CC BY
2
2. Federal reserve bank of St. Louis [Электронный ресурс] URL: https://fred.stlouisfed.org
УДК 336.64
Uralova D.Zh. Master's student 1st course, the faculty of "International Finance" Financial University under the government of Russian Federation
Russia, Moscow
MODERN TENDENCIES IN THE PORTFOLIO FORMATION OF
RUSSIAN SECURITIES
Keywords: securities, investment portfolio, liquidity, Black-Litterman model, Sharpe ratio, Sortino Ratio, modern tendencies
The most well-known and widely used model for the formation of the securities portfolio is a model described in the classical works and G.Markovits A.Roy [6; 10]. This model generally involves maximizing investor's utility function, defined by the expected return and risk of the securities portfolio. As a general rule, to assess the expected return and risk the historical data is used.
At the same time, the Russian stock market's historical data can be an extremely unreliable source of information, especially in times of change in the market trend. As a result, there is a need for incorporation of predictive and analytical information into the model, which is not included in classical approaches.
The main features of Russian economy that should be remembered are as follows:
• Russian financial market is relatively undeveloped;
• Crediting rates are set too high;
• The peculiarities of inflation in Russia. The inflation is rather high, irregular, heterogeneous and poorly forecast;
• Several currencies are actually used in Russian economy simultaneously;
• Complexity of tax structure in Russia;
• The difference between Russian accounting standards and International Financial Reporting Standards (IFRS);
• Lack of government financing of the investment projects;
• Fluctuations in paying capacity of population and contracting parties;
• Legislation instability. [1]
Also it should be noted that one of the peculiarities of the Russian securities market is its relatively low liquidity, which is expressed in the high level of the spread between the lowest and the highest sales price of the purchase price (bid-ask spread).
In addition, analysis of Russian investors' preferences indicates that the most adequate behavior is not described by utility functions, but by the
performance indicators - e.g by Sharpe ratio, which is based on the standard deviation as a measure of risk, and the coefficient of Sortino, based on the "alternative" measure " left-hand "risk (" risk of shortfall ").
Thus, the model of the portfolio, taking into account the peculiarities of the Russian stock market should have the following properties:
a) the objective function should be the maximization of the Sharpe ratio or Sortino ratio;
b) the model must take into account the forecasts of the dynamics of asset prices;
c) the model must take into account the impact of liquidity of the assets on their expected return and risk.
In accordance with the desired properties we should define the formalized objective function of the proposed model. To maximize the Sharpe ratio:
where: SharpeR -Sharpe ratio;;
Rp - the actual yield of the investment portfolio;
Rf - risk-free rate of return;;
op - risk (standard deviation) of the portfolio;;
xi h xj - the desired share of the assets i and j in the portfolio;
^i - expected profitability of the i-th asset;
oij - returns the covariance of assets i and j;
N - number of assets in the portfolio.
To maximize the Sortino ratio:
где: SortR - Sortino ratio;
Rt - the target rate of return;
DSRp - shortfall risk (the risk of left-sided) for the portfolio.
It is appropriate to use the approach developed by Black and R. F. Litterman for Goldman Sachs in 1992 to take into account the formation of a portfolio of securities and asset price dynamics forecasts in the model. The basic model has been presented in the article «Global Portfolio Optimization» [4]. A more detailed analysis of the model contained in the works of K. Bevan and Vinkelman [3], T.M Idzoreka [5], as well as A. Meucci [4; 7; 8].
Formation of of investment portfolio in accordance with the Black-Litterman model is carried out in several stages:
a) the definition of the assets that make up the market portfolio;
b) the calculation of the covariance matrix based on historical data;
c) calculation of yield estimates based on historical data;
d) determining the subjective evaluations of the investor;
e) combining equilibrium and subjective assessments by the model;
f) usage of estimates obtained as input data for optimization;
g) the choice of efficient portfolio, an appropriate degree of risk aversion particular investor.
The resulting estimates in the Black-Littermana models are non-linear combination of objective and subjective assessments. With low reliability of the estimates resulting distribution of asset returns will be slightly different from the original. A high degree of reliability of the estimates, in contrast, leads to the expectation displacement towards distribution estimates.
Model building was carried out by the following algorithm. In the first stage, the analysis of historical data was made:
a) analyzed period was divided into weekly segments;
b) from the list of shares listed on the Moscow Stock Exchange (in the former part of the MICEX), securities with 40 closing price values in the reporting period , the maximum purchase price and minimum sale price at the relevant date of the end of the week segments were selected;
c) for selected securities: the expected average weekly logarithmic yields (expectation), risk (standard deviation and risk unkind), the amount of direct losses (the expectation of the logarithm of the ratio of the maximum selling price to the closing price and the actual logarithm of the ratio of the minimum purchase price to the closing price) were determined; corresponding covariance matrix was built
d) the weighted average shortfall (in terms of net asset) value of the yield of open mutual fund shares for the respective year was used as the target rate of return for the calculation of risk indicators
On the second stage, the forecasts of dynamics of asset prices were built.
In this case, two approaches were used:
a) an approach based on the factor model of return on assets, depending on
the change in Brent crude oil prices;
b) approach based on the determination of the average analysts' forecasts, published on the website of RBC [2]. Next, with a method of regression analysis the parameters of the following equation were determined:
R, = a + bRBrem +e, (5)
where: Ri - logarithmic returns from the i-th asset;
RBrent - logarithmic relative change in the price of Brent crude;
a, b - regression parameters;
e - random error.
After evaluating the parameters of the equation for all the assets involved in the analysis, the expected return for the next period was determined by substituting into the equation (5) the cost of the logarithm of the ratio of the annual futures for Brent crude oil to the current spot price on the relevant date.
When constructing estimates based on analysts' forecasts on the website of RBC, the average target price level of the last three months (October-December) of the respective year was determined. Since these projections are focused on the RTS stock exchange and determine the value of assets in US dollars, the transformation them to "ruble" value was done by multiplying the value of the futures contract on the US dollar on the RTS FORTS market at the relevant date.
In the third step, the obtained priori values (the result of step 1) and forward-looking assessment (result of step 2) were combined on the basis of the Litterman model.
This data was used as an input parameters to optimize the functional (1) for the Sharpe ratio and functional (3) for the Sortino ratio. At the same time, in addition to the constraints (2) and (4) the restrictions on the maximum share of the asset which do not exceed 15% of the portfolio were applied, which meets the requirements of the Regulations on the composition and structure of assets of joint-stock investment funds and assets of mutual funds approved by the Federal Financial Markets Service of the Russian Federation.
To determine the Sharpe ratio the risk-free yield was used, determined by multiplying the average US Treasury bill yields in the corresponding period (generally recognized benchmark risk-free yield) by the ratio of the forward annual ruble to its current spot rate.
To determine the Sortino ratio as the target level the rate of weighted average yield of open mutual funds shares for the period was used.
After getting the results of the procedure of determining the optimal proportion of assets held in the portfolio, the analysis of the effectiveness of the model was made.
The yield performance, risk, Sharpe and Sortino ratios for the resulting portfolio in the year following the considered were determined for this ( ie if the analysis is carried out based on data in 2014, the effectiveness of the model was determined based on 2015 data).
The results of the analysis of the effectiveness of the model during 20142015.
The results of the analysis of the effectiveness of the proposed model, between the years 2014-2015 are presented in Table 1. This period corresponds to the "growing" market. Dynamics of the best on the Sharpe ratio and Sortino ratio model portfolio in 2015 is shown in Figure 1.
Figure 1. Dynamics of model portfolios in 2010 In this period, almost all the models considered in terms of efficiency surpassed the MICEX index. At the same time the best value of the Sharpe ratio and Sortino ratio showed a model based on the Sharpe ratio with forecasts based on oil prices, taking into account the liquidity.
Table 1
Performance indicators of the model during 2014-2015.
Used model Calculation method Profitability Risk (stall dart deviation) Shortfall risk Sharpe ratio Sortino ratio the number of assets ш the portfolio
Sharpe ratio with forecasts based on oil prices and forecasts of analysts Closing prices 34,4% 0,187 0,102 1,477 0,887 18
Sharpe ratio with forecasts based on oil prices and forecasts of analysts (taking into account the liquidity) Closing prices 36,4% 0,187 0,100 1,577 1,095 18
Sharpe ratio with forecasts of analysts Closing prices 33,9% 0,183 0,100 1,480 0,847 19
Sharpe ratio rath forecasts based on oil prices and forecasts of analysts (taking into account the liquidity) Sales prices 35,8% 0,184 0,100 1,573 1,035 19
Sharpe ratio Closing prices 32, S% 0,190 0,107 1,371 0,698 18
S harpe ratio with forecasts о f analysts (taking into account the liquidity ) Closing prices 34,8% 0,190 0,106 1,468 0,886 18
Sharpe ratio with forecasts based on oil pricrs and forecasts of analysts Sales prices 35,2% 0,189 0,104 1,499 0,939 19
Sharpe ratio with forecasts based on oil prims Closing prices 37,0% 0,190 0,104 1,591 1,122 19
Sort ino ratio with forecasts of analysts (taking into account the liquidity) Closing prices 34,3% 0,189 0,103 1,454 0,872 18
Sharpe ratio (taking into account the liquidity 1 Closing prices 36,3% 0,190 0,101 1,554 1,079 18
Sortino ratio with forecasts of analysts Closing prices 33.8% 0.185 0,101 1.461 0,835 19
Sortino ratio (taking into account the liquidity) Closing prices 35,7% 0,186 0,101 1,555 1,024 19
Sharpe ratio with forecasts based 011 the price of oil (taking into account the liquidity) Closing prices 33,0% 0,193 0,109 1,359 0.699 18
Sortino ratio Closing prices 34,9% 0,193 0,107 1.458 0.888 18
Sortmo ratio with forecasts based on oil puces and forecasts of analysts Closing prices 33,8% 0,189 0,106 1.425 0,789 19
Sharpe ratio with forecasts based 011 the price of oil and foiecasts of analysts (taking into account the liquidity) Closing prices 35,7% 0.190 0,106 1,517 0,966 19
Sharpe ratio with forecasts of analysts (taking into account the liquidity) Sales prices 24,8% 0,180 0,101 0.998 -0,061 15
Sharpe ratio with forecasts of analvsts Sales prices 27,2% 0,187 0,107 1,093 0,170 15
Sharpe ratio Sales prices 25,2% 0,174 0,096 1,058 -0,017 18
Sharpe ratio (taking into account the liquidity) Sales prices 27,6% 0.180 0,101 1.154 0,218 18
Sortino ratio with forecasts based on the price of oil (taking into account the liquidity) Sales prices 26,2% 0,185 0,106 1,051 0,078 16
Sharpe ratio with forecasts based on the price of oil Sales prices 28,9% 0,193 0,112 1.144 0,311 16
Sharpe ratio with foiecasts based 011 the puce of oil (taking into account the liquidity) Sales prices 30,2% 0,176 0,100 1,329 0,485 15
Sortmo ratio with forecasts based on the price of oil Closing prices 32,8% 0,184 0,105 1.415 0.709 15
Conclusion
The analysis suggests the following conclusions:
a) with an extended positive trend of the stock market, the highest rates are shown in a model based on the Sharpe ratio with forecasts based on oil prices and / or analysts' forecasts, taking into account the liquidity.
b) keeping the liquidity in most cases leads to an improvement in the efficiency of a model;
c) portfolios, produced on the basis of the models, are poorly diversified, which demonstrates the limited number of attractive ratio of "risk - yield" instruments;
d) it should be noted that none of shares of major issuers, such as "Gazprom", "LUKOIL", "Rosneft "and a number of others were included, which reflects their relatively low investment attractiveness in terms of the ratio of "risk -yield" (perhaps the reason is the increased attention to these assets on the part of analysts and investors, causing them to set prices that are close to "fair", which eliminates the possibility of obtaining additional yield)
e) the negative sequence of the previous conclusion is the need for the investor to analyze the entire market in search of "investment ideas", despite the fact that the final portfolio may enter no more than 20 assets.
Literature:
1. Tregub I.V., Oblakova A.V. Investment project risk analysis in the environment of Russian economy // International Journal of Applied and Basic Research. — 2009. — №1. — C. 31-34.
2. Forecasts and recommendations of professional participants on the Russian
stock [electronic resource]. - JSC "RosBusinessConsulting". - 2012. - Access: http://consensus.rbc.ru/shares.
3. Bevan A. Using the Black-Litterman Global Asset Allocation Model: Three Years of Practical Experience [Report] / A. Bevan, K. Winkelmann. - Goldman Sachs Fixed Income Research, 1998.
4. Black F. Global Portfolio Optimization / F. Black, R. Litterman // Financial Analysts Journal. - 1992. - Vol. 48. - №5. - pp. 28-43.
5. Idzorek T.M. Step-by-Step Guide to The Black-Litterman Model / T.M. Idzorek, G. Jacoby, K. Smimou, A.A. Gottesman, M.C. Jensen // Journal of Business. - 2004. - Vol. 42. - pp. 167-247.
6. Markowitz H.M. Portfolio Selection / H.M. Markowitz // The Journal of Finance. - 1952. - Vol. 4. - №7. - pp. 77-91.
7. Meucci A. Enhancing the Black-Litterman and related approaches: Views and stress-test on risk factors / A. Meucci // Journal of Asset Management. - 2009. -10. - №2. - 89-96.
8. Meucci A. Fully Flexible Views: Theory and Practice / A. Meucci // Risk Magazine. - 2008. - Vol. 21. - №10. - pp. 97-102.
9. Meucci A. The Black-Litterman Approach: Original Model and Extensions / A. Meucci, R. Cont // Encyclopedia of Quantitative Finance: Wiley, 2010.
10. Roy A.D. Safety First and the Holding of Assets / A.D. Roy // Econometrica. -1952. - Vol. 20. - №3. - pp. 431-449.
11. Walters J. The Black-Litterman Model: A Detailed Exploration [Report] / J. Walters, 2008.
УДК 330
Алексеева О. А. студент 4 курса факультет Менеджмент ФГОБУ ВПО «Финансовый университет при Правительстве РФ»
Мокрова Л. П. научный руководитель, доцент Россия, г. Москва ОБЗОРНАЯ МОДЕЛЬ ЧЕТЫРЕХ СФЕР ВЛИЯНИЯ КОМПАНИИ "APPLE". ПРЕПЯТСТВИЯ И ПУТИ ИХ ПРЕОДОЛЕНИЯ Аннотация:
Статья посвящена рассмотрению влияния четырех сфер на деятельность организации, среди которых структурная и политическая сферы, человеческие ресурсы и корпоративная культура. Анализируются барьеры на пути изменений и способы их преодоления в данных сферах.
Ключевые слова: сферы влияния, организационные изменения, стратегия, структура
