAnnualized ReturnAnnualizedStandard DeviationSharpe RatioMaximumDrawdownAnnualized StandartNegative DeviationSortino RatioGain-To-Pain Ration352.8%17.22%Momentum12m,Top-50%495.7%20.66%MICEXTotalReturn60.4%5.10%31.96%27.97%27.93%26.34%0.720.400.620.740.1972.06%68.53%76.64%68.35%65.19%67.91%22.0%19.8%20.9%20.1%21.3%22.5%0.770.231.070.310.620.170.860.250.970.320.230.08Value Top30%GrowthTop-40%DividendsTop-30%Profitability Top-30%339.8%16.86%522.1%21.21%217.8%12.94%36.17%29.45%0.47In addition, it is appropriate to consider the possible costs associated with managing stylizedportfolios. Table 2 shows the average annual turnover of the portfolios and the averagetransaction costs as a percentage of the portfolio value.
Transaction costs are assumed to be thefee for the transaction (accepted at 0.15% per transaction, which is a rather high estimate for theRussian brokerage services) and slippage, that is, the difference between the current price andthe price at which it was actually possible make a trade (accepted at the level of 0.2%, which isexpert estimate). As can be seen from Table 2, the impact of transaction costs on the return ofstylized portfolios is limited, although in the case of momentum portfolios, costs may be morethan 1% per year. Therefore for the purpose of cost efficiency growth stocks portfolio will bemore preferable as the performance is similar.
On the other hand, such insignificant transactioncosts can be associated with a relatively small number of stocks, from which the constituents ofthe portfolio are selected. Perhaps the application of the proposed methodologies in markets witha larger number of stocks will result in higher transaction costs.Table 2 Analysis of transaction costs for stylized portfoliosInvestment StyleAverage annualTurnoverAverage AnnualTransaction Costs25.9%41.2%28.1%16.3%287.4%0.09%0.14%0.12%0.06%1.01%Value Stocks Top-30%Growth Stocks Top-40%Dividend Stocks Top-30%Profitability Stocks Top-30%12 month Momentum Stocks Top-50%This study also has to consider whether the use of copulas improves optimizing of stylizedportfolios.
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