The inputs to our models are the SIP indicators. The SIP indicators are published by Adaptive Trading Systems on a daily basis and are used for modeling the 3 to 15 trading day price trends of the SP futures contract. The SIP indicators include Buy Pressure, Sell Pressure, Net Pressure, High Buy Pressure, High Sell Pressure, Advancing Pressure and Declining Pressure. You can download the indicators by installing the ATS Mercury application that is available toward the bottom of the Trading Signals page. The indicator values are delayed by 1 trading day for non-subscribers.

Method:

Step 1. Adding the SIP Indicators to the Securities List

This step assumes that you have downloaded the SIP indicators to your computer. For further information on downloading the SIP indicators go to the Trading Signals page at AdaptiveTradingSystems.com.

Start Profit 8 and click on the Add Text File toolbar button to open the file selection dialog. Browse to the location of the SIP indicator text files and open the first file. The File Definition Dialog will then appear.

Step-1. Adding the SIP Indicators

Click on the SIP indicator column name (in the example it is SIPAP) and click on the Close radio button in the Settings section. Click on Ok to finish adding the SIP indicator to the Securities list in Profit 8. Repeat this step for each of the SIP indicators.

Step 2. Adding the Data Series for Modeling

On the Data tab in Profit 8, double click on the security name of the data series that you are modeling. This example models the continuously linked non-adjusted SP futures contract data from Pinnacle Data Corp. Scroll down the list of securities until you see the the SIP indicators. Double click on each SIP indicator until they have all been added to the list of ‘Data to Use’.

Step 2. Adding the Data Series for Modeling

The most recent 2.5 years of data will held back for validating the models. This is referred to as the out-of-sample (OOS) period. To ensure that the last 2.5 years of data is not used, the end date for importing data is set to 07/15/2009.

Step 3. Setting the Data Import Dates

The modeling end date of 07/15/2009 was chosen so that the modeling period overlaps the start of the ‘GFC period’ whilst providing for a reasonable amount of OOS data.

Step 4. Importing the Data

Click on the ‘Import Data’ toolbar button to import data from 07/01/1997 to 07/15/2009.

Step 4. Importing the Data

No transaction costs are applied in this example. Change the Slippage and Commission values to zero on the Equity Calculations tab.

Step 5. Equity Engine Parameters

Change the ‘Project the signal by’ to 1 to apply a trading delay of 1 bar. Signals generated on any given day are executed on the close of the next trading day when using a trading delay of 1 bar.

Step 6. Setting the Trading Delay

The available inputs and predicted series used to build mesh models are defined on the Indicators tab in Profit 8. In this case, there is no need to modify the dates that optimizations are applied to because no optimizations will be run. Go to the Indicators tab and delete series SP.NON_VOLUME from the list of indicators. Apply the Ln() transform to series SP.NON_CLOSE, the transformed series will then appear at the bottom of the list of indicators.

Step 7. Building the Predicted Series

Select the Ln(SP.NON_Close) series at the bottom of the list and apply the 1 period Chg transform. Making sure the same series is still selected, apply the 2 period Shift transform. This completes the construction of the target / predicted series. The target series represents an ideal trading signal. Profit 8 will attempt to predict this series using the SIP indicators as the model inputs.

Step 8. Nominating the Predicted Series

Select the Model Building tab and then select the newly constructed target series in the Indicators list. Click on the drop down menu above the Indicators list and select ‘Predicted’.

Step 8. Selecting the Predicted Series

Change the modeling start date to 7/15/1997 and the modeling end date to 7/15/2009. Set the Modeling, Optimization and Selection percentages to 60, 20 and 20. Change the modeling parameters so that Random data points are used.

Step 9. Data Handling Settings

The default Model Settings are used as pictured below.

Step 10. Model Settings

The default Performance Settings are used as pictured below. Note that the Optimization Metric is set to Relative Accuracy. Use of the Relative Accuracy tends to result in systems with lower profit margins over the modeling period. However, use of the Relative Accuracy metric has a strong tendency to produce systems that are more robust post the modeling period. I spent a considerable amount of time comparing Profit 8 to other similar neural network and state vector machine software solutions and Profit 8 using the Relative Accuracy optimization metric was the clear winner.

Step 11. Performance Settings

Click on the Start Modeling button to begin the modeling process.

Step 12. Start Modeling

Check the Profit 8 status bar at the bottom left of the application window to see when model construction has completed.

Step 13. Change Import End Date

To view the performance of the system over the out-of-sample period the data importation dates need to be modified. Change the end date to the last date that you have SP data for.

Step 13. Change Import End Date

After updating the end date, click on the Import Data toolbar button to import the data. The system will process the new data automatically.

Step 14. View the Results

Click on the Results tab to see the in-sample and out-of-sample performance. Finally, save the system if you haven’t done so already.

Step 14. View the Results

As a market timing model developer I like to see the shape of the equity curve and the percent of perfect trading statistic. The majority of people reading this article are probably wondering how many points the system hypothetically made over the OOS period. A total of 71 positions were taken over the OOS period. The first trade post the modeling end date was opened on 7/17/2009 and the last trade in the OOS period was closed on 1/17/2012. The net points made was 667.8. This equates to $33,390 if trading the ES contract and $166,950 if trading the SP contract. Note that these figures are not net of trading costs. To calculate the total hypothetical trading cost multiply your estimate of the cost per completed trade by 71 or the cost per side by 142.

What I like about this system is:
- The SIP indicators have been published daily with no in hind-sight adjustments for years.
- Absolutely no optimization of inputs is done.
- Absolutely no model ‘pruning’ post construction is required or done.
- The OOS period spans one of the most difficult trading periods to date.

What I don’t like about the system is:
- The percent of perfect over the in-sample and out-of-sample periods is a little on the low side.

Regards,

James
Developer of Trading Systems that Adapt

The Sharpe Ratio is calculated by subtracting the risk free rate from the compound annual growth rate and dividing the result by one standard deviation of the bar by bar returns. The risk free rate is a user defined equity engine setting. The one period standard deviation of log returns is initially calculated, annualized and converted to a nominal return to form the denominator. There is no need to take the risk free rate into account when calculating the denominator because it is constant in this implementation.

Formula / Pseudo Code:

    NominalStdDevReturns = e^(StdDevLogReturns x BarsPerYear ^ 0.5) – 1
    If (StdDevReturns != 0)
    {
        SharpeRatio = (CAGR – RiskFreeRate) / NominalStdDevReturns
    }
    Else
    {
        SharpeRatio = 0
    }

Example:

    Given,
        RiskFreeRate = 0.05
        StdDevLogReturns = 0.01092566
        CAGR = 0.27026727
    Compute the Sharpe Ratio,
        NominalStdDevReturns = e^( 0.01092566 x 252^0.5) – 1
        NominalStdDevReturns = 0.18938870
        SharpeRatio = (0.27026727 – 0.05) / 0.18938870
        SharpeRatio = 1.16304332

Regards,

James
Developer of Trading Systems that Adapt

Compound Annual Growth Rate is calculated by accumulating the signal log returns over the lookback period, transforming the result to a nominal return and then calculating the corresponding annualized rate of return.

Formula / Pseudo Code:

    For (n = EndBar – LookbackPeriod + 1 To EndBar)
    {
        If (Signal(I& – 1)) > 0
            SignalSign = 1
        ElseIf (Signal(I& – 1) < 0)
            SignalSign& = -1
        Else
            SignalSign& = 0

        SumSignalLogReturns = SumSignalLogReturns + SignalSign * Log(Price(n) / Price(n - 1))
    }

    NbrYears = LookbackPeriod / BarsPerYear
    NominalReturn = e^SumSignalLogReturns - 1
    CAGR = (NominalReturn + 1) ^ (1 / NbrYears) - 1

Example:

    NominalReturn = 2.75 (275%)
    NbrYears = 5.88
    CAGR = (2.75 + 1) ^ (1 / 5.88) – 1
    CAGR = 0.25205776

A CAGR value of 0.25205776 is equivalent to a CAGR of 25.21% (rounded to 2 decimal places).

Regards,

James
Developer of Trading Systems that Adapt

Proportion of Perfect Trading while in Position is calculated by subtracting the points lost over the performance lookback period from the points gained and then dividing the result by the sum of the points lost and gained. When the signal value is zero no points are lost or gained from the current bar to the next bar.

Formula / Pseudo Code:

    For (n = EndBar – LookbackPeriod + 1 To EndBar)
    {
        If (Signal(n – 1) > 0)
            SignalSign = 1
        ElseIf (Signal(n – 1) < 0)
            SignalSign = -1
        Else
            SignalSign = 0

        SignalReturn = SignalSign x (Price(n) – Price(n-1))

        If (SignalReturn > 0)
            SumPointsGained = SumPointsGained + SignalReturn
        ElseIf (SignalReturn < 0)
            SumPointsLost = SumPointsLost + Abs(SignalReturn)
    }

    If (SumPointsGained + SumPointsLost > 0)
    {
        PPIP = (SumPointsGained - SumPointsLost) / (SumPointsGained + SumPointsLost)
    Else
    {
        PPIP = 0
    }

Example:

    SumPointsGained = 1043.1

    SumPointsLost = 738.4

    PPIP = (1043.1 – 738.4) / (1043.1 + 738.4)

    PPIP = 0.17103564

A PPIP value of 0.17103564 is equivalent to 17.10% of perfect trading (rounded to 2 decimal places).

Proportion of Perfect Log Returns while in Position is calculated by subtracting the sum of the natural log returns lost over the performance lookback period from the sum of the log returns gained and then dividing the result by the sum of the log returns lost and gained. When the signal value is zero no points are lost or gained from the current bar to the next bar.

    For (n = EndBar – LookbackPeriod + 1 To EndBar)
    {
        If (Signal(n – 1) > 0)
            SignalSign = 1
        ElseIf (Signal(n – 1) < 0)
            SignalSign = -1
        Else
            SignalSign = 0

        SignalLogReturn = SignalSign x Log(Price(n) / Price(n-1))

        If (SignalLogReturn > 0)
            SumLogReturnsGained = SumLogReturnsGained + SignalReturn
        ElseIf (SignalReturn < 0)
            SumLogReturnsLost = SumLogReturnsLost + Abs(SignalReturn)
    }

    If (SumLogReturnsGained + SumLogReturnsLost > 0)
        PPLIP = (SumLogReturnsGained - SumLogReturnsLost) / (SumLogReturnsGained + SumLogReturnsLost)
    Else
        PPLIP = 0

Regards,

James
Developer of Trading Systems that Adapt

Net Direction Correct ratio computes the equivalent of the percent direction correct scaled so that the minimum value is -1 and the maximum is +1. If the signal value at bar(n-1) is greater than zero then the change in price or smoothed price series from bar(n-1) to bar(n) would have to be greater than zero for the signal to be considered correct and vica versa. If the signal value at bar(n-1) is zero then that signal is not included in the tally of correct/incorrect signal values.

The signal can be applied to a smoothed price series by setting the Trend Period equity engine parameter to a value greater than 1. A custom designed digital FIR filter is used to do the smoothing. The filter has the same lag as a simple moving average with smoother output. The lag is taken into account when applying the signal series.

Formula / Pseudo Code:

        For (n = EndBar – LookbackPeriod + 1 To EndBar)
        {
                FilterDelta = CMASeries(n) – CMASeries(n – 1)

                If (Signal(n – CMALag – 1) > 0)
                        SignalSign = 1
                ElseIf (Signal(n – CMALag – 1) < 0)
                        SignalSign = -1
                Else
                        SignalSign = 0

                SignalReturn = SignalSign * FilterDelta

                If (SignalReturn > 0)
                        DirCorrectCount = DirCorrectCount + 1
                ElseIf (SignalReturn < 0)
                        DirIncorrectCount = DirIncorrectCount + 1
        }

        If (DirCorrectCount + DirIncorrectCount > 0)
                NDC = (DirCorrectCount – DirIncorrectCount) / (DirCorrectCount + DirIncorrectCount)
        Else
                NDC = 0

Example:

        DirCorrectCount = 56
        DirIncorrectCount = 42
        NDC = (56 – 42) / (56 + 42)
        NDC = 0.14285714

A NDC value of 0.14285714 is equivalent to a percent direction correct of 57.14% (rounded to 2 decimal places).

Weighted Net Direction Correct ratio is similar to the net direction correct ratio. Each correct / incorrect signal is assigned a weighting that corresponds to the bar number within the performance lookback period. At bar(n-lookback+1) the weighting will be 1 and at bar(n) the weighting will be equal to the lookback period.

Formula / Pseudo Code:

        If (SumDirCorrectWeights + SumDirIncorrectWeights > 0)
                WNDC = (SumDirCorrectWeights – SumDirIncorrectWeights) / (SumDirCorrectWeights + SumDirIncorrectWeights)
        Else
                WNDC = 0

Regards,

James
Developer of Trading Systems that Adapt

NbrBars is the number of trading bars over the performance lookback period. The Lookback Period is a user defined equity engine parameter.

BarsPerYear is the number of trading bars per year. # Bars per Year Period is a user defined equity engine parameter.

NbrYears is the fractional number of years spanned by the performance lookback period.

Formula:

    NbrYears = NbrBars / BarsPerYear

NominalReturn is the arithmetic or simple return. For example, a nominal return of 20% on $50,000 is $10,000. To transform a natural log return to a nominal return the mathematical constant e (2.718281828…) is raised to the power of the log return and 1 is subtracted from the result.

Formula:

    NominalReturn = e^LogReturn – 1

SignalSign is determined by the value of the signal at a given trading bar. If the signal value is positive then SignalSign is set to +1, if the signal value is negative then SignalSign is set to -1 and if the signal value is equal to zero then SignalSign is set to zero. Dakota automatically shifts the signal series in relation to the price series so that the signal value at bar(n-1) applies to the change in price from bar(n-1) to bar(n). Therefore, there is no need to account for the Trading Delay.

Formula / Pseudo Code:

    For (n = EndBar – LookbackPeriod + 1 To EndBar)
    {
        If (Signal(n – 1) > 0)
            SignalSign = 1
        ElseIf (Signal(n – 1) < 0)
            SignalSign = -1
        Else
            SignalSign = 0
    }

SignalLogReturn is determined by applying the signal to the price series. The log return gained/lost from bar to bar is calculated by multiplying the SignalSign at bar(n-1) by the log return from bar(n-1) to bar(n).

Formula:

    SignalLogReturn = SignalSign(n-1) x log(Price(n) / Price(n-1))

SumSignalLogReturns is the cumulated bar to bar natural logarithmic returns generated by applying the signal to the price series.

Formula / Pseudo Code:

    For (n = EndBar – LookbackPeriod + 1 To EndBar)
    {
        If (Signal(n – 1) > 0)
            SignalSign = 1
        ElseIf (Signal(n – 1) < 0)
            SignalSign = -1
        Else
            SignalSign = 0

        SignalLogReturn = SignalSign(n-1) x log(Price(n) / Price(n-1))
        SumSignalLogReturns = SumSignalLogReturns + SignalLogReturn
    }

SignalReturn is determined by applying the signal to the price series. The number of points gained/lost from bar to bar is calculated by multiplying the SignalSign at bar(n-1) by the change in price from bar(n-1) to bar(n).

Formula:

    SignalReturn = SignalSign(n-1) x (Price(n) – Price(n-1))

SumSignalReturns is the cumulated bar to bar returns in points generated by applying the signal to the price series.

Formula / Pseudo Code:

    For (n = EndBar – LookbackPeriod + 1 To EndBar)
    {
        If (Signal(n – 1) > 0)
            SignalSign = 1
        ElseIf (Signal(n – 1) < 0)
            SignalSign = -1
        Else
            SignalSign = 0

        SignalReturn = SignalSign(n-1) x (Price(n) – Price(n-1))
        SumSignalReturns = SumSignalReturns + SignalReturn
    }

That’s it for the basic variables and operations. Note that it is likely that this series of articles will be expanded or edited to correct errors or provide more information.  i.e. this is a dynamic article.

Regards,

James
Developer of Trading Systems that Adapt

One of the primary functions of an equity engine is to provide the swarm adaptation engine with the performance of each trade bot over the performance lookback period. Dakota calls function CalculateAdaptationPerformance() once for each trade bot when processing a trading bar. The array of historical trading signals for a particular bot and the price history for the traded market are passed into the function.

Trade bot performance can be measured in a variety of ways. A programmer can develop an equity engine to measure performance using any algorithm that he chooses. We provide 12 types of equity engines that each measure trade bot performance in their own unique way. An example is the ATS Sharpe Ratio equity engine. As the name suggests, the performance metric is the Sharpe Ratio. In this case, function CalculateAdaptationPerformance() is computing and returning the annualized Sharpe Ratio for a given trade bot over the performance lookback period.

It is worth noting that the calculation of the trade bot performance by function CalculateAdaptationPerformance() is distinct from the calculation of any corresponding measure of performance that appears in the body of the Dakota Trades report. The statistics appearing in the body of the Trades report are calculated using all available system signal and price data histories and they optionally include trading costs. The system signal is derived from the set of trade bot signals. For example, one method is to average all trade bot signals to determine the system signal.

The minimum, maximum and average trade bot performance over the lookback period is included in the header section of the Trades report. This information is particularly useful if you are not familiar with the performance data produced by a particular equity engine. The image below is of the Trade report header.

Trades Report Header

In the above report, we can see that the average trade bot performance over the performance lookback period of 500 trading bars was 0.188. An average bot performance of 0.188 is equivalent to a CAGR of 18.8%. Future articles in this series will describe the performance metrics used by AdaptiveTradingSystems.com.

Regards,

James
Developer of Trading Systems that Adapt

The up and coming release of the ‘new trading systems reports’ will not incorporate any money management techniques. Future releases might include some basic money management techniques if there is sufficient demand. Personally, I will mostly be interested in ‘pure’ signal performance. At some point there will be an option to adjust exposure based on the signal value. This approach would rely on the signal value corresponding to a measure of confidence. The introduction of this option will be the result of the (good) influence of Michael Stokes.

A screen image of an example futures trading system report follows.

New Futures Trading Systems Report Example

The trading stats are now arranged into two columns for all simulation types. The reason the list of trades does not appear in this image is that they are written to the report when processing the last bar. When running a Futures Trading simulation, the equity curve that is plotted in Dakota is the cumulative net profit (not shown for this example).

Where appropriate, I have added descriptions of the options for the equity engine settings.

Trading System Equity Engine Parameters

You may have noticed the # Bars per Year parameter. If running Dakota R/T (real time) then modifying this value enables the accurate calculation of the annualized metrics for the trading report.

Regards,

James
Developer of Trading Systems that Adapt

The Signal Performance trading simulation type doesn’t report $ returns etc. on trading capital and trading is frictionless. This is the type of trading simulation that I normally run. Stock and Futures Trading simulation types are available as well.

New Trading Systems Report Example

When running the Signal Performance trading simulation the equity curve is the cumulative log returns. Notice how this is more useful when comparing periods of relatively high / low prices.

Trading System Equity Curve

The following image lists most of the settings that are available. Where appropriate, I would love to be able to create drop-down lists for the Equity Engine settings rather than using numbers to represent different options. No doubt a future version of Dakota will enable this.

Dakota Equity Engine Settings

All feedback is appreciated!

Regards,

James
Developer of Trading Systems that Adapt

By default, only the signal history over the performance lookback period is passed into function CalculateAdaptationPerformance(). Some performance metrics require a more extensive history. Thus, the need to make the following modification. Assuming that you are using the Visual Basic 6 development platform, select the CPerformance class and go to the Public Property Get PerformanceLookback() function. Then modify the following statement,

PerformanceLookback = Me.Parameters(4).Value          ‘ Parameter 4 is the performance lookback period.

so that the function return value is set to a number that will be more than sufficient such as,

PerformanceLookback = 20000000.

The screen image below shows you the modified code within the VB6 project.

Modified Public Property Get PerformanceLookback

Conveniently, when Dakota determines how many elements (trading bars) the Signal array should have, it will take into account the number of trading bars in the data history and will not exceed this. Provided that our data history does not exceed twenty million bars, we will always have the full signal history available in function CalculateAdaptationPerformance(). Important note, if you are going to implement this modification then be well aware that you might have to change the way you process the Signal array because the number of elements now correspond to that of the data array.

Regards,

James
Developer of Trading Systems that Adapt