Automated Foreign Exchange Trading Strategies: Improving Performance Without Strategy Modification

Automated Foreign Exchange Trading Strategies: Improving Performance Without Strategy Modiﬁcation

Degree Project in Computer Science

DENNIS EKSTRÖM TOBIAS WIKSTRÖM

Bachelor’s Thesis at KTH CSC Supervisor: Pawel Herman Examiner: Örjan Ekeberg

2014-04-29

ABSTRACT Trading indicators are frequently used among foreign exchange traders in attempts to predict future market events. Automated trading strategies can easily be implemented to act on such predictions.

Motivated by a curiosity about whether the use of trading indicators could be improved without actually changing the indicators themselves, this study was conducted in an attempt to investigate opportunities in enhancing strategy profits by restricting strategies from trading during periods deemed as unfavorable.

However, conditionally restricting strategies’ trading capabilities by introducing thresholds for strategy activation did not show significant effects on the performance. By examining the accumulated strategy profits both with and without applied thresholds, it was derived that the general characteristics of the performance were withheld. Consequently, it cannot be concluded that this study provides a reliable method of enhancing profits through applying restrictions to foreign exchange strategies.

Nevertheless, the effects from applying thresholds to strategies, albeit not mainly profitable in this study, motivates further research on advantages from conditionally restricting foreign exchange strategies.

TABLE OF CONTENTS

1. Terminology ………………………………………………………………………………………………………………..3 2. Introduction………………………………………………………………………………………………………………...5 2.1 Problem Definition………………………………………………………………………………………….5 2.2 Aims and Scope ………………………………………………………………………………………………5 3. Background…………………………………………………………………………………………………………………6 3.1 Moving Average Convergence-Divergence (MACD)………………………………………….7 3.2 Linear Regression Trend Channel (LRTC)………………………………………………………..8 3.3 Similar Studies ………………………………………………………………………………………………..9 4. Method…………………………………………………………………………………………………………...... 10 4.1 Implementing the Strategies………………………………………………………………………….10 4.1.1 MACD Strategy………………………………………………………………………………...11 4.1.2 LRTC Strategy………………………………………………………………………………….13 4.2 Backtesting and Retrieving Results………………………………………………………………..16 4.2.1 Analysis on Profitable Periods………………………………………………………….16 4.2.2 Strategy Performance and Market Patterns……………………………………...16 4.2.3 Strategy Activation………………………………….……………………………………….16 4.2.4 Backtesting With Thresholds……………………………………….…………………...18 5. Results…………………………………………….……………………………………….………………………………..18 5.1 Backtest……………………………………….……………………………………………………………….18 5.2 Market Patterns ……………………………………….…………………………………………………...19 5.3 Strategy Performance Correlations……………………...………………………………………...20 5.4 Optimization of strategies ……………………………………….……………………………………..22 6. Discussion…………………………………………….……………………………………….…………………………..23 6.1 Method……………………………………….………………………………………………………………...23 6.2 Results……………………………………….…………………………………………………………………23 6.3 Limitations……………………………………….…………………………………………………………...25 6.4 Conclusion……………………………………….……………………………………………………………26 8. References…………………………………………….……………………………………….………………………….27

1. TERMINOLOGY Backtesting The process of testing a trading strategy on prior time periods.

Breakaway A sudden increase in market momentum, causing the market to abandon ongoing trends.

Crossover The action of a numerical value changing sign (e.g. going from positive to negative).

Forex Foreign exchange

Fractal A type of pattern used in technical analysis to predict a reversal in the current trend. The fractal value is the market rate at the time of reversal.

Indicator Statistical tool used to measure current conditions as well as to forecast financial or economic trends.

Instrument A currency pair. Conventionally written on the format XXX/YYY where XXX is the base currency and YYY is the quote currency (e.g. EUR/USD).

Leverage The use of various financial instruments or borrowed capital, such as margin, to increase the potential return of an investment. Leverage is expressed as the ratio between the actual invested amount and the money put into the trade by the trader.

Liquidity The availability of assets in a market. High liquidity means a higher chance of executing a trade with low slippage.

Long position An executed buy order.

Lot 100,000 units of the quote currency in a forex trade.

M5 Five minutes. The format (M1, M5, H1, etc.) is conventionally used by brokers to represent data of specific intervals.

Market momentum A measure of overall market sentiment, calculated as the change in market rate multiplied by the aggregate trading volume.

Pip 1/10,000th of the rate unit.

Point 1/10th of a pip.

Position An executed market order.

Rate The quotient of the base currency and the quote currency for a given

instrument.

Recoil The event of the rate rapidly changing direction at a specific price.

Resistance level A rate considered unlikely for the rate to climb above.

Short position An executed sell order.

Slippage The difference between the expected price of a trade, and the price the trade actually executes at.

Spread Difference between ask and bid rate.

Stop-loss An order placed with a broker to close a position when it reaches a certain price, as a precaution if the market would head in the unintended direction.

Support level A rate considered unlikely for the rate to fall below.

Take-profit An order placed with a broker to close a position when it reaches a certain price, defining a level at which to lock in profits.

Technical Analysis The academic study of historical market trends and patterns, performed with the purpose of forecasting future market development.

Tick The change in the price of an instrument from trade to trade.

Timeframe The period of the data used for analysis.

Trading strategy A programmatically implementable algorithm with the ability to open and close market positions.

Trend The general direction of a market or of the price of an asset.

2. INTRODUCTION One could reasonably argue that widely used technical analysis indicators earned their popularity from historically providing good market predictions. However, fundamental properties of financial markets contradict the existence of a widely used and ever correct indicator. The reason is that an indicator being known to the public to always give perfect predictions would cause the market liquidity to drop and the rate to potentially experience massive fluctuations in an attempt to adjust to supply and demand (Shefrin, 2002). Accordingly, it would be mindless to believe that popular indicators, such as historical rate averages and various trend identifiers, could generate large profits in the long run.

Consequently, as popular indicators seem unlikely to show long run profits, their popularity may have been gained from historically proven abilities to perform well during certain periods in time. If this was the case, traders would benefit from being able to identify and characterize such profitable periods (Murphy, 1999). Such analysis of multiple indicators would provide knowledge about what indicator is preferable at specific points in time. Furthermore, performing such analysis on indicators that have been derived from fundamentally different ideas and assumptions could increase the chances for a trader to frequently be able to choose a trustworthy indicator. These arguments are reasonable as fundamentally different indicators are more likely to perform well during periods of different market conditions, such as high volatility, consolidation or other market patterns, than indicators based on similar grounds.

Given the approach of analysis presented above, this study was motivated by a curiosity about whether the use of existing indicators could be improved without actually changing the indicators themselves. Instead, ignoring the indications given during periods deemed as unreliable for a specified indicator was seen as the potential source of improvement. Such an approach to enhance profits of indicator based trading strategies would differ fundamentally from the ideas of the vast majority of strategies (Larsen, 2010). While classical strategy development is concerned with assumptions on a market’s mathematical properties or psychological impact from traders (Chen, 2009), the strategy development conducted in this study would mainly depend on the fact that there exists strategies which occasionally performs well.

2.1 PROBLEM DEFINITION How can automated foreign exchange trading strategies that are based on widely used indicators within the field of technical analysis be conditionally restricted to enhance profits?

2.2 AIMS AND SCOPE Evidently, one of the motivating factors for conducting studies within the field of technical analysis inherits from the fact that knowledge in the area increases chances of one’s personal success as a trader. Naturally, potential monetary revenues that could emerge from results of the study could not be neglected as an incentive to conduct it. However, the main purpose of this study is to gain knowledge within the field of technical analysis in financial markets and to explore progressive

5 techniques in indicator and strategy design. Specifically, by characterizing profitable periods for specific indicators, the study aims to present an innovative trading analysis approach that makes use of already existing indicators and strategies.

In conclusion, the aim of the study is to investigate an alternative approach in indicator analysis and trading strategy improvement. The main purpose being learning, as opposed to monetizing, corresponds to the fact that the results of this study is publicly available, since publishing a trading strategy may affect its performance due to changed market conditions caused by the strategy itself.

The study does not rely on any particular strategy performing well individually. As it aims to find similarities in the periods of successful strategy performance, it is more important that each strategy performs well on occasion. Although the discussion will not go into depth in analyzing the risk of the chosen strategies never performing well, that risk is assumed to be negligible simply due to the extensive use of the indicators that the strategies in this study are based on.

3. BACKGROUND Trading the foreign exchange market has become increasingly popular over the last couple of years. Huge trading volumes, high leverage and low margins, has made the market attractive to financial organizations as well as private investors. Frequent activity on forex web forums and a vast amount of material being published on the subject of technical analysis of the forex market indicate a widespread belief in the market being predictive to some degree if appropriate tools are applied. Accordingly, numerous approaches to trading strategy design have been taken in attempts to automate successful trading systems. Variants of well known indicators, such as moving averages and trend channels, are commonly used in strategy development, but alternative approaches such as genetic algorithms that evolve to maximize profits, or neural networks that “learn” to do so, are growing in popularity. (Rosén, 2011)

As the study aims to investigate opportunities in optimal use of strategies based on commonly known indicators, emphasis has been put on researching indicators that would generally be referred to as basic indicators. These indicators are founded on ideas that are fairly easily understood and that do not require much trading experience or mathematical expertise.

The view on whether the fact that an indicator being widely used affects its reliability varies among technical analysts. Writing about technical indicators in general, Neely and Weller (2011) indicates that continuous development of indicators is necessary by arguing that profit opportunities will generally exist in financial markets, but that learning and competition will gradually erode these opportunities. However, opposite views are introduced by Marshall and Moubray (2005), as they present the major strength of common indicators as the fact that they are widely used and thus self-fulfilling to some extent. Moreover, full-time trader McDonald (2010) agrees with the theoretical concept of self-fulfilling indicators, but dismisses any substantial effects in practice due to the numerous ways of using a specific indicator. Given these three different standpoints, it would be hard to make any assumptions on whether the strategies being used for this study would perform well on its own over a period of time. Taking the standpoint of Neely and Weller, the strategies, 6 being based on commonly known indicators, would most probably show mediocre performance. However, taking the standpoint of Marshall and Moubray, such strategies are likely to be successful given that the used indicators are indeed commonly used. Consequently, no assumptions are being made regarding the strategies’ individual long-term performances.

Since this study aims to investigate strategies based on widely used indicators, research regarding such indicators was conducted. The following sections presents the fundamentals of the MACD and LRTC indicators.

3.1 MOVING AVERAGE CONVERGENCE-DIVERGENCE (MACD) A moving average is the arithmetic mean of data observations equally spaced in time. As new data is available, the average is recomputed by appending the new data and removing the oldest data from the series.

In technical analysis, moving averages are commonly used as indicators to highlight trends and momentum in the currency market. Popular variations of this indicator includes simple and exponential moving averages, as well as moving average convergence-divergence.

The Moving Average Convergence-Divergence (MACD) indicator is possibly the most widely used variation of the moving average indicators, mainly because of its versatility. MACD is defined as the difference between two Exponential Moving Averages (EMA), one reflecting a short-term trend subtracted by another reflecting a long-term trend, these periods are generally set to 12 and 26 timeframes. By analyzing the characteristics, such as the slopes and crossovers, of a MACD indicator, current trends and patterns in the market can be derived. Additionally, another EMA is applied to the MACD curve itself, called the signal line, usually interpreted such that whenever the signal line crosses the MACD, a directional change in the market is soon about to happen. (Appel & Appel, 2008)

figure 1: Visualization of the MACD indicator on EUR/USD, showing the EMA’s used for calculation, the MACD itself and the signal line.

Possible benefits of MACD come from its characteristics being able to identify both momentum and trend. The indicator will eventually follow the movements of a currency pair if given enough time. The immediate drawback would be potentially slow adjustment times to sudden changes in the market. Since MACD uses absolute subtraction in its calculation, a long-term analysis comparison of two MACD levels is potentially deceptive in cases when the currency pair has had an exponential change. (Murphy, 1999)

3.2 LINEAR REGRESSION TREND CHANNEL (LRTC) A trend channel consists of two linear trend lines, commonly referred to as support and resistance lines. In the case of LRTC, each of these lines are calculated using the least square of local extreme points, peaks for the resistance and troughs for the support trend line. This way, in the event of a downward trend (as depicted in figure 3), the resistance line connects a series of low highs (peaks in a downward trend) while the support line connects a series of low lows (troughs in a downward trend).

According to technical analysis theories, the rate will be trapped inside the lines, recoiling from both

8 levels, or breaking through one, causing the market to break away from the area of congestion.

Trend channels are thought to be the most common method of identifying trends in the currency market; this is primarily because of its intuitive visualization of a trend, giving distinct points of directional market changes to an eventual trading strategy’s algorithm. (Rosén, 2011)

figure 2: Visualization of LRTC, including the Stop-loss, Take-profit levels, and high and low fractals (blue/red arrows).

3.3 SIMILAR STUDIES Prominent studies concerning the subject of optimizing automatic trading strategies tend to construct optimal strategies by adjusting input parameters to reach optimal backtesting performance. Maymin & Maymin (2011) aim to provide traders with a general framework for constructing the best strategy for a given historical indicator by interpreting strategies as mathematical functions. In short, claiming to enhance the performance of any strategy by maximizing the corresponding function.

Optimization utilities are included in multiple trading platforms. Such tools optimizes strategies by

9 running them on historical data numerous times, modifying the input parameters to obtain the highest net profit.

What separates this study from other studies is mainly its approach to add an exterior constraint to existing strategies as opposed to modifying them or optimizing their input parameters.

4. METHOD The method of this report can shortly be summarized to consist of the following components:

● Implementation of two simple strategies, each being based on one indicator.

● Backtesting of the strategies on historical data from Jan 1, 2005 to Dec 31, 2008.

● Analysis regarding during what periods the strategies were profitable.

● Analysis to find correlations between strategy performance and market patterns.

● Implementation of constrained strategies that takes such correlations into account during execution by applying thresholds that prevent the strategies to open orders when the market conditions are deemed as unfavorable.

● Backtesting of the strategies with and without applied thresholds on historical data from Jan 1, 2009 to Dec 31, 2012.

In accordance with the generality of the problem definition, the chosen course of action was developed in an attempt to define a procedure that could be applied to any strategy. The above steps are intended to present an approach to how widely used indicators can be analyzed to find market patterns during which the indicator performs well. Finding such patterns enables development of conditional restrictions (further referred to as thresholds) to enhance strategy profits, providing an answer to the problem definition. Accordingly, the method of choice was considered appropriate for the study.

The two initially developed trading strategies were based on the two conceptually different publicly known and widely used indicators, MACD and LRTC, respectively (Schlossberg, 2006) . The backtesting of these two strategies was then performed using the EUR/USD instrument for the period of Jan 1, 2005 to Dec 31, 2012, a period considered long enough to eliminate major abnormalities in the data set caused by large financial events. Moreover, the EUR/USD currency pair was considered to have sufficient volatility to provide significant strategy activity during backtesting. Further details on the course of actions are described in detail below.

4.1 IMPLEMENTING THE STRATEGIES The strategies were written in MQL4, a script language specifically designed for MetaTrader 4, a trading platform common among traders and supported by multiple brokers. Both strategies were implemented to act on every market change being broadcasted by the broker; this is referred to as

10 acting on every tick.

A common trading amount was set to 0.1 lots for each trade, using a leverage of 200. In practice, this means a traded amount of 50 USD per trade, reacting to market changes enhanced by a factor of 200.

The two indicators to base the strategies on were chosen to be:

● Moving Average Convergence-Divergence (MACD)

● Linear Regression Trend Channel (LRTC)

The MACD strategy was implemented using the iMACD indicator, available in the MQL4 indicator library, whereas the trend channel indicator and strategy were implemented without use of existing library indicators. Having the sole purposes of opening buy or sell positions in accordance with the indications from the corresponding indicator, the strategies were simply tools to apply the indicator output in the market. The logic that defines the strategies, representing one indicator each, is presented below.

4.1.1 MACD STRATEGY The MACD indicator follows a widely used convention (Murphy, 1999) of using 12 bars for the short-term EMA interval and 26 bars for the long-term EMA interval. The bar period used for execution was M5.

For each trade made by the strategy, a trailing stop-loss was set to 3 pips and a static take-profit set to 5 pips. Trailing meaning that the stop-loss was updated to never be more than 3 pips from the current market rate. This was achieved by moving the stop-loss in the direction of the trade as the rate changes.

Additionally, a moving average applied on the 26 bar interval determines whether the market rate has upwards or downwards momentum.

The underlying logic of the MACD strategy was specified as follows:

A buy order is executed if:

● The MACD value is negative, and

● the MACD value has just crossed the signal line in the positive direction, and

● the MA of the long-term period has upwards momentum.

A sell order is executed on the exact opposite conditions, that is if:

● The MACD value is positive, and

● the MACD value has just crossed the signal line in the negative direction, and

● the MA of the long-term period has downwards momentum.

A close order on an open buy position is executed if:

● The MACD value is positive, and

● the MACD value has just crossed the Signal Line in the negative direction.

figure 3: Buy order scenarios and their respective close order scenarios for the MACD strategy.

A close order on an open sell position is executed if:

● The MACD value is negative, and

● the MACD value has just crossed the signal line in the positive direction.

figure 4: Sell order scenarios and their respective close order scenarios for the MACD strategy.

All open orders may also be closed as a result of the rate crossing the specified take-profit or trailing stop-loss.

Lastly, a condition was set to disallow the strategy having more than one open position. This was simply implemented such that potential buy or sell signals were ignored if an order was already open.

4.1.2 LRTC STRATEGY The implemented LRTC indicator uses high and low fractals (defined in terminology) as estimations of peaks and troughs in order to calculate the high and low linear regression trend lines.

The strategy considers fractals among the 72 previous M5 bars, motivated by the assumption that five hours are enough to get a reasonably large set of fractals for the M5 period and thus determine a reliable channel (Schlossberg, 2006). Both trend lines were calculated using conventional linear regression on the two sets of fractals. As the main purpose of the strategy was to trade in accordance with the indications from an LRTC indicator, the ideas of the implementation were based on the assumptions that trends are common market patterns and that the rate has a tendency to stay between the two trend lines. The conditions listed below were constructed with the intent of

13 achieving such trading behavior.

Conditions that must be fulfilled in order to consider opening a position are:

● There must be at least two high fractals, forming the high trend line.

● There must be at least two low fractals, forming the low trend line.

● Both trend lines must slope in the same direction (positive or negative slope).

● In the case of an upward trend, the slope of the low trend line must be at least 5 points per M5 period.

● In the case of a downward trend, the slope of the high trend line must be at least -5 points per M5 period.

● The vertical difference between the current trend line rates is at least 10 pips.

Given that the above conditions are fulfilled:

A buy order is executed if:

● The slope of both lines are positive, and

● the current rate has just crossed the low trend line in the negative direction.

A sell order is executed if:

● The slope of both lines are negative, and

● the current rate has just crossed the high trend line in the positive direction.

The triggering conditions for opening a position relies on the assumed tendency for the rates to stay inside the channel.

A close order on an open buy position is executed if:

● The current rate has just crossed the stop-loss

● the current rate has just crossed the take-profit.

A close order on an open sell position is executed if:

● The current rate has just crossed the stop-loss

● the current rate has just crossed the take-profit.

figure 5: Buy order scenarios and their respective close order scenarios for the LRTC strategy. Includes the scenario where a close order is caused by the stop-loss line.

Similar to the MACD strategy, a condition was set to disallow the strategy having more than one open position. This was simply implemented such that potential buy or sell signals were ignored if an order was already open.

Furthermore, an open position is continuously adjusted with regard to stop-loss and take-profit:

● The stop-loss is updated to:

o Stay 3 pips below the current low trend line rate in the case of a long position.

o Stay 3 pips above the current high trend line rate in the case of a short position.

● The take-profit is updated to stay at the rate between the current trend line rates.

The update was necessary for the strategy to fulfill its purpose of acting in accordance with the trend channel indicator since the trend slopes and the rates are expected to stay between the trend lines.

4.2 BACKTESTING AND RETRIEVING RESULTS Backtesting of strategies were done using the MetaTrader backtesting utility to generate a report with position openings and closings, order types and profits for each trade. The backtesting was performed on tick data in an attempt to achieve as realistic results as possible. However, as spreads rely on market liquidity that would be affected by trades performed by the strategy itself, historical liquidity cannot be simulated. Thus, a constant spread of 1 pip was set on the grounds that spreads in the EUR/USD market commonly lies around this level.

Both strategies were run on historical data of the period Jan 1, 2005 to Dec 31, 2008. The period of Jan 1, 2009 to Dec 31, 2012 was spared for future backtesting of the theories developed using the result from the first period. This approach was taken in an attempt to minimize the risk of the analysis ending up in mere curve fitting (Larsen, 2010).

4.2.1 ANALYSIS ON PROFITABLE PERIODS When determining during what periods strategies should be active to maximize profits, trades for each strategy were grouped such that profits from orders that were placed within the same hour were summed together, representing the total profits for that strategy and hour. The hour intervals were considered as the minimum time unit for a strategy to be active for. In practice, this would imply restricting a strategy to trade only during the interval, yet allowing it to modify already open positions outside the interval (such as adjusting the stop-loss and take-profit). The decision to group profits made within the same hour was made in order to limit the amount of data to handle for the analysis. As the study aims to recognize strategy behavior in periods of different market conditions, an assumption was made that an hour, given the eight year test period, is a small enough time unit for many significant changes in market patterns to be noticeable.

4.2.2 STRATEGY PERFORMANCE AND MARKET PATTERNS The output resulting from the analysis on profitable periods were illustrated visually in charts that were programmed to show market rates as well as the accumulated profit (the sum of all previous hourly profits) for each strategy. This utility was implemented to provide a visual representation of the data gathered up until this point in order to assist in the attempts to find correlations between market patterns and strategy performance.

4.2.3 STRATEGY ACTIVATION For each strategy, the visual representation of the market rates and strategy performance was examined to identify market patterns during which the strategy performed well. The identified market patterns were interpreted numerically such that strategy profit and the value depicting the market conditions were assumed to correlate (this value will further be referred to as the strategy’s correlation quantity). For each hour of historical data, the strategy performance was plotted against its correlation quantity for the same period. The result was examined to determine a threshold, defined in terms of the value depicting the market conditions, which had to be exceeded for the strategy to be active.

The correlation quantity for the MACD strategy was chosen as the standard deviation of the close rates of the previous 72 M5 bars. In the same way, the correlation quantity for the LRTC strategy was chosen as the absolute value of the slope of the linear regression trend line of the close rates of the previous 72 M5 bars. The reasoning behind these decisions are described in the results section.

figure 6: Visualization of the period where correlation quantity is calculated (red) and the current active strategy period (green). The time vector (x-axis) is described in discrete one hour intervals and the y-axis is the EUR/USD rate.

The threshold values for each strategy, being defined in terms of the strategy’s correlation quantity, was determined by the following procedure:

● The trades for each strategy were sorted descendingly with regard to the strategy’s correlation quantity corresponding to each trade.

● The profits were then accumulatively summed together, such that the accumulated profit for each trade was the sum of all profits of trades with a higher or equal correlation quantity.

● The threshold was chosen as the lowest correlation quantity of the trades with a positive accumulated sum.

Choosing the threshold this way was considered reasonable as the total profits of the backtest period were clearly negative (see result section for further details), although the total profits for the trades with a correlation value higher than or equal to the threshold were positive, indicating that market conditions were more profitable with a correlation quantity above the threshold.

The threshold for the correlation quantity of the LRTC strategy (being the absolute value of slope of the linear regression trend channel from the last 72 M5 bars as previously described) was calculated analogously as the relation between the slope and profits was similar to the corresponding relationship of the MACD strategy.

4.2.4 BACKTESTING WITH THRESHOLDS Finally, after calculating threshold values assumed to improve strategy performance, backtesting was done on the period of Jan 1, 2009 to Dec 31, 2012. The result from the final backtesting provides an indication to whether the assumed correlations between strategy performance and market patterns have any validity or if the correlations were simply the outcome of mere curve fitting over the Jan 1, 2005 to Dec, 31 2008 period.

5. RESULTS Conducting the previously described method, results where established and are presented below. Most results are presented in charts or tables to be easily assimilated.

5.1 BACKTEST The backtest result, depicted in figure 7, shows the accumulated profits (being significantly negative) for the MACD and LRTC strategy during the period Jan 1, 2005 to Dec 31, 2008.

figure 7: Backtest results. Accumulated profits for strategies MACD and LRTC during the period Jan 1, 2005 to Dec 31, 2008.

5.2 MARKET PATTERNS With the obtained backtest result, the strategies’ profits were plotted parallel to the market rates to provide a visual representation of what market conditions seemed favorable for each strategy.

figure 8: Market rates with accumulated profits for strategies MACD and LRTC during the period Jan 1,2005 to Dec 31, 2008.

Indications were that the MACD strategy generated higher profits during volatile periods, and the LRTC strategy generated higher profits during trending periods. As mentioned in the methods section, the correlation quantities were chosen as follows:

● The correlation quantity for the MACD strategy was chosen as the standard deviation of close prices of the last 72 M5 bars , being a measurement of market volatility for the last six hours.

● The correlation quantity for the LRTC strategy was chosen as the absolute value of the slope of the linear regression trend line of the close prices of the previous 72 M5 bars, being a measurement of market trend tendencies for the last six hours.

5.3 STRATEGY PERFORMANCE CORRELATIONS The MACD (figure 9) and LRTC (figure 10) strategy profits were plotted in scattered graphs, to visualize a potential correlation between the profit and its correlation quantity.

The correlation quantity thresholds for each strategy, which were chosen in accordance with the procedure described in the methods section, are specified below and represented in figure 9 and 10 with blue vertical lines.

● MACD standard deviation threshold: 0.00209

● LRTC linear regression trend line slope threshold: 0.00013

figure 9: Profits for each hour by the MACD strategy, plotted against the standard deviation calculated for the close rates of the 72 M5 bars previous to the start of that hour.

figure 10: Profits for each hour by the LRTC strategy, plotted against the slope of the linear regression trend line for the close rates of the 72 M5 bars previous to the start of that hour.

The Pearson correlation between the strategies’ profits and their correlation quantities are depicted in table 2, together with the confidence interval of the pearson correlation value.

Pearson Correlation Confidence interval of Strategy Correlation Quantity Value (PCV) PCV*

MACD Standard Deviation 0.0274 [0.0034, 0.0515]

LRTC Trend Line Slope 0.0160 [–0.0039, 0.0360] table 2: The Pearson Correlation Values for the assumed correlations between strategy profits and correlation quantities. * Assuming normal distribution and a confidence level of 95%.

5.4 OPTIMIZATION OF STRATEGIES The accumulated profit for the MACD and LRTC strategies using their respective correlation quantity threshold are represented in figure 10 together with the respective strategies without a threshold. The LRTC strategy with a threshold showed a higher accumulated profit than the same strategy without a threshold, while the MACD strategy with a threshold showed a lower accumulated profit than the same strategy without a threshold.

figure 11: Accumulated profits of MACD and LRTC with and without applied thresholds during the period of Jan 1, 2009 to Dec 31, 2012.

6. DISCUSSION Analysis and thoughts regarding methodology, results and limitations of this study are presented below. Many of the addressed subjects and concerns originates from the fact that the time provided to conduct the study was limited. In general, better accuracy and more trustworthy results could naturally have been achieved given more time to examine the subject further.

6.1 METHOD Since the study aims to investigate an alternative approach in strategy development, the conclusion would preferably be presented as a general effect on strategy performance from taking the developed approach in an attempt to optimize any strategy. However, the method in this study cannot be considered general enough to expect such an outcome. Firstly, none of the two developed strategies, MACD and LRTC, can be guaranteed to show similar performance if any of the parameters for the strategy were changed or if the strategy implementation was adjusted due to different interpretations on how to best respond to indications from the initially chosen indicators. Moreover, the performance further relies on the period for which the backtesting was performed on and, fundamentally, what two indicators that were chosen for this study to begin with.

The method used to derive correlations between market patterns and strategy performance should be considered a potential source of inaccuracy. Knowledge of strategy implementation when searching for correlations between market patterns and strategy profit introduces the risk of a confirmation biased conclusion regarding what correlation is the most prominent. A more trustworthy approach would be to utilize an algorithm to find correlations. However, although this risk is important to note, it was assumed to have a small impact on this study since the two strategies used were implemented based on common indicators, each with documented behavior in various market patterns.

Due to the many factors potentially affecting the outcome of this study, the methodology should not be considered a general recipe to optimize any trading strategy, but rather as a method to gather information to be used in eventual further analysis regarding strategy performance improvement.

6.2 RESULTS The initial backtesting of the two strategies, depicted in figures 7 and 8, shows poor performance with no tendencies of making profit before 2008. However, going into 2008, both strategies begin to produce profits. This could be an effect of the dramatic market change caused by the financial crisis during the period. It is important to note that strategy profitability is of low importance in this study since it aims for improvement rather than explicit profits. However, variations in strategy performance over different periods are important in the process of finding correlations between strategy performance and market patterns.

Before going into details about the result, it is important to note that any strategy active in the foreign exchange market would affect the market as every trade has an impact on market liquidity.

As previously stated, the effects from this phenomena are nearly impossible to simulate and results from backtesting must therefore be viewed as potentially misleading. However, due to the relatively small trading amount used to conduct this study, the strategies’ effects on market liquidity are negligible.

Moreover, the constant spread used for the backtesting poses a potential error as it does not reflect a real market situation. The effects from applying constant spread cannot be assumed to be negligible. However, as the constant spread of 1 pip was based on average spreads for the EUR/USD instrument the long term effects should be small as profits from low spreads should even out losses from high spreads.

The final backtest result (shown in figure 11) indicates that the introduction of thresholds did not have a significant effect on strategy performance. From studying the performance with and without thresholds, it can be derived that the general characteristics of the performance were withheld. One could assume that the impact from applying thresholds would differ depending on the strategy and period, but to draw such a conclusion would require analysis of more sample strategies and more historical data.

As the thresholds were determined from backtesting over the period of Jan 1, 2005 to Dec 31, 2008, they naturally had a positive effect on strategy performance during that period. This is shown in figure 12 (below), which clearly indicates a positive impact from applying the threshold. However, no positive impact is indicated in figure 11, showing the same results but for the period of Jan 1, 2009 to Dec 31, 2012. This can be viewed as an example of curve fitting for the interval initially used to develop theories. It is completely rational that threshold values, causing occasional deactivation of strategies, show positive results when backtests are ran over a period for which the general trend of the original strategy was clearly negative. However, if the thresholds were merely blocking trades at random, strategies with active thresholds would simply cause the accumulated profits to be closer to zero than the same strategies without thresholds, regardless of whether the strategy was profiting or losing. Figure 11 indicates that this is not the case since the general characteristics of the strategy performance were withheld with active thresholds during the shown period. Thus, even if the thresholds were not able to enhance profits of an already profiting strategy, indications are that the thresholds used for this study had some sort of relevance for strategy performance, rather than just randomly blocking trades. Further, comparing figure 11 and 12, it is reasonable to believe that the thresholds in this study could have an ability of cutting of the really bad periods with none or only a small tradeoff in profits during profitable periods.

figure 12: Accumulated profits of MACD and LRTC with and without applied thresholds during the period of Jan 1, 2005 to Dec 31, 2008.

6.3 LIMITATIONS Certain aspects regarding the study were estimated to have an impact on the result of varying degree. The most limiting factor is the fact that no more than two widely used indicators have been subject to analysis. As factors such as indicator parameters, choice of currency pair and the chosen time interval for backtesting the strategies naturally affect the results of this study, limitations in the implementation of strategies and indicator parameters were necessary to consider. Only simple approaches to indicator-based strategies have been pursued in order to gain the most representative depiction on two of the most common public indicators used in strategies during the 2005-2012 period.

Rationally, using a larger set of in indicators and including more advanced strategies, would potentially have lead to different, more detailed, results and a more substantial conclusion as to how strategies can be optimized to maximize profit. However, taking more indicators and strategies into account would require a greater amount of time assigned for this study.

Another limitation that was applied was the fact that the only instrument used was EUR/USD. Also, the period for historical testing was limited to the years 2005-2012 and the strategy profits were analyzed on an hourly basis, meaning that profits from trades initiated within the same hour were summed together. These limitations were established since EUR/USD is the largest instrument regarding trading volumes, hence being likely to provide high liquidity, low spreads and minimal impact from fundamental analysis (Schlossberg, 2006). Moreover, the decision to analyze on an hourly basis was motivated by the needs for a substantial quantity of data in order to perform the analysis for characterizing strategy behavior, still limiting the data to some extent. As the used

25 indicators are highly scalable according to the technical analysis interpretation (Chen, 2009), the period intervals were not viewed as problematic.

Lastly, having indicators depending solely on technical analysis, no impact of fundamental analysis on the EUR/USD market has been taken into account in the results and analysis. This introduces a potential risk of misleading results caused by aspects such as corporate and political events affecting the currency market.

6.4 CONCLUSION The result indicates that the conditional restrictions applied in this study, being thresholds for strategy activation, did not have a significant effect on strategy performance. From studying the accumulated profits both with and without thresholds, it can be derived that the general characteristics of the performance were withheld. Consequently, it cannot be concluded that this study provides a reliable method of enhancing profits through applying restrictions to foreign exchange strategies.

Expecting significant increases in profit would not be reasonable without using more reliable methods for analyzing the correlations between strategy performance and market patterns. However, albeit being small, the impact from applying simple conditional restrictions, such as the thresholds developed in this study, motivates further research on advantages from conditional restrictions.

To conclude, this study can be viewed upon as introducing a new approach to develop and apply conditional restrictions with a future potential of improving performance of foreign exchange strategies.

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Chen, J. (2009). Essentials of Foreign Exchange Trading. Hoboken, New Jersey: John Wiley & Sons, Inc.

Larsen I., J(2010). Predicting Stock Prices Using Technical Analysis and Machine Learning, Norwegian University of Science and Technology.

Marshal, K., & Moubray, R. (2005). Practical Fibonacci Methods for Forex Trading. Forex Systems Research Company.

Maymin, P. Z., & Maymin, Z. G (2011). Constructing the Best Trading Strategy: A New General Framework. New York: NYU-Polytechnic Institute.

McDonald, N (2010). Fibonacci Retracements. www.traders-mag.com.

Murphy, J. (1999). Technical Analysis of the Financial Markets. New Jersey: Prentice Hall Press.

Neely, C. J., & Weller, P. A. (2011). Lessons from the Evolution of Foreign Exchange Trading Strategies . St. Louis: FEDERAL RESERVE BANK OF ST. LOUIS.

Rosén, T. (2011). Winning Trading. Kristianstad: Vinnarbyrån.

Ruggiero Jr., M. A. (2011). How to backtest trading systems and avoid curve fitting. Futures Magazine.

Shefrin, H. (2002). Beyond Greed and Fear: Understanding Behavioral Finance and the Psychology of Investing. Oxford University Press.

Schlossberg, B. (2006). Technical Analysis of the Currence Market. Hoboken, New Jersey: John Wiley & Sons, Inc.