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73 Seiten, Note: A
The emergence of technical trading
The academic community’s attitude towards technical trading
The efficient market hypothesis
Data snooping and pre-testing bias
II. Problem Statement
Returns and the significance of technical trading rules
Can econometric models explain the patterns of technical trading?
Is there an optimal simple trading rule?
III. Literature Review
The profitability of technical trading rules – Early results
Confirmatory Research about Technical Trading Rules
Brock, Lakonishok and LeBaron (1992)
Levich and Thomas (1991)
Ratner and Leal (1999)
Evidence for Declining Returns of Trading Rules in Recent Sub Periods
Sullivan, Timmermann and White (1999)
The issue of trading costs
Simple Technical Trading Rules
Variable length moving average (VMA) rules
Fixed length moving average (FMA) rules
Trading Range Break (TRB) rules
The statistical significance of technical trading rules
Random Walk Null Model
AR(1) Null Model
AR(1)-GARCH(1,1) Null Model
V. Empirical results
Why future contracts?
Returns of VMA strategies
Returns of FMA strategies
Returns of TRB strategies
Negative standard deviation assessment
Time Series Dependencies
Are there optimal trading rule parameters?
Appendix – Program Code
Most banks and the recently upcoming hedge fund industry rely to a different extent on technical trading rules and technical analysis. The fact that these technical trading rules yield superior returns in practice raises several questions that will be examined in the thesis. First, one of the most crucial questions is in which assets technical trading rules perform extraordinarily well. This analysis is based on a risk-return approach with an assessment of the negative standard deviation of each asset as a risk indicator. Second, the statistical significance of technical trading is examined by using a simulation method known as bootstrap. Third, null models are simulated to answer the question to what extent autoregressive models and GARCH models are able to capture the dependencies in the time series. Finally, a rule optimizer is used to assess if any rule parameters yield superior returns over a wide range of assets.
We find that under a risk-return perspective trading rules look very attractive as most rules are able to significantly reduce the negative standard deviation compared to a buy-and-hold strategy. However, not all rules are able to outperform a simple buy-and-hold strategy in terms of absolute return. Statistical significance is generally weak and only some rules can be qualified as highly statistically significant. We do not find much evidence that autoregressive and GARCH null models perform well in capturing the dependencies that lead to superior returns of technical trading rules. With respect to trading rule parameters we find that shorter rules generally perform better when trading costs are not considered and that currencies benefited from a larger standard deviation trading band.
List of Tables
Table 1: Summary Statistics
Table 2: VMA Strategy – Mean Results
Table 3: FMA Strategy – Mean Results
Table 4: TRB Strategy – Mean Results
Table 5: VMA Strategy – Negative Standard Deviations
Table 6: FMA Strategy – Negative Standard Deviations
Table 7: TRB Strategy – Negative Standard Deviations
Table 8: AR(1) and AR(1)-GARCH(1,1) Null Model Bootstrap Test
Table 9: Optimal Trading Rule Parameter Results
List of Figures
Figure 1: 50 days moving average with trading signals
Figure 2: Local maximum line with trading signal
Figure 3: Histogram of actual DJIA returns and two simulated series
Figure 4: Unconditional PNLs vs. trading rule PNLs
Figure 5: Actual and simulated coffee future series
The past years at international stock markets have been characterized by increased activity of so called hedge funds and a significant increase of bank’s trading floor activity. Compared to past decades, banks are increasingly hiring quantitative analysts, often educated on a PhD level in sciences such as mathematics, physics, engineering or economics. What determines the need for these “Quants” and why have they only been hired in recent years in such a large number by banks and hedge funds?
One rationale for the increase in quantitative staff is the emergence of complex derivative products such as exotic options or synthetic swaps in today’s financial markets. Pricing these products involves complex mathematical equations and forecasting models that can only be handled by specialised staff.
A second reason can be found in the emergence of technical trading systems that aim to outperform other trading strategies by solely relying on quantitative investment criteria. In essence these systems do not assess any market information other than past quantitative characteristics such as prices or volatility.
Although technical trading grew significantly in past years and has become a big source of income for banks and hedge funds, the concept is far away from being something new. In fact, technical trading is often considered to be the first form of trading at stock markets, applied long before financial disclosure information enabled market participants to trade on fundamentals rather than on past prices.
To answer the question why technical trading has been booming over the past years, an obvious answer can be found in the technical revolution with the rise of computer based trading that was not possible in earlier years. While simple technical trading rules did not require strong computing power or could even be calculated without large computer systems, a whole new generation of sophisticated models is in use today often involving supercomputing systems to derive an investment decision or a trading signal. Today, state of the art computer systems are able to perform extremely complex calculations in a time that is sufficient for models that include much more variables and equations than ever been used before. In addition to extended computer power capacities, new and more powerful data storage solutions today provide an amount of backward-analyzable data not known until the 1990’s.
Not only the technical equipment available to analyse stock markets has increased; it was also the rise of whole new interdisciplinary disciplines and theories that changed trading towards a more technical approach. Most notably, physicist in the 1990’s started the sub-field of Econophysics in an attempt to explain financial time series and other economic data by using concepts that were previously only used to explain natural phenomena. Trading systems, for example, were built around the concept of gravity and velocity where volatility is inversely proportional to gravity and the change of prices is modelled as velocity (see Ingber and Mondescu, 2001, for such a trading model). While Econophysics remains a relatively small research area, financial engineering, the use of engineering concepts in finance, has gained increased popularity. Top universities such as Berkeley or Princeton today offer specialised master courses for this scientific mixture.
Although one can say that finance is increasingly becoming integrated with other scientific disciplines, technical trading as a market strategy is regarded with huge suspicion by the scientific finance community. Basically, two points of technical trading are criticised. The first refers to the efficient market hypothesis and is of theoretical nature while the second problem referred to as “data snooping” is related to the way empirical results from technical trading are obtained; both will be discussed subsequently here.
The efficient market hypothesis introduced by Fama (1970) can be separated into three different forms: the strong form, the semi-strong form and the weak form. Under the weak form, current prices only reflect information contained in all past prices. Contrary, the semi-strong form assumes that current prices reflect information not only of past prices but also all publicly available information such as financial statements, analyst reports and newspaper articles. Under the strong form, current prices reflect all information; no matter if it is of public or of private nature.
What follows from these definitions, is the fact that fundamental analysis based on the assessment of companies’ key figures such as cash flows or ratios should be possible under the paradigm of a weak form efficient market because the actual price of an asset would not only be defined by its past prices but also by publicly available information, i.e. fundamental data. Contrary, technical analysis that does not take fundamentals into account, significantly contradicts any form of the efficient market hypothesis.
To restate all forms of the efficient market hypothesis in other words one could say that past prices alone should never be enough information to outperform any stock market with any trading strategy. The conjecture that past price information alone might be enough to reach superior performance will be evaluated by the technical trading strategies applied in this thesis.
A second point often raised against technical trading is the possible application of data snooping by empirical researchers that analyse data. Data-snooping, also sometimes referred to as pre-testing bias, refers to the finding of artificial patterns that show a statistically significant relationship to each other. When such a relationship is found and this is then used to formulate a theory or a research question afterwards, researchers qualify this type of work as data snooping. Although few if any empirical tests in finance are free of pre-test biases as discussed by Leamer (1978), the sole mass of data available for technical trading rules creates a big suspicion towards sensational returns sometimes reported by applying technical trading rules.
To minimize the risk of data snooping, one has to come up with as many tools and convincing arguments as possible to mitigate the issue. With respect to the empirical studies conducted in this thesis, several approaches will be followed.
First, we will apply the same trading rules for all assets that are going to be tested. This means that there is no ex-ante calibration of trading rules to reach superior performance.
Second, the trading rules applied in this thesis are not newly designed rules but rather taken from reliable academic papers. Returns are computed in a way that makes easy comparison with other papers in the area applicable.
Third, the thesis is focussed on simple trading rules, i.e. we do not try to describe advanced models from the area of Econophysics or artificial intelligence. We thereby implicitly assume that our trading rules are at the lower end of the possible return horizon as there is most likely additional optimization room for any rule outlined.
Fourth, we apply a bootstrap approach, inspired by Efron (1979) and applied in a similar fashion as in this thesis by Brock et al. (1992). The bootstrap approach will be explained in more depth in the following chapters. As for now, its outstanding characteristic is the fact that all trading rules are not only tested against one real time series but rather against a large number of simulated time series that exhibit similar characteristics as the original time series.
Three simple trading rules are tested in this thesis: variable length moving average (VMA) rules, fixed length moving average (FMA) rules, and trading range break (TRB) rules. The exact parameters and the market forces that might explain these rules are further discussed in Section IV. As for now, it is sufficient to know that both moving average trading rule families provide a trading signal when the moving average of a short time horizon (e.g. one day) breaks through the moving average of a longer time horizon (e.g. 50 days). Contrary, the trading range break rule emits a signal when a local maximum or minimum was reached, e.g. when the stock price moved to a level, higher than observed in any of the preceding 100 days.
The rest of the thesis is organized as follows: Chapter II outlines the research problems covered in this thesis. In Chapter III literature about technical trading rules is discussed and important findings are summarized. Chapter IV explains the methodology of the empirical analysis and Chapter V presents the findings of the empirical tests. Chapter VI contains a brief summary and conclusions.
As a matter of fact trading rules are widely used by banks as can be seen by the numerous publications about the topic that all major banks publish. From an academic point of view, however, the question remains how significant the returns of these rules are. Obviously, technical trading contradicts the efficient market hypothesis but there are also other fundamental principles related to the efficient market hypothesis that are challenged by possible superior returns of technical trading rules.
Modern finance theory was founded by Louis Bachelier in his doctoral dissertation “Théorie de la Spéculation” (1900). One fundamental assumption of Bachelier’s work is that prices follow a random walk, i.e. the likelihood of a price rise on the next day is equal the likelihood of a price fall on the next day given the current price. As Bachelier wrote in his dissertation:
“The exchange reacts to itself, and the current trading is a function, not only of prior trading, but also of its relationship to the rest of the market. It is thus impossible to hope for mathematical forecasting. Contradictory opinions about these variations are so evenly divided that at the same instant buyer expect a rise and sellers a fall.”
Opening lines of “Théorie de la Spéculation”, Quoted in Mandelbrot and Hudson (2004)
In essence, technical trading should not be possible as there is no given higher likelihood for rising or falling prices. Subsequent theories were founded on Bachelier’s work such as Markovitz’s portfolio theory (1952), the capital asset pricing model developed by Sharpe (1964) and the option pricing formula introduced by Black and Scholes (1973).
Consequently, any phenomenon that challenges fundamental principles of modern finance will be assessed with big scrutiny. With respect to technical trading, opponents are keen to point out exceptional circumstances such as that a superior return from one asset over one observed time frame is more likely to be pure luck than a proof for working technical trading. We therefore have to find statistical tests that indicate with a certain probability that one technical trading rule is not only able to outperform a buy-and-hold strategy once but to a higher statistically significant degree, for example in 95 per cent of the cases. Consequently we perform multiple statistical tests for different assets and report all results obtained from our tests.
A second area of interest is the determinants that may be the source for successful technical trading rules. Models such as autoregressive processes or the generalized autoregressive constant heteroskedasticity (GARCH) model that will be explained later in this thesis might be able to capture the determinants that lead to a superior performance of technical trading rules. Basically, these models take past prices or past volatility into account. If prices are not independently identical distributed (IID) as assumed in random walk models, these models might explain the performance of trading rules. We will therefore define various econometric models as null models under the hypothesis that they are able to explain technical trading pattern and generate artificial time series from these models. Then, we will test our trading rules against these models to derive a conclusion to the question to what extent the models are able to contribute to the performance of technical trading rules. Afterwards we will calculate probability statistics to assess how often econometric models reached returns from technical trading that outperformed the returns of an actual stock market series.
As discussed earlier we put strong emphasis on the mitigation of data snooping issues. Because of that we will only apply widely used standard technical trading rules for the initial tests, not varying trading rule parameters in any way. Nevertheless, we will report the results of some brute force computing exercises to show the best achieved return based on the variation of trading rule parameters. Our interest in this section is not the absolute return of the found trading rule but rather an answer to the question if brute force computing can find similar optimal parameters for different assets. Furthermore, we will assess if the common rules used in earlier research papers underestimate the returns of technical trading significantly. This would be the case if we find better trading parameters for a broad range of different assets.
This section provides an overview of research undertaken in the field of simple technical trading rules. After providing a short historical summary of early results, we present evidence for the success of the rules as well as counter-evidence that questions the usefulness of trading rules, especially in recent years. The literature review is not limited to any specific market or any specific time period but puts careful attention to recent results because different researchers independently confirmed a declining performance of simple trading rules in various markets. At the end of the section we finally provide an overview of research concerning the important issue of transaction costs and present break even transaction cost levels.
The first author that confirmed a possible profitability of technical trading rules was Alexander (1961). In a subsequent article published three years later, Alexander (1964) accounts for trading costs in technical trading. As soon as these costs are taken into account, the author finds a disappearing profitability of the rules. Similar findings are obtained by Fama and Blume (1966) who do not find successful trading rules for US equity markets once trading costs are considered. As capital markets have significantly changed in past decades we will not discuss these early results in much detail. Especially trading costs were significantly higher in the 1960’s and 1970’s before the commission deregulation that was undertaken in May 1975.
One of the widely recognized papers about the profitability of technical trading rules was written by Brock et al. in 1992. The fact that the paper was published in the prestigious and extensively read Journal of Finance most likely contributed to the success of this paper. Based on this article, succeeding research was undertaken and part of the empirical section of this thesis is based on the research methodology of Brock et al..
The paper tests two popular trading strategies, the moving average strategy and the trading range break strategy, both by utilizing long term daily Dow Jones Industrial Average index data. The full sample tested by the authors consisted of 25,026 observations and covered the index period from 1897 to 1986. In addition to technical rule-testing, the authors employed t-statistics and a bootstrap methodology to test for statistical significance and to simulate various null models. Thus, the innovation of the article lies in the combination of trading rules with null model bootstrap testing. As the authors acknowledge: “Neither the bootstrap methodology nor the use of technical analysis to evaluate model specifications are in particular new to finance literature. The contribution of this paper lies in the combination of these two techniques.”
To evaluate the returns of technical trading rules, the authors create a universe of 26 trading rules, consisting of 10 variable length moving average (VMA) rules, 10 fixed length moving average (FMA) rules, and 6 trading range break (TRB) rules. To further refine their findings Brock et al. divide one of the VMA rules into four sub-periods to evaluate the performance of technical trading over time. Results of the rules applied are striking: For the VMA strategy, the average one-day return of all rules was 0.042 per cent, resulting in a yearly return of about 12 per cent. Compared to a buy-and-hold strategy that would have returned approximately 5 per cent per year, this represents a significant excess return. The best VMA rule 1-50-0.01 (short moving average one day, long moving average 50 days, one per cent trading band) would have returned impressive 13.2 per cent p.a. over the whole time horizon. With respect to different sub-periods, the period between 1915 and 1938 slightly outperformed the other periods. However, there is no general observable trend of declining returns with respect to the rules examined. All rules are highly significant, soundly rejecting the null hypothesis that technical rules do not produce useful signals.
The universe of FMA rules results in an even higher average return of about 15 per cent per year. However, only 7 of the 10 rules are significant on a 5 per cent level with the other 3 rules being only marginally significant. The largest return obtained by the 5-150-0 FMA rule amounts to 20.8 per cent each year. This return was obtained with only 133 signals over the complete time horizon, an observation that will turn out to be remarkable later when transaction costs are discussed in detail.
The six TRB rules were able to gain a yearly return of about 18 per cent with the best rule returning approximately 24 per cent on average each year. All TRB rules were significant and according to the authors the results for sub-periods were very similar but not presented to save space.
Overall, the paper presents strong evidence for superior returns of simple technical trading rules in equity markets. Although, trading costs were not explicitly discussed, the excess returns of up to 19 per cent compared to a buy-and-hold strategy let us conclude that there should be reasonable space to deduct trading costs from these returns while still outperforming the market.
The paper by Levich and Thomas focuses on the foreign exchange futures market in the period 1976 to 1990. Similar to Brock et al. (1992), Levich and Thomas apply a bootstrap methodology to test for statistical significance. Overall, the authors find a highly unusual rate of return for their trading rules with 39 out of their 45 rules being significant at a 5 per cent level. Yearly returns for moving average and trading range break rules are lower compared to the equity market findings of Brock et al.. However, it should be noted that average excess returns are only an indicator for the successful application of trading rules and trading costs. The absolute return can often be altered by using financial derivatives such as futures that allow trading with high leverage, i.e. doing trades on large amounts with little money.
The paper finds, depending on the currency combination an average return between 2.7 and 9.0 per cent for VMA rules and a 2.0 to 8.1 per cent return for FMA rules, both on an annual basis. Overall the largest profit of 11.2 per cent p.a. is reported for a 5-20-0 VMA rule with Deutsch Mark / US Dollar trading.
Levich and Thomas estimate the trading costs for a one-way transaction to be between 2.5 and 4.0 basis points. Although the amount of trades needed for each rule differs, even the rule with the most trades (70 trades per year) would only have caused trading costs between 1.75 and 2.8 per cent. Regarding different sub-periods, the authors find a declining rate of return of many rules for the last period between 1986 and 1990.
In addition to the return tests, possible explanations why trading rules in the foreign exchange market work, are given. One reason the authors explain is central bank intervention that tends to change the direction of exchange rate movements. When these changes are strong and undertaken over some time, moving average rules can benefit from it. Another reason mentioned are speculative bubbles that cause prices to follow in one direction for some time. Both, moving average and trading range break rules can potentially benefit from these bubbles.
 Yearly returns are calculated by dividing the total number of observations by years under observation and then multiplying the result by daily log-returns. Yearly returns therefore do not necessarily imply 252 trading days as often used in today’s calculations.
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