Russian mutual funds: skill versus luck

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National Research University

Higher School of Economics

Perm Branch

School of Economics and Finance

RUSSIAN MUTUAL FUNDS: SKILL VERSUS LUCK

Perm 2015



Contents

Introduction

Theoretical background

Research Design

Methodology

Results

Conclusion

References

Appendix



Introduction

An estimated 584 billion rubles is managed by Russian mutual funds, as of 2014. Among them 113 billion belongs to open-end funds, 40% of which are equity funds. Most of these funds are actively managed. The costs of professional management are from 1% to 4% per year, sometimes even higher. It depends on fund`s type and who is operating the fund. [National League of Managers, available at: http://www.nlu.ru/stat-scha.htm] Equity funds do not have the biggest share among other types of mutual funds on Russian market, but they provide higher returns and the frequency of portfolio changes is usually higher. That makes them attractive to many investors. Smaller amount of money under management of funds operating with stocks compared to bonds only means that people invest less in more risky assets because bonds are less volatile. Funds operating real estate, commodities, hedge funds and others that are not connected to stock exchange are close-end or interval. Thus makes equity funds most important and interesting to analyze in terms of skill. Especially since they are most volatile. There are different parameters that can give information about funds management. They are: sharp coefficient that shows the ratio of excess returns and risk, Jensen alpha, the constant of “outperforming” the market or that can be described as contribute of the manager. These coefficients help investors to pick a fund. But are they sufficient enough to tell which fund is managed skillfully? In the 20^th century it was said the higher alpha the more skilled are the managers. The main problem is that the results or alphas should be not only high but also stable for at least a few years. There wasn't a fund that was able to stand on the top for many years in a row. And that is the problem. High coefficients do not necessarily mean high returns in the future because former great performance can be explained by luck. Another way to measure skill and to choose the fund is needed. A few answer for these problem where found in the papers described below and more detailed in next chapters. One of them is bootstrap approach, which will be the key method in our research. Using it luck can be distinguished from skill. According to this approach funds can be managed skillfully without top alphas and vice versa - top alphas do not mean top skill.

Investors look for managers to skillfully manage their money for a fee. But there is asymmetry of information on the market as the complete information of managing skills have only managers. In most cases an investor want to know the presence of managers skill not it`s quantity estimation. The question is what fund should get the money or should people even invest in equity funds in Russia. It means that this research can be useful to investors and the approach can be used to reduce asymmetry of information. They can then decide to pick a fund or it is better to open a deposit in a bank or invest their money elsewhere. What is more, mutual funds' managers can measure the effectiveness of their performance and make key decisions to obtain “skilled alphas” using this approach.

The purpose of this paper is to measure the role of skill in Russian equity funds management during the last 9 years. Is it luck that explains their performance or is it skill? In order to achieve the main goal several steps should be taken: first is to collect the necessary data; then it should be analyzed and used according to the main papers in this field, using bootstrap or synthetic portfolio approach in the search of answer why funds have such alphas - luck or skill; finally, present the results and then make this paper`s conclusion. But these steps are practical part. Before that it is important to choose and understand methods that should be used to answer solve the research`s problem.

There are few researches and papers in this field about Russian market. Especially, recently with fresh data. The originality of this paper lies in sample and variety of models used to distinguish skill from luck as well as analyzing different from bootstrap simulations method - synthetic portfolio approach. There were analyzed Russian open-end equity funds from January 2005 to the beginning of 2014, meaning that the sample is fresh and it has not been analyzed much by other researchers yet. The main idea behind starting with 2005 is connected with extremely fast growth of Russian market during 1999-2006. During which indexes like Micex and RTS increased by 10 times or even more. The reason of this growth was probably because stock exchange in Russia was young and new to the country which only recently has been changed from socialism to capitalism. So, the period of abnormal growth was excluded. During the time the research was conducted one paper with fresh data was published, but the sample itself and models used were different. There was no papers with recent data, more complicated models in bootstrap approach on Russian market. Moreover, there would be introduced with explanation from economic point of view a parameter special for Russian market.

The basic papers are: “Luck versus Skill in the Cross Section of Mutual Fund Returns” by E. Fama and K. French, “Can Mutual Fund “Stars” Really Pick Stocks? New Evidence from a Bootstrap Analysis” by R. KosowskiI, A. Timmermann, R. Wermers, and H. White. They used the same bootstrap approach on US market with different models and period to distinguish luck from skill. The results were similar and can be found in the next chapter. But the idea of measuring fund's performance goes back more than 50 years. The authors presented next tried to estimate the effectiveness of funds` managers. W. Sharpe studied mutual funds and in his paper “Mutual Funds Performance” (1966), he introduced the Sharpe Ratio, which was already mentioned earlier. Also, important for this paper was the research of M. Jensen “The performance of mutual funds in the period 1945-1964” (1968). Jensen alpha is the core to bootstrap approach. Two more related papers are concentrated on US market: “The persistence of mutual fund performance” by M. Grinblantt and S. Titman (1992), “On persistence in mutual fund performance” by M. Carhart (1997). They test returns on stability in time. The paper on Russian market analyzed in this research is “Do Russian Mutual Funds Overperform the Market?” by D. Muravyev (2006). Last paper is similar to E.Fama`s and K.French`s in terms of methodology and is one of the basic papers for this research. The methods and results of mentioned papers are presented in the next chapter.

financial market mutual fund



Theoretical background

This topic first appear in 1960-s and one of the first papers was the work of W. Sharpe “Mutual Funds Performance” (1966). He studied the effectiveness of open-end mutual funds in USA. He created Sharpe coefficient that considers returns and risk simultaneously. His conclusion was that funds didn`t provide returns above benchmark. But he found evidence of stable returns provided by mutual funds. This paper is one of the first and major steps in analyzing performance of mutual funds. Sharpe ratio is still one of the most popular ways to measure fund`s performance. Most investors take it into account in their decisions. “Mutual Funds Performance” may be not the primary paper for this research since its ideas are not used in this paper`s methodology but it is still one of the first and basic papers in analyzing and estimating mutual funds` effectiveness. Also, in this paper Sharpe ratio will be used to check if the funds with skill chosen according to our approach are among the top in terms of Sharpe coefficient or not. The first formula introduced in 1966 is:

,

where: Sh - Sharpe coefficient;

E(R) - average returns;

Var(R) - variance of asset;

- risk-free rate.

A year before in 1965 J. Treynor made a coefficient called Treynor Ratio with similar idea - to represent returns and risk in one coefficient. But for the risk was used в with the market. The main difference is that it concentrates on systematic or market risks (systematic part of variability) and Sharpe coefficient also take into account idiosyncratic risks (like transitory effects). In other words Treynor Index works well only on well-diversified portfolios.

In 1994 Sharpe acknowledged that instead of risk-free rate should be used benchmark, which changes in time. It changes the initial formula adding benchmarks` returns () to it:

.

But Sharpe Ratio was criticized for several reasons. The main one of them is that the risk in the coefficient should represent something bad and it is measured by volatility. But the last one includes not only bad events but high profits too. Abnormal high return for an asset increases it`s volatility and reduces Sharp ratio. That means that big positive returns are treated as a negative thing. Also, the returns should be stationary or the ratio will be sensitive to time period, meaning that Sharp ratio changes in time and one should carefully pick the period while estimating the ratio. One of modifications that tries to solve the mentioned problems is Sortino ratio. It uses minimum acceptable return instead of risk-free rate and downside deviation. The last means negative part of deviation or when assets lose their value. It has formula:

,

where: So - is Sortino ratio;

- is return for i period of time;

N - total number of returns;

MAR - minimum acceptable return or target return.

Sortino ratio will be also used to check the results of this research. Would the skilled funds have high ratio or not?

Another famous paper that was one of the first to analyze mutual funds' performance was written by M. Jensen in 1968. As already mentioned, it is named “The performance of mutual funds in the period 1945-1964”. The author assessed the abilities of mutual funds` managers provide abnormal returns for the period from 1945 to 1964. The evidence of abilities which can provide returns above benchmark wasn't found. This paper is one of the key to this research`s methodology. Bootstrap approach that will be described later is based on Jensen alpha. The last represents abnormal returns that a manager of a fund or portfolio can provide. Jensen alpha is alpha extracted from regression like CAPM. The formula can be viewed as:

,

where: - is Jensen alpha;

- returns of asset or portfolio;

- risk-free rate;

- beta with the market or benchmark;

- returns of the market or benchmark.

The beta coefficient is constant and is estimated as average through the period. Beta is responsible for timing skills. More about timing can be obtained from J.Graham and C.Harvey in “Market timing ability and volatility implied in investment newsletters` asset allocation recommendations” (1996). Since beta does not change it is assumed that managers do not have timing skills and abnormal returns are provided by picking skills. It mean that alpha represents returns above benchmark by picking assets and beta is the moment of possession of assets on market. Since beta is average across the whole period the moments of changes cannot be tracked. Jensen alpha and CAPM model have more issues. There is a problem with diversification of risks. By increasing weight of one asset with high returns and the same deviation in portfolio the risks according CAPM do not change. One of possible solutions came in 1973 when J.Treynor and F.Black published “How to use security analysis to improve portfolio selection”. They suggested correction of alpha by standard deviation of regression errors:

,

where: - is alpha with corrections;

- standard deviation of regression errors.

CAPM is a basic model, which was many times transformed and used in many papers. From CAPM came famous three-factor model and then four-factor model. In 1993 E.Fama and K.French in “Common risk factors in the returns of stocks and bonds” suggested a modification of CAPM. By observing the market they choose the most significant factors: SMB (small minus big) and HML (high minus low). SMB represents a portfolio with long position on small and short on big capitalization companies, HML - portfolio with long on companies with high book-to-market value and short on low B/M. By adding these two factors to CAPM they create three-factor model. From this idea come another well-known model: four-factor model by M.Carhart. In 1997 was published “On persistence in mutual fund performance”. In this paper was introduced new model based on Fama-French three-factor model. The model includes new factor WML, meaning winners minus losers or a portfolio with long on best companies in the last period (usually a year) and short on worst in terms of returns. M.Carhart concluded that most mutual funds cannot have returns above benchmark for a long period of time, very few can provide stable returns above market. He proposed to analyze top alphas of mutual funds during a long period of time. No fund was able to hold top positions for the whole period. Since Fama-French three-factor and Cathart four-factor models are not used in this paper there will be not much said about these two papers.

In this research Jensen alpha is used but not as a single criteria of fund`s performance but as a part of a process that is necessary to distinguish luck from skill. At first, it was thought that alpha shows manager`s skills. The higher alpha - the better fund is operated. But it is not always true. By observing it is clear that the funds with big alphas are not always with high returns. If a fund has top alpha every year for many years then it can be said that it is managed skillfully. But there is either no such funds or there are few of them. Most funds do not have stable alphas for a long period of time. Jensen alpha by itself cannot separate luck from skill, which makes alpha unstable in time and cannot predict future abnormal returns.

As it was mentioned earlier it were assumed that managers have no timing skills since beta is constant and average from the whole retrospective period. In 1989 M.Grinblatt and S.Titman in “Portfolio performance evaluation: old issues and new insights” showed that a manager with positive expectations will increase his portfolio`s beta with the market and his reaction function depends on his risk appetite. Also, authors found evidence that simple passive strategies can be beaten. [M.Grinblatt and S.Titman, 1989]. Later in 1992 in their paper “The persistence of mutual fund performance” they found out that the difference in different mutual funds` returns are stable in time and have connections with abilities to provide abnormal returns. In this paper only picking skills are tested, so there is no need to discuss timing further.

The core papers for this research with which the last share similar methodology and main ideas are: “Luck versus Skill in the Cross Section of Mutual Fund Returns” by E.Fama and K.French, Can Mutual Fund “Stars” Really Pick Stocks? New Evidence from a Bootstrap Analysis” by R.KosowskiI, A.Timmermann, R.Wermers, and H.White. As it can be noticed from the titles: the topic and the question authors raised are similar to this paper`s. The last is based on the ideas and methods described in core papers. These papers are concentrated on American market, meaning mutual funds in USA. Authors determine the skill contribution to funds alphas in USA. Thus the main goal of current research is to analyze and use their ideas on Russian market as it was done by D.Muravyev in 2006 and then go further with more models and recent data with changes in some assumptions. More detailed information about approaches that were used in these papers can be found in chapter “Methodology”. The main results and research process of core papers are described in short below.

All the core papers are based on bootstrap approach. Authors use different assumptions but general idea is the same. The approach is based on idea of zero skill contribution. It can be achieved through random returns created with zero-alpha model and random errors. The basic form of bootstrap approach with Jensen alpha as a parameter to measure skill is presented below:

a) Estimate real alphas for each fund in the sample using one model. Below is presented an example with CAPM. These real alphas are Jensen alphas. In the equation beta is covariance of funds returns and benchmark returns divided by variation of benchmark returns:

,

where: - means returns above risk-free rate,

- is from regression or Jensen alpha,

- is beta with the market,

- is risk market premium or benchmark returns minus risk-free rate,

- represents errors of the model.

b) Store beta and residuals from the regression for each fund;

c) Use residuals to create new series of pseudo residuals by resampling observations in random order with possibility to replace. It means not only to change order of observations but some of them will be duplicated and some excluded. An example of series of pseudo errors:

,

where: - is series of pseudo returns,

- is t observation of returns е errors from the CAPM.

d) Create new returns using pseudo errors and stored beta, alpha in the model should be zero, so that there would be no skill contribution:

,

where: - is pseudo returns series.

e) Use new returns in CAPM model to estimate alpha. This alpha is one of many zero-skill alphas;

f) Paragraphs from “c” to “a” represents one iteration. Repeating them many times (1000 in core papers) brings out the distribution of zero-skill alphas or distribution of luck;

g) Compare real alpha with distribution of luck for each fund. If alpha is in the left tail then the hypothesis of random returns is false for the fund (it has non-random positive returns that are not only due to luck, positive skill), if to the left the hypothesis is also false, if in the central area than there is no evidence of skill for the fund (it is not just bad luck, negative skill). The significance level is usually 5%, meaning the central area occupies 95%.

In current paper bootstrap approach is a core method to distinguish luck from skill. It is used with several models and assumptions on treating funds with missing values. But in core papers they are different. More can be found below.

R. KosowskiI, A. Timmermann, R. Wermers, and H. White in 2006 tested picking skills of US mutual funds` managers. The authors present a method of measuring picking skills and distinguishing skill from luck of a fund - bootstrap simulations. This approach is used on monthly returns from 1975 to 2002 of open-end equity funds. The models they use are based on Carhart four-factor model. As measure of skill they use alpha and t-statistic of alpha. As already mentioned earlier, alpha is a measure of abnormal performance provided by manager`s skills. T-statistic of alpha “is a pivotal statistic (one that is not a function of nuisance parameters, such as Var) with better sampling properties”. Their method - bootstrap approach is resistant to heteroscedastisity of time series and cross-section, autocorrelation and cross-correlation in funds` returns. Their conclusion was that very few managers have sufficient skills to cover more than the costs of management. Also, the authors uncover “differences in cross-section of funds with different investment objectives”. They find “evidence of superior performance and performance persistence among growth-oriented funds… but no evidence of ability among managers of income-oriented funds”. [R. KosowskiI, A. Timmermann, R. Wermers, and H. White, 2006]

E. Fama and K. French in 2010 published another paper about bootstrap approach on US mutual funds. The sample is equity funds of the USA for the period from 1984 to 2006. As a main parameter of skill measurement the authors use t-statistic of alpha. The main models are CAPM, Fama-French three-factor model and Carhart four-factor model. The authors divide funds into groups by assets under management amount of money. Also, the approach is run on both net and gross returns. Net returns are investors' returns, in gross returns management costs are added. They uncover the evidence of manager skill in situation with no management costs. But by adding these costs very few managers have sufficient skills to beat the market. In aggregate mutual funds underperform CAPM. The authors claim: “Bootstrap simulations suggest that few funds produce benchmark adjusted expected returns sufficient to cover their costs”. [E. Fama and K. French, 2010]

The topic is fresh and still popular among economists all over the world. The most recent papers for foreign markets are: “Fixed-income Fund Performance: Role of Luck and Ability in Tail Membership” (2011) on Canadian market by M.Audi L.Kryzanowski; “The Truth About Mutual Funds Across Europe” (2011) on European market by L.M.Doncel, P.Grau, J.Otamendi, J.Sainz; “Control of Luck in Measuring Investment Fund Performance” (2011) on Korean market (many funds are skilled) by S.Suh and K.Hong; “Separating skill from luck in REIT mutual funds” (2011) on US market of real estate investment trust mutual funds by L.Layfield and S.Stevenson; “UK Mutual Fund Performance: Skill or Luck?” (2008) on UK market by K. Cuthbertson, D.Nitzsche, N.O`Sullivan.

As it was mentioned papers with similar methodology on Russian market are: “Do Russian Mutual Funds Overperform the Market?” by D. Muravyev and the most recent paper "Estimation of skill of Russian mutual fund managers" by P. Parshakov. D. Muravyev in 2006 used the same bootstrap approach to get distribution of t-statistics of alpha of simulations. The sample is 59 funds from September 1999 to the end of 2005. He introduce a new six-factor model for Russian market. If in CAPM there is only one factor and it`s a market itself, in the new model this market is divided into six parts by industries. Some of industries are presented by indexes and some by the company with biggest capitalization. The result is unexpected - most of funds have nonrandom returns, meaning managers have sufficient skills. The author also run another method of estimating luck distribution of t-statistics of alpha - simulation portfolio. According to this method actual distribution of t-statistics of alpha is to the left of simulated, which gives no evidence of skill. The results can be explained by time period but further investigation and research is needed on Russian market with new models and accurate methodology.

The most recent paper on this topic on Russian market was published by P. Parshakov in 2014. He uses Jensen alpha as a measure of risk not t-statistics of alpha. He tests open-end funds that operate with stocks and funds operating bonds on period from July 2001 to July 2012. The returns are daily. The main model used to estimate alpha is CAPM. The author finds evidence of skill for a few equity funds on Russian market (a little more than 10% of the sample). In aggregate equity funds do not have enough skill to provide abnormal benchmark adjusted returns to cover the costs of management. Also, was analyzed the frequency of data and finds the answer to the question: daily, weekly or monthly returns should be used to get most accurate results. The evidence of better accuracy with more frequent data was found. Tests that use returns with longer period are tend to overestimate managers` skills. There some questions about assumptions in bootstrap approach. Also, there funds in the sample that are operating less than an year, their skill can be overestimated since Jensen alpha is used as a measure and not t-statistics of alpha. A fund can have high returns in short run but in a long period it is almost impossible to show stable abnormal high returns (more 100% a year). More models with more complicated specification can be used on Russian market, the results will differ.

To sum up the question of measuring fund`s performance is not new, the recent approach of distinguishing luck from skill is reflected in several papers including on Russian market. But the results still differ a lot, meaning there are different assumptions in the approaches. Most of them are connected with sample, treating funds with different number of observations, choosing a measure of skill, model`s specifications. To progress further on Russian market it is important to choose these differences wisely on new data. One of the most important parts of the mentioned approach is to deal with funds with missing values during bootstrap simulations. This can bring different results and thus the conclusion may differ too. Unlike other papers on Russian market current research claims that very few equity funds are managed with skill and the results are close to papers on US and Great Britain markets. Also, this paper suggests synthetic portfolio settings that should be used to achieve proper results.

Research Design

The purpose of this paper is to develop a method of measuring Russian mutual funds' performance in terms of skill to provide returns above benchmark and apply it to Russian market. What is more, along with the primary goal the objective is to get evidence or to estimate skill of Russian mutual funds managers. This method should be useful for investors to help to make decision of investments or pick a well-managed fund. Managers lacking skill won`t get enough money and thus the whole market can become more efficient by eliminating unskilled participants. Then, the object of this research can be defined as Russian equity funds, the subject - performance of managers of equity funds. As it was described in introduction equity funds are most important to analyze, since they are more volatile and need more skill to operate. This research can show a method of analyzing and picking funds to invest and present current situation on Russian market of mutual funds. Most equity funds have negative 3-year returns. Only about 20% have positive. On such market there is need for a process to find funds with skilled managers. This research can help with decision-making process.

To achieve the primary goal the following plan can be applied:

a) Systematize and analyze existing knowledge on the topic - papers from previous chapter. This step is already described earlier, it is important to take into account not only recent papers about distinguishing luck from skill but also basic ones about measuring funds` performance. As their ideas will be used to compare with this research`s results to make accurate conclusions;

b) Outline the main aspects of research (estimation) process from core papers and create a suitable method to distinguish luck from skill for Russian market. It means to take into account previous experience and choose the most fitting specifications and assumptions while building a method to distinguish luck from skill for Russian mutual funds;

c) Choose benchmark, risk-free rate and sample based on economic point of view. It is also an important part since there are many alternatives and they may provide different results;

d) Analyze data and make interim conclusions and hypothesis. Some crucial assumptions in the approach are made after analyzing initial data; Use selected approach to get distribution of luck (simulated alphas), distinguish skill from luck and present the results. Only bootstrap approach is run completely, synthetic portfolio is only described how it should be conducted and it is explained why this approach isn`t applied in this research ;

e) Make conclusions about funds` performance and Russian market of equity funds. The conclusion is based on bootstrap approach, it provides general idea about mutual funds in Russia and it also suggests funds that are managed skillfully.

The key idea of presented process is to get distribution of luck for each fund. This distribution is nothing else but the results of portfolios managed randomly or in other words without any skill. The whole distribution consists of many of these random portfolios, 1000 in this research. If a certain fund is among the best of these 1000 random portfolios creating especially for this fund, then it has nonrandom returns. It means the fund is managed skillfully. More about the process will be in next chapter. There are two ways of getting distribution of luck (in case of this research - distribution of simulated alphas) described in theoretical part: bootstrap approach and synthetic portfolio approach. This paper is concentrated on first approach and there will be given hints of how should be used the second one and why it is much more time-consuming. Bootstrap approach involves model errors to create random portfolios, synthetic portfolio approach is based on sample of liquid stock for each fund that are picked randomly for a lot of simulated portfolios with zero skill.

From the description above hypothesis H0 for a certain fund is suggested: A fund has random benchmark adjusted returns (result of performance), meaning no skill contribution to fund`s performance. Then H1 should be: A fund has nonrandom benchmark adjusted returns, which means the results cannot be described solely by luck. Since the hypothesis contains both negative and positive returns, it can be divided into two parts: random positive and random negative returns. The difference with the initial hypothesis is only in significance level: 10% level for initial H0 equals 5% significance level for two new H0. For the whole Russian market of equity funds the hypothesis are: H0 - at aggregate there is no evidence of skill in funds` benchmark adjusted returns, H1 - at aggregate skill is distinguished from luck and is significant for equity funds, meaning many managers operate funds skillfully. All the hypothesis are made for Russian equity funds for period January 2005 - December 2013. While testing the hypothesis primary goal will be achieved: to test them there will be needed a method to distinguish luck from skill (it measures the performance of a fund) and the method should be tested or applied on real data. Also, as it was mentioned earlier bootstrap approach is a proper way to distinguish luck from skill. In the next chapter the whole process of this research method will be described and applied on Russian market of equity funds.

The idea of using bootstrap approach to distinguish luck from skill for mutual funds was generated in early 2000`s and is still popular among economists all over the world. As it was mentioned in previous chapter - new papers on the topic are published every year with different markets and types of funds as an object to test. This paper is also one of them: bootstrap approach idea as basement, Russian market, equity funds, period up to 2014.

Methodology

To solve the research question it is needed to value the skill contribution to the result of a particular fund. This contribution can be evaluated by bootstrap and synthetic portfolio approach which provide us with distribution of luck. Compare fund's alpha with this distribution will help to make a conclusion about skills of fund's managers.

A short plan of the research process to get distribution of luck and estimate skill is presented below:

a) Collect data: equity funds` share price, benchmark, risk-free rate, Brent oil prices and currency prices of USD in rubles;

b) Form an appropriate sample and prepare data;

c) Analyze this data and give notes;

d) Estimate real alphas of funds with different models;

e) Run bootstrap simulations and get distribution of luck for each fund with each model;

f) Estimate critical values for each fund based on simulated distribution of alphas;

g) Compare real alpha with critical values and make a conclusion on fund`s performance.

To work through this plan in this research is used software for statistical computing - R. The script is written in programming language R and is available in Appendix 1.

As it was mentioned in other chapters the sample consists of Russian open-end equity funds for period from January 2005 to December 2013. Initial sample includes observations of 219 funds. All the prices for all variables are closing prices. The data can be obtained from National Liege of Managers [NLU, available at: http://nlu.ru/export-excel.htm] and from investfunds.ru portal [available at: http://pif.investfunds.ru/quotes/quotation.phtml]. All the funds were functioning in December 2013, meaning funds that were closed due to bad performance or any other reason are not presented in the sample. These funds are not crucial to research process because it is assumed that the research is needed to make an investment decision in 2014 and not existing funds are unnecessary for this decision. Also, they cannot affect the results for other funds. The period starts from 2005 for several reasons:

a) First and most important is that Russian market and stock exchange are rather young: the process of changing from socialism to capitalism take some time and during it the market changes quickly. It means that old information is not valuable and can harm the research, as it will affect the alphas of models. So, it is better to include data after the market has recovered from crisis 1998;

b) From September 1998 to April 2004 the index of Russian market has risen by 1460% or more than 15 times;

c) In the research is used daily data and since alpha is measured as daily it is important that all returns are daily, meaning that missing dates can harm the results. The daily data availability for more than 9 years ago is limited, not all funds have values for all working days (or at least it is hard to obtain such data)

The period does not include 2014 so that the results of research can be tested ex-post. Will the skilled funds provide good performance in 2014? Would the investors that believe in this research results earn money as they expect? The answer is given in chapter “Results”.

MSCI Russia index in rubbles was chosen as a benchmark. There are several alternative indexes: MICEX, RTS, Russian indexes from S&P and Morgan Stanley. They have differs in weighting and other parameters. MSCI Russia is chosen as the most suitable for this particular case: it includes dividends and corporate events (MICEX and RTS do not), which is important since equity funds invest in shares and get dividends, index is weighted by market capitalization (free float amount) taking into account size of companies. MSCI Russia is also revised frequently - each quarter to consider changes on the market. It can be found on MSCI official site [available at: http://app.msci.com/products/indexes/performance/country_chart.html].

Risk-free rate can be obtained from Central Bank site. There three rates: short, middle and long run rates estimated from GKO-OFZ market [Central Bank of Russia, available at: http://www.cbr.ru/hd_base/Default.aspx?Prtid=gkoofz_mr]. Short rate is too volatile and is for investment less than 1 year. It is not suitable as a risk-free rate for our research. Long run rate has the lowest volatility and is optimal for long investments. It can be used as risk-free, but for long-term investments. The middle one is not volatile and is measured as 1-3 year rate. Investments in equity funds are usually oriented for not more than a few years. Then the appropriate choice is to use middle-term rate from GKO-OFZ market as risk-free rate in this research.

Aside from benchmark, risk-free rate and funds` prices some models also need prices of Brent oil and USD. There are many sources this data can be downloaded from. USD/RUB is obtained from site of Russian stock exchange - Moex or Moscow exchange [available at: http://moex.com/ru/issue/USD000000TOD/CETS]. Brent oil is represented by compilation of futures and can be found on investing.com or any other portal with market information (like yahoo finance, google finance or marketwatch) [available at: http://www.investing.com/commodities/brent-oil-historical-data].

After downloading all the necessary data it should be prepared. Since the instruments described above are traded on different stock exchanges they have different dates. That is because there are different holidays and thus working days in different countries. For example, Brent oil futures that are used in this research are from London Stock Exchange, while funds` shares are on Moscow Exchange. First is to match the dates. So that observations for each variable will be on the same date, observations with unmatched dates should be adjusted or excluded. The prices are needed only to estimate returns. Thus brings a dilemma: to estimate returns before matching dates, so that only daily returns will be presented but some changes will be missed ; to match dates before estimating returns, then all the changes will be included but some returns will be not for one day but for two or three. In this research the second option was chosen. It is important to represent the whole information and changes on the market. Thus the first step in data preparation is matching dates. Since there are more holidays in Russia and stock exchange has fewer working days, most changes are connected with exclusion observations in variables from London and US stock exchanges. After the matching the returns for all variables are estimated using the formula:

,

where: - is returns for period t;

- is a price of a certain asset in period t;

- is a price of a certain asset in period t-1.

It is important to mention that returns are daily and are not converted into per annum format. The same goes for alphas and all the results are presented in daily format. The reason is simple, even if 247 working days in a year are chosen (which is true for 2013 year) then 3% increase in one day (which is rather usual for Russian market) is more than 148000% per annum. After the mentioned changes the sample is still not ready for future analysis. Not all funds should be used, some of them have too small number of observations or too young. As it was mentioned in all the core papers a fund has to have at least 100 observations in order to be used in the bootstrap approach. But foreign papers use monthly returns and this research operates daily returns. As it was mentioned earlier P. Parshakov has found evidence of increasing accuracy of bootstrap approach with an increase in frequency of observations. That is why this research is concentrated on daily data. Funds with 100 daily observations can be managed for less than a year. They can have high returns during this time and thus have high alphas. But with time their mean returns fall as they cannot show abnormal high returns for a long period of time. So, another assumption should be made: funds with less than one year history should be excluded.

Statistical information of returns and of observation number before any changes is presented in Table 1 and the distribution of number of observation before any changes is illustrated on Picture 1.

Table 1

Statistics of funds` returns and number of observations before changes.

	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.	St.Dev.	NA's
Funds_returns	-0,9900	-0,0062	0,0006	0,0003	0,0076	4,0240	0,0217	189684
num_obs	4	615,5	1562	1356	2034	2222	779,04

From the table it is clear that adjustment and changes in sample are needed. There is fund with 99% decline in one day and fund with 402% growth in one day. Also, there is a fresh fund with only 4 observations. The number of missing values is rather big, it is 39% from the whole sample.

Pic. 1 Distribution of number of observations for funds

Picture one shows that the sample is divided into two parts - most funds have number of observations about 1600, also there are many funds with less than 200 observations. The values are scattered and not uniform. As it was mentioned earlier low number of observations can harm the results and such funds should be excluded from the sample.

After matching the dates and excluding funds with observation less than 247 (number of working days in year) the sample changes and is more suitable for analysis and bootstrap approach. The result of changes are presented in Table 2 and distribution of new number of observations can be seen in Picture 2.

Table 2

Statistics of funds` returns and number of observations after changes.

	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.	St.Dev.	NA's
Funds_returns	-0,4819	-0,0062	0,0006	0,0002	0,0076	0,6244	0,0176	95080
num_obs	279	1506	1667	1666	2193	2209	497,37

The statistics presented above demonstrate that the goal of sample improvement is achieved. Number of missing values decreased by half and most funds have more than 1500 observations. Standard deviation dropped by formidable amount. Impossibly high amounts of returns (both positive and negative) also disappeared. The sample has become more homogeneous.



Pic. 2. Distribution of number of observations for funds after sample adjustment

The third peak on the graph is 2209 observations. It is the maximum value of 9 years working days after date adjustment. This distribution is proof that after changes sample is more appropriate but the graph is still fragmented. The three parts are: below 1000, around 1500 and around 2200. But at least most funds are functioning for more than 6 years.

After sample adjustment the returns can be analyzed. Descriptive statistics of cross-section data can provide information about the aggregate performance of equity funds and their market. On Picture 3 is presented distribution of funds` returns.

Pic. 3 Distribution of returns (peak)

As it can be seen from the illustration the long tails are excluded and the graph concentrates on the peak. Most returns are around zero. It means funds usually are managed trying to minimize deviation to minimize risks and thus most daily changes are small. The peak is slightly to the right, also mean and median returns are above zero, meaning funds shares in general can be rising by small amount. But it is important to remember: losing 1% and then gaining 1% will bring the asset below the initial 100% value. Further information can be obtained from distribution of mean in comparison with distribution of median. The graphs can be seen on Picture 3 and Picture 4. On these graphs are also shown benchmark statistics.

Pic. 4 Distribution of mean of funds` returns

The red line is benchmark`s mean. Since the red line is to the right from the peak, most funds are losing to benchmark in terms of mean returns. At least this peak is slightly positive but still all the values are close to zero. Picture 3 confirms the Efficient Market Hypothesis (see P. Samuelson, E.Fama, A.Lo - evolution of EMH), that market is efficient and no strategy can outperform the market (at least, for a long period of time).

Pic. 4 Distribution of median of funds` returns

The red line is benchmark`s median. The situation with median is better than with mean. Mean value of benchmark is to the left from the peak. It means that most funds have more high positive returns than benchmark. Benchmark has roughly the same mean and median values for research`s period. They are 0,058% and 0,056% respectively. The mean underperform benchmark and median outperform while most funds` median is higher than mean. This can be caused by comparatively huge negative returns. Most funds have more positive returns but negative are higher (not sum, but single returns). In general funds try to level the risks and thus mean value is small and funds have many positive but small returns.

Pic. 5 Distribution of min and max of funds` returns

Picture 5 describes distribution of min and max of funds` returns. The graph confirms once again the opinion about funds controlling their risks. From the illustration it is clear that most funds are managed with the goal of minimum risk first and then maximum returns. The high peak of min returns is higher than peak of max returns and to the right of benchmark. It means that most funds are concentrating on minimization of loses and they are better than benchmark in there terms. But the price for loss minimization is small max returns. Most of funds have maximum returns lower than benchmark. Also, picture 5 shows that there are different funds with different policies in the sample. The long tails of the graph are proving that some funds have higher volatility and can provide higher returns. But if such funds have bad luck or not enough skill they can show negative performance like the funds on the left part of the graph. One more evidence can be obtain from distribution of standard deviation, which is illustrated on Picture 6.

Pic. 6 Distribution of standard deviation of funds` returns

As expected, most funds have standard deviation lower than benchmark. They are less volatile and are oriented on stable positive returns. But as it was mentioned earlier there are risky funds. They have much higher standard deviation, minimum and maximum of returns.

The description of statistics above suggests that in general funds are less risky than benchmark. They have more stable returns but lesser volatility also means smaller positive returns. There is small number of funds that are oriented on high and risky investments. These statistics are not enough to make a conclusion about funds under- or outperforming the market (benchmark) or about their managers` skill. Detailed statistics for each fund can be found in Appendix 2.

After preparing and analyzing data (sample) real alphas should be estimated as the first step of estimating managers` skills. The research has three models to estimate alphas. First is CAPM, others have new factors added. The specifications of the models:

a) CAPM, basic model that was described in chapter “Theoretical background”. It is the simplest model, which can be used as comparison to other models.

,

where: - fund`s returns for period t;

- risk-free rate for period t;

- beta with the market (benchmark - MSCI Russia);

- benchmark`s returns;

- error for period t.

It is important to mention that all the variables have to be in daily format. Risk-free rate and returns, even alpha, beta and errors are for one working day. If needed they can be switched to yearly format with 247 working days per year.

b) The second model includes Brent oil index in rubles and everything from previous one. Commodities and especially crude oil and gas have strong influence on Russian economy and market. Brent oil is standard and other types of oil and also gas are guided by Brent. This index has become a common factor for Russian market. But Brent oil futures are traded in dollars while oil companies have a huge part of costs in rubles, also paying taxes in rubles. If oil price drops while US dollar is rising in pair with ruble for the same or even greater amount, then the market in rubles will not suffer. And since all the variables in the model are in Russian currency, it can be logical to use Brent oil index in rubles too. New factor has apparent correlation with risk market premium though. It is a around 0,3. If correlation was higher it could cause instability of factors` coefficients, meaning higher standard deviation in coefficients among funds. To proper analyze the significance of correlation between factors can be used vif coefficient. Variance inflation factor has formula:

,

where: VIF - is variance inflation factor;

- is the coefficient of determination of a regression of explanator j on all the other explanators.

Vif for these model is 1,1 which is less than critical value 5. It means that existing correlation between factors will not harm the estimated coefficients and results. The equation for this regression is:

,

where: - is beta for factor Brent oil in rubles;

- returns or changes in prices of Brent oil in rubles for period t.

c) The last model has the same idea as the second one. The difference is only in how factors are used in the regression. This model separates Brent oil and US dollar so that both factors have their own beta. Changes in national currency also influence the market and share prices. So, USD factor has two meanings: the first one to cooperate with Brent oil, the second one - as separate factor that influence the market. Also there are funds that have foreign assets. Such funds can be influenced by changes in US dollar prices in rubles. Vif coefficients are again below the critical value, which permit the usage of these factors.

,

where: - is beta for factor Brent oil in US dollars;

- returns or changes in prices of Brent oil in US dollars for period t;

- is beta for factor USD/RUB;

- returns or changes in prices of currency pair USD/RUB for period t.

Using regressions above real alphas for funds can be estimated. As it was mentioned earlier M. Jensen claims that alpha represents manager`s skill. The higher the alpha - the more skillfully fund is managed. But before estimating regression coefficients some important assumptions should be made. The funds have different number of observations because they were established in different periods of time. And that is the reason why there would be missing value for many funds. It is important to run the regression only on the existing period. So all the variables should have the same length: if a fund has less observations, then other variables should be shorten to match funds` returns. There 175 funds in the sample and three models meaning that total number of regressions is 525. For each regression alpha coefficient is stored. The statistics for alphas of all models are presented in Table 4.

Table 4

Statistics of alphas for different regression specifications.

Model	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.	St.Dev.
Brent in Rub	-1,50E-03	-2,57E-04	-1,70E-05	-3,97E-05	1,62E-04	2,07E-03	4,09E-04
Brent and Rub	-1,50E-03	-2,46E-04	-1,43E-07	-2,20E-05	1,91E-04	2,04E-03	4,03E-04
CAPM	-1,51E-03	-2,58E-04	-8,99E-07	-3,50E-05	1,59E-04	2,08E-03	4,08E-04

Results have to be presented in scientific way because values are very small and some have six zero after the point. They are small because the data is daily and even a tenth of percent is enough to provide 28% each year of managers` contribution to the returns. The results are unpromising: most funds have negative alpha and the mean is also negative. From the statistics it is clear that more than a half funds cannot have positive skill. The median is higher than the mean. That suggests that most negative alphas are further from zero than most positive alphas. The distribution of alphas for each model specification can provide further information and is needed in bootstrap approach. The distributions for daily alphas can be seen below. Yearly alphas can be found in Appendix 3.

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