AbstractThis Moreover, several statistical techniques such as Bootstrapping

AbstractThis paper focuses on testing market efficiency in the respective stock markets of the 28 official European Union members, as at 2018, by empirically evaluating the profitability of the Moving Average Convergence/Divergence, alias MACD, a commonly used Technical Analysis indicator. The MACD is a trend-following indicator which gauges changes in Trend by outlining differences between two different moving averages.  The methodology used is based on the application of an optimized trading rule for each national stock market exchange, for a 10-year time sample spanning from the 1st of January 2006 to the 31st of December 2016. In pursuance of obtaining optimized MACD parameters for each of the 28 sample elements, a Backtesting cross-validation is applied ranging from 2000 to 2005. Moreover, several statistical techniques such as Bootstrapping and {} are applied as to validate estimators, thus ensuring bias-free results and more consistent conclusions. RESULTS (What level of transaction cost would eliminate gains, if there are any?)CONCLUSIONIntroductionstate the general topic and give some backgroundprovide a review of the literature related to the topicdefine the terms and scope of the topicoutline the current situationevaluate the current situation (advantages/ disadvantages) and identify the gapidentify the importance of the proposed researchstate the research problem/ questionsstate the research aims and/or research objectivesstate the hypothesesoutline the order of information in the thesisoutline the methodologyEMH INTROTA INTRO AND CONTRADICTIONREVIEW OF LITERATURE RELATED CURRENT SITUATION: Self-defeating discoveryRESEARCH IMPORTANCE, PROBLEMS AND OBJECTIVES -Contribution of paperLimitation: Transaction Costs, Overfitting, Using a single indicator, Using an old indicator that may have been incorporated into prices, Data snooping, Feasibility of MACD trading given numerous trader bias and timeliness of signalMETHODOLOGYLiterature ReviewTechnical Analysis and the MACDTechnical analysis is a technique which utilises patterns of price history of a financial instrument with the aim of providing indications on the future behaviour of prices (Caginalp and Balevonich (2003)). The popularity, and a critic (which will be discussed further in this paper), of Technical Analysis is its relative simplicity {R. Batchelor}. In fact, to estimate future price movements it is simply necessary to analyse historical price behaviour and the relative level of Volume and open interest. Primary evaluation of past prices, while alterations in the other factors are studied mainly to confirm the correctness of an identified price trend. At the beginning of the century, in the 1900, Charles Dow begun writing several editorials reflecting his view on market price action. His work published on the Wall Street Journal sets out theories that represent the basis for the modern Technical Analysis. Of the many theorems put forth by Dow, three emerge:Price Discounts Everything, so that the market reflects all available information. Prices represent and incorporates the sum of all the hopes, fears and expectations of all participants.   (Murphy, 1999)Price Moves with the Trend, differently from a chaotic process, decision making arises from the analysis of markets fluctuations. This assumption represents the basis for all technical analysis methods. (Murphy, 1999)History Repeats Itself, it is believed among Practitioners and Academics that the repetitive nature of price fluctuations is often attributed to human psychology, whereby common human emotions like fear and optimism tend to create repetitive patterns. (Murphy, 1999)Technical analysis is applicable to stocks, indices, commodities, futures or any tradable instrument where the price is influenced by the forces of supply and demand. More accurately, for its principles to be successful, it is accepted that price should only be influenced by forces of demand and supply. In fact, technical analysis makes three key assumptions about the securities that are being analysed: Level of Volume: Heavily-traded stocks allow investors to trade quickly and easily without dramatically changing the price of the stock. On the other hand, low liquidity stocks are often very low priced, meaning that their prices can be more easily manipulated by individual investors. These forces cause thinly traded securities to be unsuitable for Technical Analysis.No Artificial Price Changes: elements such as splits, dividends and distributions are considered common artificial reasons for price changes and can dramatically affect the price chart and make technical analysis difficult to apply. No Extreme News: Technical analysis cannot predict extreme events and consistently fails in delivering accurate prediction when “extreme news” are influencing price behaviour. (StockChart)It is necessary that a security meets all the criteria, and only then a trader can put capital at risk.  INDEX BEHAVIOUR FOR THIS PAPER?Moving Average Convergence DivergenceMACD (Moving Average Convergence/Divergence) is a technical indicator created by Gerald Appel in the late 1970s, used to spot changes in the strength, direction, momentum, and duration of a trend in a stock’s price. The MACD is a computation of the difference between two exponential moving averages (EMAs) of closing prices, conventionally a 12 days-EMA against a 26-days EMA. This difference is charted over time, alongside a 9-day which will function as a triggering signal. Finally, a histogram is constructed measuring the difference between the MACD and signal line. By comparing EMAs of different periods, the MACD line illustrates changes in the trend of a stock. A trader typically reacts to 3 types of signals:the MACD line crosses the signal linethe MACD line crosses the zerothere is a divergence between the MACD line and the price or between the histogram and the price.PICTUREThe period for the moving averages on which an MACD is based can vary, for example for this paper each of the MACD tested on the 28 stock exchanges within the sample will hold optimized parameters. The most commonly used parameters involve a faster EMA of 12 days, a slower EMA of 26 days, and the signal line as a 9-day EMA of the difference between the two. It is written in the form, MACD(faster, slower, signal) or commonly, MACD(12,26,9).Like any other indicator, the MACD is subject to evident limitations, and its accuracy can be compromised if applied to unfavourable conditions. This indicator has often been criticized for failing to respond in very low or alternately very high volatility market conditions. Since the MACD measures the divergence between averages, it can give meaningful feedback only as trends change. Thus, it would be less useful if the market is not trending, that is, if it is trading sideways, or if the market is trading erratically, making sudden, dramatic, or countervailing moves.Efficient Market HypothesisTechnical Analysis is an analysis methodology for forecasting future price behaviours based on past market Data, such as Price and Volume. This means that trading by virtue of technical analysis tools, such as the MACD for example, could allow for abnormal trading profits, beyond investor compensation for the level of risk tolerated. This characterization, however, stands in perfect contradiction to much of current financial archetype, the Efficient Market Hypothesis (EMH).The EMH is a theory in financial economics developed by Eugene F. Fama in the 1970, which implies that all relevant information is fully incorporated and reflected by the asset price level, thus suggesting that no investor has the capability to forecast price movements and consequently generate abnormal returns. (Fama, 1970)  If the stock market is efficient, share prices must reflect all available information which is relevant for the evaluation of a company’s future performance, and therefore the market price of share must be equal to its intrinsic value. Assuming the veracity of these statement, no amount of analysis can provide investors an advantage over another investor. Additionally, any new information becoming available to investors, will be instantly and accurately absorbed by the market price, thus denying investors risk-less profits.Eugene Fama outlines three types of market efficiency: weak, strong and semi-strong. The weak-form efficiency, implies that historical data cannot be used for future price prediction thus excluding any form of proficiency in the use of technical analysis techniques. Antithetically the use of fundamental analysis may allow the identification of undervalued and overvalued assets. The purpose of this paper will be to test specifically weak form efficiency using technical analysis, hence attempting at generating abnormal returns through the use of historical Data. If markets are weak form efficient, then MACD should be incorporated into market prices, thus not allowing for abnormal returns. The semi-strong form implies that all public information is calculated in the stock’ current price, while the strong form states that all available information, public and private, are incorporated by the stock price. Note that a stronger form of efficiency also holds any previous form.In addition to Fama’s work, Shleifer (2000,p.2-3) propounded three assumptions as the premise for the EMH theory, reported as follows:  Investors are rational, in a way that they undertake fundamental analysis, way up the expected risk and return of each stock before making any investment. Suggesting that rational investors are basically professional economists.  Where there are irrational investors, their trading activities are random. According to this assumption, the market belongs to rational investors; because the activities of irrational investors end up nullifying each other.  “Market arbitrage can correct price when it deviates from its efficient level. Because both investors are rational, they will do the arbitrage once there are imbalances existing in stock prices. Through this way, stock price will always stay in an efficient level.” (Geng and Wang, 2009)A close link can be established between Fama’s theory and the Random Walk Hypothesis, a concept traced from 1963 to French broker Jules Regnault and subsequently popularized by Burton G. Malkiel. Malkiel argues that asset prices typically exhibit signs of random walk and that one cannot consistently outperform market averages. (Malkiel, 1973) Expanding his theory, a clear and unequivocal critic stands at downgrading Technical Analysis efficiency and popularity. The economist openly diverges from the view of technicians, arguing that “correlation of past price movements with present and future price movements is very close to zero”, and that technicians fail to accept the idea of randomness and constantly attempt at providing potential reasons to random market price movements. In its book, Malkiel compares technical analysis to astrology, a pseudoscience. Since then, to the eyes of many academics and fundamental practitioners, chartists techniques completely lost credibility. Let’s focus on past researches, as to demonstrate at what stage empirical findings are.Theoretical and empirical researches on the weak-form efficiency of stocks traded on the world’s major exchanges is abundant, whereas investigations of technical analysis techniques and more specifically the MACD indicator have not been as popular.  (W. Brock, J. Lakonishok, B. leBaron, 1992) Early studies focused on the potential profitability of simple technical trading rules, such as resistance-support levels and the moving average. Noteworthy is the research from Brock, Lakonishok and leBaron (1992), which sampled a 90 years collection of daily Data from the Dow Jones Industrial, from 1897 to 1986. Their findings provide strong support for the moving average indicator, also emphasizing at what potential degree the simplest trading rule can still possess predicting power. However, transaction costs have been omitted in their computation revealing that excess returns are likely to be impoverished, if not totally erased, once considered. (Bessembinder, Chan, 1995) A similar study was experimented in Asian markets with the profitability testing of 3 simple trading rules. For instance, Bessembinder and Chan (1995) studies provide substantial evidence that technical trading rules predict changes in Asian stock price indices to an economically significant degree. The estimated “break-even” round-trip transactions costs, which would eliminate gains from technical trading, stands at 1.57% on average. Moreover, their paper suggests that rules tend to be more profitable in emerging markets, such as Malaysia, Taiwan and Thailand, compared to the more developed stock markets, namely Honk Kong and Japan. A phenomenon that could be expected for this European market analysis.A potential extension of Bessembinder and Chan work, is the recent comparative review between Developed and Emerging markets profitability carried on by Wafi in 2015. (A. Wafi, 2015)  Findings indicate that technical trading rule applied to Developed markets seemed to achieve returns only up to 1980s. Sub-sequential market efficiency, hence technical unprofitability, can be attributed to the general technological developments, transparency of information and finally the massive size of the market. Although the application of advanced models such as genetic algorithm, genetic programming, and neural network analysis leads to the increase in prediction accuracy as explained by Pai and Lin (2005)MACD (G. Anghel, 2015) Although the Moving Average Convergence Divergence oscillators is of a popular use among real-life traders, little attention has been paid to the performance of this trading rules (also considering oscillator relative youth since it was developed only in the late 1970s). Regarding MACD studies, the most prominent assessment is observed in the fresh work of G. Anghel (2015). An optimized MACD rule has been applied to national stock exchange, for 75 countries and 1336 companies.  After adjusting returns for risk, by using the geometric M2 for Sortino excess return, and subtracting all observable direct trading costs, G. Anghel detected a total of 34 inefficient markets, thus proving that time to time investors may obtain abnormal cost and risk adjusted returns. On the contrary, when looking at yearly profitability, not enough evidence is yet provided to disregard EMH: 2008 and 2011 proved to be profitable, but it is still unknown how an investor could have recognized it ex-ante, also given the unsatisfactory results of previous years. In 2013, Lui and Chong pointed out major differences in performance between experienced technical analyst and novice traders in a controlled experiment. By assumption of random walk there shouldn’t be differences between the two kinds of traders. Knowledge technicians proved to significantly outperform those with no or little experience, hence providing a valid proof for believing that experience is highly correlated with profitability in Technical Analyst. (K.M. Lui, T.T.L. Chong, 2013)EVIDENCE OF EMH (Van Horne Parker 1967)  http://0-www.jstor.org.wam.city.ac.uk/stable/pdf/4470248.pdf Abnormal returns identified in previous empirical analysis, and that may be regarded as EMH opposition, are possibly constrained by crucial limitations that would severely alter their respective conclusions. In many of the empirical analysis transaction costs have been omitted. In real life though, broker commissions, spreads and fund fees often diminish return, if any is generated. In fact, according to an article published by FT in 2016, 99% of US equity funds underperform, failing to beat the S&P 500 benchmark. Additionally, Data snooping biases may have again altered conclusions. This Bias, also referred as data mining, is the process of uncovering patterns in data that can be presented as statistically significant, without first devising a specific hypothesis as to the underlying causality. This is known as finding results simply by chance.From Developed to Emerging market efficiency discrepancies, to the generation of abnormal returns with the use of technical analysis tools, concluding with a majority of underperforming hedge funds and retail investors, the preceding papers seem to generate mixed judgments regarding EMH credibility, particularly targeting semi-strong and strong forms.http://0-onlinelibrary.wiley.com.wam.city.ac.uk/doi/10.1002/9781119200697.ch8/pdfMethodology and Data