Excerpt

## Table of Content

1 Part A

1.1 Principles of the Efficient Market Hypothesis Approach

1.2 Evaluation and Interpretation of Results

2 Part B

2.1 Forms of Market Efficiency

2.2 Review of empirical evidence of the Efficient Market Hypothesis

3 Appendix

3.1 One tail independent samples t-test

Bibliography

List of References

## List of Abbreviations

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## List of Symbols

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## List of Illustrations and Tables

Tab. 1: portfolio Overview

Fig. 1: One-tail upper-tail test

Fig. 2: One-tail independent samples t-test

## 1 Part A

### 1.1 Principles of the Efficient Market Hypothesis Approach

This project will focus on Efficient Market Hypothesis which is used in the form of its abbreviation EMH during the next sections. In this context, in Part A EMH, will be examined in the context of the Dow Jones Industrial Average, which includes 30 components and is America's most prominent and globally applied stock index. To differentiate Dow Jones and Dow Jones Industrial Average, the Dow Jones Industrial Average was created to illustrate the importance of the most powerful companies in the US economy from an economically point of view.^{1}

EHM in its origin assumes that share prices in the form of assets fully reflect available information at any time in a specific market.^{2} Accordingly, stocks are investigated to always trade at their fair value on stock exchanges due to the reflection of several information. As a result, it is impossible for investors to purchase undervalued stocks or sell stocks for inflated prices.^{3} The terminology efficient implies that historical price and market developments from capital markets, information of companies, states and raw materials in the form of knowledge as well as expectations from market participants is representative for stock markets. According to Fama, an efficient market is “where there are large numbers of rational profit maximizers actively competing, with each trying to predict future market value of individual securities, and where important current information is almost freely available to all participants”.^{4} The predictability of stock market returns is often questioned by analysts as analysis showed that prices rapidly adjust to information by increasing or decreasing. Thus, the efficiency of share prices depends on the speed of price adjustments to any available information. For investors, predicting future price movements to constantly derive higher profits than the market average is theoretically disproved, assuming the efficiency of stock markets is given.^{5} However, opportunities to identify over- or undervalued stocks are constantly investigated by analysts.

The inability to predict stock market developments by analyzing historical price movements is called Weak Form Market Efficiency. Part A of this assignment will assess the validity of Weak Form Market Efficiency by empirically analyzing historical data on two equally weighted stock portfolios. Part A serves as an evidence to verify or reject the underlying concept.^{6} Simultaneously, a second theory, referred to as Random Walk Theory or RWT is tested to be valid by analyzing two equally weighted stock portfolios. The RWT suggests that price movements base on new information which, by definition, are random, hence changes in price are seen as random. The validation of RTW will additionally show future price changes to be unpredictable and independent from historical stock price developments.^{7} ^{8}

In the analytical report of this assignment, the returns of a randomly composed portfolio A have been compared to a portfolio B, composed from top performers in terms of historical price movements. Portfolio A consists of three randomly selected components of the Dow Jones Industrial index, referred to as DJI, with 30 components in total. To ensure that the components of portfolio A won't match those from portfolio B, a top, middle and low performing component measured by its share price from the 5th of August 2018 is selected. Portfolio B comprises of the DJI's three top performers which have been identified based on their beta ranking.

Tab. 1: Portfolio Overview8

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By definition, Beta is a measure of a stocks volatility in relation to the market. The market is defined to have a beta coefficient of 1.00. Individual stocks show positive or negative, from the markets beta coefficient which inform about risky (ß>1.00) or less risky (ß<1.00) stocks. In detail, Beta is calculated by regression analysis which shows security's response with the response of the market, usually reflecting the slope of 60-month regression line.^{9} This assignment presumes the three most positive deviations to the markets beta coefficient to represent the steepest positive slopes and, as a result, the three top performing companies of Portfolio B.

Considering the above-mentioned thesis of Weak Form Market Efficiency and RTW, a comparison of Portfolio A and Portfolio B's monthly returns of a 24-month observation period starting from May 2016 to April 2018 should provide statistically equal returns. According to this information, the following null hypothesis will be assessed:

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In contrast, assuming that the returns of the three top performing companies in Portfolios B exceed the returns of the randomly selected companies of Portfolio A, the following alternative hypothesis will be assessed:

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In step 1, the monthly logarithmic returns for each company in the specific portfolio are investigated by applying the Microsoft Excel function LN() which returns the natural logarithm.^{10} In step 2, average returns of both portfolios have been detected by calculating the mean value of logarithmic returns of all returns within the selected period of 24 months. The calculated logarithmic returns as well as mean values for each portfolio are shown in Tab. 1: portfolio Overview. In step 3, a one tail independent samples t-test is applied for hypothesis testing, performed in utilization of Microsoft Excel.

### 1.2 Evaluation and Interpretation of Results

The mean value of logarithmic returns for each month of portfolio A and B as well as average returns, variance and TSTAT- value serve as a basis for performing a one tail independent samples t-test. In order to minimize the probability to incorrectly rejecting the null hypothesis, known as Type I error, some key figures have to be determined in advance. In this context, the level of significance is predetermined to 5%, a=0.05, which is analytically seen as a balanced mean value between a relatively tiny area of rejection with an alpha level of 1% and a relatively large area with an alpha level of 10%.^{11} The degree of freedom is calculated to be 44 due to a sample size (n) of 23 monthly logarithmic returns (df = nA + nB - 2).^{12}

The results of the one tail independent samples t-test show a p-value of approximately 0.2406 and a calculated tSTAT-value of approximately -0.7107. Comparing tSTAT to the critical tSTAT -value, this value equates to a value of approximately 1.6838 for a onetailed t-test at a 5% level of significance.^{13} ^{14}

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Figure 3: *One tail upper-tail test* again underlines the critical tSTAT as a value which marks the inner edge of the rejection area and presents the minimum value for hypothesis rejection.14 In this assignment, the tsTAT value of -0.7107 doesn't exceed the critical value of 1.6838. As a result, there is insufficient evidence to reject the null hypothesis. Hypothesis testing has shown incapability to reveal subsequent differences between the mean returns of Portfolio A and Portfolio B. Considering the RWT and Weak Form Market Efficiency principles, the results of hypothesis testing on the example of the Dow Jones Industrial Average index seem to be inappropriate to disprove the validity of both principles.

However, generalizability of the weak form market efficiency principles is increasingly questioned by known researcher such as Malkiel who outlines attacks especially on the efficient market hypothesis and the belief that stock prices could be partially predictable. One of the most meaningful limitation is the incapability of empirical tests on EMH to reflect short term price movements due to investors activities in actual markets which affect prices and cause expenses. Malkiel also questions the validity of noticeable patterns to be valid in the future as they might self-eliminate because of dependability in different sample periods. Moreover, research has shown self-destruction of various patterns in the long-term.^{15} However, some investigations detected anomalies in market efficiency which were revealed by studies and technical analysis in the context of EMH. The example of the January Effect describes a seasonal increase in stock prices which is based on observations in consuming behavior, taxloss harvesting to offset realized capital gains and year-end cash bonuses which cause purchasing of investments. This hypothesis implies that markets at that time are inefficient, as EMH usually make this effect nonexistent.^{16}

## 2 Part B

### 2.1 Forms of Market Efficiency

Multiple economists have taken studies of efficient market hypothesis to their main subject, subsequently, efficient market hypothesis is one of the most common and observed theories in modern finance. Today, EMH is widely used and prospers from frequent testing, which, in the past, has led to new findings, more precisely, different emphasis of EMH.^{17} During his research, the previously mentioned economist Fama investigated in his test that there must be three emphasis of EMH, which he differentiated into weak form market efficiency, semi-strong form market efficiency as well as strong form market efficiency.^{18}

As already explained in Part A section 1.1: *Principles of the Efficient Market Hypothesis Approach,* Weak Form Market Efficiency assumes that stock prices already reflect all information that can be derived by examining market trading data such as the history of past prices. The theory says that future stock price returns are insufficient to be predicted by the examination of past returns. As a result, no extraordinary returns can be derived for investors.^{19}

Semi-strong form market efficiency implies that stock prices are not only reflective of past historical information but comprise all publicity available information which additionally include fundamental data on the company and macro-economic factors, such as economic or political events, annual reports, forecasts or announcements to M&A intentions.^{20} Because public information includes the past history of prices, a market that is semi-strong form efficient is necessarily weak-form efficient. Due to immediately changing prices based on those information, no extraordinary profits can be derived. It implies, that even insiders cannot make abnormal profits.^{21}

The third form of efficient market hypothesis, strong-form market efficiency stipulates that stock prices reflect all publicity and privately available data.^{22} Consideration of this data may have the effect of monopolistic access, possibly enabling advantages in comparison to other investors. However, research has outlined that even exclusive and unannounced information is insufficient to generate extraordinary profits due to the fact that strong markets are characterized to anticipate future market developments, trends and market participants expectations.^{23} Insiders, who earn profits with non-public information based on trading are accused to be lawbreaker. As a result, companies try to publish every important event which may have impact on stock prices.^{24} In general, efficient market hypothesis and its variations assumes that the stock market is a rational market.^{25}

**[...]**

^{1} Cf. Onvista 2018.

^{2} Cf. Fama 1970, p. 383.

^{3} Cf. Investopedia 2018a.

^{4} Cf. Sapate 2017, p. 2.

^{5} Cf. Gonedes 1976, p. 612.

^{6} Cf. Sapate 2017, p. 3.

^{7} Cf. Malkiel 2015, p. 26.

^{8} Please see document Analytical Report, p. 5.

^{9} Cf. Investopedia 2018b.

^{10} Cf. Jelen 2013, p. 572 et seq.

^{11} Cf. Statistics How To 2018.

^{12} Cf. Depoy, Gitlin 2013, p. 262.

^{13} Cf. Appendix 3.1: One-tail independent samples t-test, p. 10.

^{14} Cf. DePoy, Gitlin 2013, p. 262.

^{15} Cf. Malkiel 2003, p. 71.

^{16} Cf. Investopedia 2018c.

^{17} Cf. Schubert 2009, p. 1.

^{18} Cf. Titan 2015, p. 443.

^{19} Cf. Madura 2016, p. 287

^{20} Cf. Clarke/Jandik/Mandelker 2001, p. 5.

^{21} Cf. Hussin 2010, p. 30.

^{22} Cf. Schubert 2009, p. 1.

^{23} Cf. Clarke/Jandik/Mandelker 2001, p. 6.

^{24} Cf. Malkiel 2010, p. 192.

^{25} Cf. Thomsett 2014 p.173.

- Quote paper
- Anonymous, 2018, Principles of the Efficient Market Hypothesis, Munich, GRIN Verlag, https://www.grin.com/document/1150190

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