Return based investment strategies on the Russian stock market: the empirical study

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Master

of

Science

in

Business

Administration

Applied

Economy

and

Finance

Returnbased investment strategies on the Russian

stock market: the empirical study

Student: Vladimir Ioffe

Supervisor: Lisbeth La Cour

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Abstract

Market efficiency theory is one of the cornerstones of modern finance. It has now been disputed for

several decades whether market efficiency holds on different types of markets. One of the most

common interpretations of market efficiency theory is that trading strategies based on historical returns

could not earn higher than normally expected return on the market. However, some of the recent

research suggests that profitable trading strategies with abnormal returns do exist on international

stock markets.

The purpose of this paper is to examine the profitability of return‐based investment strategies in the

Russian stock market. 16 such strategies are examined for the period from January 1996 to December

2009. The methodology used for the testing is widely accepted in academic literature.

The paper shows that as opposing to international evidence, market efficiency holds rather well on the

Russian stock market. In essence, no persistently profitable strategies are found. Controlling for

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2. MARKET EFFICIENCY THEORY ... 10

2.1. INTRODUCTION ... 10

2.2. EARLY DEVELOPMENTS OF MARKET EFFICIENCY THEORY ... 10

2.3. RANDOM WALK MODEL ... 11

2.4. FORMULATION OF MARKET EFFICIENCY THEORY ... 12

2.4.1. Introduction ... 12

2.4.2. General case for market efficiency (“fair game” model)... 13

2.4.3. The Submartingale model ... 15

2.4.4. The Random Walk model as extension to “fair game” model ... 15

2.4.5. Sufficient conditions for market efficiency ... 16

2.5. CRITICISM OF FAMA’S ORIGINAL DEFINITION ... 16

2.6 “EFFICIENT CAPITAL MARKETS: II” – FAMA’S REVISION ... 17

2.7. SUMMARY ... 18

3. EMPIRICAL EVIDENCE ON MARKET EFFICIENCY ... 19

3.1. INTRODUCTION ... 19

3.2. TESTS FOR RETURN PREDICTABILITY ... 19

3.2.1. Predicting returns from past returns ... 20

3.2.2. Company related forecasting variables ... 21

3.2.3. Seasonality effects in predicting returns ... 22

3.3. EVENT STUDIES ... 24

3.3. TESTS FOR PRIVATE INFORMATION ... 26

Insider trading ... 27

Security analysis ... 28

Professional portfolio management ... 29

3.4. INTERNATIONAL EVIDENCE ON CONTRARIAN AND MOMENTUM STRATEGIES ... 31

3.6. SUMMARY ... 36

4. RUSSIAN STOCK MARKET ... 37

4.1 INTRODUCTION ... 37

4.2 EARLY DEVELOPMENTS OF RUSSIAN STOCK MARKET ... 37

4.3. ECONOMIC CRISIS OF 1998‐1999 ... 40

4.4. RUSSIAN ECONOMY RECOVERY AND STOCK MARKET DEVELOPMENT, 2000‐2007 ... 41

4.5. GLOBAL FINANCIAL CRISIS AND ITS INFLUENCE ON RUSSIAN ECONOMY ... 43

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5. DATA AND METHODOLOGY ... 48

5.1. INTRODUCTION ... 48

5.2. DATA ... 48

5.2.1. Data description ... 48

5.2.2. Adjustments of RTS data ... 49

Data Retrieval and Screening ... 51

5.3. METHODOLOGY ... 56

5.3.1. Choice of an appropriate empirical testing methodology ... 56

5.3.2. Portfolios formation procedure ... 57

5.4. THE MODEL AND THE HYPOTHESIS ... 60

6. RESULTS OF EMPIRICAL ANALYSIS ... 62

6.1. INTRODUCTION ... 62

6.2. PROFITABILITY OF RETURN‐BASED INVESTMENT STRATEGIES, 1996‐2009 ... 62

6.3. CORRECTION FOR THE BID‐ASK BOUNCE ... 65

6.5. PROFITABILITY OF RETURN‐BASED INVESTMENT STRATEGIES, 2000‐2006 ... 67

6.6. SUMMARY ... 72

7. CONCLUSION ... 73

8. BIBLIOGRAPHY ... 75

9. APPENDIXES ... 82

APPENDIX 9.1. MICEX DATA RETRIEVAL CRITERIA (DATASTREAM) ... 83

APPENDIX 9.2. RTS DATA RETRIEVAL PROCEDURE ... 85

APPENDIX 9.3. THE LIST OF RUSSIAN COMPANIES SELECTED FOR THE SAMPLE ... 87

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1. Introduction and Problem Statement

1.1. Introduction

Market efficiency is being disputed in academic debates for several decades. Efficient Market

Hypothesis (EMH) states that all available information about any single stock is already incorporated

into its price. That means it should not be possible to earn an abnormal return on the stock market by

pursuing investment strategy based on selection of over‐ and undervalued stocks. There exist a large

number of empirical studies that are testing this statement. Earlier research on the field has mostly

produced evidence supporting market efficiency. In his famous work Fama (1970) has introduced the

term “Efficient Market Hypothesis”, outlined its basic postulates and assumptions, and made an

overview of existing empirical evidence, most of which have supported the theory by that time.

However, later international studies have revealed some controversial results. That’s why when two

decades later Fama and French (1996) have revisited the theory their assessment of its validity was not

so strong. By then growing body of empirical evidence has contained various examples of market

efficiency violations. Besides other occurrences, they were expressed in terms of abnormal contrarian

and momentum profits. Fama and French (1996) have raised a question of whether the US stock market

evidence of such violations could be a result of data snooping. They called for more out‐of‐sample tests

on international data.

While theoretical base for market efficiency was slowly emerging throughout 20th century, stock market

practitioners had to come up with profitable investment strategies. Growing number of stock brokers,

portfolio managers, and trading advisors have been creating and applying various trading strategies that

would (presumably) allow them to beat the market. Two main approaches were used: fundamental

analysis and technical analysis. Fundamental analysis of a company is based on evaluation of its financial

statements, management practices, competitive advantages, and macroeconomic environment. The

outcome of the analysis is used to predict future stock price movements. By contrast, technical analysis

is not considering any of these factors and purely concentrated on the creation of the buy/sell decision

rules triggered by the signals of technical indicators, which are calculated on historical values of the

stock prices. Both approaches imply that share prices sometimes deviate from its fair values and thereby

contradict EMH.

There have been some attempts to find theoretical explanation of why EMH might not always work.

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Overreaction hypothesis stipulates that market overreacts in response to both good and bad news

announcements. This results in the initial stock price movement that is higher in magnitude than it takes

to reflect the newly announced information. That creates presence of temporarily over‐ and

undervalued stocks on the market, whose prices after some time revert back to their fundamental

values. This allows for applying the contrarian investment strategy, where one invests into stocks with

the worst performance (losers) and sells the ones with the best performance to date (winners). The

profit in this case is realized when the stocks prices adjust back to their fair values. Completely opposite

approach is used by the pursuers of the momentum investment strategy, who believe that the past

winner stocks will continue to perform well in future, while past losers will lose even more in their value

over time. The psychological background behind this type of investor sentiment is explained by the herding behaviour theory, which indicates that many investors tend to follow the crowd in buying and

selling securities. The implication for the investors here is to create portfolios by investing into winners

and at the same time selling loser stocks. This strategy works on the markets where one can find the

presence of the strong momentum that is driving the stock prices in either positive or negative direction.

Empirical testing of the profitability of both contrarian and momentum strategies has seen a lot of

academic interest. Extensive research have been made not only on the stock markets of all developed

countries (US, UK, Japan, Australia, Canada, New Zealand, Germany, Spain and other western European

countries), but also covered many of the emerging markets (among others Brazil, Sri Lanka, Taiwan,

China, Korea, Thailand). The outcome of this research is not unified: in several countries the presence of

the strong momentum effect has allowed to earn significant abnormal returns (US, New Zealand, UK and

most European countries), in others it was the contrarian strategy that could significantly outperform

the market (Japan, Spain, and Brazil) 1. Finally, in some countries researchers were not able to find the

presence of either overreaction or momentum (Australia and several Asian countries).

Very little research in this regard was made on the stock markets of Central and Eastern European

countries (CEE countries)2. In fact, only one academic paper has specifically studied implementation of

momentum strategies in the region. Avizinis and Pajuste (2007) have studied seven CEE countries

(Poland, Slovenia, Hungary, Lithuania, Croatia, Estonia, and Latvia) for the years 2002 through 2006. By

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More detailed review of the findings is presented in section 3.4 of this paper 2

The OECD definition of CEE countries (dated 2002) includes the following states: Albania, Bosnia and

Herzegovina, Bulgaria, Croatia, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Macedonia, Poland, Romania,

Slovakia, Slovenia, Yugoslavia (Serbia and Montenegro). Even though Russian Federation is not included here, in

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constructing composite portfolios including most liquid stocks from all countries, they found the

presence of significantly positive momentum returns. The profitable momentum strategies were even

more significant when Polish stocks (accounted for nearly 40% of all stocks) have been excluded from

the sample. Other than this, there were no publicly available academic articles focused on evaluation of

contrarian and momentum strategies in the CEE region. It was impossible to retrieve neither studies

conducting research on the stock market of a particular CEE country, nor devoted to the stock market of

the region as a whole. There were, however, several empirical papers that have been assessing

investment opportunities on the emerging markets, where some CEE states have been included into the

sample. Fernandes and Ornelas (2008) have used a sample of 15 countries including Czech Republic,

Hungary, Poland, and Romania with the study period of 1995‐2005. They have reported long‐term

reversal effect for Czech Republic, Poland, and Romania. In the short‐term the contrarian strategy was

outperforming in Romania, while in Poland the short‐term momentum effect has prevailed. The results

of this study were significant on the 5% level. Hart et. al (2003) used the sample of 20 countries

including Czech Republic, Hungary, Poland, Russia, and Slovakia with varying time periods. They

evaluated whether particular stock selection strategies based on fundamental analysis can outperform

the market and found some evidence of successful trading strategies. In particular, on the Russian stock

market with the study period of 1997‐2001 the only profitable trading strategy was the one using

earnings‐to‐price ratios for portfolio formation (it was significantly profitable on 10% level). Bohl and

Siklos (2008) have compared the developed stock markets of Germany, UK, and US with the emerging

stock markets of Czech Republic, Hungary, Poland, and Russia. They were looking for the presence of

feedback traders and found some evidence supporting their existence on both emerging and developed

stock markets. The presence of feedback trading implies deviation of stock prices from their

fundamental values, which contradicts market efficiency propositions. Other than in the above

mentioned papers, the CEE region hardly ever mentioned in the empirical literature.

There could be several reasons behind the lack of empirical studies using stock returns data from CEE

countries. First of all, the stock markets in most of these countries have started to operate normally no

more than 15 years ago. That creates a limitation in the statistical sense, the number of observations is

simply too small to make a valid statistical inference. Secondly, it is very likely that stock market studies

performed by local researchers are published in the native language and never reach English speaking

audience. Finally, it could simply be the lack of interest to this region’s stock market or potential

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Regardless of the cause, the lack of empirical research on the CEE regional stock market as a whole and

Russian stock market in particular presents a great opportunity for contribution. It is the main purpose

of this paper to test whether internationally recognized contrarian and momentum strategies will work

on the Russian stock market. Such empirical test would have several implications. Firstly, it would

constitute another out‐of‐sample test of Efficient Market Hypothesis, which has lately received a lot of

academic criticism. Secondly, it would be interesting to see whether Russian stock market on its current

state of development exhibits properties similar to the stock markets of the developed countries.

Thirdly, invoking academic interest to expand empirical tests of investment strategies to CEE countries

would eventually benefit stock market development of the region. Finally, from the potential outside

investor’s point of view it would be interesting to know whether portfolio diversification to the Russian

stock market can add some value to the existing holdings.

1.2. Problem Statement

The main objective of this paper is to test for profitability of contrarian and momentum strategies on the Russian stock market and to assess whether the obtained results will still hold after accounting for

market efficiency anomalies and other well known sources of statistical disturbances.

This assessment is important since it has been shown in several studies that momentum profits could

partially or completely vanish after such disturbances are accounted for. The widely accepted

disturbance factors generating spurious momentum are:

• Bid‐ask bounce when share price in the end of formation period is the same as in the beginning

of holding period

• Differences in systematic risk between winners and losers

Additionally, market efficiency anomalies could potentially affect the empirical study results. Therefore

it has become a common practice to test findings against size effect, liquidity effect, and January effect,

and more recently discovered Halloween effect.

Finally, in portfolio management practice it is often argued that transaction costs can substantially alter

profitability of empirically tested investment strategies. Some researchers therefore attempt to account

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In accordance with general research practice the empirical findings of this paper, whenever appropriate,

will be tested against the above mentioned factors.

1.3. Delimitation

There are some theoretical and practical aspects which go beyond the scope of this paper.

First of all, the literature covering topics of efficient markets, contrarian and momentum strategies, and

market efficiency anomalies is very extensive and cannot be fully reviewed in this paper. The choice of

literature is therefore limited by author’s subjective assessment of its relevancy and applicability in the

context of this study.

Secondly, time period of the study poses some limitation on the number of observation for statistical

inference. Even though the total period of study is 14 years, it has to be reduced in order to exclude the

effect of economic crises which Russian economy was subject to in the years 1998‐99 and 2007‐2009.

This exclusion shrinks the study period to years 2000‐2006, which corresponds to 7 years under

“normal” market conditions, or 84 monthly observations. Even though this number still allows for

statistical analysis, some caution must be exercised while making long‐term interpretation of the results.

Thirdly, transaction costs will not be included into the analysis. This decision was made because the

inclusion of such costs would require detailed information on which stocks are traded, from which stock

exchange3, which trading system (electronic or manual) is used, and which stock broker has placed an

order. Moreover, trading strategies used in this paper require small part of the holdings in the

constructed portfolios to be rebalanced on the monthly basis, which in conjunction with the above

mentioned factors makes calculation of transaction costs to be a nontrivial task.

Finally, liquidity could be an issue challenging basic assumptions of the model under testing. It is

assumed that position in any stock in the constructed portfolios can be easily liquidated whenever

trading strategy would require doing so. During early years of its development Russian stock market was

characterized by having a certain number of illiquid stocks, for which liquidation of holdings was not

easily achievable or was associated with large commission charges. Even though the most illiquid stocks

have been excluded from the sample, there is still big portion of stocks that are potentially problematic

in the sense of positions liquidation. 3

The data used in this paper comes from two Russian stock exchanges (MICEX and RTS), some stocks are quoted

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1.4. Thesis structure

The remainder of this paper is structured as follows:

Section 2 deals with theoretical foundation for Market Efficiency Theory

Section 3 gives overview of research on the field with particular focus on studies of contrarian

and momentum strategies

Section 4 contains the outline of the Russian stock market development during the study period.

It describes various processes that took place in the country’s economy during the last 15 years

and assesses their role for development of the Russian stock market

Section 5 describes data and methodology used in this paper. It includes discussion of data

validity, sample selection criteria, and choice of methodology as well as the reasoning behind

this choice

Section 6 is the main part of this paper. It presents the results of the conducted research and

gives interpretation of the outcome

Section 7 concludes this paper. It summarizes the findings of the study and their interpretation,

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2. Market Efficiency Theory

This chapter describes one of the fundamental concepts of modern finance – the concept of market

efficiency. It provides theoretical foundation for the empirical research of this paper.

The first two sections deal with early developments of market efficiency theory and random walk model.

In the third section the original formulation of the theory by Fama (1970) is presented. The chapter

proceeds by the section describing the academic criticism of Fama’s propositions. Next, the revised

definitions of market efficiency postulates by Fama (1991) are reviewed. The chapter is then concluded

by short summary.

2.2. Early developments of Market Efficiency Theory

The first cornerstone of market efficiency theory was laid in the beginning of the 20th century, when

French mathematician Louis Bachelier has submitted his PhD dissertation to the Sorbonne. His thesis

was called “The theory of speculation” and has been investigating stochastic processes and their

application in the analysis of price fluctuations on the stock market. In his opening paragraph, Bachelier

recognizes that “past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes”4. This recognition of informational efficiency of the market

has anticipated many of the analytical studies made by finance academics of the second half of 20th

century. Unfortunately, Bachelier’s work has not been appreciated at his time. It has only been

rediscovered in the 1950s, when the topic of random stock price fluctuations was discussed in the

research made by Kendall (1953) and later by Samuelson (1965). At that time Bachelier’s dissertation

has been also reviewed by Cootner (1962).

Effectively, by the end of the first half of the 20th century there was no widely accepted economic theory

being able to explain processes behind stock price fluctuations. The general agreement, however, was

that it should not be possible to conduct an investment strategy that would constantly outperform the

market. Several empirical studies available at that time were broadly confirming this statement

(e.g. Working (1934), Cowles and Jones (1937)). There was a need for a theory explaining the observed

stock market behavior, and it has arrived with introduction of the concept of random walk model.

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2.3. Random Walk Model

The properties of random processes have been discussed in the scientific literature from the beginning

of the 20th century. The randomness of stock price fluctuation has been realized by Kendall when he was

looking for price cycles in the time series containing stock price data. Instead of discovering patterns he

concludes that “in series of prices which are observed at fairly close intervals the random changes from

one term to the next are so large as to swamp any systematic effect which may be present. The data

behave almost like wandering series”5. Kendal has further noted that in statistical sense stock prices

exhibited nearly zero serial correlation. This empirical observation has been confirmed by several

researchers and later has been labeled random walk hypothesis or random walk model.

Practitioners of the 1950s have continued to investigate properties of time series of equity prices.

Roberts (1959) have demonstrated that time series generated from a sequence of random numbers was

indistinguishable from a record of US stock prices. At the same time Osborne (1959) has shown that

common stock prices have properties analogous to the movement of molecules. Despite the prevailing

evidence for randomness of price fluctuations in some occasions there were found stock price series

that followed deterministic path. It was first realized in 1960 that autocorrelation in stock returns could

be one explanation for this tendency. This has been independently discovered by Working (1960) and

Alexander (1961).

The turning point in the development of economic theory of market efficiency came in 1965 when

Eugene Fama has published his doctoral dissertation called “The behavior of stock market prices”. In this

study he reviews the existing literature on the subject, analyses distribution and serial correlation of

stock market returns, and concludes that “it seems safe to say that this paper has presented strong and voluminous evidence in favour of the random walk hypothesis”6. Academic justification of random walk

hypothesis made it possible few years later to develop theoretical framework for the new market

efficiency theory. 5 Kendall (1953) 6 Fama (1965)

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2.4. Formulation of Market Efficiency Theory

2.4.1. Introduction

In the same year when Fama has published his doctoral dissertation, another academic paper has set

another milestone in the development of market efficiency theory. In 1965 MIT Professor Paul

Samuelson publishes his “Proof that properly anticipated prices fluctuate randomly”. The paper begins

with an observation that “In competitive markets there is a buyer for every seller. If one could be sure that a price would rise, it would have already risen”7. It is further argued that “arguments like this are used to deduce that competitive prices must display price changes... that perform a random walk with no predictable bias”. In the core of his manuscript Samuelson provides theoretical proof of this statement,

which is presented in the form of mathematical theorem. Starting from the simple theorem he has

generalized it to demonstrate that “market quotation already contains in itself all that can be known

about the future and in that sense has discounted future contingencies as much as is humanly possible”.

In the conclusion he states that “the theorem is so general that I must confess to having oscillated over

the years in my own mind between regarding it as trivially obvious (and almost trivially vacuous) and

regarding it as remarkably sweeping. Such perhaps is characteristic of basic results”.

Based on Samuelson’s approach, Fama (1970) made a comprehensive review of the theory and evidence

of market efficiency. According to his definition, “a market in which prices always ’fully reflect’ available information is called ‘efficient’.” In his outstanding paper Fama has also introduced the notion of market

efficiency theory (which was later labeled efficient market hypothesis). He has made a distinction

between three different forms of market efficiency: weak, semi‐strong, and strong8. The weak form of

market efficiency means that current prices fully reflect all information contained in the historical

returns. The semi‐strong form of market efficiency asserts that in addition to historical returns all

publicly available relevant information is already incorporated into current prices, and strong form

presumes that any relevant information known to any market participant is already reflected in the

market prices. All empirical tests could therefore be classified according to the form of market efficiency

they are dealing with.

After outlining theoretical standpoints Fama (1970) notes that “statement that in efficient market prices “fully reflect” available information is so general that it has no empirically testable implications”. He

further argues that “to make the model testable, the process of price formation must be specified in

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Samuelson (1965) 8

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more detail”. The approach that is normally taken by researchers to derive testable models is to assume

that expected return on security is a function of its underlying “risk”. Different theories would therefore

primarily differ in the ways this “risk” is defined. Fama remarks that conditions of market equilibrium do

not necessarily have to be stated in the terms of expected returns, since they are only one of many

possible measures of probability distribution of returns. By assuming expected returns to be appropriate

descriptors of market equilibrium market efficiency theory implicitly “elevates the purely mathematical

concept of expected value to a status not necessarily implied by the general notion of market efficiency”.

The assumption is, however, unavoidable to make possible empirical testing of market efficiency theory.

2.4.2. General case for market efficiency (“fair game” model)

To generalize the testable model for expected returns, Fama uses the following expression:

E(p̃j,t+1|Φt) = [1 + E( r̃j,t+1|Φt)] pjt (2.1)

where

E – expected value operator;

pjt – price of security j at time t;

pj,t+1 – price of security j at time t+1 (with reinvestment of any intermediate income);

rj,t+1 – one‐period percentage return (pj,t+1 – pjt)/pjt;

Φt – general symbol for whatever set of information is assume to be “fully reflected” in the price at t; Tildes indicate that pj,t+1 and rj,t+1 are random variables at time t.

This expression was labeled “fair game” model9 and presents the general case of market efficiency

theory. The two assumptions of the model – that market equilibrium can be stated in terms of expected

returns and that equilibrium expected returns are formed utilizing information set Φt – have important empirical implication: they prevent any trading strategies based on Φt to have expected returns exceeding equilibrium expected returns. By letting x to be difference between expected and realized

value of security price in the time t+1 it can be shown that:

xj,t+1 = pj,t+1 – E(pj,t+1|Φt) (2.2)

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With inspiration from Samuelson (1965), Fama builds his argument by applying game theory to his generalized

model of market efficiency. Description of game theory and its concepts goes beyond the scope of this paper.

However, it’s necessary to note that establishment of the fact that the model is a “fair game” allows him to derive

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from which follow that

E(x̃j,t+1|Φt) = 0 (2.3)

This outcome, by definition, means that sequence {xjt} is a “fair game” with respect to the information

sequence {φt}. Equivalently, this property of the model can be presented in the terms of expected and realized returns. By denoting z to be difference between realized and expected returns one gets:

zj,t+1 = rj,t+1 – E(rj,t+1|Φt) (2.4)

from which follow that

E(z̃j,t+1|Φt) = 0 (2.5)

So, the sequence {zjt} is a “fair game” with respect to the information sequence {φt}.

Continuing with Fama’s notation, any trading strategy in the efficient market universe could be

expressed as:

α(Φt) = [ α1(Φt), α2(Φt), α3(Φt), … , αn(Φt) ] (2.6)

where α1…. αn are the amounts to be invested into n available securities. The investment takes place at the time t. Total excess return of the strategy at time t+1 will be described by the following equation:

n

Σ

j=1

vt+1 = αj(Φt) [rj,t+1 – E(r̃j,t+1|Φt)] (2.7)

which from the “fair game” property of (2.5) has expectation:

n

Σ

α j=1

E(ṽt+1|Φt) = j(Φt) E(z̃j,t+1|Φt) = 0 (2.8)

That means any trading strategy based on the available information set Φt is not expected to earn any return above the equilibrium expected return on the market.

After derivation of the general market efficiency model Fama describes two special cases: the submartingale model and random walk model. These models are reviewed in the following sections.

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2.4.3. The Submartingale model

The submartingale10 model assumes that, given the information set Φt at the time t the price of the security j in the next period t+1 is expected to be higher or equal to its current price. In other words, this

security value is expected to grow over time.

In Fama’s notation the model will be expressed as follows:

E(p̃j,t+1|Φt) ≥ pjt or equivalently E(r̃j,t+1|Φt) ≥ 0 (2.9)

There is an important empirical implication to this return’s non‐negativity property. There exists set of

investment strategies based on “one security and cash” mechanical trading rules. These strategies for

every period of time generate signals prescribing either holding security, selling it short, or simply

holding cash. The profitability of such strategies based on the same information set Φt under assumptions of (2.9) can never exceed simple buy‐and‐hold strategy, since the maximum expected

return will always be achieved by simply holding the security till the next time period. Consequently,

empirical testing of such rules will present valuable evidence for or against market efficiency theory. 2.4.4. The Random Walk model as extension to “fair game” model

When testing for market efficiency two assumptions were made by researchers looking for patterns in

the time series data: successive price changes (returns) are independent and identically distributed.

Combining these assumptions together one would get a simple random walk model. In Fama’s notation

it is described as

f(rj,t+1|Φt) = f(rj,t+1) (2.10)

which means that conditional probability distribution of independent random variable equals to its

marginal probability distribution. In addition, density function f must be the same for all t.

Fama (1970) considers random walk model to be extension of his “fair game” efficient market model,

since it’s “making a more detailed statement about the economic environment”. The argument here is

that the “fair game” model only implies that conditions of market equilibrium are stated in the terms of

expected returns, but no information is given about the stochastic process of price generation. In that

sense random walk model is superior, because it provides information about distribution of the future

10

Martingale, submartingale, and supermartingale are the concepts of the Probability theory. Their description is

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prices, which is independent of information set Φt and is derived from the historical price distribution. Fama concludes that “empirical tests of the “random walk” model … are in fact tests of “fair game”

properties” and they are “more strongly in support of the model than tests of the … pure independence

assumption”.

2.4.5. Sufficient conditions for market efficiency

Fama (1970) concludes theoretical part of his paper by presenting sufficient conditions for market

efficiency. He puts them as follows:

• Transaction costs are not incurred in security trading;

• Market agents have a free access to all publicly available information; • All market agents have homogeneous expectations.

Fama admits that these conditions are hardly achievable in the real world settings. However, since the

conditions are sufficient but not necessary, violation of one or more conditions will not immediately

invalidate market efficiency theory. For instance, the market can still be efficient if “sufficient number”

of investors have access to all publicly available information. Similarly, all market agents don’t have to

have homogeneous expectations as soon as different expectations do not allow some investors to

consistently make better predictions for future prices movements.

2.5. Criticism of Fama’s original definition

Fama’s foundation of EMH has triggered a lot research on the field and resulted in popularization of

market efficiency theory. Many researchers have found prominent supporting evidence for the theory.

For instance, Jensen (1978) stated that “there is no other proposition in economics which has more solid

empirical evidence supporting it than the Efficient Markets Hypothesis”. At the same time it has

received considerable amount of criticism.

Leroy (1973) has demonstrated that under risk aversion the martingale property of returns in the “fair

game” model would only approximately hold in the multi‐period investment horizons. Going further,

Leroy (1976) argued that Fama’s definitions are tautologies and points out the need for correction for

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Figlewski (1978) has studied heterogeneous expectations of market agents. His conclusion was that in

the short term market prices tend to fully reflect information, weighted according to the wealth of

investor who possesses such information. However, increasing period of investment decisions,

decreasing risk aversion of market agents, and presence of more agents with heterogeneous

expectations would adversely affect the level of efficiency achieved on the market. Figlewski’s

conclusion was that markets are neither entirely efficient, nor entirely inefficient.

Grossman and Stiglitz (1980) have criticized the “prices fully reflect all available information”

assumption and pointed out that there must be “sufficient profit opportunities, i.e. inefficiencies, to

compensate investors for the cost of trading and information‐gathering”.

Lo and MacKinlay (1988) have shown that random walk hypothesis is strongly rejected on the US stock

price data for the entire sample period (1962‐1985). They admit that the rejection of random walk

hypothesis doesn’t automatically invalidate market efficiency model. It is argued that “these results do

not necessarily imply that the stock market is inefficient or that prices are not rational assessments of

“fundamental” values” because “without a more explicit economic model of the price‐generating

mechanism, a rejection of the random walk hypothesis has few implications for the efficiency of market price formation. Although our test results may be interpreted as a rejection of some economic model of

efficient price formation, there may exist other plausible models that are consistent with the empirical

findings”.

As a response to this extensive academic criticism, Fama (1991) has revisited the market efficiency

theory and revised some of the definitions. His article called “Efficient Capital Markets: II” was published

in 1991. The details of Fama’s revision are presented in the next section.

2.6 “Efficient Capital Markets: II” – Fama’s revision

After approaching market efficiency theory in 1991 and evaluating the developments of the last two

decades, Fama has decided to alter the definitions of different tests of market efficiency used in his

original article in 1970. Instead of weak form market efficiency tests he has introduced the notion of tests for return predictability. In the new definition these tests have not only considered forecast power

of past returns, but also covered tests of forecasting abilities of variables like dividend yield, interest

rates, P/E ratios and other company specific factors. Additionally, tests for all kind of market anomalies

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semi‐strong market efficiency tests, was renamed to event studies. The idea behind such tests is to

check how quickly the market adapts to the newly announced information in the terms of news,

company earnings releases, and so on. If the market is efficient, it should immediately absorb the

information contained in the news announcements and security price should be accordingly adjusted.

Finally, the strong form market efficiency tests have been labeled tests for private information. They

evaluate whether small groups of investors possess not publicly available information (“inside

information”), which can be consistently used to outperform the market.

After revision of market efficiency definitions Fama presents the updated review of empirical findings on

the field. He admits that the strong version of market efficiency hypothesis with zero transaction costs is

not economically feasible and points to weaker and more economically sensible version presented by

Jensen (1978). In Jensen’s interpretation “prices reflect information to the point where the marginal

benefits of acting on information (the profits to be made) do not exceed the marginal costs”.

Fama also asserts that transaction costs are not the central issue for tests on market efficiency. The

main empirical challenge lies in the “joint hypothesis” problem, which only allows conduction of joint

tests of market efficiency and some model of equilibrium, an asset‐pricing model. According to Fama,

that is the reason why “market efficiency per se is not testable”. Still, he believes that this fact doesn’t

make the empirical research on the field uninteresting or redundant. On the opposite, he argues that

“judged on how it has improved our understanding of the behavior of security returns, the past research

on market efficiency is among the most successful in empirical economics, with good prospects to remain so in the future”.

2.7. Summary

This chapter has outlined one of the central theories of modern finance: market efficiency theory. The

original “fair game” model and its modifications (submartingale and random walk models) were

presented and discussed. The model’s criticism and Fama’s later revision of the definitions have also

been documented.

In the next section of the paper the empirical evidence coming from various tests of market efficiency

will be reviewed. This review will include the evidence on the tests for return predictability, event

studies, and tests for private information. The recent studies of momentum and contrarian strategies,

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3. Empirical evidence on market efficiency

The empirical evidence on market efficiency has grown enormously during the last four decades.

Nowadays it covers wide range of regularly discussed topics in the academic literature: profitability of

investment strategies, reliability of technical trend indicators, market reaction to news announcements,

forecasting abilities of professional market analysts, and many more. The comprehensive review of all

the relevant literature is not possible in the context of this study. Therefore this chapter will only cover

the most influential research on the field along with some related concepts and hypotheses. Special

attention will be paid to empirical studies of contrarian and momentum strategies, which were the main

source of inspiration for writing this paper.

In several occurrences researchers who were conducting tests for market efficiency came across

puzzling expected return irregularities. Such irregularities were labeled anomalies to market efficiency.

Some of these “anomalies” were later proven to be sample specific phenomena, while others were

persisting even in cross‐country data. It has now become common practice for any market efficiency

study to verify whether the obtained abnormal profits (if any) could be explained by some of the widely

recognized market efficiency anomalies.

The first three sections of this chapter are structured according to Fama’s revised classification of

market efficiency tests. The first section is devoted to the tests for return predictability, the second one

deals with event studies, and third one describes tests for private information. Some of the well known

market efficiency anomalies are also described in the course of the first three sections. The fourth

section illustrates the historical development of evidence on contrarian and momentum strategies.

Methodologies, arguments, and criticism of the reported results are presented and reviewed. The final

section of this chapter summarizes the discussed evidence.

3.2. Tests for return predictability

Generally speaking, return predictability could be estimated from both cross‐sectional and time series

data. However, any cross‐sectional study immediately runs into the joint hypothesis problem: one can

either test market efficiency conditionally on some asset‐pricing model or test asset‐pricing model

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more sensible: one would rather test the explanatory power of famous Capital Asset Pricing Model

(CAPM) under the assumption of market efficiency than the other way around. In other words, the

ability of any asset pricing model to capture all cross‐sectional variations in the data is much stronger

assumption than the ability of market to be efficient, hence any test with such strict assumption don’t

have much value in terms of its results interpretation. Therefore tests for return predictability are

mainly concerned with assessment of market efficiency based on time‐varying expected returns. Fama

(1991) provides comprehensive overview of existing literature on the field. He makes a distinction

between three groups of tests for time‐varying return predictability. In the first group of tests future

returns are predicted solely based on past returns. Second group of tests evaluates whether company

related variables could be associated with return patterns. Finally, the last group of tests is concerned

with seasonality factors. All three groups of tests are discussed in more detail below.

3.2.1. Predicting returns from past returns

Short‐horizon stock returns. Market efficiency assumes no predictive power of past returns, so the best

estimate for future return values should be historical mean of past returns. It has been demonstrated,

however, that daily, weekly, and monthly returns are often found to have some degree of

autocorrelation, which allows to some extent make predictions about future return values. Lo and

MacKinlay (1988) have tested random walk hypothesis on the US data and have rejected it. They found

that weekly stock returns are positively correlated, and autocorrelation is stronger for portfolios of small

stocks. The rejection of random walk hypothesis could not be completely explained by infrequent

trading or time‐varying volatilities. Lo and MacKinlay (1988) have further argued that implications of

their results would not invalidate market efficiency per se, but would put some restrictions on the

plausible asset pricing models that were used to describe the process of price formation. The

variance‐ratio test methodology introduced by Lo and MacKinlay (1988) is still widely used (with some

corrections) to test for random walk on the international stock markets. The results of such tests are

mixed. However, even when random walk hypothesis is rejected, the percentage of predictable return

variability is too low to declare strong violations of market efficient hypothesis.

Long‐horizon returns. Until it was challenged by Shiller (1984) and Summers (1986), the general view

was that since autocorrelation found in stock returns is economically insignificant even for short‐horizon

studies, it would completely die out when moving to long horizons test. Shiller and Summers have

presented some models in which stock prices take slowly move away from their fundamental values

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settings the market would be highly inefficient, but such inefficiency would not be detected in the tests

of short‐horizon returns. Fama and French (1988) have found empirical evidence for long‐horizon

dependencies predicted by Shiller‐Summers model. They have pointed out, however, that such

dependencies could either be interpreted as rational long‐term change of return expectations or

irrational price bubble. Therefore they argued that existence of autocorrelation in long‐horizon returns

could not be clearly attributable to violations of market efficiency.

Contrarian and momentum strategies. Tests for the presence of either contrarian or momentum effect

also fall under the category of return predictions solely based on past return data. Because of its

importance to this paper the accumulated empirical evidence on contrarian and momentum strategies

will be presented separately under section 3.4.

3.2.2. Company related forecasting variables

The statistical problem with any predictions solely based on historical returns is that it is past returns

that are used as proxies for expected returns. That is not very convenient, because variation in past

returns is only partially explained by return expectations. In other words, past returns are very noisy

measure of expected returns. Tests for company related forecasting variables are made in attempt to

overcome this statistical limitation by introducing some variables which serve as better proxies for

expected returns estimation.

Size Effect. One of the earliest and most quoted empirical articles on size effect was published by

Banz (1981). He has studied excess returns for US stocks in the period 1936‐1977 and has documented

persistent excess return when holding a portfolio of small stocks. The effect was significant in both

statistical and economic terms (small stocks have outperformed the large ones by the annual 19.8%).

Strong evidence of size effect was later found in many studies of US and international stock markets.

Because of its statistical importance company size (in terms of market capitalization) was even included

as one of the factors in the famous Fama and French three‐factor model11.

Several explanations were offered to deal with size effect anomaly. One reason for its existence could be

underestimation of CAPM betas for small stocks, which makes small stocks returns appear to be

11

The model was originally developed by Fama and French (1993) to explain variation in the data that was not

captured by CAPM. Besides traditional CAPM beta the model includes two additional explanatory variables: the

return differences between small and big companies and the return differences between high and low book‐to‐

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excessive, while in fact they are “normal” compensation for correctly measured level of risk. Another

explanation states that size effect arises from the presumption that CAPM is not appropriate model for

measuring expected return. This view is taken by Chan et. al (1985), who deployed an alternative asset

pricing model to measure the performance of small firms portfolios relative to the large ones. They

found that under the alternative model small firms have only outperformed large ones by an average of

1.5% per year, which was a huge difference in comparison with the standard CAPM estimate of 11.5%

per year.

Market to Book ratio. Lakonishok et. al (1994) have examined the portfolios of stocks bought on the

basis of stock’s book to market value. After controlling for size effect they found that average difference

between returns of firms with high and low book‐to‐market ratios is 7.8% per year. Lakonishok et. al

(1994) have also demonstrated that the reported results cannot be explained by compensation for

increased risk. Fama and French (1993) have used market to book ratio as another explanatory variable

in their three‐factor asset pricing model.

Earnings to Price Ratio. Basu (1977) has shown that earnings to price ratio (E/P), which is often used for

valuation of company growth perspectives, can explain some variations in expected returns that are not

captured by standard CAPM. However, Fama and French (1992) have demonstrated that after

controlling for size effect and market to book ratio the E/P effect disappears. Similar results have been

later achieved in other studies, therefore it was widely accepted that E/P relationship can be seen as a

proxy for other effects.

3.2.3. Seasonality effects in predicting returns

Large number of studies has documented the presence of time patterns in security returns, which have

been labeled “seasonality effects”. In essence, this term refers to the situation when the observed

returns are systematically higher or lower depending on the time of the day, day of the week, and

month of the year. Some of the reported seasonality effects are described below. The special focus is

made on the most well‐known January effect along with the more recently discovered Halloween indicator.

January effect. Numerous research papers found that returns in January are substantially higher than

returns in other months. The effect is especially pronounced for small stocks and is found both on the

US and international security markets. Fama (1991) has presented some evidence of January effect on

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average 8.06% (and 1.34% for large stocks). At the same time, the average return for the rest of the year

was 0.92% for small and 0.88% for large stocks. Furthermore, in the following decade (years 1982‐1991)

the January return was 5.32% for small and 3.2% for large stocks. The respective numbers for the rest of

the year were 0.17% and 1.23%. Fama (1991) noted, that even though the difference between large and

small stocks January returns has become smaller during the last decade, both groups of stocks have

continued experiencing significantly larger average returns in January than in all other calendar months.

Gultekin and Gultekin (1983) have tested for presence of the January effect on the international data.

Their sample included stock returns data for 18 industrialized countries, and they have found significant

abnormal returns in January in all countries except Australia.

In the last two decades January effect was found in many stock markets worldwide. Some researchers

claimed that because of such extensive popularization some investors will attempt to exploit it, so the

power of January effect will inevitably decline. This proposition was tested by Moller and Zilca (2008),

who analyzed the US stock data. They found the overall magnitude of January effect to be similar across

the whole study period (years 1927‐2004). The researchers concluded that the basic forces behind the

January effect still persisted and were as strong as they had been in the past.

There were some attempts to find explanation of systematic abnormal returns experienced by stocks in

January. The most well known explanation is called tax‐selling hypothesis. It is based on the fact that

investment advisors at the year end often recommend selling securities for which an investor incurred

substantial losses. The sale needs to be done before the end of the tax year, and equivalent securities

can be purchased again in the beginning of the next year. This creates a tax loss for the investor, which

can fully or partially cover transaction costs. The argument here is this: since all the selling happens in

December and the repurchasing takes place in January, the stock prices are depressed in December and

elevated in January, thus creating excessive returns for this particular month.

Despite the appealing argumentation of tax‐selling hypothesis, some evidence has shown that January

effect could not be fully explained by it. International research has shown that abnormal returns in

January exist even in countries without capital gain tax. Moreover, January effect was found in the US

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“Sell in May and go away”. This investment strategy has its roots in the old British saying “Sell in May

and go away, but buy back on St. Leger Day12”. The strategy prescribes selling the shares in May and

staying away from the stock market for half a year until September, where one has to buy the shares

back. Similar strategy on the US stock market has received the name “Halloween indicator” (because the

purchase of shares happens in October around the time when Halloween is celebrated). In several

studies the profit made by following this strategy is significantly higher than from simple buy‐and‐hold

strategy. Bouman and Jacobsen (2002) have been able to found the evidence for this anomaly in the UK

as early as in 1964. They have analyzed data across 37 different countries and observed that the “Sell in

May” effect tends to be especially strong in European countries and it is persistent over time. For 36 out

of 37 countries the returns during November ‐ April period are significantly larger than for the

remainder of the year. Bouman and Jacobsen (2002) have shown that even after controlling for risk,

January effect, and sector‐specific factors the “Sell in May” strategy was still demonstrating superior

performance throughout the research period.

Quite notable, Bouman and Jacobsen’s study included Russia as one of the countries in the sample, and

Russia was the only country where no significant return differences were observed between November‐

April and May‐October periods. However, Bouman and Jacobsen (2002) had only 44 monthly

observations for Russian stock market (all other countries had at least three times more observations),

so the statistical inference of their results should be made with precaution. Additionally, their sample

included years 1998‐1999 when Russia has been going through serious economic crisis, so the returns

were totally different from what one can expect under “normal” market conditions.

Other seasonality effects. There’ve been made numerous studies of other seasonality effects in the

attempt to find the exploitable profitability patterns. Evidence on such effects would not be reviewed in

this paper, but it makes sense to name some of them for readers’ reference. Ziemba (1994) made an

overview of evidence on reported market efficient anomalies to date. Besides the most famous January

effect the list of known seasonality effects included day of the week, holiday, turn of the month, turn of

the year effects, and Golden Week effects.

3.3. Event studies

Event studies are market efficiency tests evaluating adjustment of prices to public announcements.

Fama (1991) argued that out of all types of tests the event studies “come closest to allowing a break

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between market efficiency and equilibrium‐pricing issues” and in that sense they give “the most direct evidence on efficiency”. The idea here is to isolate the effect of an announcement on the price of a stock.

This is done by calculating relative performance of a stock in the months surrounding the

announcement. The outcome of such study shows how quickly stock prices adapts to the newly arrived

information, which will allows to draw conclusions on the level of market efficiency.

Most of the evidence accumulated so far suggests that stock market prices rather quickly adapt to the

new information. Fama et. al (1969) have analyzed the adjustment of equity prices to stock splits. Since

stock splits are generally associated with substantial divided increases, on efficient markets anticipation

of such increases would affect share prices immediately after the stock split is announced. During

empirical testing on the US data this tendency was confirmed. Moreover, Fama et. al (1969) were able

to verify that stock splits only cause price adjustments necessary to accommodate to the new

anticipated stream of future dividend earnings. The conclusion of the study was that stock market is

efficient in the sense of accommodation of new information into security prices.

Patell and Wolfson (1984) have studied the effects of earnings and dividend announcements on the

intraday behavior of stock prices. They have analyzed the consecutive US stock prices changes

surrounding the minute at which news messages appear on the Dow Jones News Service (the Broad

Tape). According to their estimations, the major part of a stock price adjustment occurs within 5 to 10

minutes of the relevant announcement. The researchers note that “dividend announcements, as a class,

do not appear to induce large increases in the intraday price change variance, but significant

disturbances can be detected at the announcement of dividend changes”. This behavior is consistent

with market efficiency hypothesis, since all information about dividends is known beforehand and is

already incorporated into stock prices, while changes in dividend payouts constitute new pieces of

information.

On the international data event studies on announcements effects have been conducted by Brown and

Niederhoffer (1968) for Australia, by Emanuel (1984) for New Zealand, and by Ariff and Finn (1989) for

Singapore. The behavior of these stock markets was generally consistent with efficient market

hypothesis.

Out of recently published research papers, Norden and Weber (2004) investigated the response of stock

and credit default swap (CDS) markets to rating announcements made by the three major rating

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downgrades by all three agencies. Additionally, it was identified that reviews for downgrade by Standard

& Poor’s and Moody’s are associated with significant abnormal negative performance in both markets,

whereas actual downgrades are not. At the same time, neither reviews for downgrade nor actual

downgrades by Fitch exhibit a significant impact on the stock and CDS markets. Market reaction of

adjusting returns in the time of announcements of downgrade reviews is consistent with the notion

market efficiency. By the time the actual rating downgrade takes place the market anticipation of stock’s

performance is already incorporated into its price.

Some events studies came across results not consistent with market efficiency. One of the most well

documented anomalies here is called post‐earnings announcement drift. The first studies of this

phenomenon date back to the 1960’s, where Ball and Brown (1968) have discovered that after

company’s announcement of annual income report its stock’s cumulative abnormal returns drift in the

direction of an earnings surprise for several weeks (or even several months) following the day of

earnings announcement. Since then this behavior was thoroughly tested both on the US and

international data. Chan et. al (1996) have tested the sample of US stocks in the period 1977‐1993 and

found strongly significant post‐earnings announcement drift, which lasted for at least six months. Their

results remained significant even after controlling for size effect and risk factors. The most recent

international research was made by Liu et. al (2003) for the UK, by Burghof and Johannsen (2009) for

Germany, and by Forner et. al (2009) for Spain. All three studies confirmed the presence of post‐

earnings announcement drift effect on the underlying stock markets. The empirical evidence of its

presence means that initially market underreacts to the corporate earnings announcements and only�