這篇dissertation是博士學(xué)位花了四年時間編寫而成。學(xué)生中心的非線性動力經(jīng)濟學(xué)和金融學(xué)(CeNDEF)以及定量經(jīng)濟學(xué)院經(jīng)濟學(xué)、計量經(jīng)濟學(xué)是阿姆斯特丹大學(xué)的一個組成部分。在過去的四年里我的銀行帳戶在股票市場之中上下波動，但幸運的是,波動的頻率在我的研究中都穩(wěn)步上升。本文在撰寫過程之中得到無數(shù)人的幫助和支持,我在這里表示感謝。首先,我感謝我的主管和彼得。沒有他們我就不會開始經(jīng)濟學(xué)博士學(xué)位的攻讀。是他們說服我開始學(xué)術(shù)界的職業(yè)生涯并且可以使用我的知識得到回報。我感謝他們給我這個機會。接下來,我感謝彼得為我的研究而做出了許多貢獻。我很喜歡我們的定期會議可以討論工作并可以獲得進步。

 

只要經(jīng)濟市場存在,人們都可以來嘗試預(yù)測它的走向,當(dāng)然我們也希望好的預(yù)測會帶來巨大的財富。實踐并不是質(zhì)疑而是可以預(yù)測,但未來的道路如何，我們需要更多的預(yù)測時間序列規(guī)律來分析。在學(xué)術(shù)界,這僅僅是一系列投機策略，它是否可以預(yù)測還有待我們商榷。因此實踐派學(xué)者在研究經(jīng)濟是沿著不同路徑進行時間序列來預(yù)測數(shù)據(jù)。例如,從業(yè)人員基本知識和技術(shù)分析技巧是可以在實踐中根據(jù)時間序列加以預(yù)測。他們可以提供不同的商品何時賣出是最為合適的，以及相關(guān)的分析數(shù)據(jù)。

 

This thesis is the result of four years of research as a Ph.D. student at the Center for Nonlinear Dynamics in Economics and Finance (CeNDEF) at the Department of Quantitative Economics of the Faculty of Economics and Econometrics of the University of Amsterdam. During these past four years my bank account followed the stock market in its up and down swings. Luckily, the peaks and throughs in my research were steadily rising. This thesis would not have been written without the encouragement, help and support of numerous people, whom I like to thank here. First of all, I thank my supervisors Cars Hommes and Peter Boswijk. Without Cars I would never have started my Ph.D. in economics. He convinced me to start my career Þrst in academia instead of using my knowledge in business. I thank him for this opportunity. Next, I thank Peter for his interest in and many contributions to my research. I appreciate our regular meetings in discussing my work. I want to thank the other members of my Ph.D. committee, Jaap van Duijn, Philip Hans Franses, Frank de Jong, Blake LeBaron, Florian Wagener and Claus Weddepohl, for reading an earlier version of the manuscript. I thank my Italian Ph.D. colleague Sebastiano Manzan, with whom I shared an o?ce and the frustrations of doing research for four years. Next I thank the people in the CeNDEF group, Jan Tuinstra, Cees Diks, Sander van de Hoog, Henk van de Velden and Roy van der Weide. Also I thank the many other people at the Department of Quantitative Economics, Frank Kleibergen, Dawit Zerom, Maurice Bun, Antoine van der Ploeg, Noud van Giersbergen, Angela van de Heerwaarden, Cees Jan van Garderen and Jan Kiviet. I thank the people of the cocoa-trading Þrm Unicom International B.V., Bart Verzaal and Guido Veenstra, for providing me the data used in Chapter 2 and for keeping me informed of all what was happening in the cocoa markets. Finally, I thank my mother and my father for always encouraging and supporting me. They gave me the opportunity to study at the university and I will always be grateful for that. Thanks to my sister Siemone, who followed me in studying econometrics, which caused many heavy debates when doing the dishes.www.400190.com/jr/3988.html

 

As long as Þnancial markets have existed, people have tried to forecast them, in the hope that good forecasts would bring them great fortunes. In Þnancial practice it is not the question whether it is possible to forecast, but how the future path of a Þnancial time series can be forecasted. In academia, however, it is merely the question whether series of speculative prices can be forecasted than the question how to forecast. Therefore practice and academics have proceeded along di?erent paths in studying Þnancial time series data. For example, among practitioners fundamental and technical analysis are techniques developed in Þnancial practice according to which guidelines Þnancial time series should and could be forecasted. They are intended to give advice on what and when to buy or sell. In contrast, academics focus on the behavior and characteristics of a Þnancial time series itself and try to explore whether there is certain dependence in successive price changes that could proÞtably be exploited by various kinds of trading techniques. However, early statistical studies concluded that successive price changes are independent. These empirical Þndings combined with the theory of Paul Samuelson, published in his inßuential paper “Proof that Properly Anticipated Prices Fluctuate Randomly” (1965), led to the e?cient markets hypothesis (EMH). According to this hypothesis it is not possible to exploit any information set to predict future price changes. In another inßuential paper Eugene Fama (1970) reviewed the theoretical and empirical literature on the EMH to that date and concluded that the evidence in support of the EMH was very extensive, and that contradictory evidence was sparse. Since then the EMH is the central paradigm in Þnancial economics. Technical analysis has been a popular and heavily used technique for decades already in Þnancial practice. It has grown to an industry on its own. During the 1990s there was a renewed interest in academia on the topic when it seemed that early studies which found technical analysis to be useless might have been premature. 

 

Number of trend-following technical trading techniques are studied and applied to various speculative price series. Their proÞtability as well as their forecasting ability will be statistically tested. Corrections will be made for transaction costs, risk and data snooping to answer the question whether one can really proÞt from perceived trending behavior in Þnancial time series. This introductory chapter is organized as follows. In section 1.1 the concepts of fundamental and technical analysis are presented and the philosophies underlying these techniques are explained. Also something will be said about the critiques on both methods. Next, in section 1.2 an overview of the academic literature on technical analysis and efÞcient markets is presented. Finally section 1.3 concludes with a brief outline of this thesis.

 

Fundamental analysis found its existence in the Þrm-foundation theory, developed by numerous people in the 1930s, but Þnally worked out by John B. Williams. It was popularized by Graham and Dodd’s book “Security Analysis” (1934) and by Graham’s book “The Intelligent Investor” (1949). One of its most successful applicants known today is the investor Warren Bu?et. The purpose of fundamental securities analysis is to Þnd and explore all economic variables that inßuence the future earnings of a Þnancial asset. These fundamental variables measure di?erent economic circumstances, ranging from macro-economic (inßation, interest rates, oil prices, recessions, unemployment, etc.), industry speciÞc (competition, demand/supply, technological changes, etc.) and Þrm speciÞc (company growth, dividends, earnings, lawsuits, strikes etc.) circumstances. On the basis of these ‘economic fundamentals’ a fundamental analyst tries to compute the true underlying value, also called the fundamental value, of a Þnancial asset. According to the Þrm-foundation theory the fundamental value of an asset should be equal to the discounted value of all future cash ßows the asset will generate. The discount factor is taken to be the interest rate plus a risk premium and therefore the fundamental analyst must also make expectations about future interest rate developments. The fundamental value is thus based on historical data and expectations about future developments extracted from them. Only ‘news’, which is new facts about the economic variables determining the true value of the fundamental asset, can change the fundamental value. If the computed fundamental value is higher (lower) than the market price.

 

The fundamental analyst concludes that the market over- (under-) values the asset. A long (short) position in the market should be taken to proÞt from this supposedly under- (over-) valuation. The philosophy behind fundamental analysis is that in the end, when enough traders realize that the market is not correctly pricing the asset, the market mechanism of demand/supply, will force the price of the asset to converge to its fundamental value. It is assumed that fundamental analysts who have better access to information and who have a more sophisticated system in interpreting and weighing the inßuence of information on future earnings will earn more than analysts who have less access to information and have a less sophisticated system in interpreting and weighing information. It is emphasized that sound investment principles will produce sound investment results, eliminating the psychology of the investors. Warren Bu?et notices in the preface of “The Intelligent Investor” (1973): “What’s needed is a sound intellectual framework for making decisions and the ability to keep emotions from corroding that framework. The sillier the market’s behavior, the greater the opportunity for the business-like investor.” However, it is questionable whether traders can perform a complete fundamental analysis in determining the true value of a Þnancial asset. An important critique is that fundamental traders have to examine a lot of di?erent economic variables and that they have to know the precise e?ects of all these variables on the future cash ßows of the asset. Furthermore, it may happen that the price of an asset, for example due to overreaction by traders, persistently deviates from the fundamental value. In that case, short term fundamental trading cannot be proÞtable and therefore it is said that fundamental analysis should be used to make long-term predictions. Then a problem may be that a fundamental trader does not have enough wealth and/or enough patience to wait until convergence Þnally occurs. Furthermore, it could be that Þnancial markets a?ect fundamentals, which they are supposed to reßect. In that case they do not merely discount the future, but they help to shape it and Þnancial markets will never tend toward equilibrium. Thus it is clear that it is a most hazardous task to perform accurate fundamental analysis. Keynes (1936, p.157) already pointed out the di?culty as follows: “Investment based on genuine long-term expectation is so di?cult as to be scarcely practicable. He who attempts it must surely lead much more laborious days and run greater risks than he who tries to guess better than the crowd how the crowd will behave; and, given equal intelligence, he may make more disastrous mistakes.” On the other hand it may be possible for a trader to make a fortune by free riding on the expectations of all other traders together. Through the market mechanism of demand and supply the expectations of those traders will eventually be reßected in the asset price in a more or less gradual way. If a trader is engaged in this line of thinking.

 

Technical analysis is the study of past price movements with the goal to predict future price movements from the past. In his book “The Stock Market Barometer” (1922) William Peter Hamilton laid the foundation of the Dow Theory, the Þrst theory of chart readers. The theory is based on editorials of Charles H. Dow when he was editor of the Wall Street Journal in the period 1889 − 1902. Robert Rhea popularized the idea in his.

 

1930s market letters and his book “The Dow Theory” (1932). The philosophy underlying technical analysis can already for most part be found in this early work, developed after Dow’s death in 1902. Charles Dow thought that expectations for the national economy were translated into market orders that caused stocks to rise or fall in prices over the long term together - usually in advance of actual economic developments. He believed that fundamental economic variables determine prices in the long run. To quantify his theory Charles Dow began to compute averages to measure market movements. This led to the existence of the Dow-Jones Industrial Average (DJIA) in May 1896 and the Dow-Jones Railroad Average (DJRA) in September 1896. The Dow Theory assumes that all information is discounted in the averages, hence no other information is needed to make trading decisions. Further the theory makes use of Charles Dow’s notion that there are three types of market movements: primary (also called major), secondary (also called intermediate) and tertiary (also called minor) upward and downward price movements, also called trends. It is the aim of the theory to detect the primary trend changes in an early stage. Minor trends tend to be much more inßuenced by random news events than the secondary and primary trends and are said to be therefore more di?cult to identify. According to the Dow Theory bull and bear markets, that is primary upward and downward trends, are divisible in stages which reßect the moods of the investors. The Dow Theory is based on Charles Dow’s philosophy that “the rails should take what the industrials make.” Stated di?erently, the two averages DJIA and DJRA should conÞrm each other. If the two averages are rising it is time to buy; when both are decreasing it is time to sell. If they diverge, this is a warning signal. Also the Dow Theory states that volume should go with the prevailing primary trend. If the primary trend is upward (downward), volume should increase when price rises (declines) and should decrease when price declines (rises). Eventually the Dow Theory became the basis of what is known today as technical analysis. Although the theory bears Charles Dow’s name, it is likely.

 

That he would deny any allegiance to it. Instead of being a chartist, Charles Dow as a Þnancial reporter advocated to invest on sound fundamental economic variables, that is buying stocks when their prices are well below their fundamental values. His main purpose in developing the averages was to measure market cycles, rather than to use them to generate trading signals. After the work of Hamilton and Rhea the technical analysis literature was expanded and reÞned by early pioneers such as Richard Schabacker, Robert Edwards, John Magee and later Welles Wilder and John Murphy. Technical analysis developed into a standard tool used by many Þnancial practitioners to forecast the future price path of all kinds of Þnancial assets such as stocks, bonds, futures and options. Nowadays a lot of technical analysis software packages are sold on the market. Technical analysis newsletters and journals ßourish. Bookstores have shelves full of technical analysis literature. Every bank employs several chartists who write technical reports spreading around forecasts with all kinds of fancy techniques. Classes are organized to introduce the home investor to the topic. Technical analysis has become an industry on its own. Taylor and Allen (1992) conducted a questionnaire survey in 1988 on behalf of the Bank of England among chief foreign exchange dealers based in London. It is revealed that at least 90 percent of the respondents place some weight on technical analysis when forming views over some time horizons. There is also a skew towards reliance on technical, as opposed to fundamental, analysis at shorter horizons, which becomes steadily reversed as the length of the time horizon is increased. A high proportion of chief dealers view technical and fundamental analysis as complementary forms of analysis and a substantial proportion suggest that technical advice may be self-fulÞlling. There is a feeling among market participants that it is important to have a notion of chartism, because many traders use it, and may therefore inßuence market prices. It is said that chartism can be used to exploit market movements generated by less sophisticated, ‘noise traders’. Menkho? (1998) holds a questionnaire survey among foreign exchange professionals from banks and from fund management companies trading in Germany in August 1992. He concludes that many market participants use non-fundamental trading techniques. Cheung and Chinn (1999) conduct a mail survey among US foreign exchange traders between October 1996 and November 1997. The results indicate that in that time period technical trading best characterizes 30% of traders against 25% for fundamental analysis. All these studies show that technical analysis is broadly used in practice. The general consensus among technical analysts is that there is no need to look at the fundamentals, because everything that is happening in the world can be seen in the price charts. A popular saying among chartists is that “a picture is worth a ten thousand words.”

 

Price as the solution of the demand/supply mechanism reßects the dreams, expectations, guesses, hopes, moods and nightmares of all investors trading in the market. A true chartist does not even care to know which business or industry a Þrm is in, as long he can study its stock chart and knows its ticker symbol. The motto of Doyne Farmer’s prediction company as quoted by Bass, 1999, p.102, was for example: “If the market makes numbers out of information, one should be able to reverse the process and get information out of numbers.” The philosophy behind technical analysis is that information is gradually discounted in the price of an asset. Except for a crash once in a while there is no ‘big bang’ price movement that immediately discounts all available information. It is said that price gradually moves to new highs or new lows and that trading volume goes with the prevailing trend. Therefore most popular technical trading rules are trend following techniques such as moving averages and Þlters. Technical analysis tries to detect changes in investors’ sentiments in an early stage and tries to proÞt from them. It is said that these changes in sentiments cause certain patterns to occur repeatedly in the price charts, because people react the same in equal circumstances. A lot of ‘subjective’ pattern recognition techniques are therefore described in the technical analysis literature which have fancy names, such as head & shoulders, double top, double bottoms, triangles, rectangles, etc., which should be traded on after their pattern is completed.

 

 

Most popular technical trading rules is based on moving averages. A moving average is a recursively updated, for example daily, weekly or monthly, average of past prices. A moving average smoothes out erratic price movements and is supposed to reßect the underlying trend in prices. A buy (sell) signal is said to be generated at time t if the price crosses the moving average upwards (downwards) at time t. Figure 1.1 shows an example of a 200-day moving average applied to the Amsterdam Stock Exchange Index (AEXindex) in the period March 1, 1996 through July 25, 2002. The 200-day moving average is exhibited by the dotted line. It can be seen that the moving average follows the price at some distance. It changes direction after a change in the direction of the prices has occurred. By decreasing the number of days over which the moving average is computed, the distance can be made smaller, and trading signals occur more often. Despite that the 200-day moving-average trading rule is generating signals in some occasions too late, it can be seen that the trading rule succeeds in detecting large price moves that occurred in the index. In this thesis we will develop a technical trading rule set on the basis of simple trend-following trading techniques, such as the above moving-average strategy, as well as reÞnements with %-band-Þlters, time delay Þlters, Þxed holding periods and stop-loss. We will test the proÞtability and predictability of a large class of such trading rules applied to a large number of Þnancial asset price series.
 

Technical analysis has been heavily criticized over the decades. One critique is that it trades when a trend is already established. By the time that a trend is signaled, it may already have taken place. Hence it is said that technical analysts are always trading too late. As noted by Osler and Chang (1995, p.7), books on technical analysis fail in documenting the validity of their claims. Authors do not hesitate to characterize a pattern as frequent or reliable, without making an attempt to quantify those assessments. ProÞts are measured in isolation, without regard for opportunity costs or risk. The lack of a sound statistical analysis arises from the di?culty in programming technical pattern recognition techniques into a computer. Many technical trading rules seem to be somewhat vague statements without accurately mathematically deÞned patterns. However Neftci (1991) shows that most patterns used by technical analysts can be characterized by appropriate sequences of local minima and/or maxima. Lo, Mamaysky and Wang (2000) develop a pattern recognition system based on non-parametric kernel regression. They conclude (p.1753): “Although human judgment is still superior to most computational algorithms.

 

The area of visual pattern recognition, recent advances in statistical learning theory have had successful applications in Þngerprint identiÞcation, handwriting analysis, and face recognition. Technical analysis may well be the next frontier for such methods.” Furthermore, in Þnancial practice technical analysis is criticized because of its highly subjective nature. It is said that there are probably as many methods of combining and interpreting the various techniques as there are chartists themselves. The geometric shapes in historical price charts are often in the eyes of the beholder. Fundamental analysis is compared with technical analysis like astronomy with astrology. It is claimed that technical analysis is voodoo Þnance and that chart reading shares a pedestal with alchemy. The attitude of academics towards technical analysis is well described by Malkiel (1996, p.139): “Obviously, I’m biased against the chartist. This is not only a personal predilection but a professional one as well. Technical analysis is anathema to the academic world. We love to pick on it. Our bullying tactics are prompted by two considerations: (1) after paying transaction costs, the method does not do better than a buy-and-hold strategy for investors, and (2) it’s easy to pick on. And while it may seem a bit unfair to pick on such a sorry target, just remember: It’s your money we are trying to save.” However, technical analysts acknowledge that their techniques are by no means foolproof. For example, Martin Pring (1998, p.5) notices about technical analysis: “It can help in identifying the direction of a trend, but there is no known method of consistently forecasting its magnitude.” Edwards and Magee (1998, p.12) notice: “Chart analysis is certainly neither easy nor foolproof .” Finally, Achelis (1995, p.6) remarks:“..., I caution you not to let the software lull you into believing markets are as logical and predictable as the computer you use to analyze them.” Hence, even technical analysts warn against investment decisions based upon their charts alone.

 

The big advantage of technical analysis over fundamental analysis is that it can be applied fairly easily and cheaply to all kinds of securities prices. Only some practice is needed in recognizing the patterns, but in principle everyone can apply it. Of course, there exist also some complex technical trading techniques, but technical analysis can be made as easy or as di?cult as the user likes. Martin Pring (1997, p.3) for example notices that although computers make it more easy to come up with sophisticated trading rules, it is better to keep things as simple as possible. Of course fundamental analysis can also be made as simple as one likes. For example, look at the number of cars parked at the lot of the shopping mall to get an indication of.

 

Consumers’ conÞdence in the national economy. Usually more (macro) economic variables are needed. That makes fundamental analysis more costly than technical analysis. An advantage of technical analysis from an academic point of view is that it is much easier to test the forecasting power of well-deÞned objective technical trading rules than to test the forecasting power of trading rules based on fundamentals. For testing technical trading rules only data is needed on prices, volumes and dividends, which can be obtained fairly easily. An essential di?erence between chart analysis and fundamental economic analysis is that chartists study only the price action of the market itself, whereas fundamentalists attempt to look for the reasons behind that action. However, both the fundamental analyst and the technical analyst make use of historical data, but in a di?erent manner. The technical analyst claims that all information is gradually discounted in the prices, while the fundamental analyst uses all available information including many other economic variables to compute the ‘true’ value. The pure technical analyst will never issue a price goal. He only trades on the buy and sell signals his strategies generate. In contrast, the fundamental analyst will issue a price goal that is based on the calculated fundamental value. However in practice investors expect also from technical analysts to issue price goals. Neither fundamental nor technical analysis will lead to sure proÞts. Malkiel shows in his book “A Random Walk down Wall Street” (1996) that mutual funds, the main big users of fundamental analysis, are not able to outperform a general market index. In the period 1974 − 1990 at least two thirds of the mutual funds were beaten by the Standard.

 

Poors 500 (Malkiel, 1996, p.184). Moreover, Cowles (1933, 1944) already noticed that analysts report more bullish signals than bearish ones, while in his studies the number of weeks the stock market advanced and declined were equal. Furthermore, fundamental analysts do not always report what they think, as became publicly known in the Merrill Lynch scandal. Internally analysts judged certain internet and telecommunications stocks as ‘piece of shit’, abbreviated by ‘pos’ at the end of internal email messages, while they gave their clients strong advices to buy the stocks of these companies. In 1998 the “Long Term Capital Management” (LTCM) fund Þled for bankruptcy. This hedge fund was trading on the basis of mathematical models. Myron Scholes and Robert Merton, well known for the development and extension of the Black & Scholes option pricing model, were closely involved in this company. Under leadership of the New York Federal Reserve Bank, one the twelve central banks in the US, the Þnancial world had to raise a great amount of money to prevent a big catastrophe. Because LTCM had large obligations in the derivatives markets, which they could not fulÞll anymore, default of payments would.

 

Despite the fact that chartists have a strong belief in their forecasting abilities, in academia it remains questionable whether technical trading based on patterns or trends in past prices has any statistically signiÞcant forecasting power and whether it can profitably be exploited after correcting for transaction costs and risk. Cowles (1933) started by analyzing the weekly forecasting results of well-known professional agencies, such as Þnancial services and Þre insurance companies, in the period January 1928 through June 1932. The ability of selecting a speciÞc stock which should generate superior returns, as well as the ability of forecasting the movement of the stock market itself is studied. Thousands of predictions are recorded. Cowles (1933) Þnds no statistically signiÞcant forecasting performance. Furthermore Cowles (1933) considered the 26-year forecasting record of William Peter Hamilton in the period December 1903 until his death in December 1929. During this period Hamilton wrote 255 editorials in the Wall Street Journal which presented forecasts for the stock market based on the Dow Theory. It is found that Hamilton could not beat a continuous investment in the DJIA or the DJRA after correcting for the e?ect of brokerage charges, cash dividends and interest earned if no position is held in the market. On 90 occasions Hamilton announced changes in the outlook for the market. Cowles (1933) Þnds that 45 of the changes of position were unsuccessful and that 45 were successful. Cowles (1944) repeats the analysis for 11 forecasting companies for the longer period January 1928 through July 1943. Again no evidence of forecasting power is found. However, although the number of months the stock market declined exceeded the number of months the stock market rose, and although the level of the stock market in July 1943 was lower than at the beginning of the sample period, Cowles (1944) Þnds that more bullish signals are published than bearish. Cowles (1944, p.210) argues that this peculiar result can be explained by the fact that readers prefer good news to bad.

 

 

While Cowles (1933, 1944) focused on testing analysts’ advices, other academics focused on time series behavior. Working (1934), Kendall (1953) and Roberts (1959) found for series of speculative prices, such as American commodity prices of wheat and cotton, British indices of industrial share prices and the DJIA, that successive price changes are linearly independent, as measured by autocorrelation, and that these series may be well deÞned by random walks. According to the random walk hypothesis trends in prices are spurious and purely accidentally manifestations. Therefore, trading systems based on past information should not generate proÞts in excess of equilibrium expected proÞts or returns. It became commonly accepted that the study of past price trends and patterns is no more useful in predicting future price movements than throwing a dart at the list of stocks in a daily newspaper. However the dependence in price changes can be of such a complicated form that standard linear statistical tools, such as serial correlations, may provide misleading measures of the degree of dependence in the data. Therefore Alexander (1961) began deÞning Þlters to reveal possible trends in stock prices which may be masked by the jiggling of the market. A Þlter strategy buys when price increases by x percent from a recent low and sells when price declines by x percent from a recent high. Thus Þlters can be used to identify local peaks and troughs according to the Þlter size. He applies several Þlters to the DJIA in the period 1897 − 1929 and the S&P Industrials in the period 1929 − 1959. Alexan-der (1961) concludes that in speculative markets a price move, once initiated, tends to persist. Thus he concludes that the basic philosophy underlying technical analysis, that is prices move in trends, holds. However he notices that commissions could reduce the results found. Mandelbrot (1963, p.418) notes that there is a ßaw in the computations of Alexander (1961), since he assumes that the trader can buy exactly at the low plus x percent and can sell exactly at the high minus x percent. However in real trading this will probably not be the case. Further it was argued that traders cannot buy the averages and that investors can change the price themselves if they try to invest according to the Þlters. In Alexander (1964) the computing mistake is corrected and allowance is made for transaction costs. The Þlter rules still show considerable excess proÞts over the buy-and-hold strategy, but transaction costs wipe out all the proÞts. It is concluded that an investor who is not a ßoor trader and must pay commissions should turn to other.

 

Sources of advice on how to beat the buy-and-hold benchmark. Alexander (1964) also tests other mechanical trading rules, such as Dow-type formulas and old technical trading rules called formula Dazhi, formula DaÞlt and Þnally the also nowadays popular moving averages. These techniques provided much better proÞts than the Þlter techniques. The results led Alexander (1964) still to conclude that the independence assumption of the random walk had been overturned. Theil and Leenders (1965) investigate the dependence of the proportion of securities that advance, decline or remain unchanged between successive days for approximately 450 stocks traded at the Amsterdam Stock Exchange in the period November 1959 through October 1963. They Þnd that there is considerable positive dependence in successive values of securities advancing, declining and remaining unchanged at the Amsterdam Stock Exchange. It is concluded that if stocks in general advanced yesterday, they will probably also advance today. Fama (1965b) replicates the Theil and Leenders test for the NYSE. In contrast to the results of Theil and Leenders (1965), Fama (1965b) Þnds that the proportions of securities advancing and declining today on the NYSE do not provide much help in predicting the proportions advancing and declining tomorrow. Fama (1965b) concludes that this contradiction in results could be caused by economic factors that are unique to the Amsterdam Exchange. Fama (1965a) tries to show with various tests that price changes are independent and that therefore the past history of stock prices cannot be used to make meaningful predictions concerning its future behavior. Moreover, if it is found that there is some dependence, then Fama argues that this dependence is too small to be proÞtably exploited because of transaction costs. Fama (1965a) applies serial correlation tests, runs tests and Alexander’s Þlter technique to daily data of 30 individual stocks quoted in the DJIA in the period January 1956 through September 1962. A runs test counts the number of sequences and reversals in a returns series. Two consecutive returns of the same sign are counted as a sequence, if they are of opposite sign they are counted as a reversal. The serial correlation tests show that the dependence in successive price changes is either extremely small or non-existent. Also the runs tests do not show a large degree of dependence. ProÞts of the Þlter techniques are calculated by trading blocks of 100 shares and are corrected for dividends and transaction costs. The results show no proÞtability. Hence Fama (1965a) concludes that the largest proÞts under the Þlter technique would seem to be those of the broker. The paper of Fama and Blume (1966) studies Alexander’s Þlters applied to the same data set as in Fama (1965a). A set of Þlters is applied to each of the 30 stocks quoted in the DJIA with and without correction for dividends and transaction costs. 

 

Set is divided in days during which long and short positions are held. They show that the short positions initiated are disastrous for the investor. But even if positions were only held at buy signals, the buy-and-hold strategy cannot consistently be outperformed. Until the 1990s Fama and Blume (1966) remained the best known and most inßuential paper on mechanical trading rules. The results caused academic skepticism concerning the usefulness of technical analysis.

 

DiversiÞcation of wealth over multiple securities reduces the risk of investing. The phrase “don’t put all your eggs in one basket” is already well known for a long time. Markowitz (1952) argued that every rule that does not imply the superiority of diversiÞcation must be rejected both as hypothesis to explain and as a principle to guide investment behavior. Therefore Markowitz (1952, 1959) published a formal model of portfolio selection embodying diversiÞcation principles, called the expected returns-variance of returns rule (E-V-rule). The model determines for any given level of anticipated return the portfolio with the lowest risk and for any given levels of risk the portfolio with the highest expected return. This optimization procedure leads to the well-known e?cient frontier of risky assets. Markowitz (1952, 1959) argues that portfolios found on the e?cient frontier consist of Þrms operating in di?erent industries, because Þrms in industries with di?erent economic characteristics have lower covariance than Þrms within an industry. Further it was shown how by maximizing a capital allocation line (CAL) on the e?cient frontier the optimal risky portfolio could be determined. Finally, by maximizing a personal utility function on the CAL, a personal asset allocation between a risk-free asset and the optimal risky portfolio can be derived. An expected positive price change can be the reward needed to attract investors to hold a risky asset and bear the corresponding risk. Then prices need not be perfectly random, even if markets are operating e?ciently and rationally. With his work Markowitz (1952, 1959) laid the foundation of the capital asset pricing model (CAPM) developed by Sharpe (1964) and Lintner (1965). They show that under the assumptions that investors have homogeneous expectations and optimally hold mean-variance e?cient portfolios, and in the absence of market frictions, a broad-weighted market portfolio will itself be a meanvariance e?cient portfolio. This market portfolio is the tangency portfolio of the CAL with the e?cient frontier. The great merit of the CAPM was, despite its strict and unrealistic assumptions, that it showed the relationship between the risk of an asset and its expected return. The notion of trade-o? between risk and rewards also triggered the question whether the proÞts generated by technical trading rule signals were not just the reward of bearing risky asset positions. Levy (1967) applies relative strength as a criterion for investment selection to weekly closing prices of 200 stocks listed on the NYSE for the 260-week period beginning October 24, 1960 and ending October 15, 1965. All price series are adjusted for splits, stock dividends, and for the reinvestment of both cash dividends and proceeds received from the sale of rights. The relative strength strategy buys those stocks that have performed well in the past. Levy (1967) concludes that the proÞts attainable by purchasing the historically strongest stocks are superior to the proÞts of the random walk. Thus in contrast to earlier results he Þnds stock market prices to be forecastable by using the relative strength rule. However Levy (1967) notices that the random walk hypothesis is not refuted by these Þndings, because superior proÞts could be attributable to the incurrence of extraordinary risk and he remarks that it is therefore necessary to determine the riskiness of the various technical measures he tested. Jensen (1967) indicates that the results of Levy (1967) could be the result of selection bias. Technical trading rules that performed well in the past get most attention by researchers, and if they are back-tested, then of course they generate good results. Jensen and Benington (1969) apply the relative strength procedure of Levy (1967) to monthly closing prices of every security traded on the NYSE over the period January 1926 to March 1966, in total 1952 securities. They conclude that after allowance for transaction costs and correction for risk the trading rules did not on average earn signiÞcantly more than the buy-and-hold policy. James (1968) is one of the Þrsts who tests moving-average trading strategies. That is, signals are generated by a crossing of the price through a moving average of past prices. He Þnds no superior performance for these rules when applied to end of month data of stocks traded at the NYSE in the period 1926 − 1960.Besides testing the random walk theory with serial correlation tests, runs tests and by applying technical trading rules used in practice, academics were searching for a theory that could explain the random walk behavior of stock prices. In 1965 Samuelson published his “Proof that properly anticipated prices ßuctuate randomly .” He argues that in an informational e?cient market price changes must be unforecastable if they are properly anticipated, i.e., if they fully incorporate the expectations and information of all market participants. 

 

News anymore, prices must ßuctuate randomly. This important observation, combined with the notion that positive earnings are the reward for bearing risk, and the earlier empirical Þndings that successive price changes are independent, led to the e?cient markets hypothesis. Especially the notion of trade-o? between reward and risk distinguishes the e?cient markets hypothesis from the random walk theory, which is merely a purely statistical model of returns. The inßuential paper of Fama (1970) reviews the theoretical and empirical literature on the e?cient markets model until that date. Fama (1970) distinguishes three forms of market e?ciency. A Þnancial market is called weak e?cient, if no trading rule can be developed that can forecast future price movements on the basis of past prices. Secondly, a Þnancial market is called semi-strong e?cient, if it is impossible to forecast future price movements on the basis of publicly known information. Finally, a Þnancial market is called strong e?cient if on the basis of all available information, also inside information, it is not possible to forecast future price movements. Semi-strong e?ciency implies weakform e?ciency. Strong e?ciency implies semi-strong and weak e?ciency. If the weak form of the EMH can be rejected, then also the semi strong and strong form of the EMH can be rejected. Fama (1970) concludes that the evidence in support of the e?cient markets model is very extensive, and that contradictory evidence is sparse. The impact of the empirical Þndings on random walk behavior and the conclusion in academia that Þnancial asset prices are and should be unforecastable was so large, that it took a while before new academic literature on technical trading was published. Financial analysts heavily debated the e?cient markets hypothesis. However, as argued by academics, even if the theory of Samuelson would be wrong, then there are still many empirical Þndings of no forecastability. Market technicians kept arguing that statistical tests of any kind are less capable of detecting subtle patterns in stock price data than the human eye. Thus Arditti and McCollough (1978) argued that if stock price series have information content, then technicians should be able to di?erentiate between actual price data and random walk data generated from the same statistical parameters. For each of Þve randomly chosen stocks from the NYSE in the year 1969 they showed 14 New York based CFAs (Chartered FiR nancial Analyst, the CFA° program is a globally recognized standard for measuring the competence and integrity of Þnancial analysts) with more than Þve years of experience.

 

 

One of the earliest studies of the proÞtability of technical trading rules in foreign exchange markets is Dooley and Shafer (1983). Very high liquidity, low bid-ask spreads and roundthe-clock decentralized trading characterize exchange rate markets for foreign currency. Furthermore, because of their size, these markets are relatively immune to insider trading. Dooley and Shafer (1983) address the question whether the observed short-run variability in exchange rates since the start of generalized ßoating exchange rates in March 1973 is caused by technical traders or is caused by severe fundamental shocks. In the former case the exchange rate path could be interpreted in terms of price runs, bandwagons, and technical corrections, while in the latter case frequent revisions on the basis of small information occurs and the market is e?cient in taking into account whatever information is available. They follow the study of Fama (1965, 1970) by applying serial correlation tests, runs tests and seven Þlter trading rules in the range [1%, 25%] to the US Dollar (USD) prices of the Belgium Franc (BF), Canadian Dollar (CD), French Franc (FF), German Mark (DEM), Italian Lira (IL), Japanese Yen (JPY), Dutch Guilder (DGL), Swiss Franc (SF), and the British Pound (BP) in the period March 1973 through November 1981. Adjustment is made for overnight Eurocurrency interest rate di?erentials to account for the predictable component of changes in daily spot exchange rates. In an earlier study Dooley and Shafer (1976) already found that the Þlters yielded substantial proÞts from March 1975 until October 1975 even if careful account was taken of opportunity costs in terms of interest rate di?erentials and transactions costs. It is noted that these good results could be the result of chance and therefore the period October 1975 through November 1981 is considered to serve as an out-of-sample testing period for which it is unlikely that the good results for the Þlters continue to hold if the exchange markets are really e?cient. Dooley and Shafer (1983) report that there is signiÞcant autocorrelation present in the data and that there is evidence of substantial proÞts to all but the largest Þlters, casting doubt on the weak form of the e?cient markets hypothesis. Further, they Þnd a relation between the variability of exchange rates, as measured by the standard deviation of the daily returns, and the Þlter rules’ proÞts. A large increase in the variability is associated with a dramatic increase in the proÞtability of the Þlters. They also compare the results generated in the actual exchange rate data with results generated by random walk and autoregressive models, which in the end cannot explain the Þndings.

 

Sweeney (1986) develops a test of the signiÞcance of Þlter rule proÞts that explicitly assumes constant risk/return trade-o? due to constant risk premia. Seven di?erent Þlter rules in the range [0.5%, 10%] are applied to the US Dollar against the BF, BP, CD, DEM, FF, IL, JPY, SF, Swedish Krone (SK) and Spanish Peseta (SP) exchange rates in the period 1975 − 1980. It is found that excess rates of return of Þlter rules persist into the 1980s, even after correcting for transaction costs and risk. After his study on exchange rates, Sweeney (1988) focuses on a subset of the 30 stocks in the DJIA for which the 0.5% Þlter rule yielded the most promising results in the Fama and Blume (1966) paper, which comprehends the 1956 − 1962 period. He Þnds that by ocusing on the winners in the previous period of the Fama and Blume (1966) paper signiÞcant proÞts over the buy-and-hold can be made for all selected stocks in the period1970 − 1982 by investors with low but feasible transaction costs, most likely ßoor traders. 

 

Sweeney (1988) questions why the market seems to be weak-form ine?cient according to his results. Sweeny argues that the costs of a seat on an exchange are just the riskadjusted present value of the proÞts that could be made. Another possibility is that if a trader tries to trade according to a predeÞned trading strategy, he can move the market itself and therefore cannot reap the proÞts. Finally Sweeney (1988) concludes that excess return may be the reward for putting in the e?ort for Þnding the rule which can exploit irregularities. Hence after correcting for research costs the market may be e?cient in the end. Schulmeister (1988) observes that USD/DEM exchange rate movements are characterized by a sequence of upward and downward trends in the period March 1973 to March 1988. For two moving averages, two momentum strategies, two combinations of moving averages and momentum and Þnally one support-and-resistance rule, reported to be widely used in practice, it is concluded that they yield systematically and signiÞcant proÞts. Schulmeister (1988) remarks that the combined strategy is developed and truly applied in trading by Citicorp. No correction is made for transaction costs and interest rate di?erentials. However, for the period October 1986 through March 1988 a reduction in proÞts is noticed, which is explained by the stabilizing e?ects of the Louvre accord of February 22, 1987. The goal of this agreement was to keep the USD/DEM/JPY exchange rates stable. The philosophy behind the accord was that when those three key currencies were stable, then the other currencies of the world could link into the system and world currencies could more or less stabilize, reducing currency risks in foreign trade.

 

Little work on technical analysis appeared during the 1970s and 1980s, because the efÞcient markets hypothesis was the dominating paradigm in Þnance. Brock, Lakonishok and LeBaron (1992) test the forecastability of a set of 26 simple technical trading rules by applying them to the closing prices of the DJIA in the period January 1897 through December 1986, nearly 90 years of data. The set of trading rules consists of moving average strategies and support-and-resistance rules, very popular trading rules among technical trading practitioners. Brock et al. (1992) recognize the danger of data snooping. That is, the performance of the best forecasting model found in a given data set by a certain speciÞcation search could be just the result of chance instead of truly superior forecasting power. They admit that their choice of trading rules could be the result of survivorship bias, because they consulted a technical analyst. However they claim that they mitigate the problem of data snooping by (1) reporting the results of all tested trading strategies, (2) utilizing a very long data set, and (3) emphasizing the robustness of the results across various non-overlapping subperiods for statistical inference. Brock et al. (1992) Þnd that all trading rules yield signiÞcant proÞts above the buy-and-hold benchmark in all periods by using simple t-ratios as test statistics. Moreover they Þnd that buy signals consistently generate higher returns than sell signals and that the returns following buy signals are less volatile than the returns following sell signals. However t-ratios are only valid under the assumption of stationary and time independent return distributions. Stock returns exhibit several well-known deviations from these assumptions like leptokurtosis, autocorrelation, dependence in the squared returns (volatility clustering or conditional heteroskedasticity), and changing conditional means (risk premia). The results found could therefore be the consequence of using invalid signiÞcance tests. To overcome this problem Brock et al. (1992) were the Þrst who extended standard statistical analysis with parametric bootstrap techniques, inspired by Efron (1979), Freedman and Peters (1984a, 1984b) and Efron and Tibshirani (1986). Brock et al. (1992) Þnd that the patterns uncovered by their technical trading rules cannot be explained by Þrst order autocorrelation and by changing expected returns caused by changes in volatility. Stated di?erently, the predictive ability of the technical trading rules found is not consistent with a random walk, an AR(1), a GARCH-in-mean model, or an exponential GARCH model. Therefore Brock et al. (1992) conclude that the conclusion reached in earlier studies that technical analysis is useless may have been premature. However they acknowledge that the good results of the technical trading rules can be o?set by transaction costs. The strong results of Brock, Lakonishok and LeBaron (1992) led to a renewed interest in academia for testing the forecastability of technical trading rules. 

 

It was the impetu for many papers published on the topic in the 1990s. Notice however that Brock et al. (1992) in fact do not apply the correct t-test statistic, as derived in footnote 9, page 1738. See section 2.5 in Chapter 2 of this thesis for a further discussion on this topic. Levich and Thomas (1993) criticize Dooley and Shafer (1983) for not reporting any measures of statistical signiÞcance of the technical trading rule proÞts. Therefore Levich and Thomas (1993) are the Þrst who apply the bootstrap methodology, as introduced by Brock et al. (1992), to exchange rate data. Six Þlters and three moving averages are applied to the US Dollar closing settlement prices of the BP, CD, DEM, JPY and SF futures contracts traded at the International Monetary Market of the Chicago Mercantile Exchange in the period January 1973 through December 1990. Levich and Thomas (1993) note that the trading rules tested are very popular ones and that the parameterizations are taken from earlier literature. Just like Brock et al. (1992) they report that they mitigate the problem of data mining by showing the results for all strategies. It is found that the simple technical trading rules generate unusual proÞts (no corrections are made for transaction costs) and that a random walk model cannot explain these proÞts. However there is some deterioration over time in the proÞtability of the trading rules, especially in the 1986 − 1990 period. Lee and Mathur (1995) remark that most surveys, whose Þndings are in favor of technical trading if applied to exchange rate data, are conducted on US Dollar denominated currencies and that the positive results are likely to be caused by central bank intervention. Therefore to test market e?ciency of European foreign exchange markets they apply 45 di?erent crossover moving-average trading strategies to six European spot cross-rates (JPY/BP, DEM/BP, JPY/DEM, SF/DEM and JPY/SF) in the May, 1988 to December, 1993 period. A correction for 0.1% transaction costs per trade is made. They Þnd that moving-average trading rules are marginally proÞtable only for the JPY/DEM and JPY/SF cross rates, currencies that do not belong to the European exchange rate mechanism (ERM). Further it is found that in periods during which central bank intervention is believed to have taken place, trading rules do not show to be proÞtable in the European cross rates. Finally Lee and Mathur (1995) propose to apply a recursively optimizing test procedure with a rolling window for the purpose of testing out-of-sample forecasting power. Every year the best trading rule of the previous half-year is applied. Also this out-of-sample test procedure rejects the null hypothesis that moving averages have forecasting power. It is concluded that the e?ect of target zones on the dynamics of the ERM exchange rates may be partly responsible for the lack of proÞtability of moving-average trading rules. The dynamics of ERM exchange rates are di?erent from those of common exchange ranges in that they have smaller volatility.

 

Has forecasting power when applied to the stock market indices of Japan, Hong Kong, South Korea, Malaysia, Thailand and Taiwan in the period January 1975 through December 1989. Break-even transaction costs that eliminate the excess return of a double or out strategy over a buy-and-hold are computed. The rules are most successful in the markets of Malaysia, Thailand and Taiwan, where the buy-sell di?erence is on average 51.9% yearly. Break-even round-trip transaction costs are estimated to be 1.57% on average (1.34% in the case if a one-day lag in trading is incorporated). It is concluded that excess proÞts over the buy-and-hold could be made, but emphasis is placed on the fact that the relative riskiness of the technical trading strategies is not controlled for. For the UK stock market Hudson, Dempsey and Keasey (1996) test the trading rule set of Brock et al. (1992) on daily data of the Financial Times Industrial Ordinary index, which consists of 30 UK companies, in the period July 1935 to January 1994. They want to examine whether the same set of trading rules outperforms the buy-andhold on a di?erent market. It is computed that the trading rules on average generate an excess return of 0.8% per transaction over the buy-and-hold, but that the costs of implementing the strategy are at least 1% per transaction. Further when looking at the subperiod 1981 − 1994, the trading rules seem to lose their forecasting power. 

 

Hudson et al. (1996) conclude that although the technical trading rules examined do have predictive ability, their use would not allow investors to make excess returns in the presence of costly trading. Additionally Mills (1997) simultaneously Þnds in the case of zero transaction costs with the bootstrap technique introduced by Brock et al. (1992) that the good results for the period 1935 − 1980 cannot be explained by an AR-ARCH model for the daily returns. Again, for the period after 1980 it is found that the trading rules do not generate statistically signiÞcant results. Mills (1997) concludes that the trading rules mainly worked when the market was driftless but performed badly in the period after 1980, because the buy-and-hold strategy was clearly dominating. Kho (1996) tests a limited number of double crossover moving-average trading rules on weekly data of BP, DEM, JPY, SF futures contracts traded on the International Monetary Market (IMM) division of the Chicago Mercantile Exchange from January 1980 through December 1991. The results show that there have been proÞt opportunities that could have been exploited by moving-average trading rules. The measured proÞts are so high that they cannot be explained by transaction costs, serial correlation in the returns or a simple volatility expected return relation (GARCH-in-mean model). Next, Kho (1996) estimates a conditional CAPM model that captures the time-varying price of risk. 

 

Bessembinder and Chan (1998) redo the calculations of Brock et al. (1992) for the period 1926 − 1991 to assess the economic signiÞcance of the Brock et al. (1992) Þndings. Corrections are made for transaction costs and dividends. One-month treasury bills are used as proxy for the risk-free interest rate if no trading position is held in the market. Furthermore, also a correction is made for non-synchronous trading by lagging trading signals for one day. It is computed that one-way break-even transaction costs are approximately 0.39% for the full sample. However they decline from 0.54% in the Þrst subperiod 1926 − 1943 to 0.22% in the last subperiod 1976 − 1991. Knez and Ready (1996) estimate.

 

The average bid-ask spread between 0.11 and 0.13%, while Chan and Lakonishok (1993) estimate commissions costs to be 0.13%. Together this adds to approximately 0.24 to 0.26% transaction costs for institutional traders in the last subperiod. In earlier years trading costs were probably higher. Thus the break-even one-way transaction costs of 0.22% in the last subperiod are clearly smaller than the real estimated transaction costs of 0.26% per trade. Although Bessembinder and Chan (1998) conÞrm the results of Brock et al. (1992), they conclude that there is little reason to view the evidence of Brock et al. (1992) as indicative of market ine?ciency. Fern´ andez-Rodr´ õguez, Sosvilla-Rivero, and Andrada-F´ elix (2001) replicate the testing procedures of Brock et al. (1992) for daily data of the General Index of the Madrid Stock Exchange (IGBM) in the period January 1966 through October 1997. They Þnd that technical trading rules show forecastability in the Madrid Stock Exchange, but acknowledge that they didn’t include transaction costs. Furthermore, the bootstrap results show that several null models for stock returns such as the AR(1), GARCH and GARCH-in-mean models cannot explain the forecasting power of the technical trading rules. Ratner and Leal (1999) apply ten moving-average trading rules to daily local index inßation corrected closing levels for Argentina (Bolsa Indice General), Brazil (Indice BOVESPA), Chile (Indice General de Precios), India (Bombay Sensitive), Korea (Seoul Composite Index), Malaysia (Kuala Lumpur Composite Index), Mexico (Indice de Precios y Cotaciones), the Philippines (Manila Composite Index), Taiwan (Taipei Weighted Price Index) and Thailand (Bangkok S.E.T.) in the period January 1982 through April 1995. After correcting for transaction costs, the rules appear to be signiÞcantly proÞtable only in Taiwan, Thailand and Mexico. However, when not looking at signiÞcance, in more than 80% of the cases the trading rules correctly predict the direction of changes in prices. Isakov and Hollistein (1999) test simple technical trading rules on the Swiss Bank Corporation (SBC) General Index and to some of its individual stocks UBS, ABB, Nestle, Ciba-Geigy and Zurich in the period 1969 − 1997. They are the Þrst who extend moving.

 

Average trading strategies with momentum indicators or oscillators, so called relative strength or stochastics. These oscillators should indicate when an asset is overbought or oversold and they are supposed to give appropriate signals when to step out of the market. Isakov and Hollistein (1999) Þnd that the use of oscillators does not add to the performance of the moving averages. For the basic moving average strategies they Þnd an average yearly excess return of 18% on the SBC index. Bootstrap simulations show that an AR(1) or GARCH(1,1) model for asset returns cannot explain the predictability of the trading rules. However it is concluded that in the presence of trading costs the rules are only proÞtable for a particular kind of investor, namely if the costs are not higher than 0.3-0.7% per transaction, and that therefore weak-form e?ciency cannot be rejected for small investors. LeBaron (2000b) tests a 30-week single crossover moving-average trading strategy on weekly data at the close of London markets on Wednesdays of the US Dollar against the BP, DEM and JPY in the period June 1973 through May 1998. It is found that the strategy performed very well on all three exchange rates in the subperiod 1973 − 1989, yielding signiÞcant positive excess returns of 8, 6.8 and 10.2% yearly for the BP, DM and JPY respectively. However for the subperiod 1990 − 1998 the results are not signiÞcant anymore. LeBaron (2000b) argues that this reduction in forecastability may be explained by changes in the foreign exchange markets, such as lower transaction costs allowing traders to better arbitrage, foreign exchange intervention, the internet or a better general knowledge of technical trading rules. Another possibility is that trading rules are proÞtable only over very long periods, but can go through long periods in which they lose money, during which most users of the rules are driven out of the market. LeBaron (2000a) reviews the paper of Brock et al. (1992) and tests whether the results found for the DJIA in the period 1897 − 1986 also hold for the period after 1986. Two technical trading rules are applied to the data set, namely the 150-day single crossover moving-average rule, because the research of Brock et al. (1992) pointed out that this rule performed consistently well over a couple of subperiods, and a 150-day momentum strategy. LeBaron (2000a) Þnds that the results of Brock et al. (1992) change dramatically in the period 1988 − 1999. The trading rules seem to have lost their predictive ability.

 

Out rules yield better results than the moving averages. Although the trading rules show signiÞcant forecasting power, it is concluded that after correcting for transaction costs the trading rules cannot proÞtably be exploited. In contrast, Ming Ming, Mat Nor and Krishnan Guru (2000) Þnd signiÞcant forecasting power for the strategies of Brock et al. (1992) when applied to the Kuala Lumpur Composite Index (KLCI) even after correction for transaction costs. Detry and Gregoire (2001) test 10 moving-average trading rules of Brock et al. (1992) on the indices of all 15 countries in the European Union. They Þnd that their results strongly support the conclusion of Brock et al. (1992) for the predictive ability of movingaverage rules. However the computed break-even transaction costs are often of the same magnitude as actual transaction costs encountered by professional traders. In his master’s thesis Langedijk (2001) tests the predictability of the variable movingaverage trading rules of Brock et al. (1992) on three foreign exchange rates, namely USD/DEM, JPY/DEM and USD/JPY, in the period July 1973 through June 2001. By using simple t-ratios he Þnds that technical trading rules have predictive ability in the subperiod July 1973 through June 1986, but that the results deteriorate for the period thereafter. Because for the USD/JPY exchange rate the strongest results in favor of technical trading are found, standard statistical analysis is extended by the bootstrap methodology of Brock et al. (1992). It is found that random walk, autoregressive and GARCH models cannot explain the results. However Langedijk (2001) shows that only large investors with low transaction costs can proÞtably exploit the trading rules.

 

Most papers written on the proÞtability of technical trading rules use daily data. But there is also some literature testing the strategies on intra-day data. Ready (1997) shows that proÞts of technical trading rules applied to the largest 20% stocks of the NYSE in the period 1970 − 1995 disappear, if transaction costs as well as the time delay between the signal of a trading rule and the actual trade are taken into account. Further, he also Þnds that trading rules perform much worse in the period 1990 − 1995. 

 

Goodhart, Guillaume and Payne (1997) apply technical trading rules, based on supportand-resistance levels, identiÞed and supplied by technical analysts, to intra-daily data of foreign exchange markets (DEM/USD, JPY/USD, BP/USD). They Þnd that no proÞts can be made on average when transaction costs, due to bid-ask spreads, are taken into account.

 

Academic research on the e?ectiveness of technical analysis in Þnancial markets, as reviewed above, mainly implements Þlters, moving averages, momentum and support-andresistance rules. These technical indicators are fairly easy to program into a computer. However the range of technical trading techniques is very broad and an important part deals with visual pattern recognition. The claim by technical analysts of the presence of geometric shapes in historical price charts is often criticized as being too subjective, intuitive or even vague. Levy (1971) was the Þrst to examine 32 possible forms of Þve point chart patterns, i.e. a pattern with two highs and three lows or two lows and three highs, which are claimed to represent channels, wedges, diamonds, symmetrical triangles, (reverse) head-and-shoulders, triple tops, and triple bottoms. Local extrema are determined with the help of Alexander’s (1961) Þlter techniques. After trading costs are taken into account it is concluded that none of the 32 patterns show any evidence of proÞtable forecasting ability in either bullish or bearish direction when applied to 548 NYSE securities in the period July 1964 through July 1969. Neftci (1991) shows that technical patterns can be fully characterized by using appropriate sequences of local minima and maxima. Hence it is concluded that any pattern can potentially be formalized. Osler and Chang (1995) were the Þrst to evaluate the predictive power of head-and-shoulders patterns using a computer-implemented algorithm in foreign exchange rates. The features of the headand-shoulders pattern are deÞned to be described by local minima and maxima that are found by applying Alexander’s (1961) Þlter techniques. The pattern recognition algorithm is applied to six currencies (JPY, DEM, CD, SF, FF and BP against the USD) in the period March 1973 to June 1994. SigniÞcance is tested with the bootstrap methodology described by Brock et al. (1992) under the null of a random walk and GARCH model. It is found that the head-and-shoulders pattern had signiÞcant predictive power for the DEM and the JPY, also after correcting for transaction costs and interest rate di?erentials. Lo, Mamaysky and Wang (2000) develop a pattern recognition algorithm based on non-parametric kernel regression to detect (inverse) head-and-shoulders, broadening tops and bottoms, triangle tops and bottoms, rectangle tops and bottoms, and double tops and bottoms - patterns that are the most di?cult to quantify analytically. The pattern recognition algorithm is applied to hundreds of NYSE and NASDAQ quoted stocks in the period 1962 − 1996. 

 

Data snooping is the generic term of the danger that the best forecasting model found in a given data set by a certain speciÞcation search is just the result of chance instead of the result of truly superior forecasting power. Jensen (1967) already argued that the good results of the relative-strength trading rule used by Levy (1967) could be the result of survivorship bias. That is, strategies that performed well in the past get the most attention by researchers. Jensen and Benington (1969, p.470) go a step further and argue: “Likewise given enough computer time, we are sure that we can Þnd a mechanical trading rule which works on a table of random numbers - provided of course that we are allowed to test the same rule on the same table of numbers which we used to discover the rule. We realize of course that the rule would prove useless on any other table of random numbers, and this is exactly the issue with Levy’s results.” Another form of data snooping is the publication bias. It is a well-known fact that studies presenting unusual results are more likely to be published than the studies that just conÞrm a well-known theory. The problem of data snooping was addressed in most of the work on technical analysis, but for a long time there was no test procedure to test for it. Finally White (2000), building on the work of Diebold and Mariano (1995) and West (1996), developed a simple and straightforward procedure for testing the null hypothesis that the best forecasting model encountered in a speciÞcation search has no predictive superiority over a given benchmark model. The alternative is of course that the best forecasting model is superior to the benchmark. Summarized in simple terms, the procedure bootstraps the original time series a great number of times, preserving the key characteristics of the time series. White (2000) recommends the stationary bootstrap of Politis and Romano (1994a, 1994b). Next, the speciÞcation search for the best forecasting model is executed for each bootstrapped series, which yields an empirical distribution of the performance of the best forecasting model. The null hypothesis is rejected at the α percent signiÞcance level if the performance of the best forecasting model on the original time series is greater than the α percent cut o? level of the empirical distribution. This procedure was called White’s Reality Check (RC) for data snooping. Sullivan, Timmermann and White (1999, 2001) utilize the RC to evaluate simple technical trading strategies and calendar e?ects applied to the DJIA in the period 1897 − 1996. Sullivan et al. (1999) take the study of Brock et al. (1992) as starting point and construct an extensive set of 7846 trading rules, consisting of Þlters, moving averages, support-andresistance, channel break-outs and on-balance volume averages. It is demonstrated that the results of Brock et al. (1992) hold after correction for data snooping, but that the forecasting performance tends to have disappeared in the period after the end of 1986.

 

For the calendar e?ects, for example the January, Friday and the turn of the month e?ect, Sullivan et al. (2001) Þnd that the RC in all periods does not reject the null hypothesis that the best forecasting rule encountered in the speciÞcation search does not have superior predictive ability over the buy-and-hold benchmark. If no correction were made for the speciÞcation search, then in both papers the conclusion would have been that the best model would have signiÞcant superior forecasting power over the benchmark. Hence Sullivan et al. (1999, 2000) conclude that it is very important to correct for data snooping for otherwise one can make wrong inferences about the signiÞcance of the best model found. Hansen (2001) identiÞes a similarity condition for asymptotic tests of composite hypotheses, shows that this condition is a necessary condition for a test to be unbiased. He shows that White’s RC does not satisfy this condition. This causes the RC to be an asymptotically biased test, which yields inconsistent p-values. Moreover, the test is sensitive to the inclusion of poor and irrelevant models in the comparison. Further, the test has poor power properties. Therefore, within the framework of White (2000), he applies the similarity condition to derive a test for superior predictive ability (SPA). The null hypothesis of this test is that none of the alternative models in the speciÞcation search is superior to the benchmark model, or stated di?erently, the benchmark model is not inferior to any alternative model. The alternative is that one or more of the alternative models are superior to the benchmark model. Hansen (2001) uses the RC and the SPA-test to evaluate forecasting models applied to US annual inßation in the period 1952 − 2000. He shows that the null hypothesis is neither rejected by the SPA-test p-value, nor by the RC p-value, but that there is a large di?erence between both p-values, likely to be caused by poor models in the space of forecasting models. Grandia (2002) utilizes in his master’s thesis the RC and the SPA-test to evaluate the forecasting ability of a large set of technical trading strategies applied to stocks quoted at the Amsterdam Stock Exchange in the period January 1973 through December 2001. He Þnds that the best trading strategy out of the set of Þlters, moving averages and trading range break-out rules can generate excess proÞts over the buy-and-hold even in the presence of transaction costs, but is not superior to the buy-and-hold benchmark after correction for the speciÞcation search. The results are stable across the subperiods 1973 − 1986 and 1987 − 2001.

 

Technical analysis is heavily used in practice to make forecasts about speculative price series. However, early statistical studies found that successive price changes are linearly independent, as measured by autocorrelation, and that Þnancial price series may be well deÞned by random walks. In that case technical trading should not provide valuable trading signals. However, it was argued that the dependence in price changes might be of such a complicated nonlinear form that standard linear statistical tools might provide misleading measures of the degree of dependence in the data. Therefore several papers appeared in the academic literature testing the proÞtability of technical analysis. The general consensus in academic research on technical analysis is that there is some but not much dependence in speculative prices that can be exploited by nonlinear technical trading rules. Moreover, any found proÞtability seems to disappear after correcting for transaction costs and risk. Only ßoor traders who face very small transaction costs can possibly reap proÞts from technical trading. Most papers consider a small set of technical trading rules that are said to be widely known and frequently used in practice. This causes the danger of data snooping. However, after correction for the speciÞcation search, it is still found that those technical trading rules show forecasting power in the presence of small transaction costs. It is noted by many authors that the forecasting power of technical trading rules seems to disappear in the stock markets as well as in the currency markets during the 1990s, if there was any predictive power before. It is argued that this is likely to be caused by computerized trading programs that take advantage of any kind of patterns discovered before the mid 1990s causing any proÞt opportunity to disappear.

 

 

The e?cient markets hypothesis states that in highly competitive and developed markets it is impossible to derive a trading strategy that can generate persistent excess proÞts after correction for risk and transaction costs. Andrew Lo, in the introduction of Paul Cootner’s “The Random Character of Stock Prices” (2000 reprint, p.xi), suggests even to extend the deÞnition of e?cient markets so that proÞts accrue only to those who acquire and maintain a competitive advantage. Then, those proÞts may simply be the fair reward for unusual skill, extraordinary e?ort or breakthroughs in Þnancial technology. The goal of this thesis is to test the weak form of the e?cient markets hypothesis by applying a broad range of technical trading strategies to a large number of di?erent data sets. In particular we focus on the question whether, after correcting for transaction costs.

 

Data snooping, technical trading rules have statistically signiÞcant forecasting power and can generate economically signiÞcant proÞts. This section brießy outlines the di?erent chapters of the thesis. The chapters are written independently from each other with a separate introduction for each chapter. Now and then there is some repetition in the text, but this is mainly done to keep each chapter self contained. Chapters 2 through 5 are mainly empirical, while Chapter 6 describes a theoretical model. In Chapter 2 a large set of 5350 trend-following technical trading rules is applied to the price series of cocoa futures contracts traded at the London International Financial Futures Exchange (LIFFE) and the New York Co?ee, Sugar and Cocoa Exchange (CSCE), in the period January 1983 through June 1997. The trading rule set is also applied to the Pound-Dollar exchange rate in the same period. It is found that 58% of the trading rules generates a strictly positive excess return, even if a correction is made for transaction costs, when applied to the LIFFE cocoa futures prices. Moreover, a large set of trading rules exhibits statistically signiÞcant forecasting power if applied to the LIFFE cocoa futures series. On the other hand the same set of strategies performs poor on the CSCE cocoa futures prices, with only 12% generating strictly positive excess returns and hardly showing any statistically signiÞcant forecasting power. Bootstrap techniques reveal that the good results found for the LIFFE cocoa futures price series cannot be explained by several popular null models like a random walk, autoregressive and GARCH model, but can be explained by a structural break in trend model. The large di?erence in the performance of technical trading may be attributed to a combination of the demand/supply mechanism in the cocoa market and an accidental inßuence of the Pound-Dollar exchange rate, reinforcing trends in the LIFFE cocoa futures but weakening trends in the CSCE cocoa futures. Furthermore, our case study suggests a connection between the success or failure of technical trading and the relative magnitudes of trend, volatility and autocorrelation of the underlying series. In the next three chapters, Chapters 3-5, a set of trend-following technical trading rules is applied to the price history of several stocks and stock market indices. Two di?erent performance measures are used to select the best technical trading strategy, namely the mean return and the Sharpe ratio criterion. Corrections are made for transaction costs. If technical trading shows to be proÞtable, then it could be the case that these proÞts are merely the reward for bearing the risk of implementing technical trading. Therefore Sharpe-Lintner capital asset pricing models (CAPMs) are estimated to test this hypothesis. Furthermore, if technical trading shows economically and statistically signiÞcant forecasting power after corrections are made for transaction costs and risk, then it is tested whether the selected technical trading strategy is genuinely superior to the buy.

 

 

And-hold benchmark also after a correction is made for data snooping. Tests utilized to correct for data snooping are White’s (2000) Reality Check (RC) and Hansen’s (2001) test for superior predictive ability (SPA). Finally, it is tested with a recursively optimizing and testing method whether technical trading shows true out-of-sample forecasting power. For example, recursively at the beginning of each month the strategy with the highest performance during the preceding six months is selected to generate trading signals in that month. In Chapter 3 a set of 787 trend-following technical trading rules is applied to the DowJones Industrial Average (DJIA) and to 34 stocks listed in the DJIA in the period January 1973 through June 2001. Because numerous research papers found that technical trading rules show economically and statistically signiÞcant forecasting power in the era until 1987, but not in the period thereafter, we split our sample in two subperiods: 1973 − 1986 and 1987 − 2002. For the mean return as well as the Sharpe ratio selection criterion it is found that in all periods for each data series a technical trading rule can be found that is capable of beating the buy-and-hold benchmark, even if a correction is made for transaction costs. Furthermore, if no transaction costs are implemented, then for most data series it is found by estimating Sharpe-Lintner CAPMs that technical trading generates riskcorrected excess returns over the risk-free interest rate. However, as transaction costs increase the null hypothesis that technical trading rule proÞts are just the reward for bearing risk is not rejected for more and more data series. Moreover, if as little as 0.25% transaction costs are implemented, then the null hypothesis that the best technical trading strategy found in a data set is not superior to the buy-and-hold benchmark after a correction is made for data snooping, is neither rejected by the RC nor by the SPA-test for all data series examined. Finally, the recursive optimizing and testing method does not show economically and statistically signiÞcant risk-corrected out-of-sample forecasting power of technical trading. Thus, in this chapter no evidence is found that trend-following technical trading rules can forecast the direction of the future price path of the DJIA and stocks listed in the DJIA. In Chapter 4 the same technical trading rule set is applied to the Amsterdam Stock Exchange Index (AEX-index) and to 50 stocks listed in the AEX-index in the period January 1983 through May 2002. For both selection criteria it is found that for each data series a technical trading strategy can be selected that is capable of beating the buy-and-hold benchmark, also after correction for transaction costs. Furthermore, by estimating Sharpe-Lintner CAPMs it is found for both selection criteria in the presence of 1% transaction costs that for approximately half of the data series the best technical trading strategy has statistically signiÞcant risk-corrected forecasting power and even.

 

Duces risk of trading. Next, a correction is made for data snooping by applying the RC and the SPA-test. If the mean return criterion is used for selecting the best strategy, then both tests lead for almost all data series to the same conclusion if as little as 0.10% transaction costs are implemented, namely that the best technical trading strategy selected by the mean return criterion is not capable of beating the buy-and-hold benchmark after correcting for the speciÞcation search that is used to select the best strategy. In contrast, if the Sharpe ratio selection criterion is used, then for one third of the data series the null of no superior forecasting power is rejected by the SPA-test, even after correction for 1% transaction costs. Thus in contrast to the Þndings for the stocks listed in the DJIA in Chapter 3, we Þnd that technical trading has economically and statistically signiÞcant forecasting power for a group of stocks listed in the AEX-index, after a correction is made for transaction costs, risk and data snooping, if the Sharpe ratio criterion is used for selecting the best technical trading strategy. Finally, the recursive optimizing and testing method does show out-of-sample forecasting proÞts of technical trading. Estimation of Sharpe-Lintner CAPMs shows, after correction for 0.10% transaction costs, that the best recursive optimizing and testing method has statistically signiÞcant risk-corrected forecasting power for more than 40% of the data series examined. However, if transaction costs increase to 0.50% per trade, then for almost all data series the best recursive optimizing and testing procedure has no statistically signiÞcant risk-corrected forecasting power anymore. Thus only for su?ciently low transaction costs technical trading is economically and statistically signiÞcant for a group of stocks listed in the AEX-index. In Chapter 5 the set of 787 trend-following technical trading strategies is applied to 50 local main stock market indices in Africa, North and South America, Asia, Europe, the Middle East and the PaciÞc, and to the MSCI World Index in the period January 1981 through June 2002. We consider the case of an US-based trader and recompute all proÞts in US Dollars. It is found that half of the indices could not even beat a continuous risk-free investment. However, as in Chapters 3 and 4 it is found for both selection criteria that for each stock market index a technical trading strategy can be selected that is capable of beating the buy-and-hold benchmark, also after correction for transaction costs. Furthermore, after implementing 1% costs per trade, still for half of the indices a statistically signiÞcant risk-corrected forecasting power is found by estimating CAPMs. If also a correction is made for data snooping, then we Þnd as in Chapter 4 that both selection criteria yield di?erent results. In the presence of 0.50% transaction costs the null hypothesis of no superior predictive ability of the best technical trading strategy selected by the mean return criterion over the buy-and-hold benchmark after correcting for the speciÞcation search is not rejected for most indices by both the RC.

 

SPA-test. However, if the Sharpe ratio criterion is used to select the best strategy, then for one fourth of the indices, mainly the Asian ones, the null hypothesis of no superior forecastability is rejected by the SPA-test, even in the presence of 1% transaction costs. Finally, the recursive optimizing and testing method does show out-of-sample forecasting proÞts, also in the presence of transaction costs, mainly for the Asian, Latin American, Middle East and Russian stock market indices. However, for the US, Japanese and most Western European stock market indices the recursive out-of-sample forecasting procedure does not show to be proÞtable, after implementing little transaction costs. Moreover, for su?ciently high transaction costs it is found, by estimating CAPMs, that technical trading shows no statistically signiÞcant risk-corrected out-of-sample forecasting power for almost all of the stock market indices. Only for low transaction costs (≤ 0.25% per trade) economically and statistically signiÞcant risk-corrected out-of-sample forecasting power of trend-following technical trading techniques is found for the Asian, Latin American, Middle East and Russian stock market indices. In Chapter 6 a Þnancial market model with heterogeneous adaptively learning agents is developed. The agents can choose between a fundamental forecasting rule and a technical trading rule. The fundamental forecasting rule predicts that the price returns back to the fundamental value with a certain speed, whereas the technical trading rule is based on moving averages. The model in this chapter extends the Brock and Hommes (1998) heterogeneous agents model by adding a moving-average technical trading strategy to the set of beliefs the agents can choose from, but deviates by assuming constant relative risk aversion, so that agents choosing the same forecasting rule invest the same fraction of their wealth in the risky asset. The local dynamical behavior of the model around the fundamental steady state is studied by varying the values of the model parameters. A mixture of theoretical and numerical methods is used to analyze the dynamics. In particular we show that the fundamental steady state may become unstable due to a Hopf bifurcation. The interaction between fundamentalists and technical traders may thus cause prices to deviate from their fundamental value. In this heterogeneous world the fundamental traders are not able to drive the moving average traders out of the market, but fundamentalists and technical analysts coexist forever with their relative importance changing over time.

 

This chapter is an attempt to answer questions raised by a Þnancial practitioner, Guido Veenstra, employed at the leading Dutch cocoa-trading Þrm, Unicom International B.V. at Zaandam. Unicom is part of a bigger consortium that buys crops of cocoa at the Ivory Coast, where it has a plant to make some Þrst reÞnements of the raw cocoa. The cocoa beans are shipped to Europe where they are transformed to cocoa-butter, cocoapowder and cocoa-mass in plants in France and Spain. These raw cocoa products serve as production factors in the chocolate industry. The Þrst goal of Unicom is to sell the raw cocoa beans as well as the raw cocoa products to chocolate manufacturers. A second important task of Unicom is to control the Þnancial risks of the whole consortium. The consortium faces currency risk as well as cocoa price risk. Unicom monitors the product streams and uses cocoa futures contracts, mainly those traded at the London International Financial Futures Exchange (LIFFE), to hedge the price risk. Unicom trades cocoa futures through brokers. However, the commission fees give the brokers an incentive to contact their clients frequently and to give them sometimes unwanted advice to trade as much as possible. Brokers’ advices are partly based on technical analysis. In addition to cocoa producers, more and more speculators seem to be trading on the cocoa futures markets who use technical analysis as a forecasting tool. If a lot of speculators with a large amount of money are trading in a market, they may a?ect realized.

 

futures prices through their behavior. The question “Can cocoa futures prices be predicted by technical analysis?” thus becomes important from a practitioner’s viewpoint. This question is not only important to cocoa producers, but in general to producers of any commodity hedging price risk. If technical analysis has forecasting power and speculators take positions in the market on the basis of technical analysis, these speculators can a?ect market prices. Why should a (cocoa) producer go short in the futures market to hedge his price risk exposure if he knows that a lot of speculators in the market are buying long positions driving up the price? Knowledge of the behavior of speculators in the market may be useful to adapt a producers’ price hedging strategy. Until fairly recently, the academic literature has paid little attention to technical trading strategies. Until the 1980s the e?cient markets hypothesis (EMH) was the dominating paradigm in Þnance, see e.g. Fama (1970) and Samuelson (1965). According to a strong form of the EMH, Þnancial time series follow a random walk and are thus inherently unpredictable. All information is discounted in the prices already and prices will only adapt if new information becomes available. Because news arrives randomly, prices will move randomly. According to the EMH, Þnancial time series are unpredictable and technical analysis is useless and cannot lead to statistically signiÞcant prediction or economically signiÞcant proÞts. In the last decade however, technical analysis has regained the interest of many economic researchers. Several authors have shown that Þnancial prices and returns are forecastable to some extent, either from their own past or from some other publicly available information, see e.g. Fama and French (1988), Lo and MacKinlay (1988, 1997, 1999) and Pesaran and Timmermann (1995, 2000). In particular, it has been shown that simple technical trading rules used in Þnancial practice can generate positive proÞts and can have statistically signiÞcant forecasting power. For example Brock, Lakonishok and LeBaron (1992) test 26 simple technical trading rules on daily data of the Dow-Jones Industrial Average (DJIA) in the period 1897-1986. Each of the trading rules Brock et al. (1992) test generates higher returns during buy days, that is periods following buy signals, than during sell days, that is periods following sell signals. Further they Þnd that returns following buy signals are less volatile than returns following sell signals. By applying bootstrap techniques they show that their results are not consistent with some popular null models like the random walk, the AR(1), the GARCH-in-mean and the exponential GARCH model. LeBaron (2000) performs the same analysis as Brock et al. (1992) for the period 1988-1999 and Þnds that trading rules perform much worse in this period, but that volatility remains di?erent between buy and sell periods. Levich and Thomas (1993) test Þlter and moving-average trading rules on foreign currency futures prices in the period.

 

1976-1990. Applying bootstrap techniques they conclude that the proÞts of the technical trading strategies cannot be explained by a random walk model or by autocorrelation in the data. LeBaron (1993) applies trading rules to exchange rates based on interest rate di?erentials, moving averages and volatility comparison and concludes that the trading rules tested have forecasting power. Several authors have emphasized the danger of data snooping, meaning that if one searches long enough in a data set, there will always appear one trading strategy that seems to work. Many authors mitigate this problem by using only trading rules that are frequently used in Þnancial practice or by reporting the robustness of their results across di?erent subperiods. However, Sullivan, Timmermann and White (1999) noted that such trading strategies could be the result of survivorship bias, since the currently used trading rules in practice can be the result of a continuous search for the best strategy. Therefore they propose to use White’s (2000) Reality Check bootstrap methodology to correct for data snooping. Sullivan et al. (1999) take the results of Brock et al. (1992) on the DJIA in the period 1897-1986 as starting point. They Þnd that the results of Brock et al. (1992) are robust to data snooping in the period 1897-1986, but that in the period 1987-1997 the performance of the best trading rule is not signiÞcant when corrected for data snooping. Sullivan et al. (1999) show that the same results hold for a universe of 7846 trading rules and conclude that the worse performance of trading rules in the period 1987-1997 may be explained by a change of the market mechanism, e.g. an increase of market e?ciency due to lower transaction costs and increased liquidity. The present chapter is empirical and tests the proÞtability and predictability of objective trend-following technical trading techniques in the cocoa futures markets in the period 1983:1-1997:6. In order to avoid the problem of data snooping our approach is to test a large set of more than 5000 trading strategies, moving average, trading range break-out and Þlter rules, and to investigate the magnitude of the fraction generating strictly positive excess returns and statistically signiÞcant forecasting power. Cocoa futures contracts are traded at two di?erent exchanges, namely at the Co?ee, Sugar and Cocoa Exchange (CSCE) in New York and the London International Financial Futures Exchange (LIFFE). The results for the two cocoa futures contracts are strikingly di?erent. When applied to the LIFFE cocoa futures prices, 58.3% of all trading rules generate strictly positive excess returns, even when correcting for transaction costs. Furthermore, a large set of trading rules exhibits statistically signiÞcant forecasting power of the LIFFE cocoa futures series, with e.g. 26.6% having signiÞcantly positive mean buy minus sell return; for the 5 year subperiod 1983:1-1987:12 even 46.7% of all trading rules has a signiÞcantly positive mean buy minus sell return. However, the same set of strategies performs poorly on the CSCE.

 

Cocoa futures prices, with only 12.2% generating positive net excess returns and hardly any statistically signiÞcant forecasting power. The large di?erence in the performance of technical trading is surprising, because the underlying asset in both markets is more or less the same. Our Þndings may be attributed to a combination of the demand/supply mechanism in the cocoa market and an accidental inßuence of the Pound-Dollar exchange rate. Due to a spurious relation between the level of the Pound-Dollar exchange rate and the excess demand/supply mechanism in the cocoa market, especially in the period 1983:1-1987:12, trends caused by the demand/supply mechanism were reinforced in the LIFFE cocoa futures price, but the same trends were weakened in the CSCE cocoa futures price. Many technical trading rules are able to pick up these su?ciently strong trends in the LIFFE cocoa futures but almost none of them pick up the weaker trends in the CSCE cocoa futures. The chapter is organized as follows. In section 2.2 we describe our data set and the construction of a long, continuous time series of 15 years out of 160 di?erent (overlapping) futures contracts of 18 months. Section 2.3 gives an overview of the 5350 trading rules we apply; the parameterizations of these rules can be found in Appendix B. In section 2.4 the performance measure, i.e. the excess return net of transaction costs generated by the trading rules, is calculated. Section 2.5 focuses on the economic performance as well as the statistical signiÞcance of the predictability of returns by technical trading rules. The statistical tests are performed Þrst under the assumption of iid returns but later also by correcting for dependence in the data. This is done by estimating exponential GARCH models with a dummy for the trading position in the regression equation, but also by applying bootstrap techniques, the results of which are presented in section 2.6. In section 2.7 a possible explanation of the large di?erences in the performance between CSCE and the LIFFE cocoa futures prices is given. Finally, section 2.8 concludes.

 

For trading. The CSCE and LIFFE cocoa futures contracts di?er somewhat in their speciÞcations. First, cocoa is grown in many regions in Africa, Asia and Latin America and therefore the crops di?er in quality. In the futures contracts a benchmark is speciÞed and the other crops are traded at premiums. The benchmark in the LIFFE contract has a higher quality than the benchmark in the CSCE contract. Therefore the benchmark in the LIFFE contract is traded at a $160/ton1 premium in the CSCE contract. Second, the place of delivery in the CSCE contract is near New York, while the places of delivery in the LIFFE contract are nominated warehouses at di?erent places in Europe. Third, the tick sizes of the CSCE and LIFFE contract are respectively one Dollar and one Pound. Cocoa producers and farmers hedge their price risk exposure with futures contracts. This guarantees them that they buy or sell cocoa against a predetermined price. The futures price will depend on the current and expected future demand and supply. When new information becomes available the price will adapt. Normally a futures price is the derivative of the spot price and can be computed by the cost of carry relationship. But in the case of soft commodities such as cocoa the spot price is not relevant, because a farmer with his crop on the land only wants to know what he can get in the future. For cocoa there is no actual spot price, but the “notional” spot price is in fact determined by the futures prices. We investigate data on the settlement prices of 160 cocoa futures contracts that expire in the period January 1982 through December 1997 at the CSCE and the LIFFE2 , as well as data on the Pound-Dollar exchange rate (WM/Reuters) and 1-month UK and US certiÞcates of deposit (COD) interest rates in the same period.

 

 

Price of contract 2 which expires later is higher than the futures price of contract 1 which expires earlier. But if the utility of having an asset in stock is high, e.g. when there is a shortage of the commodity in the short run, then the futures price of contract 2 can be lower than the futures price of contract 1. Thus the prices of di?erent futures contracts can move at di?erent price levels. A long continuous time series of futures prices will be constructed, in order to be able to test technical trading strategies with long memory. The continuous time series must be constructed out of the many price series of the di?erent futures contracts that have the same price trends, but move at di?erent price levels. In particular roll over dates must be deÞned at which the price movements of the di?erent contracts are pasted together. In practice most trading occurs in the second nearest contract, that is the futures contract that has the one but nearest expiration date. We investigated the liquidity of the cocoa futures contracts and decided to take as roll over dates the date one month before most of the practitioners switch to the next contract, so that the continuous time series always represents a high liquidity futures contract. Figure 2.1 exhibits graphically the roll over procedure used in this chapter. Murphy (1986) suggests pasting the prices of two successive futures contracts to study price movements over a long period of time. But the pasting of prices will introduce price.

 

Figure 2.1: Roll over scheme. The time axis shows the roll over dates from Dec. 1, 1993 until

March 1, 1995. The arrows above the time axis show in which period which futures contract is used in constructing the continuous futures price series.jumps in the continuous time series, because the prices of two di?erent contracts move at di?erent levels. These price jumps can have an impact on the results and may trigger spurious trading signals if technical trading rules are tested. Therefore a continuous time series must be constructed in another way. The holder of the long position in a futures contract pays a time premium to the holder of the short position. According to (2.1) the time premium paid at time t is T Pt = Ft − St = (e(rt +ut −yt )(T −t) − 1) St .

 

According to (2.4) the time premium that must be paid will be less when the duration of the contract is shorter other things being equal. However, (2.4) also implies that if a continuous time series of futures prices is constructed by pasting the prices of di?erent contracts, at each pasting date3 a new time premium to the time series is added, because at each pasting date the time until expiration will be longer than before the pasting date. This time premium will create price jumps and therefore an upward force in the global price development. In fact, if the return of the underlying asset is not greater than the cost of carry a spurious upward trend can be observed in the continuous price series, as illustrated in Þgure 2.2, which may a?ect the performance of long memory trading strategies. Therefore we constructed a continuous time series of futures prices by pasting the returns of each futures contract at the roll over dates and choosing an appropriate starting value; see Þgure 2.2. For this continuous series, discontinuous price jumps and spurious trends will disappear and the trends will show the real proÞtability of trading positions in futures contracts.

 

Figure 2.2: Two continuous time series of CSCE cocoa futures prices in the period 1982:11997:6. The upper time series is constructed by pasting the futures prices at the roll over dates. The time premium of a futures contract leads to price jumps and spurious trends. In this chapter we use the lower continuous time series, constructed by pasting the returns of the futures prices at the roll over dates and by choosing as starting value the futures price of the May contract at January 3, 1983. Any trends that are present in the lower series reßect real proÞtability of trading positions.

 

In Þgure 2.3 time series are shown of the continuation of the CSCE and LIFFE cocoa futures prices and returns as well as the Pound-Dollar exchange rates and returns for the period 1982:1-1997:6. The long-term and short-term trends can be seen clearly. Each technical trading strategy needs a di?erent time horizon of past prices to generate its Þrst signal. Therefore the Þrst 260 observations in each data set will be used to initialize the trading rules, so that on January 3, 1983 each rule advises some position in the market. All trading rules will be compared from this date. Table 2.1 shows the summary statistics of the daily returns of the sample 1983:1-1997:6 and three subperiods of Þve years. Returns are calculated as the natural log di?erences of the level of the data series. The Þrst subperiod, 1983:1-1987:12, covers the period in which the price series exhibit Þrst a long term upward trend and thereafter a downward trend; see Þgure 2.3. It is remarkable that the upward and downward trends of both cocoa futures series CSCE and LIFFE (accidentally) coincide with similar trends in the Pound-Dollar exchange rate series. In the second subperiod, 1988:1-1992:12, the cocoa series exhibit a downward trend, while the Pound-Dollar series is ßuctuating upwards and downwards. The third subperiod, 1993:1-1997:6, covers a period in which the cocoa series as well as the PoundDollar series seem to show no signiÞcant long term trends anymore. 

 

Can be seen that the mean daily returns are close to zero for all periods. The largest (absolute) mean daily return is negative 9.5 basis points per day, -21.2% per year, for the CSCE series in the second subperiod. The daily standard deviation of the CSCE returns series is slightly, but signiÞcantly4 greater than the daily standard deviation of the LIFFE returns series in all periods. The daily volatility of the Pound-Dollar series is much smaller, by a factor more than two measured in standard deviations, than the volatility of both cocoa series in all subperiods. All data series show excess kurtosis in comparison with a normal distribution and show some sign of skewness. The table also shows the maximum consecutive decline of the data series in each period. For example the CSCE cocoa futures continuation series declined with 85.1% in the period May 23, 1984 until February 20, 1997. The Pound lost 47.5% of its value against the Dollar in the period February 27, 1985 until September 2, 1992. Hence, if objective trend-following trading techniques can avoid being in the market during such periods of great depreciation, large proÞts can be made. Table 2.2 shows the estimated autocorrelation functions, up to order 20, for all data series over all periods. Typically autocorrelations are small with only few lags being signiÞcant.5 The CSCE series shows little autocorrelation. Only for the Þrst subperiod the second order autocorrelation is signiÞcant at a 5% signiÞcance level. The LIFFE series shows some signs of low order autocorrelation, signiÞcant at the 10% level, in the Þrst two subperiods. The Pound-Dollar series has a signiÞcant Þrst order autocorrelation at a 1% signiÞcance level, mainly in the Þrst two subperiods.

 

Murphy (1986) deÞnes technical analysis as the study of past price movements with the goal to forecast future price movements, perhaps with the aid of certain quantitative summary measures of past prices such as “momentum” indicators (“oscillators”), but without regard to any underlying economic, or “fundamental” analysis. Another description is given by Pring (1998) who deÞnes technical analysis as the “art” of detecting a price trend in an early stage and maintaining a market position until there is enough weight of evidence that the trend has reversed.

 

There are three principles underlying technical analysis. The Þrst is that all information is gradually discounted in the prices. Through the market mechanism the expectations, hopes, dreams and believes of all investors are reßected in the prices. A technical analyst argues that the best adviser you can get is the market itself and there is no need to explore fundamental information. Second, technical analysis assumes that prices move in upward, downward or sideways trends. Therefore most technical trading techniques are trend-following instruments. The third assumption is that history repeats itself. Under equal conditions investors will react the same leading to price patterns which can be recognized in the data. Technical analysts claim that if a pattern is detected in an early stage, proÞtable trades can be made. In this thesis we conÞne ourselves to objective trend-following technical trading techniques which can be implemented on a computer. In this chapter we test in total 5350 technical trading strategies divided in three di?erent groups: moving-average rules (in total 2760), trading range break-out (also called support-and-resistance) rules (in total 1990) and Þlter rules (in total 600). These strategies are also described by Brock, Lakonishok and LeBaron (1992), Levich and Thomas (1993) and Sullivan, Timmermann and White (1999). Lo, Mamaysky and Wang (2000) use non-parametric methods to implement other, geometrically based technical trading rules such as head-and-shoulder pattern formation. We use the parameterizations of Sullivan et al. (1999) as a starting point to construct our sets of trading rules. These parameterizations are presented in Appendix B. The strategies will be computed on the continuous cocoa time series and the Pound-Dollar exchange rate. If a buy (sell) signal is generated at the end of day t, we assume that a long (short) position is taken in the market at day t against the settlement price of day t.

 

According to the time delay Þlter a signal must hold for d consecutive days before a trade is implemented. If within these d days di?erent signals are given, the position in the market will not be changed. A MA rule with a Þxed holding period holds a long (short) position in the market for a Þxed number of f days after a buy (sell) signal is generated. After f days the market position is liquidated and a neutral market position is held up to the next buy or sell signal. This strategy tests whether the market behaves di?erent in a time period after the Þrst crossing. All signals that are generated during the Þxed holding period are ignored. The last extension is the stop-loss. The stop-loss is based on the popular phrase: “Let your proÞts run and cut your losses short.” If a short (long) position is held in the market, the stop-loss will liquidate the position if the price rises.

 

Our second group of trading rules consists of trading range break-out (TRB) strategies, also called support-and-resistance strategies. The TRB strategy uses support and resistance levels. If during a certain period of time the price does not fall below (rise beyond) a certain price level, this price level is called a support (resistance) level. According to technical analysts, there is a “battle between buyers and sellers” at these price levels. The market buys at the support level after a price decline and sells at the resistance level after a price rise. If the price breaks through the support (resistance) level, an important technical trading signal is generated. The sellers (buyers) have won the “battle”. At the support (resistance) level the market has become a net seller (buyer). This indicates that the market will move to a subsequent lower (higher) level. The support (resistance) level will change into a resistance (support) level. To implement the TRB strategy, supportand-resistance levels are deÞned as local minima and maxima of the closing prices. If the price falls (rises) through the local minimum (maximum) a sell (buy) signal is generated and a short (long) position is taken in the market. If the price moves between the local minimum and maximum the position in the market is maintained until there is a new breakthrough. The TRB strategy will also be extended with a %-band Þlter, a time delay Þlter, a Þxed holding period and a stop-loss. The basic TRB strategy, extended with a %-band Þlter, is described by if Pt > (1 + b) max{Pt−1 , Pt−2 , ..., Pt−n } P ost+1 = 1, P ost+1 = P ost , if (1 − b) min{Pt−1 , ..., Pt−n } ≤ Pt ≤ (1 + b) max{Pt−1 , ..., Pt−n } P ost+1 = −1, if Pt < (1 − b) min{Pt−1 , Pt−2 , ..., Pt−n } Our group of TRB strategies consists of 1990 trading strategies.

 

The Þnal group of trading strategies we test is the group of Þlter rules, introduced by Alexander (1961). These strategies generate buy (sell) signals if the price rises (falls) by x% from a previous low (high). We implement the Þlter rule by using a so called moving stop-loss. In an upward trend the stop-loss is placed below the price series. If the price goes up, the stop-loss will go up. If the price declines, the stop-loss will not be changed.

 

If the price falls through the stop-loss, a sell signal is generated and the stop-loss will be placed above the price series. If the price declines, the stop-loss will decline. If the price rises, the stop-loss is not changed. If the price rises through the stop-loss a buy signal is generated and the stop-loss is placed below the price series. The stop-loss will follow the price series at a x% distance. On a buy (sell) signal a long (short) position is maintained. This strategy will be extended with a time delay Þlter and a Þxed holding period. In total our group of Þlter rules consists of 600 trading strategies. As can be seen in Appendix B we can construct a total of 5350 trading strategies (2760 MA-rules, 1990 TRB-rules, and 600 Filter-rules) with a limited number of values for each parameter. Each trading strategy divides the data set of prices in three subsets. A buy (sell) period is deÞned as the period after a buy (sell) signal up to the next trading signal. A neutral period is deÞned as the period after a neutral signal up to the next buy or sell signal. The subsets consisting of buy, sell or neutral periods will be called the set of buy, sell or neutral days.

 

Suppose Pt is the level of the continuous futures price series at the end of day t and P ost is the position held in the market by the trader at day t. When trading a futures contract, it is required to hold some margin on a margin account to protect the broker against defaults of the traders. ProÞts and losses are directly added and subtracted from the margin. A risk-free interest rate can be earned on the margin account. Suppose a trader takes a long or short position in the market against the settlement price at day t − 1, Pt−1 , and assume that he deposits Pt−1 on his margin account. 

 

Risk-free interest rate. The proÞt or loss of the trader on the futures position in period t directly added to or subtracted from the margin account is equal to (Pt − Pt−1 )P ost . We will also consider transaction costs. Costs are calculated as a fraction c of the price. Some strategies generate trading signals very often, others not. If a strategy does not generate trading signals very often and a position in the market is maintained for a long time, then there are also trading costs due to the limited life span of a futures contract. In particular, we assume that if a certain position in the market is maintained for 20 days after a roll over date, a trade takes place since the position has to be rolled over to the next futures contract and transaction costs must be paid. 

 

Panel A of table 2.3 shows the results of the best Þve technical trading strategies applied to the CSCE cocoa futures price series in the period 1983:1-1997:6. Panel B of the table lists the results of the best strategy in each subperiod. The Þrst column of the table lists the strategy parameters. MA, TRB and FR are abbreviations for the moving average, trading range break-out and Þlter rules respectively. %b, td, fhp, and stl are abbreviations for the %-band Þlter, the time delay Þlter, the Þxed holding period and the stop-loss respectively. 

 

Holding period. The second column lists the mean daily excess return of the strategy on a yearly basis, that is the mean daily return times the number of trading days in a year, which is set to 252. The third column lists the mean daily excess returns of the trading rules net of 0.1% transaction costs, with the t-ratios beneath these numbers. The t-test statistic tests whether the mean daily excess return is signiÞcantly di?erent from zero under the assumption of iid returns. The fourth and Þfth column list the number of days classiÞed as a buy or sell day. The number of buy and sell trades is listed beneath these numbers. The sixth (seventh) column list the total number of days buy (sell) trades with a strictly positive excess return last, as a fraction of the total number of buy (sell) days. The fraction of buy and sell trades with a strictly positive excess return is listed beneath these numbers. The eight and ninth column list the mean daily return of the data series itself during buy and sell days. T-ratios to test whether the mean daily return during buy and sell days is signiÞcantly di?erent from zero are listed beneath these numbers. In this way we can detect whether the data series itself rises during buy days and declines during sell days. The last column lists the di?erences between the mean daily buy and sell returns and the corresponding t-ratios, which test whether the mean daily buy return is signiÞcantly di?erent from the mean daily sell return. 

 

Thus the expression in the denominator of (2.8) is not correct, because the covariance term in (2.9) is unequal to zero. This is because the set of buy or sell days is a subset of the total set of observations. However the adjustment would have little e?ect on the results of Brock et al. (1992), because as we have shown the variance of their test statistic is actually smaller than the one they used and therefore their tests are too conservative. The best strategy applied to the full sample has a signiÞcantly positive mean daily excess return of 0.039%, 10.38% yearly, which is considerably large. The mean daily excess return of the CSCE series during buy (sell) days is equal to 0.056% (−0.101%), 15.2% (−22.5%) yearly. The mean daily sell return is signiÞcantly negative at a 5% signiÞcance level using a one tailed test, while the mean daily buy return is not signiÞcantly positive. The mean buy-sell di?erence is signiÞcantly positive at a 5% signiÞcance level and equal to 0.158% (48.9% yearly). The four other strategies yield similar results. The mean daily excess return is signiÞcantly positive in all cases at a 10% signiÞcance level using a one tailed t-test. The mean return of the CSCE series during buy days is positive, but not signiÞcant, and the mean return during sell days is signiÞcantly negative. For all Þve strategies the mean buy-sell di?erences are signiÞcantly positive at a 5% signiÞcance level using a one sided test. The sixth and seventh column show that for all Þve listed strategies more than 50% of the buy and sell trades have a strictly positive excess return and that these trades consist of more than 50% of the total number of buy and sell days. The results above show that the best Þve technical trading strategies applied to the CSCE series in the period 83:1-97:6 have an economically as well as a statistically signiÞcant forecasting power. For the three subperiods similar results are found, but now the best Þve strategies found have a higher mean daily excess return. The best strategy has a signiÞcantly positive mean yearly excess return of about 20%. Thus when looking at subperiods, strategies can be found that perform better than when applied to the full period.

 

Panel A of table 2.4 shows the results of the best Þve technical trading strategies applied to the LIFFE cocoa series in the period 83:1-97:6. Now the best Þve strategies consist entirely of moving-average trading strategies. The best strategy is a MA strategy that compares the price series with a 40-day MA. The strategy is extended with a 0.5 %-band Þlter. The results of the mean daily excess returns and the mean daily buy and sell returns are similar to the CSCE cocoa series in the same period, but the mean excess returns are higher and the t-ratios show that the results are strongly signiÞcant. The results for the number of trades with a strictly positive excess return di?er. Now in most cases 20 − 40% of the buy and sell trades generate an excess return, but these trades.

 

Consists of more than 70% of the total number of buy and sell days. Thus most of the time the strategies are making a positive excess return, but there are a lot of short run trades that make a loss. Also for the three subperiods of the LIFFE series it is found that the best strategies perform better than the best strategy applied to the total period. But for the three subperiods the best Þve strategies generate buy and sell trades that are in more than 50% of the cases proÞtable and these trades consist of more than 70% of the total number of.

 

Buy and sell days in most cases. The above results show that also for the LIFFE series the best Þve strategies have an economically and statistically signiÞcant forecasting power in all periods. Table 2.5 shows the results of the best technical trading strategies applied to the Pound-Dollar exchange rate for the full sample. The best strategy is a 100 day trading range break-out rule with a one %-band Þlter and a 50 day Þxed holding period. This strategy has a mean daily excess return of 0.007% (1.64% yearly). The mean daily return during buy (sell) days of the Pound-Dollar series itself is equal to 0.161% (−0.017%),which corresponds to 50% (−4.2%) on a yearly basis. The mean daily buy return is signiÞcantly positive in all cases, but the mean daily sell return is not signiÞcantly negative for most of the best Þve strategies. The mean buy-sell di?erence is signiÞcantly positive for all best Þve strategies and for the best strategy equal to 0.178% (56.6% yearly). All strategies generate buy trades with a strictly positive excess return in more than 50% of the cases, and these trades consist of more than 50% of the total number of buy days. The percentage of sell trades with a strictly positive excess return is equal to zero, because in the case of a sell trade, the domestic currency is bought and the domestic interest rate is earned. Hence the excess return during sell days is always equal to zero. The results for all three subperiods are similar. Thus also in the case of the Pound-Dollar exchange rate the results show that the best Þve technical trading strategies have an economically and statistically signiÞcantly forecasting power. However the mean daily excess returns of.

 

the best Þve strategies are smaller in comparison with the excess returns of the best Þve strategies applied to the cocoa series, and much less proÞts could be made in comparison with the cocoa series. We have found technical trading rules that perform very well when applied to the CSCE and LIFFE cocoa futures series and the Pound-Dollar exchange rate. However, there will always be a strategy that generates a large proÞt if a large set of trading rules is tested as we have seen in the results above. In practice technical traders will optimize their set of trading rules and use the best one for future forecasting. Therefore Brock et al. (1992) and Levich and Thomas (1993) test a small set of strategies that are used in practice. In their bootstrap procedure which corrects for data snooping Sullivan et al. (1999) only use the best strategy. Instead, in the next section, to deal with the data snooping problem we shall look at the forecasting results of the 5350 constructed technical trading rules as a group.

 

Cocoa futures series We test for economic signiÞcance of the set of technical trading strategies by looking at the percentage of strategies that generate a strictly positive excess return. These numbers are shown in table 2.6 in the case of no transaction costs and in table 2.7 in the case of 0.1% transaction costs, for the CSCE, LIFFE and Pound-Dollar series, for all sets of technical trading rules and for all periods. Comparing table 2.6 with table 2.7 shows that after correcting for transaction costs, the percentage of trading rules generating a strictly positive excess return declines substantially. In the full period 83:1-97:6 the complete set of trading rules performs very well on the LIFFE cocoa futures prices, but much worse on the CSCE cocoa prices; 58.34% of the strategies generate a strictly positive excess return when applied to the LIFFE series, but only 12.18% generate a strictly positive excess return when applied to the CSCE series, after correcting for transaction costs. This large di?erence is remarkable, because the underlying asset in both markets is the same, except for small di?erences in quality of the cocoa. The table shows that the good results for the LIFFE series mainly appear in the Þrst subperiod 1983:1-1987:12, where 73.25% of the rules generate a strictly positive net excess return for the LIFFE series against 14.14% for the CSCE series. In the second subperiod, 1988:1-1992:12, the trading rules seem to work equally well and fairly well on both series, although the results for the LIFFE series are now weaker than in the Þrst subperiod, with 50.55% (53.90%) of the rules generating a strictly positive net excess return for the CSCE (LIFFE) series. In the third subperiod.

 

1993:1-1997:6, the trading rules perform poorer on both series, since only 15.19% (29.25%) generate a strictly positive net excess return for the CSCE (LIFFE) series. As can be seen in the tables, the results for the di?erent subsets of technical trading rules do not di?er from the complete set of trading rules for all periods. Pound-Dollar exchange rate For the full sample the trading rules do not show much economically signiÞcant forecasting power, with only 10.14% of the trading rules generating a strictly positive excess return net of 0.1% transaction costs. The same result is found for the Þrst subperiod, with 9.32% generating a strictly positive net excess return. The trading rules seem to work better when they are applied to the Pound-Dollar exchange rate in the second subperiod, with 30.81% of the trading rules generating a strictly positive net excess return. In the third subperiod the strategies work badly and only 2.07% generate a strictly positive net excess return. Thus for all three data series it is found that the set of technical trading strategies performs poorly in the subperiod 1993:1-1997:6, when compared with the preceding period 83:1-92:12. Notice that, for example under the null hypothesis of a random walk, the net excess return of technical trading rules will be negative due to transaction costs. The fact that a large set of technical trading rules generates a strictly positive net excess return, especially for the LIFFE cocoa futures series, is therefore surprising and suggestive of economically signiÞcant proÞt opportunities. It is hard however, to evaluate the statistical signiÞcance of this observation. Therefore, in the next subsection we focus on the question whether the forecasting power of returns is statistically signiÞcant.

 

 

We test for the statistical forecasting signiÞcance of the set of technical trading rules by looking at the percentage of strategies which have a mean excess return, mean buy return, mean sell return, mean buy-sell di?erence signiÞcantly di?erent from zero. Table 2.8 summarizes the results. The table shows for both the LIFFE and CSCE cocoa futures series and the Pound-Dollar exchange rate series for the full sample period 1983:1-1997:6 as well as for the three Þve year subperiods the percentages of MA, TRB and Filter trading rules, and the percentage of the complete set of trading rules for which a statistically signiÞcantly positive mean excess return is found. The table also shows the percentage of strategies that have a signiÞcantly positive (negative) mean return during buy (sell).

 

Days. Further the table shows the percentage of strategies for which the di?erence in mean return of the data series during buy and sell days is signiÞcantly positive. Finally, the percentage of strategies for which the data series at the same time has a signiÞcantly positive mean return during buy days as well as a signiÞcantly negative mean return during sell days is shown. A correction is made for 0.1% transaction costs. Table 2.9 shows in contrast to table 2.8 the percentage of strategies which generate statistically signiÞcant bad results, i.e. the percentage of strategies with a signiÞcantly negative mean excess return, with a signiÞcantly negative (positive) mean buy (sell) return, with a signiÞcantly negative mean buy-sell di?erence and the percentage of strategies which have a signiÞcantly negative mean buy return as well as a signiÞcantly positive mean sell return. These statistics are computed to test whether technical trading rules as a group show statistically signiÞcant bad forecasting power. The tables lists only the results of one sided tests with a 10% signiÞcance level, the results for a 5% signiÞcance level are similar but of course weaker. For a 1% signiÞcance level most signiÞcant results disappear. Cocoa futures series For the full sample period the strategies applied to the CSCE cocoa series show hardly any statistically signiÞcant forecasting power. For example, the di?erence in mean return during buy and sell days is signiÞcantly positive only in 1.38% of the trading rules, whereas a signiÞcantly negative mean return during sell days occurs only in 5.92% of all strategies. Only in 0.3% of the cases the mean excess return is signiÞcantly positive, hence no signiÞcant proÞts could be made. For the LIFFE series on the other hand the results are remarkably di?erent. For 26.58% of the strategies the mean buy-sell di?erence is signiÞcantly positive. In particular, the strategies seem to forecast the sell days very well, with more than half (50.53%) of all strategies having a signiÞcantly negative mean return during sell days. In contrast, the mean buy return is signiÞcantly positive only in 6.86% of all strategies. 13.86% of the strategies have a signiÞcantly positive mean excess return when applied to the LIFFE series. Looking at table 2.9 a lot of strategies perform statistically very bad when applied to the CSCE series, while the percentage of strategies that performs statistically badly is much less for the LIFFE series. Thus for the full sample the set of strategies applied to the LIFFE series shows a lot of economic signiÞcance, which is also statistically signiÞcant, and a lot of trading rules have a statistically signiÞcant forecasting power, i.e. they detect periods in which the data series rises and declines, while the percentage of trading rules which performs statistically badly is smaller than the percentage of trading rules which performs statistically good.

 

For the Þrst subperiod the trading rules show almost no statistically signiÞcant forecasting power when applied to the CSCE series. Most t-ratios stay within the critical values. The percentage of strategies that perform badly is even larger than the percentage of strategies that perform well. For example 24.17% of all strategies generate a signiÞcantly negative mean excess return. For the LIFFE series the results are totally di?erent. All subsets of trading rules show some forecasting power. 34.52% of all strategies generate a signiÞcantly positive mean excess return. For 26.73% of the strategies the mean return of the data series during buy days is signiÞcantly positive, for 39.47% of the strategies the mean return during sell days is signiÞcantly negative and for 46.65% of the strategies the Buy-Sell di?erence is signiÞcantly positive. The percentage of strategies that performs statistically badly is small. For 5.87% of the strategies the mean excess return is signiÞcantly negative. Hence, for the LIFFE series the trading rules show economic as well as statistically signiÞcant forecasting power in the Þrst subperiod. The second subperiod is characterized by a long term downward trend with short term upward corrections in both cocoa series. Economically the strategies behave quite well in the second subperiod, but the statistical signiÞcance of the mean excess return of the strategies is very poor (CSCE: 1.85% > tcrit ; LIFFE 6.31% > tcrit ). Hence the economic signiÞcance found is not statistically signiÞcant. All subsets of trading rules show a signiÞcantly negative mean return of the data series during sell days (CSCE: 44.57% < −tcrit ; LIFFE: 54.62% < −tcrit ), which is in line with the downward trend. The upward corrections are not predicted well by the strategies, and for many trading rules the mean return of the data series during buy days is even signiÞcantly negative (CSCE: 26.55% < −tcrit ; LIFFE: 31.96% < −tcrit ). The results found for the second subperiod are in line with the advices of technical analysts only to trade in the direction of the main trend and not reverse the position in the market until there is enough weight of evidence that the trend has reversed. Apparently, the short term upward corrections did not last long enough to be predictable or proÞtable. The third subperiod is characterized by upward and downward trends in prices. The trading rules show no economic signiÞcance for this period and neither do they show statistical forecasting signiÞcance. 29.25% of the strategies applied to the LIFFE series generated a strictly positive excess return, but only for 2.13% of the strategies the mean excess return is signiÞcantly positive. For the CSCE series even 32.26% of the strategies generate a signiÞcantly negative mean excess return. If there was any predictability in the data it has disappeared in the third subperiod.

 

Pound-Dollar exchange rate For the full sample 83:1-97:6 table 2.8 shows that 13.08% of the strategies have a signiÞcantly positive mean buy return and 17.13% have a signiÞcantly negative mean sell return. In 28.19% of the cases the mean Buy-Sell di?erence is signiÞcantly positive. Thus the trading rules seem to generate good trading signals. However, the mean excess return is signiÞcantly positive only in 2.07% of the trading rules, while even in 62.32% of the cases the trading rules generate a signiÞcantly negative mean excess return. Especially the moving-average trading rules perform badly. For the Þrst subperiod the results are similar (Buy: 12.42% > tcrit ; Sell: 44.29% < −tcrit ; Buy-Sell: 41.9% > tcrit ). Sell days are forecasted much better than the buy days. However, only for 0.35% of the strategies the mean excess return is signiÞcantly positive, while in 27.11% of the cases the mean excess return is even signiÞcantly negative. According to the Buy-Sell di?erence the trading rules as a group seem to have a statistically signiÞcant forecasting power in this period, but the economic signiÞcance is poor. In the second subperiod the strategies forecast the upward trends better than the downward trends, 29.63% of the strategies have a signiÞcantly positive mean buy return, while 7.73% of the trading rules have a signiÞcantly negative mean sell return. For 26.13% of the trading rules the Buy-Sell di?erence is signiÞcantly positive. Only 4.78% of the strategies have a signiÞcantly positive mean excess return, while even 17.32% of the strategies have a signiÞcantly negative mean excess return. Hence, also in this subperiod there are signs of forecastability according to the Buy-Sell di?erence, which cannot be exploited economically. In the third subperiod the Pound-Dollar exchange rate exhibits some upward and downward trends. The trading rules show hardly any signs of forecasting power in this subperiod for the Pound-Dollar exchange rate. Only in 0.09% of the cases a signiÞcantly positive mean excess return is generated, while in 66.02% of the cases a signiÞcantly negative mean excess return is generated. 2.5.3.2 SigniÞcance after correction for dependence: an estimation based approach.

 

In the previous subsection we showed that in the period 1983:1-1987:12 the technical trading strategies as a group seem to have forecasting power when applied to the LIFFE cocoa futures prices. This is the only period and data series for which good results in favor of technical analysis are found. 

 

Second moments (volatility clustering) and in section 2.2.3 we showed that our data series also exhibit some autocorrelation. Therefore we further explore the statistical signiÞcance found in the Þrst subperiod by estimating for each trading rule an econometric time series model which incorporates volatility clustering, autoregressive variables and a dummy for buy (sell) days in the regression function. We then determine the percentage of cases for which the dummy coe?cients are signiÞcant, to check whether the trading rules as a group show signs of forecasting power. 

 

This model allows that future volatility depends di?erently on the sign of the current return. The coe?cient θ measures the leverage e?ect. If θ is negative (positive), then a negative (positive) return is followed by larger volatility than a positive (negative) return. Table 2.10 shows the estimation results. The coe?cient θ is signiÞcantly positive. This indicates that there is a positive correlation between return and volatility. Note that this is in contrast with the results found on stock markets and exchange rates where a negative correlation between return and volatility is found, see for example Nelson (1991). The estimation of γ is also signiÞcantly positive and this shows that there is volatility clustering in the data. The (partial) autocorrelation function of the (squared) standardized residuals shows no sign of dependence in the (squared) standardized residuals. Hence we conclude that this model Þts the data well. To explore the signiÞcance of the trading rules after correction for dependence the following regression function in the exponential GARCH model is estimated: rt = α + δ m Dm,t + φ16 rt−16 + ²t ,Nelson (1991) replaces the normal distribution used here with a generalized error distribution. We checked for signiÞcance of the estimated coe?cients. We did diagnostic checking on the standardized residuals, to check whether there was still dependence. We used the (partial) autocorrelation.

 

The results reported in the last section show again that simple trend-following technical trading techniques have forecasting power when applied to the LIFFE series in the period 1983:1-1987:12. In this section we investigate whether the good results found can be explained by some popular time series models like a random walk, autoregressive or an exponential GARCH model using a bootstrap method. The bootstrap methodology compares the percentage of trading rules with a signiÞcantly positive mean buy return, with a signiÞcantly negative mean sell return, with a signiÞcantly positive mean buy-sell di?erence and with a signiÞcantly positive mean buy as well as a signiÞcantly negative mean sell return, when applied to the original data series, with the percentages found when the same trading rules are applied to simulated comparison series. The distributions of these percentages under various null hypotheses for return movements will be estimated using the bootstrap methodology inspired by Efron (1982), Freedman (1984), Freedman and Peters (1984a, 1984b), and Efron and Tibshirani (1986). According to the estimation based bootstrap methodology of Freedman and Peters (1984a, 1984b) a null model is Þt to the original data series. The estimated residuals are standardized and resampled with replacement to form a new residual series. This scrambled residual series is used together with the estimated model parameters to generate a new data series with the same properties as the null model. For each null model we generate 500 bootstrapped data series. The set of 5350 technical trading rules is applied to each of the 500 bootstrapped data series to get an approximation of the distributions of the percentage of strategies with a signiÞcantly positive mean buy return, with a signiÞcantly negative mean sell return, with a signiÞcantly positive buy-sell di?erence and with a signiÞcantly positive mean buy as well as a signiÞcantly negative mean sell return under the null model. The null hypothesis that our strong results found can be explained by a certain time series model is rejected at the α percent signiÞcance level if the percentage found in the original data series is greater than the α percent cuto? level of the simulated percentages under the null model. Random walk process The random walk with a drift is bootstrapped by resampling the returns of the original data series with replacement. If the price series is deÞned as {Pt : t = 1, 2, ..., T }, then the return series is deÞned as {rt = ln(Pt ) − ln(Pt−1 ) : t = 2, 3, ..., T }. 

 

This model Þts the data the best9 . Table 2.12 contains the estimation results of the autoregressive model in the period January 5, 1983 until February 4, 1985 and of the GARCH model in the period February 5, 1985 until December 31, 1987 with the t-ratios within parenthesis. Table 2.12: Coe?cient estimates structural break in trend model The autoregressive model coe?cients estimates 1/5/1983 - 2/4/1985 α φ16 0.001213 0.161887 (1.74) (3.67) The GARCH-model coe?cients estimates 2/5/1985 - 12/31/1987 α φ2 α0 α1 β1 -0.001511 -0.113115 3.85E-06 0.064247 0.905622 (-3.95) (-2.85) (1.48) (1.68) (18.6).

 

Estimates of an autoregressive model on the daily return series of the LIFFE cocoa futures prices in the period January 5, 1983 until February 4, 1985 and of a GARCH model in the period February 5, 1985 until December 31, 1987. The autoregressive model is estimated using OLS and White’s (1980) heteroskedasticity-consistent standard errors. The GARCH model is estimated using maximum likelihood using the Marquardt iterative algorithm and BollerslevWooldridge (1992) heteroskedasticity-consistent standard errors and covariance. The numbers within parenthesis are t-ratios.

 

The returns in the Þrst period show signiÞcantly positive 16-th order autocorrelation, while the returns in the second period show signiÞcantly negative second order autocorrelation. The constant is in the Þrst period signiÞcantly positive at the 10% signiÞcance level, while in the second period it is signiÞcantly negative at the 1% signiÞcance level. This is an indication that the drift is Þrst positive and then negative. With this Þnal bootstrap procedure we can test whether the good results of the technical trading rules can be explained by the trend structure in the data series and the strong autocorrelation in returns.

 

when the complete set of technical trading strategies is applied to the LIFFE cocoa futures prices in the period 1983:1-1997:6. All the results presented are the fractions of simulation results that are larger than the results for the original data series. In panel A the fractions of the 500 bootstrapped time series are reported for which the percentage of trading rules with a signiÞcantly positive mean excess return, with a signiÞcantly positive mean buy return, with a signiÞcantly negative mean sell return, with a signiÞcantly positive mean buy-sell di?erence, and with a signiÞcantly positive mean buy as well as signiÞcantly negative mean sell return at a ten percent signiÞcance level using a one sided t-test is larger than the same percentage found when the same trading rules are applied to the original data series. Panel B on the other hand reports the bootstrap results for the bad signiÞcance of the trading rules. It shows the fraction of the 500 bootstrapped time series for which the percentage of trading rules with a bad signiÞcance is even larger than the percentage of trading rules with a bad signiÞcance at a 10% signiÞcance level using a one sided t-test when applied to the original data series. For the cocoa series the mean excess return is approximately equal to the return on the futures position without correcting for the risk-free interest rate earned on the margin account, because

f e rt = ln(1 + rt +Pt − Pt−1 Pt − Pt−1 Pt − Pt−1 f f f P ost ) − ln(1 + rt ) ≈ rt + P ost − rt = P ost . 

 

Therefore the mean excess return of a trading rule applied to the bootstrapped cocoa series is calculated as the mean return of the positions taken by the strategy, so that we don’t need to bootstrap the risk-free interest rate. We have already seen in table 2.8 that for 34.5% of the strategies the mean excess return is signiÞcantly positive in the Þrst subperiod for the LIFFE cocoa futures series. The number in the column of the random walk results in the row tP erf > tc , which is 0.002, shows that for 0.2% of the 500 random walk simulations the percentage of strategies with a signiÞcantly positive mean excess return is larger than the 34.5% found when the strategies are applied to the original data series. This number can be thought of as a simulated “p-value”. Hence the good results for the excess return found on the original data series cannot be explained by the random walk model. For 26.7% of the strategies the mean buy return is signiÞcantly positive. The fraction in the row tBuy > tc shows that in only 3.2% of the simulations the percentage of strategies with a signiÞcantly positive mean buy return is larger than the 26.7% found in the original data series. However, the fraction in the row tSell < −tc , shows that in 14% of the simulations the percentage of strategies with a signiÞcantly negative mean sell return is larger than the 39.5% of strategies with a signiÞcantly negative mean sell return when applied to the original data.

 

 

series. Thus the random walk model seems to explain the signiÞcantly negative mean sell return. For 46.7% of the strategies the buy-sell di?erence is signiÞcantly positive, but the fraction in the row tBuy−Sell > tc shows that for none of the random walk bootstraps the percentage of trading rules with a signiÞcantly positive mean buy-sell return is larger than this number. 14.7% of the strategies have a signiÞcantly positive mean buy return as well as a signiÞcantly negative mean sell return. The number in the row tBuy > tc ∧ tSell < −tc , which is 0.006, shows that in only 0.6% of the simulations this percentage is larger than the 14.7% found in the original data series. Table 2.9 showed the percentage of strategies with a bad signiÞcance when applied to the original data series. For the LIFFE cocoa futures series in the Þrst subperiod the strategies as a group show no real signs of bad signiÞcance. For 5.9% of the strategies the mean excess return is signiÞcantly negative, for 3.5% of the strategies the mean buy return is signiÞcantly negative, for 3.3% of the strategies the mean sell return is signiÞcantly positive, for 3.3% of the strategies the mean buy-sell di?erence is signiÞcantly negative and for 0.82% of the strategies the mean buy return is signiÞcantly negative and also the mean sell return is signiÞcantly positive. Panel B of table 2.13 shows that under the null of a random walk the strategies as a group perform even much worse. The number in the row tP erf < −tc shows that for 96.4% of the simulations the percentage of strategies with a signiÞcantly negative mean excess return is larger than the 5.9% found in the original data series. For 87% of the simulations the percentage of strategies with a signiÞcantly negative mean buy return is larger than the 3.5% found on the original data series. For 57.2% (96.8%, 34.2%) of the simulations the percentage of strategies with a signiÞcantly positive mean sell (signiÞcantly negative mean buy-sell di?erence, a signiÞcantly negative mean buy as well as a signiÞcantly positive mean sell return) is larger than the 3.3% (3.3%,0.82%) found in the original data series. From the results reported above we can conclude that the good results found when the technical trading strategies are applied to the LIFFE cocoa futures prices in the period 1983:1-1997:6 cannot be explained by a random walk model. Autoregressive process The third column of table 2.13 repeats the previous results under the null of an autoregressive process. Now we can detect whether the good results of the technical trading strategies can be explained by the high order autocorrelation in the data. The results change indeed in comparison with the null of a random walk. Now for 3.8% of the 500 AR bootstraps the percentage of strategies with a signiÞcantly positive mean excess return is larger than the 34.5% found in the original data series. 

 

Simulations the percentage of strategies with a signiÞcantly positive mean buy return (signiÞcantly negative mean sell return) is larger than the 26.7% (39.5%) found in the original data series. Hence the autoregressive model seems to explain the good signiÞcant results of the technical trading rules as a group for selecting buy and sell days. On the other hand the autoregressive model does not explain the results found for the percentage of strategies with a signiÞcantly positive mean buy-sell di?erence and the percentage of strategies with a signiÞcantly positive mean buy as well as a signiÞcantly negative mean sell return. Panel B shows again, as in the case of the null of a random walk, that the strategies as a group perform much worse on the simulated autoregressive data series than on the original data series. We can conclude that the autoregressive model neither can explain the good results of the technical trading rules. Exponential GARCH process The results of the bootstrap procedure under the null of an exponential GARCH model are similar to those under the null of an autoregressive model. Therefore the good results of the technical trading strategies can also not be explained by the leverage e?ect, which is accounted for in the exponential GARCH formulation. Structural break in trend The last column of table 2.13 lists the bootstrap results of applying the set of trading strategies to simulated autoregressive series with a structural change to account for the di?erent trending behavior of the LIFFE cocoa futures prices. The results change completely in comparison with the other null models. For 41.4% of the simulations the percentage of strategies with a signiÞcantly positive mean excess return is larger than the 34.5% found when the same set is applied to the original data series. For 47.8% (52.8%, 24.8%) of the simulations the percentage of strategies with a signiÞcantly positive mean buy (signiÞcantly negative mean sell, signiÞcantly positive mean buy-sell di?erence) return is larger than the 26.7% (39.5%, 46.7%) found when the same set is applied to the original data series. Even for 42.6% of the simulations the percentage of strategies with a signiÞcantly positive mean buy as well as a signiÞcantly negative mean sell is larger than the 14.7% found for the original data series. Hence the Þnal model, which allows a structural change, because there is Þrst an upward trend and then a downward trend in the price series, seems to explain the good results found when the set of technical trading strategies is applied to the LIFFE cocoa futures price series in the period 1983:1-1987:12. Probably the trading rules performed well because of the strong trends in the data. 

 

B shows the bootstrap results for testing whether the bad signiÞcance of the technical trading rules can be explained by the several null models. In the case of the structural break in trend model the results show again that the set of technical trading rules behaves statistically worse when applied to the simulated series than to the original data series. For example in 96% of the simulations the percentage of strategies with a signiÞcantly negative mean excess return is larger than the 5.9% found when the same strategies are applied to the original data series. Despite that the structural break in trend model can explain the statistically signiÞcant forecasting power of the trading rules, also this model cannot explain the good results found when testing for bad signiÞcance of the strategies in the original data series. Thus the original time series has characteristics which causes the trend-following technical trading techniques to show signs of forecasting power, most probably the characteristic of the strong change in direction of the price trend. However this characteristic is not the only explanation, because it cannot explain the relatively low percentage of trend-following technical trading techniques which performed statistically badly on the original time series.

 

The technical trading strategies as a group show economic and statistically signiÞcant forecasting power when applied to the LIFFE cocoa series, especially in the period 1983:11987:12. On the other hand the same technical trading strategies show no sign of forecasting power when applied to the CSCE cocoa series in the same period. The futures contracts di?er in their speciÞcation of quality, currency and place of delivery, but it is surprising that the di?erence in economic and statistical signiÞcance is so large. Why are these di?erences so pronounced? The daily CSCE cocoa returns show somewhat stronger autocorrelation in the Þrst two lags than the LIFFE returns, which suggests more predictability. The variance of the CSCE series is slightly bigger across all subperiods than the variance of the LIFFE series, which may be an indication why trend-following rules have more di?culty in predicting the CSCE cocoa series. However, it seems that this somewhat higher variance cannot explain the large di?erences. For example, in the second subperiod, when the volatility is the strongest across all subperiods for both time series, the trading rules perform almost equally well on the CSCE and LIFFE cocoa futures prices and show forecasting power of the sell days for both series. Hence, there must be some other explanation for the di?erences of technical trading performance. 

 

Cocoa futures prices Þrst exhibit an upward trend from 83:1-84:6 for the CSCE in New York and from 83:1-85:2 for the LIFFE in London, whereas from 85:2-87:12 both cocoa series exhibit a downward trend. The upward trend until mid 84 was due to excess demand on the cocoa market, whereas after January 1986 cocoa prices declined for several years due to excess supply. See for example the graphs of gross crops and grindings of cocoa beans from 1960-1997 in the International Cocoa Organization Annual Report 1997/1998 (see e.g. p.15, Chart I).11 The demand-supply mechanism thus caused the upward and downward trends in cocoa futures prices in the subperiod 1983:1-1987:12. Figure 2.3 suggests that these trends were more pronounced in London for the LIFFE than in New York for the CSCE.

 

Figure 2.3 also showed that the Pound-Dollar exchange rate moved in similar trends in the same subperiod 1983:1-1987:12. More precisely, the Pound-Dollar exchange rate increased (the Pound weakened against the Dollar) from January 1983 to reach its high in February 1985. This caused an upward force on the LIFFE cocoa futures price in Pounds, and a downward force on the CSCE cocoa futures price in Dollars. The LIFFE cocoa futures price also peaked in February 1985, while the CSCE cocoa futures price reached its high already in June 1984. After February 1985, the Pound strengthened against the Dollar until April 1988 and the Pound-Dollar exchange rate declined. This caused a downward force on the LIFFE cocoa futures price in Pounds, but an upward force on the CSCE futures price in Dollars. Until January 1986 the LIFFE cocoa price declined, while the CSCE cocoa price rose slightly. After January 1986 cocoa prices fell on both exchanges for a long time, due to excess supply of cocoa beans. We therefore conclude that, by coincidence, the upward and downward trends in the cocoa prices coincide with the upward and downward trends in the Pound-Dollar exchange rate. For the LIFFE in London the trends in exchange rates reinforced the trends in cocoa futures, whereas for the CSCE in New York the trends in the exchange rates weakened the trends in cocoa futures prices. Table 2.14 shows the cross-correlations between the levels of the three data series across all subperiods. It is well known that if two independently generated integrated time series of the order one are regressed against each other in level, with probability one a spurious, but signiÞcant relation between the two time series will be found.

 

1986). Although the Pound-Dollar exchange rate should be independently generated from the cocoa futures series, it has some impact on the price level of the cocoa series as described above. The table shows that the Pound-Dollar exchange rate is correlated strongly with the level of the LIFFE cocoa continuation series and also (although a little bit weaker) with the CSCE cocoa continuation series. In particular, in the Þrst subperiod 1983:1-1987:12 the Pound-Dollar exchange rate is correlated strongly with the level of the LIFFE cocoa futures series (cross correlation coe?cient 0.88) and also (although a little bit weaker) with the CSCE cocoa futures series (cross correlation coe?cient 0.58). In the other subperiods, there is little cross correlation between the Pound-Dollar exchange rate and the LIFFE and/or the CSCE cocoa futures series. Apparently, due to the accidental correlation (spurious relation) in the period 1983:11987:12 between the Pound-Dollar exchange rate movements and the demand-supply mechanism in the cocoa market, trends in the LIFFE cocoa futures price are reinforced and trends in the CSCE cocoa futures price are weakened. Because the technical trading rules we tested are mainly trend-following techniques, this gives a possible explanation for the large di?erences in the performance of technical trading in the LIFFE and CSCE cocoa futures. In order to explore further the possible impact of the Pound-Dollar exchange rate on the proÞtability of trend-following technical trading techniques when applied to the cocoa data series, we test the trading rules on the LIFFE cocoa price series expressed in Dollars and on the CSCE cocoa price series expressed in Pounds. If the LIFFE and CSCE cocoa futures prices are expressed in the other currency, then the results of testing technical trading strategies change indeed. In order to test for economic signiÞcance table 2.15 lists the percentage of trading rules with a strictly positive mean excess return for all trading rules sets across all subperiods. For the full sample, 83:1-97:6, for the LIFFE cocoa series in Dollars 33.85% (versus 58.34% in Pounds) of all trading rules generate a strictly positive mean excess return, while for CSCE cocoa futures in Pounds 19.30% (versus 12.18% in Dollars) of the trading rules generate a strictly positive mean excess return. Especially in the Þrst subperiod 1983:1-1987:12 the results change dramatically. For the LIFFE cocoa series in Dollars 23.71% (versus 73.25% in Pounds) of all trading rules generate a strictly positive mean excess return, while for CSCE cocoa futures in Pounds 57.93% (versus 14.14% in Dollars) of the trading rules generate a strictly positive mean excess return. Table 2.16 summarizes the results concerning the statistical forecasting power of the trading rules applied to the LIFFE cocoa futures in Dollars and the CSCE cocoa futures in Pounds. The table shows for all periods for both data series the percentage of trading rules generating a signiÞcantly positive mean excess return. The table also shows the percentage of trading rules generating a signiÞcantly positive (negative) mean return during buy (sell) days. Further the table shows the percentage of trading rules for which the mean Buy-Sell di?erence of the data series is signiÞcantly positive and for which buy and sell days at the same time generate signiÞcantly positive respectively negative returns. The table summarizes only the results of one sided tests at the 10% signiÞcance level. The results of table 2.16 should be compared to the corresponding results of table 2.8. For the full sample, the statistical properties of the trading rules applied to the CSCE cocoa series in Pounds are only slightly better than for the CSCE cocoa series in Dollars. For example, only 2.73% (versus 1.38%) of all rules yields a signiÞcantly positive di?erence between Buy-Sell returns. The sell days are predicted better, with 14.25% (versus 5.92% of the trading rules showing signiÞcantly negative mean return during sell days. For the LIFFE series in Dollars the statistical results of the trading rules are poorer than for to the LIFFE series in Pounds. Now only 1.31% of the strategies generate a signiÞcantly positive mean excess return, while this percentage is 13.86% for the LIFFE series in Pounds. The mean Buy-Sell di?erence is signiÞcantly positive only for 5.10% (versus 26.58%) of all trading rules. The trading rules still forecast the sell days well, with 25.97% of the trading rules having signiÞcantly negative mean return during sell days, but not nearly as good as for the LIFFE cocoa series in Pounds for which 50.53% of all rules has signiÞcantly negative mean return during sell days. For the Þrst subperiod the trading rules showed no statistically signiÞcant forecasting power on the CSCE series in Dollars. When applied to the CSCE series in Pounds the results are much better. For example 8.33% (versus 0.92%) of the strategies has a signiÞcantly positive mean excess return. 19.65% (versus 0.77%) of all trading rules has a signiÞcantly negative mean return during sell days. For the buy days most t-ratios stay within the critical values and only 6.13% (versus 1.27%) has signiÞcantly positive returns. For 19.41% (versus 1.46%) of all strategies the mean Buy-Sell di?erence is signiÞcant. The strongly signiÞcant forecasting power of the strategies applied to the LIFFE series in Pounds totally vanishes when applied to the LIFFE series in Dollars. The percentage of trading rules which generates a signiÞcantly mean excess return decreases from 34.52% to 1.03%. For most trading rules the t-ratios of the mean return of the data series during buy or sell days stay within the critical values. Only 1.18% (versus 39.47%) of all trading rules has a signiÞcantly negative mean return during sell days and only 1.70% (versus 26.73%) has signiÞcantly positive returns during buy days. The percentage of strategies for which the mean Buy-Sell di?erence is signiÞcant drops from 46.65% to 2.13%. We conclude that, especially in the Þrst subperiod, the Pound-Dollar exchange rate.

 

Had a strong inßuence on the forecasting power of the trading rules applied to the LIFFE cocoa futures price in Pounds. There is a dramatic change in predictability when the LIFFE cocoa futures price is transformed to Dollars. On the other hand the forecasting power of the strategies on the CSCE cocoa series transformed to Pounds is not as strong as the forecasting power of the strategies applied to the LIFFE cocoa series in Pounds. The Pound-Dollar exchange rate mechanism thus provides only a partial explanation, in addition to the demand-supply mechanism on the cocoa market, of the predictability of trading rules applied to cocoa futures.

 

An important theoretical and practical question is: “What are the characteristics of speculative price series for which technical trading can be successful?” In order to get some insight into this general question from our case-study, it is useful to plot the price and returns series all on the same scale, as shown in Þgure 2.4. The returns series clearly show that the volatility in the Pound-Dollar exchange rate is lower than the volatility in both cocoa futures series. Furthermore, the price series on the same scale show that the trends in the LIFFE cocoa series are much stronger than in the CSCE cocoa series and the Pound-Dollar exchange rate. One might characterize the three series as follows: (i) CSCE has weak trends and high volatility; (ii) LIFFE has strong trends and high volatility, and (iii) Pound-Dollar has weak trends and low volatility. Recall from section 5 that the performance of technical trading may be summarized as follows: (i) no forecasting power and no economic proÞtability for CSCE; (ii) good forecasting power and substantial net economic proÞtability for LIFFE, and (iii) good forecasting power but no economic proÞtability for Pound-Dollar. Our case-study of the cocoa futures series and the Pound-Dollar exchange rate series suggest the following connection between performance of technical trading rules and the trend and volatility of the corresponding series. When trends are weak and volatility is relatively high, as for the CSCE cocoa futures series, technical trading does not have much forecasting power and therefore also cannot lead to economic proÞtability. Volatility is too high relative to the trends, so that technical trading is unable to uncover these trends. When trends are weak but volatility is also relatively low, as for the PoundDollar exchange rates, technical trading rules can have statistically signiÞcant forecasting power without economically signiÞcant proÞtability. In that case, because volatility is low technical trading can still pick up the weak trends, but the changes in returns, although predictable, are too small to account for transaction costs. strong and volatility is relatively high, as for the LIFFE cocoa futures series, a large set of technical trading rules may have statistically signiÞcant forecasting power leading to economically signiÞcant proÞt opportunities. In that case, the trends are strong enough to be picked up by technical trading even though volatility is high. Moreover, since volatility is high, the magnitude of the (predictable) changes in returns is large enough to cover the transaction costs.

 

In this chapter the performance of a large set of 5350 technical trading rules has been tested on the prices of cocoa futures contracts, traded at the CSCE and the LIFFE, and on the Pound-Dollar exchange rate in the period 1983:1-1997:6. The large set of trading rules consists of three subsets: 1990 moving average, 2760 trading range breakout and 600 Þlter strategies. The strategies perform much better on the LIFFE cocoa prices than on the CSCE cocoa prices, especially in the period 1983:1-1987:12. In this period a large group of the trading rules applied to the LIFFE cocoa futures price has statistically signiÞcant forecasting power and is economically proÞtable after correcting for transaction costs. Applied to the CSCE cocoa futures series the trading rules show little forecasting power and are not proÞtable. The forecasting power of the strategies applied to the Pound-Dollar exchange rate in the period 1983:1-1997:6 is also statistically signiÞcant, but most trading strategies are not proÞtable. The large di?erence in the performance of technical trading in the LIFFE or CSCE cocoa futures contracts may be explained by a combination of the demand/supply mechanism in the cocoa market and the Pound-Dollar exchange rate. In the period 1983:11987:12 the price level of the cocoa futures contracts and the level of the Pound-Dollar exchange rate were, accidentally, strongly correlated. This spurious correlation reinforced upward and downward price trends of the LIFFE cocoa futures contracts in London, while weakening the price trends of the CSCE cocoa futures contracts in New York. For the LIFFE cocoa futures price series the trends are strong enough to be picked up by a large class of technical trading rules; for the CSCE cocoa futures price series most trading rules do not pick up the trends, which are similar to the trends in the LIFFE cocoa futures but weaker. We also performed a bootstrap analysis showing that benchmark models such as a random walk, an autoregressive and an exponential GARCH cannot explain the good performance of the technical trading rules in the period 1983:1-1987:12. However a structural break in the trend model cannot be rejected as explanation of the results. Apparently many technical trading rules are able to pick up this structural break in trend.

 

For the period 1993:1-1997:12 we Þnd that the forecasting power of the technical trading strategies applied to the cocoa futures prices and the Pound-Dollar exchange rate is much less than in the preceding period 1983:1-1992:12. This is in line with many papers that found that forecasting power of trading strategies tends to disappear in the 1990s. Although the present chapter only documents the economic and statistical performance of technical trading rules applied to a single commodity market, some general conclusions that may be useful for other Þnancial series as well are suggested by our case-study. First, in order to assess the success or failure of technical trading it is useful to test a large class of trading rules, as done in this chapter. A necessary condition for reliable success of technical trading seems to be that a large class of trading rules, not just a few, should work well. If only a few trading rules are successful this may simply be due to “chance” or to data snooping. It should also be emphasized that even if a large class of trading rules has statistically signiÞcant forecasting power this is not a su?cient condition for economically signiÞcant trading proÞts after correcting for transaction costs. An example is the Pound-Dollar exchange rate for which a large fraction of trading rules exhibits statistically signiÞcant forecasting power, but these trading rules hardly generate economic net proÞtability. Our case-study of the cocoa futures series and the Pound-Dollar exchange rate series suggest a connection between the success or failure of technical trading rules and the trend and volatility of the corresponding series. When trends are weak and volatility is relatively high, technical trading does not have much forecasting power and therefore also cannot lead to economic proÞtability. Technical trading is unable to uncover these trends, because volatility is too high. When trends are weak but volatility is relatively low, technical trading rules can have statistically signiÞcant forecasting power without economically signiÞcant proÞtability. In that case, because volatility is low technical trading can still pick up the weak trends, but the changes in returns, although predictable, are too small to account for transaction costs. Finally, when trends are strong and volatility is relatively high, a large set of technical trading rules may have statistically signiÞcant forecasting power leading to economically signiÞcant proÞt opportunities. In that case, even though volatility is high the trends are strong enough to be picked up by technical trading. Moreover, since volatility is high, the magnitude of the (predictable) changes in returns is large enough to cover the transaction costs. We emphasize that this connection between predictive and economic performance of technical trading is suggestive and only documented by the market studied here. Further research, of interest from a theoretical as well as a practical viewpoint, is needed to uncover whether the success and failure of technical trading is explained by the relative magnitudes of trend and volatility.

 

Chapter 3: Technical Trading and DJIA Listed Stocks In 1884 Charles Dow started to construct an average of eleven stocks, composed ofnine railroad companies and only two non-railroad companies, because in those days railroad companies were the ?rst large national corporations. He recognized that railroad companies presented only a partial picture of the economy and that industrial companies were crucial contributors to America’s growth. “What the industrials make the railroads take” was his slogan and from this he concluded that two separate measures could act as cocon?rmers to detect any broad market trend. This idea led to the birth of the DowJones Railroad Average (DJRA), renamed in 1970 to Dow-Jones Transportation Average, and to the birth of the Dow-Jones Industrial Average (DJIA). The DJIA started on May 26, 1896 at 40.94 points and the DJRA started on September 8, 1896 at 48.55 points. Initially the DJIA contained 12 stocks. This number was increased to 20 in 1916 and on October 1, 1928 the index was expanded to a 30-stock average, which it still is. The only company permanently present in the index, except for a break between 1898-1907, is General Electric. The ?rst 25 years of its existence the DJIA was not yet known among a wide class of people. In the roaring twenties the DJIA got its popularity, when masses of average citizens began buying stocks. It became a tool by which the general public could measure the overall performance of the US stock market and it gave investors a sense of what was happening in this market. After the crash of 1929 the DJIA made front-page headlines to measure the overall damage in personal investments. The DJIA has been published continuously for more than one hundred years, except for four and a half months at the beginning of World War I when the New York Stock Exchange (NYSE) closed temporarily. Nowadays the DJIA is the oldest and most famous measure of the US stock market. The DJIA is price weighted rather than market weighted, because of the technology in Charles Dow’s days. It is an equally-weighted price average of 30 blue-chip US stocks, each of them representing a particular industry. When stocks split or when the DJIA is revised by excluding and including certain stocks, the divisor is updated to preserve historical continuity. Because the composition of the DJIA is dependent on the decision which stocks to exclude and to include, the index would have a completely di?erent value today, if the DJIA constructors had made di?erent decisions in the past. People criticize the Dow because it is too narrow. It only contains 30 stocks out of thousands of public companies and the calculation is simplistic. However it has been shown that the DJIA tracks other major market indices fairly closely. http://www.400190.com/jr/

 

laid the foundation of “the Dow Theory”, the ?rst theory of chart readers. The theory is based on editorials of Charles H. Dow when he was editor of the Wall Street Journal in the period 1889-1902. Robert Rhea popularized the idea in his 1930s market letters and his book “The Dow Theory” (1932). Although the theory bears Charles Dow’s name, it is likely that he would deny any allegiance to it. Instead of being a chartist, Charles Dow as a ?nancial reporter advocated to invest on sound fundamental economic variables, that is buying stocks when their prices are well below their fundamental values. His main purpose in developing the averages was to measure market cycles, rather than to use them to generate trading signals. After the work of Hamilton and Rhea the technical analysis literature was expanded and re?ned by Richard Schabacker, Robert Edwards and John Magee, and later by Welles Wilder and John Murphy. Technical analysis developed itself into a standard tool used by many to forecast the future price path of all kinds of ?nancial assets such as stocks, bonds, futures and options. Nowadays a lot of technical analysis software packages are sold on the market. Technical analysis newsletters and journals ?ourish. Every bank employs several chartists who write technical reports spreading around forecasts with all kinds of fancy techniques. Classes (also through the internet) are organized to introduce the home investor in the topic. Technical analysis has become an industry on its own. For example, the questionnaire surveys of Taylor and Allen (1992), Menkho? (1998) and Cheung and Chinn (1999) show that technical analysis is broadly used in practice. However, despite the fact that chartists have a strong belief in their forecasting ability, for academics it remains the question whether it has any statistically signi?cant forecasting power and whether it can be pro?tably exploited also after accounting for transaction costs and risk. Cowles (1933) considered the 26-year forecasting record of Hamilton in the period 1903-1929. He found that Hamilton could not beat a continuous investment in the DJIA or the DJRA after correcting for the e?ect of brokerage charges, cash dividends and interest earned when not in the market. On 90 occasions Hamilton announced changes in the outlook for the market. It was found that 45 of his changes of position were unsuccessful and that 45 were successful. In a later period, Alexander (1964), and Fama and Blume (1966) found that ?lter strategies, intended to reveal possible trends in the data, did not yield pro?ts after correcting for transaction costs, when applied to the DJIA and to individual stocks that composed the DJIA. The in?uential paper of Fama (1970) reviews the theoretical and empirical literature on the e?cient markets model until that date and concludes that the evidence in support of the e?cient markets model is very extensive, and that contradictory evidence is sparse. From that moment on the e?cient markets hypothesis (EMH), which states that it is not possible to forecast the future price movements of a ?nancial asset given any information set, is the central paradigm in ?nancial economics. The impact Fama’s (1970) paper was so large, that it took a while before new academic literature on technical trading was published. The extensive study of Brock, Lakonishok and LeBaron (1992) on technical analysis led to a renewed interest in the topic. They applied 26 simple technical trading strategies, such as moving averages, and support-and-resistance strategies, to the daily closing prices of the DJIA in the period 1897-1986, nearly 90 years of data. They were the ?rst who extended simple standard statistical analysis with parametric bootstrap techniques, inspired by Efron (1979), Freedman and Peters (1984a, 1984b), and Efron and Tibshirani (1986). It was found that the predictive ability of the technical trading rules found was not consistent with a random walk, an AR(1), a GARCH-in-mean model, or an exponential GARCH. The strong results of Brock et al. (1992) were the impetus for many papers published on technical analysis in the 1990s. Although numerous papers found evidence for economic pro?tability and statistically signi?cant forecasting power of technical trading rules, they did acknowledge the problem of data snooping. This is the danger that the results of the best forecasting rule may just be generated by chance, instead of truly superior forecasting power over the buy-andhold benchmark. It could be that the trading rules under consideration were the result of survivorship bias. That is, the best trading rules found by chartists in the past get most attention by academic researchers in the present. Finally White (2000), building on the work of Diebold and Mariano (1995) and West (1996), developed a simple and straightforward procedure, called the Reality Check (RC), for testing the null hypothesis that the best model encountered in a speci?cation search has no predictive superiority over a given benchmark model. Sullivan, Timmermann and White (1999) utilize the RC to evaluate a large set of approximately 7800 simple technical trading strategies on the data set of Brock et al. (1992). They con?rm that the results found by Brock et al. (1992) still hold after correcting for data snooping. However in the out-of-sample period 1986-1996 they ?nd no signi?cant forecasting ability for the technical trading strategies anymore. Hansen (2001) shows that the RC is a biased test, which yields inconsistent p-values. Moreover, the test is sensitive to the inclusion of poor and irrelevant models. Further the test has poor power properties, which can be driven to zero. Therefore, within the framework of White (2000), Hansen (2001) derives a test for superior predictive ability (SPA). In this chapter we test whether objective computerized trend-following technical trading techniques can pro?tably be exploited after correction for transaction costs when applied to the DJIA and to all stocks listed in the DJIA in the period 1973:1-2001:6.

 

Furthermore, we test whether the best strategies can beat the buy-and-hold benchmark signi?cantly after correction for data snooping. This chapter may be seen as an empirical application of White’s RC and Hansen’s SPA-test. In addition we test by recursively optimizing our trading rule set whether technical analysis shows true out-of-sample forecasting power. In section 3.2 we list the stock price data examined in this chapter and we show the summary statistics. Section 3.3 presents an overview of the technical trading rules applied to the stock price data. Section 3.4 describes which performance measures are used and how they are calculated. In section 3.5 the problem of data snooping is addressed and a short summary of White’s RC and Hansen’s SPA-test is presented. Section 3.6 shows the empirical results. In section 3.7 we test whether recursively optimizing and updating our technical trading rule set shows genuine out-of-sample forecasting ability. Finally section 3.8 concludes.