Portfolio analysis

Evidence, explanation of the cost of the award. A combination of cost and momentum strategies. Working with abnormal distributions. Testing of median values for significance. Measuring the performance of built portfolios. Conducting regression analysis.

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08.02.2017
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Introduction

cost portfolio regression

Every investor wants to outperform the market and gain abnormal return. A lot of investment strategies have been developed and applied in stock markets worldwide in order to outperform the indexes. Some strategies approved themselves as steady and robust ones, others failed.

Value and momentum effects have drawn a lot of attention as a topic for academic research, where the former is an investment paradigm proposed by Benjamin Graham (Graham and Dodd, 1934; Graham, 1949), and the last for the first time broadly examined by Jegadeesh & Titman (1993).

In general, these two capital market phenomena can be defined as the relation between company book value of equity relative to its current market value - value effect; and the relation between an asset's return and its recent relative performance history - momentum effect. The returns of value and momentum strategies have become central contradiction of efficiency market hypothesis, which states that past price information cannot be used to predict future price patterns, one of the core principles upon which momentum investing relies. Jegadeesh and Titman remark that the momentum effect might probably represent the strongest evidence against the Efficient Market Hypothesis. As for value investing, it also violates EMH as it is based on publicly available information such as price-to-earnings (P/E), price-to-book value per share (P/B) or P/E-to growth (PEG) ratios derived from accounting data of an entity.

Despite both phenomena have been widely researched in different markets and asset classes, there are a few works that examine both strategies as a combination. Finally, this topic has never been studied in Russian stock market, thus, we have a great interest of examining the profitability of combining value and momentum strategies. In this paper we provide an explanation for the profitability of value, momentum strategies and their combination in Russian stock market for the period from January 2001 to May 2015. We compare risk-adjusted returns of separate and combined portfolios.

The rest of the paper is structured as follows. In chapter 1 we recall the existing academic researches that provide the evidence and explanation of the value premium and momentum effect, and will discuss the works examining the combination of both strategies. Chapter 2 is devoted to description of collected data and applied methodology, explaining momentum, value and combo portfolio construction and regression analysis. In chapter 3 we represent our findings and interpretation. Finally, we provide outro and make recommendations for a further research in conclusion.

1. Literature overview

1.1 Evidence and explanation of the value premium

Academic research has shown consistently that value investing outperforms other investment styles. Benjamin Graham (1976) in a 51-year performance research (1925-1975) concluded that the value strategy consistently resulted in annualized return of 15 per cent or better, that is two times higher than DJIA return for that period. Then Buffett (1984) examined the performance of 9 successful investment funds that used value as the principal strategy. Seven out of nine funds showed long-term double-digit outperformance over the market average. Even the pension funds demonstrated 5 per cent to 8 per cent return above the market.

Oppenheimer (1984) chose companies listed on AMEX and NYSE from 1974 to 1981 using Graham's criteria and concluded that an investor who had applied Graham's criteria would have gained annualized return of 38 per cent versus 14 per cent of the CRSP Index of NYSE-AMEX. Chan, Hamao, and Lakonishok (1991) documented a strong value premium in Japan. Ibbotson and Riepe (1997) examined the performance of different value and growth indexes (Wilshire, Frank Russell, S&P/BARRA, Barclays Global Investors) and found that regardless of capitalization, every value index resulted in higher returns with lower risk (standard deviation) than growth one.

Using four valuation ratios, namely, P/E, price to cash flow, P/B and dividend yield, Bauman, Conover and Miller (1998) found that value stocks outperformed growth stocks both on total-return and risk-adjusted basis in 21 countries for a 10-year period. Chen and Zhang (1998) reported that value stocks offer reliably higher returns in the US, Japan, Hong Kong and Malaysia. Using a 10 years sample Capaul et al. (1993) examined value, defined as low price/book ratios, and growth, defined as high price/book ratios, for six countries over the period from January 1981 to June 1992. He found that value stocks outperformed growth stocks on average in each country during the sample period, on absolute and risk-adjusted basis.

Although academia is in agreement that value stocks outperform growth stocks, much less consensus exists about the underlying reasons behind this superior performance. For example, Fama and French (1996) reported that higher returns of value stocks are due to their higher level of risks because these stocks are more disposed to financial distress. Chen and Zhang (1998) stated that value firms are riskier as they are usually under distress, have high financial leverage, and face substantial uncertainty in future earnings.

The findings of Rozeff and Zaman (1998) also summarize growth stocks as less risky and value stocks as more risky. However, these explanations of value premium are in contradiction to some other studies like Lakonishok, Shleifer and Vishny (1994) who proposed that investors' cognitive biases and agency costs of professional investment management were the reasons for the superior performance of value portfolios. Chan, Karceski, and Lakonishok (2000) studied the relative performance of value and growth stocks in the late 1990s and found that only a behavioral argument can explain the recent relative stock price performance of the equity asset classes. Chan and Lakonishok (2004) reported that the market betas of both the value and glamour portfolios are very close to each other, so systematic risk is not an obvious variable for explaining the value premium.

Kouwenberg and Salomons found the profitability of value investing at the country level in emerging markets. A portfolio of countries with low P/B ratios significantly outperforms a portfolio of high P/B countries. Moreover, global risk factors cannot explain the outperformance of a long-short value strategy, even after taking transaction costs into account. However, Chan et al. argued that the high prices of stocks that experiencing temporal growth do not reflect their fundamentals. The authors stated that the prices reflect investors' hype expectations of future earnings growth and of the companies' ability to sustain that growth, but there is nothing common with detecting of real value stocks.

Athanassakos (2009) reported a consistently strong value effect on Canadian data within 1985-2005 observation period. The value premium prevailed not only in both bull and bear markets, but also during recessions and recoveries. The author showed that value portfolios tend to have lower betas than the growth ones, regardless of sorting criteria based on P/E or P/BV. He considered the risk argument to explain the value premium and reported that higher return attained by value stocks is due to higher risk inherent in those stocks. But lately, Athanassakos documented that value stocks add value into a mixed portfolio of different strategies applied and furthermore that value stocks are not as riskier as the non-value stocks.

The value effect can be explained if generally defined as low P/E or other similar accounting ratios, such as low P/B or low price to cash flow ratios. However, most value investors do not think this is a valid explanation for the value premium as one variable cannot distinguish between stocks with poor performance in terms of earnings, cash flow or sales growth. Thus, true value investors do not screen stocks only applying criteria of low P/B or other price ratio. In fact such an approach to investment contradicts to original value investing paradigm by proposed Benjamin Graham. The so called true value investors can purchase a stock that is experiencing a current downturn in earnings but not one with a persistent past history of poor earnings. Lately we would discuss the reasons of choosing only one ratio as criteria of finding value stocks.

1.2 Evidence and Explanation of the Momentum effect

The first mention of existence of momentum effect in the price movement, betting on winners, relates to 1967. Levi noticed that purchase of shares with profitability that is significantly higher than profitability of the other stocks within the last 27 weeks, can result in total return above the set benchmark. However, there was not detected any interest in momentum investing in the 1970's and in the early 80's. Moreover, in the mid-eighties, De Bondt and Thaler provided advantages of alternative strategy - contrarian strategy, which suggests taking a long position in stocks that have recently showed the worst results, and vice versa - take short position in stocks which have showed the explosive growth of the price. Authors found, that it is possible to receive statistically significant profit if an investor selects winners and losers on the basis of the three to five year period and hold the specified position during the same period.

Since the middle of the 1980's, De Bondt's and Thaler's research generated practical interest of investors in strategy against the market and the period of active tests of possibility of receiving profit on the basis of the analysis of the historical prices of actions began. A famous research conducted by Jegadeesh and Titman, proved the advantages of momentum investing and made shocking impression on financial community since conclusions contradicted already recognized approach of investment against the market. Practicians and analysts were impressed by convincing tests, and since the end of the 1990th the criteria based on the accounting of last price dynamics (an indicator of relative strength of Levi (relative strength)) appeared in the system of stocks rating of the known analytical company Value Line.

Jegadeesh and Titman reported that profitability of stocks of the American market have considerable positive autocorrelation on the temporary horizon from 3 to 12 months, while portfolios of winners are not associated with higher risk: a beta of the loser portfolios is higher than a beta of winner portfolios. The results of testing momentum strategy indicate that simultaneous purchase of winners and short sale of losers on the basis of six months formation period and 6 month holding period results in additional return equal on average to 1% per month, or 12% per annum. One more important conclusion is that the effect of the increased profitability of a portfolio disappears after 12 months since opened momentum position.

Jegadeesh and Titman use a sample of NYSE and AMEX stocks covering the period from 1965 to 1989. They formed portfolios according the following logic. The stocks in the sample are ranked according to their returns over the past J months and are held for the following K months. J and K refer to the formation period and to the holding period in months, respectively. A set of 16 strategies were tested; for each J = 3, 6, 9 and 12 with K = 3, 6, 9 and 12. Moreover, they form another 116 strategies but with the lag of one week between formation and holding period in order to avoid some of the bid-ask spread, price pressure and lagged reaction effects. Overall, they study all 32 zero-cost portfolios and found that the selection strategies yield positive returns. The most significant returns are generated by the K=3 and J= 12 strategy, which yields average monthly risk adjusted returns of 1.31 percent. All other strategies yield returns between 0% and 1%. Jegadeesh and Titman conclude that momentum was present on the NYSE and the AMEX in the period from 1965 to 1989 and suggest investor underreaction to firm specific information as a possible explanation.

It is worth mentioning the results of researches of emerging markets are contradictory. Positive returns are reported by Muga, Santamaria (2006) in Argentina, Mexico, Brazil, Chile. They documented that stock type and country play a dominant role in explaining the momentum effect in these markets, however stock type is much more important. At the same time the results among several countries indicate the inefficiency of the strategy, for example, in Columbia (Luis Berggruna and Oliver Rauscha, 2011), Hong Kong after adjusting for risk (Cheng, Wu, 2010), Japan and Korea. The effect of a momentum is also not found in Taiwan. However, Du, Huang and Liao (2009) reported that results can be explained by the fact the market was in negative trend. They assumed that when the market is on the rise momentum strategy works, whereas when market declines contrarian strategy prevails.

Original testing of momentum strategy was performed on American data. Successful results of testing have drawn attention of many researchers. One more direction of empirical researches is search of inter countries relations in profitability of momentum strategy. In particular, Rouwenhorst (1998) found confirmation that momentum strategy works in twelve European markets: Germany, France, Italy, Denmark, Belgium, Netherlands, Norway, Sweden, Switzerland, Austria, Spain and the UK during 1980-1995 period. Researchers Bekaert, Erb, Harvey, and Viskanta (1997) tested various trading strategies including momentum in emerging markets and came up with a conclusion that the strategy does not work. However, lately Rouwenhorst confirmed the existence of momentum effect in emerging markets. Chan, Hameed, Tong, 2000 tested the strategy in market indexes of 23 countries and asserted its profitability.

Bhojraj, Swaminathan (2001) documented the efficiency of momentum strategy in developed and emerging markets. Moreover, the strategy is mostly profitable during the first year after portfolio construction. Similar results were obtained in markets of Germany, Sweden countries of big seven by, six countries of Asian region and Saudi ArabiaEmpirical evidence worldwide prove that portfolio returns obtained by momentum strategy are economic and statistically significant.

Profitability of momentum strategy in the USA and Europe has high positive correlation, and, therefore, the effect can be caused by a certain common intercontinental factor. However the strategy shows considerably higher profitability in Europe meaning impossibility to explain profitability of momentum strategy with some common factor. At the same time Griffin et al. (2003) proved lack of correlation between strategies across different countries, and the results show that this statement is valid both for the whole world and for certain regions. Therefore, if we stick to the point of view that the phenomenon is raised by various risks, these risks have to be at the level of the certain state. However, these risks are not revealed as the main macroeconomic indicators and cannot explain the difference in profitability.

Momentum strategy like any other one has a number of limitations. In general, most of the time this strategy outperforms the results of investing in undervalued stocks and passive investing, but there is empirical evidence indicating relation of momentum returns with market condition, seasonality, liquidity and company size. A. Maslovskaya (2013) researched liquidity as a source of profitability of momentum strategy in Russian stock market. She concluded that outperformance of momentum strategy in medium run can be partially explained as premium for risk of market liquidity. Moreover, the results indicated that liquidity is the key factor of explaining the losses of the strategy

Vladimir Ioffe in research Return based investment strategies on the Russian stock market: the empirical study (2010) investigated the profitability of contrarian and momentum strategies on the Russian stock market during the period 1996?2009. He reports that unlike most previous studies of developed and emerging stock markets, his study didn't find any evidence for the presence of contrarian and momentum profits on the Russian stock market.

Undoubtedly, the attempts to explain momentum effect are based not only on empirical analysis but also theoretical frameworks. There exist a number of behavioral theories that try to find out the reasons for the presence of momentum in financial markets.

Behavioral frameworks proceed from two key psychological aspects. The first one is conservatism inherent to individuals. Investors tend to place less emphasis on new information when making investment decisions. Secondly, it is typical of investors facing uncertainty to make decisions based on previous positive experience, even if those decisions contradict to statistical expectations. Agents pay more attention to a signal rather than its significance.

Psychological traits of investors become apparent in financial markets as follows. First, investor choses a portfolio that becomes profitable. Thereafter, he receives new information but does not fully utilize it and continues keeping to initial investment decision. Thus, if the shares were profitable in past, then they would be purchased in the future, giving a positive impact on prices. However, new information becomes outdated by some moment, it becomes obvious and investor fully incorporates it. As a result, prices return to fundamental levels.

Daniel, Hirshleifer, Subrahmanyam (1998) explain momentum effect through psychology of investors' behavior. Their argument is based on two psychological aspects of individuals. First, they state that people tend to be overconfident, especially when making investment decisions whose result becomes known after some period of time. This implies that agents overestimate their skills, meaning that actual variance of portfolio returns is higher than expected. The second phenomenon is the tendency of investors to account their success as acquired skills - self-attribution bias. Self-confidence rises when external signals coincide with investor's vision of the market, whereas it does not decline when he receives information contradicting to his view. Thus, investors perceive success as they have skills while negative outcome as due to bad luck. As time flows new signals appear that return asset prices back to fair values, overall leading to negative autocorrelation of returns in long run.

This theory is supplied by empirical work. Andy Chui, Sheridan Titman, and John Wei 2010 conducted a research of momentum strategy across different countries in order to determine the influence of cultural particularities on profitability of momentum. The authors form hypothesis that profitability of momentum strategy depends on the level of individualism in a country that indicates to what extend people are egocentric, concentrated on their abilities and feel distant from each other. It is assumed that the higher the level of individualism is, the more confident investors are leading to the higher probability of mistake caused by overconfidence. Thus, investors fell stronger disposition towards their success depends on their skills, consequently the probability of application of momentum strategy will rise. Moreover they found that index of individualism is higher in developed countries. This remark corresponds to the earlier researches of momentum profitability in the USA and Europe.

Thus, the vast majority of researches show that application of momentum strategy, as well as contrarian, can make profit for the agent. Moreover, the profit is often significant even after the risk adjustment. As both strategies are based only on historical values of the prices, such evidence can be a violation of a weak form of market efficiency. However, market efficiency is violated only if strategy brings the super profit, therefore, it is important to know to what extend the expected return is correct. Thus, a problem, when it is necessary to test two hypotheses - Joint hypothesis problem, arises: we have to test market efficiency and the accuracy of the chosen model of expected returns. The existence of profitable strategy can mean the inefficiency of the market, and also the incorrectness of expected returns counted, and, that actually, profitability is not anomaly, but premium for unaccounted risk. The majority of researches use CAPM or three-factor model of Fama and French for calculation of expected returns. The models consider the market risk, risk associated with the size of the company and with its potential of growth. However, these factors are not sufficient to provide strong explanation. As the considered strategy needs frequent rebalancing of a portfolio and use of considerable number of tools, market liquidity can become an important risk factor. In other words, former winners can be more sensitive to market liquidity and, as a result, have certain premium as compensation for this risk that would explain the phenomenon of a momentum.

1.3 Combining Value and momentum strategies

The first published C. Asness's article showed the possibility of creation of profitable strategy through a combination of portfolios of stocks with high previous results of investment and stocks with low multiples, i.e. a choice from value stocks as we have defined them above. C. Asness built his research on the analysis of monthly data of the American stocks listed on NYSE, AMEX and NASDAQ during the period from July 1963 to December 1994. The indicator of PAST (2,12) average monthly returns for last 12 months was constructed For reflection of momentum-effect excepting the last month in order to tale into the account reversal or contrarian effect. He selected last winners among the value stocks screening them by two indicators: Log (BV/MV) and D/P. In order to reveal interrelation between momentum and value effects the constructed average portfolios on three variables were compared: PAST (2,12), Log (BV/MV) and D/P. Stocks were ranked on five portfolios in ascending order for every month. Then each stock quoted on one of the exchanges (NYSE, AMEX, NASDAQ) was allocated to one of five quintiles and finally portfolios were constructed with equal weights. The special attention was paid to comparison of portfolios from the fifth and first quintiles.

The testing of hypothesis for statistical significance implies the estimation of t-stat and checking the difference of returns of that opposite portfolios is not equal to 0. The test indicated the average monthly spread of returns is statistically significant and equal to 0,87%.

This work permits to draw two important inferences: investing based on past dynamics and low P/B ratio can result in additional gain; the indicators Log (BV/MV) and PAST (2,12) are positively correlated with future profitability of investment but negatively correlated with each other. Thus, an investor can predict the dynamics of stock price and build winner strategy if he knows what type of momentum/value the stock is.

Finally, he concluded, although momentum investing (taking long and short positions) demonstrates positive return for all variations of value stock selection, momentum stocks that have the highest P/B result in the highest statistically significant return of 1,47% per month. Investment based on stock selection with low P/B also brings positive return, but in order to maximize the gain it is necessary to invest in stocks with poor momentum for previous 12 months. Such strategy of portfolio construction results in statistically significant average monthly return of 0.97%. C. Asness summarized that momentum investing works better when stocks are already expensive, stocks that have high P/E or P/B ratios, stocks which are not suitable for value investors. On the other hand, value investing results in higher return if apply the strategy on stocks with poor past 12 month performance.

The relation between value and momentum effects appears to be a strong one. These results apply directly to implementing quantitative investment strategies. The interpretation of these results will be the topic for future debate in a research Value and Momentum Everywhere. The authors study the returns to value and momentum strategies jointly across eight diverse markets and asset classes: global individual stocks across four equity markets: U.S., U.K., continental Europe (excluding the U.K.), and Japan; Global Equity Indices consisting of the following 18 developed equity markets: Australia, Austria, Belgium, Canada, Denmark, France, Germany, Hong Kong, Italy, Japan, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, U.K., and U.S; the following 10 currencies: Australia, Canada, Germany (spliced with the Euro), Japan, New Zealand, Norway, Sweden, Switzerland, U.K., and U.S.; global Government Bonds (Australia, Canada, Denmark, Germany, Japan, Norway, Sweden, Switzerland, U.K., and U.S.); 27 different commodity futures.

To measure value and momentum, they use the common value signal of the ratio of the book value of equity to market value of equity, or book-to-market ratio, and for momentum, they use the common measure of the past 12 month cumulative raw return on the asset skipping the most recent month's return, MOM2-12.

The conclusion of the Asness, et al. research is that the negative correlation between value and momentum strategies in addition with their high expected returns build a simple strategy of equally weighting a portfolio with value and momentum stocks which was found out to be a powerful strategy that produces higher cumulative long term rates of return than either value or momentum alone across all studied classes of assets. The study also stresses that combining value and momentum results in a significantly higher Sharpe ratio than either a value or momentum strategy separately and makes the portfolio less volatile across markets and time periods. The so called `combo' portfolio represents a 50/50 combination of the value and momentum portfolios.

According to the study a value investor in US stocks can expect to outperform the overall stock market by 3 to 4 percent a year, while a momentum investor is expected to earn 4 to 5 percent more than the market each year. Both strategies have about the same amount of volatility, which measures the risk that the actual return investors get is different than what they expected. Combining value and momentum yields a return that is 5 percent higher per year than the market. Though this is only slightly higher than the returns from either strategy, the big difference is that volatility falls sharply by approximately 50 percent. The benefits are even larger when this mixed strategy is applied across global markets and to various asset classes resulting in an investor's expected return would be twice the return on investing in the overall US stock market given the same amount of volatility. Improving a portfolio's risk and return trade-off is important because a good investment should generate higher returns without adding more risk.

According to an article by Jim Fink there exist two ways of constructing combined portfolio. He calls the combining of value and momentum strategies as the holy grail of investing. The potential benefits of such a combination may arise due to negative correlation between the strategies which gives an opportunity to form a less volatile portfolio, and thus attaining smoother returns. Then he summarizes two distinct approaches available for investors to form a profitable combination. First, he proposes the method as we mentioned already used by C. Asness (2009) involved a 50% weight on a pure momentum stocks plus 50% weight on a pure value stocks. The combination yields annualized SR of 0.86 of combo strategy versus 0.45 of momentum and 0.26 of value strategy across US stocks; 1.21 versus 0.68 and 0.52 respectively for global stocks. Overall, he attained risk-adjusted return improvement across all eight studied assets.

But Fink also stresses another approach of forming a winning combined portfolio of value and momentum stocks. The method is enclosed in looking for stocks that share two characteristics, namely, stocks that have both value and momentum disposition simultaneously. He refers to a famous investor and portfolio manager James O'Shaughnessy who developed two investment strategies Cornerstone Growth and Cornerstone Value. Lately, O'Shaughnessy invented a stock screener known as Trending Value which ranks the stocks in two steps. First step implies looking for value stocks based on criteria of low price-to-earnings, price-to-sales and price-to-free cash flow ratio. The second step deals with selection of value stocks with the highest six-month price momentum from the obtained list at step one. Further, the screener was back tested by James O'Shaughnessy himself and Patrick O' Shaughnessy. In this new research, they have found the way to boosts returns. Authors report that an updated combination of value and momentum strategies is the best performing strategy since 1963. Finally they conclude that the strategy with annualized return of 20.58% outperforms a benchmark which has a return of 10.71%. Moreover, the Trending Value strategy attains such profitability with a lower standard deviation of 42.06% versus benchmark's 42.73%.

However, Fink argues that there is no empirical evidence that O'Shaughnessy's Trending Value screen outperforms C. Asness' 50/50 combined portfolio of two pure sets of value and momentum companies. He also notices that Asness' approach gains from impressive negative correlation (-0.65) between the pure momentum and value stocks, while Trending Value strategy lacks such benefit.

Secondly, Jim Fink states that combined portfolio constructed using Asness' method may simply perform better than O'Shaughnessy's portfolio due to mixed nature of stocks included in the former. This argument can be valid since O'Shaughnessy's stock screen is based in first turn on selection of value stocks, and only after that sorts value stocks by momentum criteria of 6 month past performance. Therefore, momentum effect is treated as a secondary effect. On the other hand, C. Asness and coauthors pay equal attention to both momentum and value stocks. Finally, C. Asness rebalances combined portfolios once a month which would definitely increase transaction costs, whereas J. O'Shaughnessy rebalances his hybrid portfolio of stocks on an annual basis.

Today it does not appear that the strategy of combining good value and good momentum has attracted attention of investors. On the one hand, value investors have been conditioned to ignore technical/momentum analysis, while many chartists do not pay significant attention, if any, to valuation multiples. Until combining value and momentum becomes more widely used, it is possible that combining low valuation and upward price momentum will be a useful strategy for individual investors.

2. Data and Methodology

2.1 Data

The research is based on the sample of data consisting of Russian companies listed on Moscow Stock Exchange. MOEX was chosen due to it is the largest Russian stock exchange and sufficiently represents the whole market. The time period of the study covers 15 years starting from January 2000 to May 2015. Most researchers on momentum strategy, and C. Asness in the work Value and momentum everywhere used monthly data. Thus, we are also dealing with monthly observations. The data set includes the following series: closing price of a stock on the first day of the month, price-to-book ratio of each selected company as well on the first day of month. The data was collected from Thompson Reuters DataStream.

The process of company selection is based on the following criteria. We excluded GDR's, preferred stocks, but include delisted companies in order to increase the sample. The total number of individual common stocks extracted from DataStream was 405. Then the data has been screened to exclude missing, invalid, and non-usable observations. Some of the price and price-to-book series didn't have any values throughout the whole study period, therefore, we deleted these series. Moreover, we exclude the unbalanced series, that is, the companies that had price-to-book ratios but missed the price values. Besides, there were some price series that were copies of already existing series, which were also eliminated from the sample. Some of the series have contained valid stock price observations, but were not applicable for this empirical study, such as preferred shares and series containing Russian stocks traded outside Russia (ADRs), and series for other than stock instruments. All such series have been removed. Overall, after screening and editing the series, we got 355 companies under consideration.

From the Table 1 it can be clearly observed that the number of companies was gradually increasing from January 2001 up to 2011. The fact is that the number of companies did not decline during the global financial crises in 2008-2009. The effect was quite opposite, and the number of listed companies experienced a sharp increase, and continued to grow up to 2011, where it reached the maximum of 273 companies. The average and minimum number of companies in the sample is 147 and 28 respectively.

Also, we have retrieved the monthly values of MICEX index from moex.ru and risk-free rate as Average Moscow Interbank Offered Rates (MIBOR-90 days as recommended by Thompson Reuters) from website of the Central Bank of the Russian Federation. MIBOR is the rate which was introduced as an attempt to create a ruble analogue to LIBOR and is calculated by the CB of the Russian Federation on a daily basis. To sum up this section, we have 28202 price values, 185 MICEX values, the same figure of risk free rate and 24338 P/B ratios and. In total, the sample consists of 52910 observations.

2.2 Value and momentum measures

To begin with, before the discussion of portfolio construction it would be important to recall the process of the preparation of sample data for empirical testing. We deal with the selection of calculation method of monthly total returns (simple or log returns). Since simple returns are linearly additive across portfolio of stocks, whereas log returns are not, our portfolio analysis would be based on simple returns as it would be possible to calculate total monthly return of a portfolio as a weighted sum of all stocks in it. Clearly, the same logic applied to calculate monthly market return for a studied period.

The aim of the analysis is to construct value and momentum portfolios, make a combination strategy and check whether the last has higher risk adjusted return. In order to do this procedure, it is necessary to define the value and momentum measures. To characterize value stocks we use common signal price-to-book ratio which shows to what extend a stock is fairly priced: if P/B>1, the stock is overpriced, P/B<1 the stock is underpriced, P/B=1, a stock is fairly priced, where B is book value per share, calculated as BVPS=BV/(# of shares outstanding). According to Fama-French three factor model, the use of P/B ratio is a consistent ratio to distinguish between value and growth stocks. Moreover, P/B is quick and easy to calculate. C. Asness selects past value winners on the basis of Log (BV/MV). Finally, in our previous study, we reported the significance of P/B ratio in explaining future returns in Russian stock market. Thus, P/B is a good value signal for creation of value portfolio.

For momentum we use common measure of past cumulative returns for 11 months with a one month lag, which was first discovered by J and T (1993). We skip the most recent month, which is standard in the momentum literature, to avoid the one month reversal in stock returns, which may be related to liquidity or microstructure issues. We motivate our choice with an argument that momentum effect in Russian market was already investigated by Vladimir Ioffe as we previously mentioned. He examined all 16 strategies with 12, 9, 6 and 3 month formation and holding periods. The results indicate that a winner-loser strategy based on 12/3 month formation/holding period skipping one month yields the highest return of 1.6% significant at 5% level among all other strategies. The 12/3 strategy showed the highest results eve when the portfolio was transformed to the quintiles. Therefore, we decided not to test all 16 strategies and limit out analysis on 12x3 and 12x1 strategies skipping one month, where the last (1 month holding period) has never been tested on Russian stock market.

2.3 Momentum Portfolio Construction

Let us start out analysis from discussion of momentum portfolio construction. The first step of building momentum portfolio is to calculate the cumulative returns based on a formation period. In our case, we consider the performance of stocks in the sample for the previous 11 months beginning from December 2000. Cumulative returns are calculated using the formula R11=, where i stands for the month. Stock return is calculated as (Pt-Pt-1)/Pt-1.

The second step is to rank the stocks according to their past performance in descending order. The sorted stocks are then divided into three portfolios: the upper 1/3 is assigned to winner portfolio, the bottom 1/3 is assigned to loser portfolio. In our work we use tertiles instead of deciles in order to attain maximum diversification on lower sample size. Consequently, equally weighted winner portfolio, loser portfolio are built. Important note here is that stocks are included in portfolio with equal weights rather than using criteria of market capitalization.

Each portfolio is then held for the next 1 and 3 months. We do not consider the middle portfolio as it is not required in building the zero cost strategy. The last is formed by taking a long position in winner portfolio and going short in loser portfolio. Profitability of this strategy is measured over 1 and 3 months holding period as well as for winner and loser portfolios. All returns are represented as monthly average figures to make the results comparable.

Since momentum is an active strategy it requires frequent rebalancing of portfolio. The classical approach proposed by J and T is based on monthly rebalancing in the following way. 1/K (where K is the holding period) of the holdings is liquidated (turned into cash) and reinvested into new winners and losers based on the new past J?month cumulative returns, while the rest of holdings is carried over to the following period. This type of rebalancing implies frequent transaction costs. First, investor pays for initial transaction, secondly he faces TC when liquidates a part of portfolio and purchases a new portfolio, and finally when he closes the position. Therefore, we decided to abandon this approach in order to reduce TC and make rebalancing simpler. Instead of 1/K liquidation, we hold the initial portfolio unchanged within a whole investing period and only adjust it every month with new winners/losers. So, the only difference is the source of funds used for rebalancing. We finance the rebalancing with free funds available to investor. It is assumed that investor has own free cash to make monthly rebalancing. Thus, we avoid the transaction costs dealt with 1/K liquidation. However, we are not dealing with direct TC in our analysis in order to make our analysis more straightforward.

For example, consider an individual investor who has available funds in amount of X. He invests 1/3 of X at t1 in winner momentum portfolio based on 11-month cumulative returns skipping one month and holds it for 3 months. At t2 he invests one more 1/3 of X in the new leaders keeping the same strategy. At t3 he invests the rest of X in the new leaders. Finally, at t4 he receives cumulative return for the winner portfolio constructed at t1. The procedure is repeated every month for winner/loser/zero cost portfolios. As a result, we would get aggregate portfolios formed on the monthly basis for the whole sample period.

We also consider one month holding period as the shortest one. Momentum is a short term strategy, thus we are interested in testing the short holding periods like 1 and 3. As already mentioned in literature overview, we believe momentum prevails due to investors overconfidence and confirmation bias, the public herds. This is the distinctive attribute of momentum investing as it mostly relies on people's emotions rather than company's fundamentals and performance as value investing does. So, we anticipate higher return of 1 month portfolio. If momentum effect exists then the return of winner stocks with positive past dynamics should be higher than return of loser stock portfolio.

One should mention an aspect that is not discussed in J and T research. It deals with calculation of stock returns that were not traded during the holding period, that were placed on MOEX after the analysis period, and that were delisted during folding period. If a company was not traded for some period during investing period then the return was calculated as -1, as investor cannot sell a stock and loses all funds in that position. We faced such stocks numerous times during observation period and adjusted their returns to -1. The intuition behind this argument is that investor cannot predict whether a stock would be delisted or stops being traded for some time, and this can definitely happen in reality. Thus, we did not eliminate such stocks, and took them into our analysis.

To sum up this section, we have constructed 6 momentum portfolios on the 11 month cumulative return skipping one month after formation period to take into the account reversal effect. The portfolios are the following: Winner 12x1, Loser 12x1, Winner-Loser 12x1, Winner 12x3, Loser 12x3, Winner-Loser (WML) 12x3. The results would are interpreted in Chapter 3.

2.4 Value portfolio construction

Now let us proceed to value portfolio construction. As we have mentioned, price-to-book ratio was used as a determinant of selecting value stocks. First of all, all stocks were ranked according to P/B criteria in ascending order, so that the stocks with lowest P/B are at the top. In order to make the results consistent and comparable with momentum profitability, we apply the same logic for value portfolio construction as for momentum. Having ranked the stocks we divide the set on three portfolios. Middle portfolio does not fall into our analysis, only top 1/3 of stocks with lowest P/B for a previous month and bottom 1/3 of stocks with the highest P/B for a previous month are under consideration. By analogy with momentum portfolio construction we invest skipping one month after formation period. Instead of cumulative returns, we take P/B for the previous month, sort the stocks, wait a month and start investing. The thing is that the current P/B already indicates whether the stocks is under - or overvalued, so that investors don not have to take some past P/B - a one month lag P/B is sufficient to claim for the fairness of the stock price. We do not invest in stocks with negative or zero P/B ratios.

Undoubtedly, true value investors can argue that one ratio is nothing in investment analysis. As Jim Fink states that value investing is a process based on discovering a limited number of stocks trading at prices significantly below their long-term intrinsic values and then holding them long term. Intrinsic value is usually derived from a discounted cash flow analysis, which is based on analyzing the entire life cycle of a company. We definitely agree with this statement, but it would be problematic to test the significance of the value strategy if consider additional widely used value factors, such as P/E ratio; PEG ratio and which are used to determine a stock's value while taking the company's earnings growth into account, and is considered to provide a more complete picture than the P/E ratio; current ratio and other multiples, then we would have probably selected much fewer companies from our sample suited for this criteria. Thus, the portfolio would consist of fewer stocks which could lead to insignificant or erroneous results. A P/B ratio proved itself as good indicator of value stocks. Thus, we admit the selection criteria based on one ratio to increase the quantity of stock in portfolio and as a result attain higher diversification. Moreover, it would be more difficult to make calculations of the intrinsic value of each 355 stocks based on DCF analysis. Besides, to make the results of both momentum and value strategies comparable we stick to common holding period of 1 and 3 months.

Finally, we constructed 6 value portfolios which are monthly rebalanced as momentum portfolios: Winner 12x1, Loser 12x1, Winner-Loser 12x1, Winner 12x3, Loser 12x3, Winner-Loser (WML) 12x3.

Overall, we generated 12 momentum and value test portfolios.

2.5 Combo portfolio construction

As we have discussed earlier in literature review there are two distinct approaches to construct a combined portfolio. It was decided to focus on the method originally proposed by C. Asness which is based on weighting momentum and value portfolios into a single one. We do not reject validity and success of the double ranking approach, though it does not suit for our sample. Screening stocks with both characteristics requires much larger sample of companies. Nowadays, it seems us impracticable to perform such ranking under current Russian stock market size due to its relative youth. Double ranking may result in higher return but higher volatility due to lower portfolio size. Perhaps, it can be a topic of the next research, but currently we apply the construction of combo portfolios which is simply based on the averaging of WML zero cost portfolios of value and momentum strategies. In particular, we form combination of 50% WML momentum, 50% WML value stocks for one and three month holding period, and perform other variations of weights. We rebalance portfolios each month as well as C. Asness did in his study. Overall, we construct 18 combinations for every variation of weight. In total, we formed 31 portfolios.

Table 4 represents the monthly average returns and standard deviations of combination portfolios. In the next chapter we will compare portfolio risk adjusted returns, analyze descriptive statistics and perform hypotheses testing.

2.6 Hypotheses and asset pricing models

In order to understand whether momentum and value effects are anomalies or fair premium for risk associated with each strategy, we have to estimate expected return for each portfolio relating to risk, and then test the hypothesis whether the difference between expected and actual returns is significant. The same logic we apply for testing combined portfolios. Overall, we have to test 31 portfolios.

The second model we apply is dual-beta CAPM which allows investors to differentiate downside risk (risk of loss) from upside risk (gain), whereas regular beta cannot distinguish between such potentials for loss and gain. The dual-beta model does not assume that upside beta and downside betas are the same but actually calculates what the values are for the two betas, thus allowing investors to make better-informed investing decisions. The dual-beta CAPM model can thus be expressed as:

,

where D is a dummy variable, which takes the value of 1 when the market index return is positive and zero if negative.

Finally, we form 3 hypotheses to test:

H1: Momentum effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns;

H2: Value effect exists in 1 and 3 month perspective, and following the strategy can bring abnormal returns;

H3: Combined portfolio can bring abnormal returns in 1 and 3 month perspective.

These hypotheses will be tested for each constructed portfolio. If any profitable momentum, value or combined strategies would are found via applying sign test for significance of difference (explained later), they would be further tested whether the findings could be explained by differences in risk using CAPM and dual-beta.

3. Results of empirical analysis

3.1 Dealing with non-normal distributions

To begin with, let us look at the Table 1: Descriptive statistics of portfolio returns. The marked values of skewness and kurtosis are too large. It is clearly seen that not all portfolio returns are distributed normally. Usually, distribution is considered to be normal if it is symmetric, that is skewness is 0, and kurtosis is equal to 3. Thus, we cannot apply standard t-test as it is constructed for normally distributed data and in our case it would be invalid.

There are various methods to deal with non-normal data. One of the reasons for non-normal portfolio returns might be too many extreme values in a data set, in particular outliers. Let us look at the histogram of momentum winner portfolio with 1 month holding period (MOMW1).

It is clearly seen that distribution is skewed to the right due to outliers. However, we are not going to eliminate them, as those outliers can be identified as truly special causes of highly speculative stocks. Besides, we expected a little percentage of outliers. Moreover, according to Zephyr StatFacts one would prefer positive skewness. However, in the real world few investments exhibit a positive skew. Therefore, one might seek investments with skew that is less negative than the alternatives. All distributions of calculated portfolio returns, except vall3, are positively skewed. Thus, we are leaving the skewness unedited. Kurtosis measures the fatness of distribution tails. High kurtosis might imply higher probability that an event occurring is extreme in relation to portfolio returns distribution. Thus, the higher the kurtosis coefficient is above the normal level of 3, the more likely that future returns will be either extremely large or extremely small. In our case all distribution of portfolio returns are positive or called leptokurtic Investopedia explains: If the past return data yields a leptokurtic distribution, the stock will have a relatively low amount of variance, because return values are usually close to the mean. Investors who wish to avoid large, erratic swings in portfolio returns may wish to structure their investments to produce a leptokurtic distribution. All our investments except one follow leptokurtic distribution, which is a positive sign as we found out. Overall, we did not make any corrections of portfolio distributions.


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