Directional Movement - Backtest Results and Implementation Issues

Directional Movement - Backtest Results and Implementation Issues
Discusses basic issues and results when attempting to back-test the Directional Movement formula.

Data: S&P500 Emini Futures
Futures Contract Rollover: Arbitrarily set on second Friday of every Mar, Jun, Sep and Dec
Period: 28 Dec 2008 - 31 Mar 2012 (Hourly Chart)
VBA Code: Method B of Code
Excel Version: 2010

Note: 1) As with the Aroon Indicator, the Directional Movement can be used for other time frames and not necessarily daily data as is the context when I wrote the Directional Movement explanation page.

2) The directional movement indicator refers to an implementation of the directional movement formula. What this page attempts to do is to backtest the directional movement formula, not the directional movement index and also not the directional movement indicator. Return to the technical analysis page for links to the respective indicators, codes and backtest results. 

Click here for background information, formula, calculation steps and the entire VBA code.

There are multiple variations on how to apply an indicator. I seek your understanding that the work done below are experiments and are for information purposes only.

Results Summary
Divergence does not signify that a trend is forming in the hourly charts based on my dataset. I inverted this trading rule and arrived with a strategy that is profitable before transaction costs, as expected. Given the large number of trades generated, the naive trading rule applied will most likely not be profitable after costs. The interesting fact is that this is the second or third indicator I found where the  usual trading rule I read from other sources has to be inverted in order for the strategy to even show before transaction cost profitability.

Procedure in Brief

Pasted the code into Excel with changes made as per comments in code to direct application to ranges with input data (High, Low, Close columns). Screen Shot 1 shows the output (the last four columns).

Screen Shot 1

Detailed Findings and Results

Summary of Trading Rules -

1) Calculate Positive DM Minus Negative DM. Recall that Negative DM is a positive value. Negative refers to the fact that a new low was created in the current bar. 

2) If (Positive DM Minus Negative DM) is greater than 0, Long 

3) If (Positive DM Minus Negative DM) is lower than 0, Short

4) Else maintain long or short position

517 index points of profit (before transaction costs) were generated on a large set of 6,687 trades. Average return is very small at just 0.08 points per trade, which means that such an application will not cover trading costs for most people (I guess?). 59% of trades were profitable. Standard deviation of returns for each trade is 4.93 points. The profit trajectory of this indicator and trading rules is shown in Chart 1. 

Chart 1: Cumulative Profit of Strategy (Before Costs)

Conclusion

Although this application of the DM generated a lot of trades, just like my attempt with the Aroon Indicator, the trading rule in this case did not generate statistically significant profitability based on the student t statistic. The low per trade profitability of this approach negated the statistical effect of a large number of trades in reducing standard error. I end this post at this juncture as we will be using this Directional Movement formula in various forms when backtesting the directional movement index and the directional movement indicator. More can be elaborated then. 

Any suggestions or comments are welcome. 

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Aroon Indicator / Oscillator - Backtest Results and Implementation Issues

Aroon Indicator / Oscillator AI / AO - Backtest Results and Implementation Issues 
Discusses basic issues and results when attempting to back-test the AI and the AO indicators

Data: S&P500 Emini Futures
Futures Contract Rollover: Arbitrarily set on second Friday of every Mar, Jun, Sep and Dec
Period: 28 Dec 2008 - 31 Mar 2012 (Hourly Chart)
VBA Code: Method B of Code
Excel Version: 2010

Note: When I wrote the post for the Aroon Indicator VBA code, I wrote it in the context as though the Aroon Indicator and Oscillator can only be used on a daily basis. This is not necessarily always the case. In this case, I used the Aroon Indicator on the same hourly data as with all other backtests. 

Click here for background information, formula, calculation steps and the entire VBA code.

There are multiple variations on how to apply an indicator. I seek your understanding that the work done below are experiments and are for information purposes only.

Summary of Results 

While the Aroon Indicator has been described as a "trend" type indicator, I found that it behaves more as a price reversion indicator in the context of hourly data. Like the adaptive price zone (APZ) indicator, commonly known applications of the Aroon Indicator turned out to be loss making, requiring an inversion of the trading rule. While the Aroon Indicator (and the final trading rules used) is profitable before transaction costs, the key challenge lies with tweaking it to be profitable AFTER costs. Average profit per trade is only 0.2 index points per trade. 

Procedure in Brief

Pasted the code into Excel with changes made as per comments in code to direct application to ranges with input data (High, Low, Close columns). Screen Shot 1 shows the output (the last two columns).  

Screen Shot 1

Detailed Findings and Results
Period is set at 5 - This means that the formula looks at only the last five hours of data in the calculation of current hour Aroon Indicator value.

Summary of Trading Rules -

1) If Aroon Up is larger than Aroon Down at the end of each hour, SHORT in the next hour
2) If Aroon Down is larger than Aroon Up at the end of each hour, LONG in the next hour.
3) Otherwise, carry forward previous hour's position.

This set of trading rules generated 869.5 index points of profit (before transaction costs) on a large set of 4,146 trades. Average return per trade is 0.210 points on a standard deviation of 6.328 points. The success rate of this strategy is very high. 63.9% of the trades were profitable (before transaction costs and slippage). The profit trajectory of this indicator and trading rules is shown in Chart 1.

Chart 1: Aroon Indicator Cumulative Profit (Before Costs)

Conclusion

This set of trading rules and the indicator used generated a lot of trades. As a result, the standard error of the mean return is very small due to the formula used, which is standard deviation of returns of each trade divided by the number of trades. In turn, standard statistical distributions, such as the student t-statistic and normal z-statistic are significant when computed for this strategy. 

However, I have my doubts over the significance of these statistics. Due to the long tail nature of financial data, standard distributions may not correctly present the distribution of the returns of this strategy. Maybe this statistical significance will disappear when the correct statistic is used. 

Furthermore, I have repeatedly emphasized that the returns I calculated exclude commissions and slippage. I believe that this naive strategy on its own may not be profitable once I incorporate these costs.

The Aroon Oscillator measures the difference between the Aroon Up and Aroon Down indicator. As such, my trading rules are a form of the application of the Aroon Oscillator. 

Further research, in my opinion, can be in the application of these naive trading rules to larger time frames, e.g. daily, half-daily charts, which are more likely to generate less trades and lower trading costs. However, at larger time frames, the behaviour between price movements and the Aroon Indicator may change and may require the trading rules to be adjusted.

Any suggestions or comments are welcome.

Like what you have just read? Digg it or Tip'd it.

The objective of Finance4Traders is to help traders get started by bringing them unbiased research and ideas. Since late 2005, I have been developing trading strategies on a personal basis. Not all of these models are suitable for me, but other investors or traders might find them useful. After all, people have different investment/trading goals and habits. Thus, Finance4Traders becomes a convenient platform to disseminate my work...(Read more about Finance4Traders)