Category Archives: Must Know EasyLanguage

A Tribute to Murray and His Inter-Market Research

Murray Ruggiero’s Inter-Market Research

Well it’s been a year, this month, that Murray passed away.  I was fortunate to work with him on many of his projects and learned quite a bit about inter-market convergence and divergence.  Honestly, I wasn’t that into it, but you couldn’t argue with his results.  A strategy that he developed in the 1990s that compared the Bond market with silver really did stand the test of time.  He monitored this relationship over the years and watched in wane.  Murray replaced silver with $UTY.

The PHLX Utility Sector Index (UTY) is a market capitalization-weighted index composed of geographically diverse public utility stocks.

He wrote an article for EasyLanguage Mastery by Jeff Swanson where he discussed this relationship and the development of inter-market strategies and through statistical analysis proved that these relationships added real value.

I am currently writing Advanced Topics, the final book in my Easing Into EasyLanguage trilogy, and have been working with Murray’s research.  I am fortunate to have a complete collection of his Futures Magazine articles from the mid 1990s to the mid 2000s.  There is a quite a bit of inter-market stuff in his articles.  I wanted, as a tribute and to proffer up some neat code, to show the performance and code of his Bond and $UTY inter-market algorithm.

Here is a version that he published a few years ago updated through June 30, 2022 – no commission/slippage.

Murray’s Bond and $UTY inter-market Strategy

Not a bad equity curve.  To be fair to Murray he did notice the connection between $UTY and the bonds was changing over the past couple of year.  And this simple stop and reverse system doesn’t  have a protective stop.   But it wouldn’t look much different with one, because the system looks at momentum of the primary  data and momentum of the secondary data and if they are in synch (either positively or negatively correlated – selected by the algo) an order is fired off.  If you simply just add a protective stop, and the momentum of the data are in synch, the strategy will just re-enter on the next bar.  However, the equity curve just made a new high  recently.  It has got on the wrong side of the Fed raising rates.  One could argue that this invisible hand has toppled the apple cart and this inter-market relationship has been rendered meaningless.

Murray had evolved his inter-market analysis to include state transitions.  He not only looked at the current momentum, but also at where the momentum had been.  He assigned the transitions of the momentum for the primary and secondary markets a value from one to four and he felt this state transition helped overcome some of the coupling/decoupling of the inter-market relationship.

However,  I wanted to test Murray’s simple strategy with a fixed $ stop and force the primary market to move from positive to negative or negative to positive territory while the secondary market is in the correct relationship.  Here is an updated equity curve.

George’s Adaptation and using a $4500 stop loss

This equity curve was developed  by using a $4500 stop loss.  Because I changed the order triggers, I reoptimized the length of the momentum calculations for the primary and secondary markets.  This curve is only better in the category of maximum draw down.  Shouldn’t we give Murray a chance and reoptimize his momentum length calculations too!  You bet.

Murray Length Optimizations

These metrics were sorted by Max Intraday Draw down.  The numbers did improve, but look at the Max Losing Trade value.  Murray’s later technology,  his State Systems, were a great improvement over this basic system.  Here is my optimization using a slightly different entry technique and a $4500 protective stop.

Standing on the Shoulders of a Giant

This system, using Murray’s overall research, achieved a better Max Draw Down and a much better Max Losing Trade.   Here is my code using the template that Murray provided in his articles in Futures Magazine and EasyLanguage Mastery.

 

// Code by Murray Ruggiero
// adapted by George Pruitt

Inputs: InterSet(2),LSB(0),Type(1),LenTr(4),LenInt(4),Relate(0);
Vars: MarkInd(0),InterInd(0);

If Type=0 Then 
Begin
	InterInd=Close of Data(InterSet)-CLose[LenInt] of Data(InterSet);
	MarkInd=CLose-CLose[LenTr];
end;

If Type=1 Then 
Begin
	InterInd=Close of Data(InterSet)-Average(CLose of Data(InterSet),LenInt);
	MarkInd=CLose-Average(CLose,LenTr);
end;

if Relate=1 then 
begin
	If InterInd > 0 and MarkInd CROSSES BELOW 0 and LSB>=0 then 
		Buy("GO--Long") Next Bar  at open;
	If InterInd < 0 and MarkInd CROSSES ABOVE 0 and LSB<=0 then
		Sell Short("GO--Shrt") Next Bar  at open;

end;
if Relate=0 then begin
	If InterInd<0 and MarkInd CROSSES BELOW 0  and LSB>=0 then 
		Buy Next Bar  at open;
	If InterInd>0 and MarkInd CROSSES ABOVE 0  and LSB<=0 then 
		Sell Short Next Bar  at open;
end;

Here the user can actually include more than two data streams on the chart.  The InterSet input allows the user to choose or optimize the secondary market data stream.  Momentum is defined by two types:

  • Type 0:  Intermarket or secondary momentum simply calculated by close of data(2) – close[LenInt] of date(2) and primary momentum calculated by close – close[LenTr]
  • Type 1:   Intermarket or secondary momentum  calculated by close of data(2) – average( close of data2, LenInt)  and primary momentum calculated by close – average(close, LenTr)

The user can also input what type of Relationship: 1 for positive correlation and 0 for negative correlation.  This template can be used to dig deeper into other market relationships.

George’s Modification

I simply forced the primary market to CROSS below/above 0 to initiate a new trade as long the secondary market was pointing in the right direction.

	If InterInd > 0 and MarkInd CROSSES BELOW 0 and LSB>=0 then 
		Buy("GO--Long") Next Bar  at open;
	If InterInd < 0 and MarkInd CROSSES ABOVE 0 and LSB<=0 then
		Sell Short("GO--Shrt") Next Bar  at open;
Using the keyword CROSSES

This was a one STATE transition and also allowed a protective stop to be used without the strategy automatically re-entering the trade in the same direction.

Thank You Murray – we sure do miss you!

Murray loved to share his research and would want us to carry on with it.  I will write one or two blogs a year in tribute to Murray and his invaluable research.

Using EXCEL VBA to Combine Equity Curves from TradeStation

A Poor Man’s Equity Curve Merger

Sometimes you just want to create a combined equity curve of several markets and for one reason or another you don’t want to use Maestro.  This post will show you an indicator that you can insert into your TradeStation chart/strategies that will output monthly cumulative equity readings.  After that I refresh my VBA skills a little bit by creating a VBA Macro/Script that will take the output and parse it into a table where the different months are the rows and the different market EOM equities, for those months, will be the columns.  Then all the rows will be summed and then finally a chart will be produced.  I will zip the Exel .xlsm and include it at the end of this post.

Part 1:  Output Monthly Data to Print Log

You can determine the end of the month by comparing the current month of the date and the month of the prior date.  If they are different, then you know you are sitting on the first trading day of the new month.  You can then reach back and access the total equity as of yesterday.  If you want you can also track the change in month equity.  Here is the indicator code in EasyLanguage.

// Non plotting indicator that needs to be applied to 
// a chart that also has a strategy applied
// one that produces a number of trades

vars: monthlyEqu(0),priorMonthEqu(0);
vars: totalEquity(0);


if month(date) <> month(date[1]) then
begin
    monthlyEqu = totalEquity[1] - priorMonthEqu;
    priorMonthEqu = totalEquity[1];
	print(getSymbolName,",",month(date[1]):2:0,"-",year(date[1])+1900:4:0,",",monthlyEqu,",",totalEquity);
end;
totalEquity = i_ClosedEquity; 
Indicator that exports the EOM equity values

The interesting part of this code is the print statement.  You can use the month and year  functions to extract the respective values from the date bar array.  I use a formatted print to export the month and year without decimals.  Remember 2021 in TradeStation is represented by 121 and all you have to do is add 1900 to get a more comfortable value.  The month output is formatted with :2:0 and the year with :4:0.  The first value in the format notation informs  the computer to allow at least 2 or 4 values for the month  and the year respectively.  The second value following the second colon informs the computer that you do not want any decimals values (:0).  Next insert the indicator into all the charts in your workspace.  Here’s a snippet of the output on one market.  I tested this on six markets and this data was the output generated.  Some of the markets were interspersed and that is okay.  You may have a few months of @EC and then a few months of @JY and then @EC again.

@EC, 7-2008,-5106.24,-5106.24
@EC, 8-2008,   0.00,-5106.24
@EC, 9-2008,   0.00,-5106.24
@EC,10-2008,   0.00,-5106.24
@EC,11-2008,   0.00,-5106.24
@EC,12-2008,25156.26,20050.02
@EC, 1-2009,   0.00,20050.02
@EC, 2-2009,   0.00,20050.02
@EC, 3-2009,   0.00,20050.02
@EC, 4-2009,   0.00,20050.02
@EC, 5-2009,   0.00,20050.02
@EC, 6-2009,   0.00,20050.02
@EC, 7-2009,   0.00,20050.02
@EC, 8-2009,   0.00,20050.02
@EC, 9-2009,   0.00,20050.02
@EC,10-2009,   0.00,20050.02
@EC,11-2009,   0.00,20050.02
@EC,12-2009,7737.51,27787.53
@EC, 1-2010,   0.00,27787.53
@EC, 2-2010,   0.00,27787.53
@EC, 3-2010,   0.00,27787.53
@EC, 4-2010,   0.00,27787.53
@EC, 5-2010,   0.00,27787.53
@EC, 6-2010,   0.00,27787.53
@EC, 7-2010,   0.00,27787.53
@EC, 8-2010,   0.00,27787.53
@EC, 9-2010,6018.76,33806.29
Indicator output

Part 2: Getting the Data into Excel

If you use this post’s EXCEL workbook with the macro you may need to tell EXCEL to forget any formatting that might already be inside the workbook.  Open my workbook and beware that it will inform/warn you that a macro is located inside and that it could be dangerous.  If you want to go ahead and enable the macro go ahead.  On Sheet1 click in A1 and place the letter “G”.  Then goto the Data Menu and then the Data Tools section of the ribbon and click Text to Columns.  A dialog will open and ask you they type of file that best describes your data.  Click the Delimited radio button and then next.  You should see a dialog like this one.

Clear Any Left Over Formatting

Now copy all of the data from the Print-Log and paste it into Column A.  If all goes right everything will be dumped in the appropriate rows and in a single column.

The fields will be dumped into a single column

First select column A and  go back to the Data Menu and the Data Tools on the Ribbon.  Select Delimited and hit next,  Choose comma because we used commas to separate our values.  Click Next again.  Eventually you will get to this dialog.

Make sure you use Date [MDY] for the second column of data.
If you chose Date format for column 2 with MDY, then it will be imported into the appropriate column in a date format.  This makes charting easier.  If all goes well then you will have four columns of data –  a column for Symbol, Date, Delta-EOM and EOM.  Select column B and right click and select Format Cells.

Clean Up column B by formatting cells and customizing the date format

Once you format the B column in the form of  MM-YYYY you will have a date like 9-2007, 10-2007, 11-2007…

Running the VBA Macro/Script

On the Ribbon in EXCEL goto the Developer Tab.  If you don’t see it then you will need to install it.  Just GOOGLE it and follow their instructions.  Once on the Develop Tab goto the Code category and click the Visual Basic Icon.  Your VBA IDE will open and should like very similar to this.

VBA IDE [integrated development environment]
If all goes according to plan after you hit the green Arrow for the Run command your spreadsheet should like similar to this.

EOM table with Months as Rows and Individual Market EOMs as columns

The Date column will be needed to be reformatted again as Date with Custom MM-YYYY format.  Now copy the table by highlighting the columns and rows including the headings and then goto to Insert Menu and select the Charts category.  

This is what you should get.

Merged Equity on Closed Trade Basis

This is the output of the SuperTurtle Trading system tested on the currency sector from 2007 to the present.

VBA Code

I have become very spoiled using Python as it does many things for you by simply calling a function.  This code took my longer to develop than I thought it would, because I had to back to the really old school of programming (really wanted to see if I could do this from scratch) to get this done.  You could of course eliminate some of my code by calling spread sheet functions from within EXCEL.  I went ahead and did it the brute force way just to see if I could do it.

Sub combineEquityFromTS()

    'read data from columns
    'symbol, date, monthlyEquity, cumulativeEquity - format
    'create arrays to hold each column of data
    'use nested loops to do all the work
    'brute force coding, no objects - just like we did in the 80s
    
    Dim symbol(1250) As String
    Dim symbolHeadings(20) As String
    Dim myDate(1250) As Long
    Dim monthlyEquity(1250) As Double
    Dim cumulativeEquity(1250) As Double
    
    'read the data from the cells
    dataCnt = 1
    Do While Cells(dataCnt, 1) <> ""
        symbol(dataCnt) = Cells(dataCnt, 1)
        myDate(dataCnt) = Cells(dataCnt, 2)
        monthlyEquity(dataCnt) = Cells(dataCnt, 3)
        cumulativeEquity(dataCnt) = Cells(dataCnt, 4)
        dataCnt = dataCnt + 1
    Loop
    dataCnt = dataCnt - 1
    
    'get distinct symbolNames and use as headers
    symbolHeadings(1) = symbol(1)
    numSymbolheadings = 1
    For i = 2 To dataCnt - 1
        If symbol(i) <> symbol(i + 1) Then
            newSymbol = True
            For j = 1 To numSymbolheadings
                If symbol(i + 1) = symbolHeadings(j) Then
                    newSymbol = False
                End If
            Next j
            If newSymbol = True Then
                numSymbolheadings = numSymbolheadings + 1
                symbolHeadings(numSymbolheadings) = symbol(i + 1)
            End If
        End If
    Next i
    
    'Remove duplicate months in date array
    'have just one column of month end dates
    
    Cells(2, 7) = myDate(1)
    dispRow = 2
    numMonths = 1
    i = 1
    Do While i <= dataCnt
        foundDate = False
        For j = 1 To numMonths
            If myDate(i) = Cells(j + 1, 7) Then
                foundDate = True
            End If
        Next j
        If foundDate = False Then
            numMonths = numMonths + 1
            Cells(numMonths + 1, 7) = myDate(i)
        End If
        i = i + 1
    Loop
    'put symbols across top of table
    'put "date" and "cumulative" column headings in proper
    'locations too
    
    Cells(1, 7) = "Date"
    For i = 1 To numSymbolheadings
        Cells(1, 7 + i) = symbolHeadings(i)
    Next i
       
    numSymbols = numSymbolheadings
    Cells(1, 7 + numSymbols + 1) = "Cumulative"
    'now distribute the monthly returns in their proper
    'slots in the table
    dispRow = 2
    dispCol = 7
    For i = 1 To numSymbols
        For j = 2 To numMonths + 1
            For k = 1 To dataCnt
                foundDate = False
                If symbol(k) = symbolHeadings(i) And myDate(k) = Cells(j, 7) Then
                    Cells(dispRow, dispCol + i) = cumulativeEquity(k)
                    dispRow = dispRow + 1
                    Exit For
                End If
                'for later use
                'If j > 1 Then
                '    If symbol(k) = symbolHeadings(i) And myDate(k) < Cells(j, 7) And myDate(k) > Cells(j - 1, 7) Then
                '        dispRow = dispRow + 1
                '    End If
                'End If
            Next k
        Next j
        dispRow = 2
    Next i
    'now accumulate across table and then down
    For i = 1 To numMonths
        cumulative = 0
        For j = 1 To numSymbols
            cumulative = cumulative + Cells(i + 1, j + 7)
        Next j
        Cells(i + 1, 7 + numSymbols + 1) = cumulative
    Next i
End Sub

This a throwback to the 80s BASIC on many of the family computers of that era.  If you are new to VBA you can access cell values by using the keyword Cells and the row and column that points to the data.   The first thing you do is create a Module named combineEquityFromTS and in doing so it will create a Sub combineEquityFromTS() header and a End Sub footer.  All of your code will be squeezed between these two statements.  This code is ad hoc because I just sat down and started coding without much forethought.  

Use DIM to Dimension an Arrays

I like to read the date from the cells into arrays so I can manipulate the data internally.  Here I create five arrays and then loop through column one until there is no longer any data.  The appropriate arrays are filled with their respective data from each row.

Dimension and Load Arrays

Once the data is in arrays we can start do parse it.  The first thing I want is to get the symbolHeadings or markets.  I know the first row has a symbol name so I go ahead and put that into the symbolHeadings array.  I kept track of the number of rows in the data with the variable dataCnt.  Here I use  nested loops to work my way down the data and keep track of new symbols as I encounter them.  If the symbol changes values, I then check my list of stored symbolHeadings and if the new symbol is not in the list I add it.

Parse different symbols from all data

Since all the currencies will have the same month values I wanted to compress all the months into a single discrete month list.  This isn’t really all that necessary since we could have just prefilled the worksheet with monthly date values going back to 2007.  This algorithm is similar to the one that is used to extract the different symbols.  Except this time, just for giggles, I used a Do While Loop.

Squash Monthly List Down

As well as getting values from cells you can also put values into them.  Here I run through the list of markets and put them into Cells(1, 7+i).  When working with cells you need to make sure you get the offset correct.  Here I wanted to put the market names in Row A and Columns: H, I, J, K, L, M.

  • Column H = 8
  • Column I = 9
  • Column J = 10
  • Column K =11
  • Column L = 12
  • Column M = 13
Put Markets as Column Headers

Cells are two dimensional arrays.  However if you are going to use what is on the worksheet make sure you are referencing the correct data.  Here I introduce dispRow and dispCol as the anchor points where the data I need to reference starts out.

Three nested loops – Whopee.

Here I first parse through each symbol and extract the EOM value that matches the symbol name and month-year value.  So if I am working on @EC and I need the EOM for 07-2010, I fist loop through the month date values and compare the symbol AND myDate (looped through with another for-loop) with the month date values.  If they are the same then I dump the value in the array on to the spreadsheet.  And yes I should have used this:

For j = dispRow to numMonths-1

Instead of –

For j = 2 to numMonths-1

Keeping arrays in alignment with Cells can be difficult.  I have a hybrid approach here.  I will clean this up later and stick just with arrays and only use Cells to extract and place data.  The last thing you need to do is sum each row up and store that value in the Cumulative column.

Across and then Down to sum accumulated monthly returns

Conclusion

This was another post where we relied on another application to help us achieve our objective.   If you are new to EXCEL VBA (working with algorithms that generate trades) you can find out more in my Ultimate Algorithmic Trading System Toolbox book.  Even if you don’t get the book this post should get you started on the right track.

Excel Workbooks – One Empty with Macro and one Filled With this Post Data.

 

Tracking Last EntryPrice While Pyramiding on Minute Bars

EasyLanguage’s EntryPrice Doesn’t Cut the Mustard

In writing the Hi-Res edition of Easing Into EasyLanguage I should have included this sample program.  I do point out the limitations of the EntryPrice keyword/function in the book.  But recently I was tasked to create a pyramiding scheme template that used minute bars and would initiate a position with N Shares and then pyramid up to three times by adding on N Shares at the last entry price + one 10 -Day ATR measure as the market moves in favor of the original position.  Here is an example of just such a trade.

Pyramid 3 Times After Initial Trade Entry. Where’s the EntryPrice?

EntryPrice only contains the original entry price.  So every time you add on a position, the EntryPrice doesn’t reflect this add on price.  I would like to be able to index into this keyword/function and extract any EntryPrice.  If you enter at the market, then you can keep track of entry prices because a market order is usually issued from an if-then construct:

//Here I can keep track of entry prices because I know
//exactly when and where they occur.

if c > c[1] and value1 > value2 then
begin
	buy("MarketOrder") next bar at market;
	lastEntryPrice = open of next bar;
end;
Last Entry Price tracking is easy if using Market Orders

But what if you are using a stop or limit order.  You don’t know ahead of time where one of these types of orders will hit up.  It could be the next bar or it could be five bars later or who knows.

AvgEntryPrice Makes Up for the Weakness of EntryPrice

AvgEntryPrice is a keyword/function that  returns the average of the entries when pyramiding.  Assume you buy at 42.00 and pyramid the same number of shares at 46.50 – AvgEntryPrice will be equal to (42.00 + 46.50) / 2 = 44.25.  With this information you can determine the two entry prices.  You already know the original price.  Take a look at this code.

// remember currentShares and avgEntryPrice ARE EasyLanguage Keywords/Functions
if mp[1] = mp and mp = -1 and currentShares > curShares then
begin
	totShorts = totShorts + 1;
	if currentShares > initShares then
	begin
		lastEntryPrice = totShorts * avgEntryPrice - entryPriceSums;
		entryPriceSums = entryPriceSums + lastEntryPrice;
		print(d," Short addon ",lastEntryPrice," ",totShorts," ",avgEntryPrice," ",entryPriceSums);
	end;
end;
Calculating the true LastEntryPrice

Remember currentShares is a keyword/function and it is immediately updated when more shares are added or taken off.  CurShares is my own variable where I keep track of the prior  currentShares , so if currentShares (real number of shares) is greater than the prior curShares (currentShares) then I know 100%, a position has been pyramided as long the the mp stays the same.  If currentShares increases and mp stays constant, then you can figure out the last entry price where the pyramid takes place.  First you tick totShorts up by 1.  If currentShares > initShares, then you know you are pyramiding so

lastEntryPrice = totShorts * avgEntryPrice – entryPriceSums

Don’t believe me.  Let’s test it.  Remember original entry was 42.00 and the add on was at 46.50.  TotShorts now equals 2.

  1. Initial entryPrice = 42.00 so entryPriceSums is set to 42.00
  2. After pyramiding avgEntryPrice is set to 44.25
  3. lastEntryPrice = 2 * 44.25 – 42.00 = 46.50
  4. entryPriceSums is then set to 42.00 + 46.50 or 88.50

So every time you add on a position, then you flow through this logic and you can keep track of the actual last entry price even if it is via a limit or stop order.

But wait there is more.  This post is also a small glimpse into what I will be writing about in the Easing Into EasyLanguage:  Advanced Topics.  This system definitely falls into what I discussed in the Hi-Res Edition.  Here is where we tip over into Advanced Topics.  The next book is not about creating dialogs or trading apps using OOEL (object oriented EasyLanguage), but we do use some of those topics to do some rather complicated back testing things.

Now that we know how to calculate the lastEntryPrice wouldn’t it be really cool if we could keep track of all of the entryPrices during the pyramid stream.   If I have pyramided four times, I would like to know entryPrice 1, entryPrice 2, entryPrice 3 and entryPrice 4.

EntryPrice Vector

Dr. VectorLove or How I Learned to Stop Worrying and Love Objects

I have discussed vectors before but I really wanted to discuss them more.  Remember Vectors are just lists or arrays that don’t need all the maintenance.  Yes you have to create them which can be a pain, but once you learn and forget it twenty times it starts to sink in.  Or just keep referring back to this web page.


Using elsystem.collections;

vars: Vector entryPriceVector(Null);

once Begin
	entryPriceVector = new Vector;
end;
The Bare Minimum to Instantiate a Vector
  1. Type – “Using elsystem.collections; “
  2. Declare entryPriceVector as a Vector and set it equal to Null
  3. Use Once and instantiate entryPriceVector by using the keyword new < object type>;

A Vector is part of elsystem’s collection objects.  Take a look at this updated code,

if mp[1] = mp and mp = -1 and currentShares > curShares then
begin
	totShorts = totShorts + 1;
	if currentShares > initShares then
	begin
		lastEntryPrice = totShorts * avgEntryPrice - entryPriceSums;
		entryPriceVector.push_back(lastEntryPrice);
		entryPriceSums = entryPriceSums + lastEntryPrice;
		print(d," Short addon ",lastEntryPrice," ",entryPrice," ",entryPrice(1)," ",totShorts," ",avgEntryPrice," ",entryPriceSums," ",entryPriceVector.back() astype double," ",entryPriceVector.count asType int);
		if not(entryPriceVector.empty()) then
		begin
			for m = 0 to entryPriceVector.count-1
			begin
				print(entryPriceVector.at(m) astype double);
			end;
		end;
	end;
end;
LastEntryPrice and Pushing It onto the Vector and Then Printing Out the Vector

After the lastEntryPrice is calculated it is pushed onto the entryPriceVector using the function (method same thing but it is attached to the Vector class).push_back(lastEntryPrice);

entryPriceVector.push_back(lastEntryPrice);

So every time a new lastEntryPrice is calculated it is pushed onto the Vector at the back end.  Now if the entryPriceVector is not empty then we can print its contents by looping and indexing into the Vector.

if not(entryPriceVector.empty()) then
begin
     for m = 0 to entryPriceVector.count-1
     begin
          print(entryPriceVector.at(m) astype double);
     end;
end;
Looping through a Vector and Printing Out its Contents

Remember if you NOT a boolean value then it turns it to off/on or just the opposite of the boolean valueIf entryPriceVector is not empty then proceed.  entryPriceVector.count holds the number of values stuffed into the vectorYou can index into the Vector by using .at(m),  If you want to print out the value of the Vector .at(m), then you will need to typecast the Vector object as what ever it is holding.  We know we are pushing numbers with decimals (double type) onto the Vector so we know we can evaluate them as a double type.  Just remember you have to do this when printing out the values of the Vector.

Okay you can see where we moved into an Advanced Topics area with this code.  But it really becomes useful when trying to overcome some limitations of EasyLanguage.  Remember keep an eye open for Advanced Topics sometime in the Spring.

Converting Method() To Function – MultiCharts

MultiCharts Doesn’t Support Methods

Methods are wonderful tools that are just like functions, but you can put them right into your Analysis Technique and they can share the variables that are defined outside the Method.  Here is an example that I have posted previously.  Note:  This was in response to a question I got on Jeff Swanson’s EasyLanguage Mastery Facebook Group.

{'('  Expected line 10, column 12  }
//the t in tradeProfit. // var: double tradeProfit;
	
vars: mp(0);
array: weekArray[5](0);



method void dayOfWeekAnalysis()   {method definition}
var: double tradeProfit;
begin
	If mp = 1 and mp[1] = -1 then tradeProfit = (entryPrice(1) - entryPrice(0))*bigPointValue;
 	If mp = -1 and mp[1] = 1 then tradeProfit = (entryPrice(0) - entryPrice(1))*bigPointValue;
 	weekArray[dayOfWeek(entryDate(1))] = weekArray[dayOfWeek(entryDate(1))] + tradeProfit;
end;

Buy next bar at highest(high,9)[1] stop;
Sellshort next bar at lowest(low,9)[1] stop;

mp = marketPosition;
if mp <> mp[1] then dayOfWeekAnalysis();
If lastBarOnChart then
Begin
 	print("Monday ",weekArray[1]);
 	print("Tuesday ",weekArray[2]);
 	print("Wednesday ",weekArray[3]);
 	print("Thursday ",weekArray[4]);
 	print("Friday ",weekArray[5]);
end;
PowerEditor Cannot Handle Method Syntax

Convert Method to External Function

Sounds easy enough – just remove Method and copy code and put into a new function.  This method keeps track of Day Of Week Analysis.  So what is the function going to return?  It needs to return the performance metrics for Monday, Tuesday, Wednesday, Thursday and Friday.  That is five values so you can’t simply  assign the Function Name a single value – right?

Create A New Function – Call It DayOfWeekAnalysis

inputs: weekArray[n](numericArrayRef);

vars: mp(0);
var: tradeProfit(0);
mp = marketPosition;

tradeProfit = -999999999;
If mp = 1 and mp[1] = -1 then tradeProfit = (entryPrice(1) - entryPrice(0))*bigPointValue;
If mp = -1 and mp[1] = 1 then tradeProfit = (entryPrice(0) - entryPrice(1))*bigPointValue;
if tradeProfit <> -999999999 then
 	weekArray[dayOfWeek(entryDate(1))] = weekArray[dayOfWeek(entryDate(1))] + tradeProfit;
print(d," ",mp," ",mp[1]," ",dayOfWeek(entryDate(1)),tradeProfit," ",entryDate," ",entryDate(1)," ",entryPrice(0)," ",entryPrice(1));

DayOfWeekAnalysis = 1;
Simple Function - What's the Big Deal

Looks pretty simple and straight forward.  Take a look at the first line of code.  Notice how I inform the function to expect an array of [n] length to passed to it.  Also notice I am not passing by value but by reference.  Value versus reference – huge difference.  Value is a scalar value such as 5, True or a string.  When you pass by reference you are actually passing a pointer to actual location in computer memory – once you change it – it stays changed and that is what we want to do.  When you pass a variable to an indicator function you are simple passing a value that is not modified within the body of the function.  If you want a function to modify and return more than one value you can pass the variable and catch it as a numericRef.  TradeStation has a great explanation of multiple output functions.

Multiple Output Function per EasyLanguage

Some built-in functions need to return more than a single value and do this by using one or more output parameters within the parameter list.  Built-in multiple output functions typically preface the parameter name with an ‘o’ to indicate that it is an output parameter used to return a value.  These are also known as ‘input-output’ parameters because they are declared within a function as a ‘ref’ type of  input (i.e. NumericRef, TrueFalseRef, etc.) which allows it output a value, by reference, to a variable in the EasyLanguage code calling the function.

I personally don’t follow the “O” prefacing, but if it helps you program then go for it.

Series Function – What Is It And Why Do I Need to Worry About It?

A series function is a specialized function that refers to a previous function value within its calculations.  In addition, series functions update their value on every bar even if the function call is placed within a conditional structure that may not be true on a given bar.  Because a series function automatically stores its own previous values and executes on every bar, it allows you to write function calculations that may be more streamlined than if you had to manage all of the resources yourself.  However, it’s a good idea to understand how this might affect the performance of your EasyLanguage code.

Seems complicated, but it really isn’t.  It all boils down to SCOPE – not the mouthwash.  See when you call a function all the variables inside that function are local to that particular function – in other words it doesn’t have a memory.  If it changes a value in the first call to the function, it has amnesia so the next time you call the function it forgets what it did just prior – unless its a series function.  Then it remembers.  This is why I can do this:

 	If mp = 1 and mp[1] = -1 then tradeProfit = (entryPrice(1) - entryPrice(0))*bigPointValue;
 	If mp = -1 and mp[1] = 1 then tradeProfit = (entryPrice(0) - entryPrice(1))*bigPointValue;
I Can Refer to Prior Values - It Has A Memory

Did you notice TradeProfit = -99999999 and then if it changes then I accumulate it in the correct Day Bin.  If I didn’t check for this then the values in the Day Bin would be accumulated with the values returned by EntryPrice and ExitPrice functions.  Remember this function is called on every bar even if you don’t call it.  I could have tested if a trade occurred and passed this information to the function and then have the function access the EntryPrice and ExitPrice values.  This is up to your individual taste of style.  One more parameter for readability, or one less parameter for perhaps efficiency?

This Is A Special Function – Array Manipulator and Series Type

When you program a function like this the EasyLanguage Dev. Environment can determine what type of function you are using.  But if you need to change it you can.  Simply right click inside the editor and select Properites.

Function Properties – AutoDetect Selected

How Do You Call Such a “Special”  Function?

The first thing you need to do is declare the array that you will be passing to the function.  Use the keyword Array and put the number of elements it will hold and then declare the values of each element.  Here I create a 5 element array and assign each element zero.  Here is the function wrapper.

array: weekArray[5](0);
vars: mp(0),newTrade(false);

Buy next bar at highest(high,9)[1] stop;
Sellshort next bar at lowest(low,9)[1] stop;
mp = marketPosition;
newTrade = False;
//if mp <> mp[1] then newTrade = true;
	
value1 = dayOfWeekAnalysis(weekArray);
If lastBarOnChart then
Begin
 	print("Monday ",weekArray[1]);
 	print("Tuesday ",weekArray[2]);
 	print("Wednesday ",weekArray[3]);
 	print("Thursday ",weekArray[4]);
 	print("Friday ",weekArray[5]);
end;
Wrapper Function - Notice I only Pass the Array to the Function

Okay that’s how you convert a Method from EasyLanguage into a Function.  Functions are more re-uasable, but methods are easier.  But if you can’t use a method you now know how to convert one that uses Array Manipulation and us a “Series” type.

 

 

EasyLanguage Programming Workshop Part 1: 2D Array, Print Format, and Loops

Storing Trades for Later Use in a 2D Array

Since this is part 1 we are just going to go over a very simple system:  SAR (stop and reverse) at highest/lowest high/low for past 20 days.

A 2D Array in EasyLanguage is Immutable

Meaning that once you create an array all of the data types must be the same.  In a Python list you can have integers, strings, objects whatever.   In C and its derivatives you also have a a data structure (a thing that stores related data) know as a Structure or Struct.  We can mimic a structure in EL by using a 2 dimensional array.  An array is just a list of values that can be referenced by an index.

array[1] = 3.14

array[2] = 42

array[3] = 2.71828

A 2 day array is similar but it looks like a table

array[1,1], array[1,2], array[1,3]

array[2,1], array[2,2], array[2,3]

The first number in the pair is the row and the second is the column.  So a 2D array can be very large table with many rows and columns.  The column can also be referred to as a field in the table.  To help use a table you can actually give your fields names.  Here is a table structure that I created to store trade information.

  1. trdEntryPrice (0) – column zero – yes we can have a 0 col. and row
  2. trdEntryDate(1)
  3. trdExitPrice (2)
  4. trdExitDate(3)
  5. trdID(4)
  6. trdPos(5)
  7. trdProfit(6)
  8. trdCumuProfit(7)

So when I refer to tradeStruct[0, trdEntryPrice] I am referring to the first column in the first row.

This how you define a 2D array and its associate fields.

arrays: tradeStruct[10000,7](0);

vars: trdEntryPrice (0),
      trdEntryDate(1), 
      trdExitPrice (2),
      trdExitDate(3),
      trdID(4),
      trdPos(5),
      trdProfit(6),
      trdCumuProfit(7);
2D array and its Fields

In EasyLanguage You are Poised at the Close of a Yesterday’s Bar

This paradigm allows you to sneak a peek at tomorrow’s open tick but that is it.  You can’t really cheat, but it also limits your creativity and makes things more difficult to program when all you want is an accurate backtest.   I will go into detail, if I haven’t already in an earlier post, the difference of sitting on Yesterday’s close verus sitting on Today’s close with retroactive trading powers.  Since we are only storing trade information when can use hindsight to gather the information we need.

Buy tomorrow at highest(h,20) stop;

SellShort tomorrow at lowest(l,20) stop;

These are the order directives that we will be using to execute our strategy.  We can also run a Shadow System, with the benefit of hindsight, to see where we entered long/short and at what prices. I call it a Shadow because its all the trades reflected back one bar.   All we need to do is offset the highest and lowest calculations by 1 and compare the values to today’s highs and lows to determine trade entry.  We must also test the open if a gap occurred and we would have been filled at the open.  Now this code gets a bit hairy, but stick with it.

Shadow System

stb = highest(h,20);
sts = lowest(l,20);
stb1 = highest(h[1],20);
sts1 = lowest(l[1],20);

buy("Sys-L") 1 contract next bar at stb stop;
sellShort("Sys-S") 1 contract next bar at sts stop;

mp = marketPosition*currentContracts;
totTrds = totalTrades;

if mPos <> 1 then
begin
	if h >= stb1 then
	begin
		if mPos < 0 then // close existing short position
		begin
			mEntryPrice = tradeStruct[numTrades,trdEntryPrice];
			mExitPrice = maxList(o,stb1);
			tradeStruct[numTrades,trdExitPrice] = mExitPrice;
			tradeStruct[numTrades,trdExitDate] = date;
			mProfit = (mEntryPrice - mExitPrice) * bigPointValue - mCommSlipp;
			cumuProfit += mProfit;
			tradeStruct[numTrades,trdCumuProfit] = cumuProfit;
			tradeStruct[numTrades,trdProfit] = mProfit;
			print(d+19000000:8:0," shrtExit ",mEntryPrice:4:5," ",mExitPrice:4:5," ",mProfit:6:0," ",cumuProfit:7:0);
		print("-------------------------------------------------------------------------");	
		end;	
		numTrades +=1;
		mEntryPrice = maxList(o,stb1);
		tradeStruct[numTrades,trdID] = 1;
		tradeStruct[numTrades,trdPOS] = 1;
		tradeStruct[numTrades,trdEntryPrice] = mEntryPrice;
		tradeStruct[numTrades,trdEntryDate] = date;
		mPos = 1;
		print(d+19000000:8:0," longEntry ",mEntryPrice:4:5);
	end;
end;
if mPos <>-1 then
begin
	if l <= sts1 then
	begin
		if mPos > 0 then // close existing long position
		begin
			mEntryPrice = tradeStruct[numTrades,trdEntryPrice];
			mExitPrice = minList(o,sts1);
			tradeStruct[numTrades,trdExitPrice] = mExitPrice;
			tradeStruct[numTrades,trdExitDate] = date;
			mProfit = (mExitPrice - mEntryPrice ) * bigPointValue - mCommSlipp;
			cumuProfit += mProfit;
			tradeStruct[numTrades,trdCumuProfit] = cumuProfit;
			tradeStruct[numTrades,trdProfit] = mProfit;
			print(d+19000000:8:0," longExit ",mEntryPrice:4:5," ",mExitPrice:4:5," ",mProfit:6:0," ",cumuProfit:7:0);
			print("---------------------------------------------------------------------");
		end;	
		numTrades +=1;
		mEntryPrice =minList(o,sts1);
		tradeStruct[numTrades,trdID] = 2;
		tradeStruct[numTrades,trdPOS] =-1;
		tradeStruct[numTrades,trdEntryPrice] = mEntryPrice;
		tradeStruct[numTrades,trdEntryDate] = date;
		mPos = -1;
		print(d+19000000:8:0," ShortEntry ",mEntryPrice:4:5);
	end;
end;
Shadow System - Generic forany SAR System

Notice I have stb and stb1.  The only difference between the two calculations is one is displaced a day.  I use the stb and sts in the EL trade directives.  I use stb1 and sts1 in the Shadow System code.  I guarantee this snippet of code is in every backtesting platform out there.

All the variables that start with the letter m, such as mEntryPrice, mExitPrice deal with the Shadow System.  Theyare not derived from TradeStation’s back testing engine only our logic.  Lets look at the first part of just one side of the Shadow System:

if mPos <> 1 then
begin
	if h >= stb1 then
	begin
		if mPos < 0 then // close existing short position
		begin
			mEntryPrice = tradeStruct[numTrades,trdEntryPrice];
			mExitPrice = maxList(o,stb1);
			tradeStruct[numTrades,trdExitPrice] = mExitPrice;
			tradeStruct[numTrades,trdExitDate] = date;
			mProfit = (mEntryPrice - mExitPrice) * bigPointValue - mCommSlipp;
			cumuProfit += mProfit;
			tradeStruct[numTrades,trdCumuProfit] = cumuProfit;
			tradeStruct[numTrades,trdProfit] = mProfit;
			print(d+19000000:8:0," shrtExit ",mEntryPrice:4:5," ",mExitPrice:4:5," ",mProfit:6:0," ",cumuProfit:7:0);
		print("-------------------------------------------------------------------------");	
		end;	

mPos and mEntryPrice and mExitPrice belong to the Shadow System

if mPos <> 1 then the Shadow Systems [SS] is not long.  So we test today’s high against stb1 and if its greater then we know a long position was put on.  But what if mPos = -1 [short], then we need to calculate the exit and the trade profit and the cumulative trade profit.  If mPos = -1 then we know a short position is on and we can access its particulars from the tradeStruct 2D arraymEntryPrice = tradeStruct[numTrades,trdEntryPrice].  We can gather the other necessary information from the tradeStruct [remember this is just a table with fields spelled out for us.]  Once we get the information we need we then need to stuff our calculations back into the Structure or table so we can regurgitate later.  We stuff date in to the following fields trdExitPrice, trdExitDate, trdProfit and trdCumuProfit in the table.

Formatted Print: mEntryPrice:4:5

Notice in the code how I follow the print out of variables with :8:0 or :4:5?  I am telling TradeStation to use either 0 or 5 decimal places.  The date doesn’t need decimals but prices do.  So I format that so that they will line up really pretty like.

Now that I take care of liquidating an existing position all I need to do is increment the number of trades and stuff the new trade information into the Structure.

		numTrades +=1;
		mEntryPrice = maxList(o,stb1);
		tradeStruct[numTrades,trdID] = 1;
		tradeStruct[numTrades,trdPOS] = 1;
		tradeStruct[numTrades,trdEntryPrice] = mEntryPrice;
		tradeStruct[numTrades,trdEntryDate] = date;
		mPos = 1;
		print(d+19000000:8:0," longEntry ",mEntryPrice:4:5);

The same goes for the short entry and long exit side of things.  Just review the code.  I print out the trades as we go along through the history of crude.  All the while stuffing the table.

If LastBarOnChart -> Regurgitate

On the last bar of the chart we know exactly how many trades have been executed because we were keeping track of them in the Shadow System.  So it is very easy to loop from 0 to numTrades.

if lastBarOnChart then
begin
	print("Trade History");
	for arrIndx = 1 to numTrades
	begin
		value20 = tradeStruct[arrIndx,trdEntryDate];
		value21 = tradeStruct[arrIndx,trdEntryPrice];
		value22 = tradeStruct[arrIndx,trdExitDate];
		value23 = tradeStruct[arrIndx,trdExitPrice];
		value24 = tradeStruct[arrIndx,trdID];
		value25 = tradeStruct[arrIndx,trdProfit];
		value26 = tradeStruct[arrIndx,trdCumuProfit];
		
		print("---------------------------------------------------------------------");
		if value24 = 1 then
		begin
			string1 = buyStr;
			string2 = sellStr;
		end;
		if value24 = 2 then
		begin
			string1 = shortStr;
			string2 = coverStr;
		end;	
		print(value20+19000000:8:0,string1,value21:4:5," ",value22+19000000:8:0,string2,
			  value23:4:5," ",value25:6:0," ",value26:7:0);
	end;
end;

Add 19000000 to Dates for easy Translation

Since all trade information is stored in the Structure or Table then pulling the information out using our Field Descriptors is very easy.  Notice I used EL built-in valueXX to store table information.  I did this to make the print statements a lot shorter.  I could have just used tradeStruct[arrIndx, trdEntry] or whatever was needed to provide the right information, but the lines would be hard to read.  To translate EL date to a normal looking data just add 19,000,000 [without commas].

If you format your PrintLog to a monospaced font your out put should look like this.

 

PrintLog OutPut

Why Would We Want to Save Trade Information?

The answer to this question will be answered in Part 2.  Email me with any other questions…..

Why Do I Need to Test with Intraday Data

Why Can’t I Just Test with Daily Bars and Use Look-Inside Bar?

Good question.  You can’t because it doesn’t work accurately all of the time.   I just default to using 5 minute or less bars whenever I need to.  A large portion of short term, including day trade, systems need to know the intra day market movements to know which orders were filled accurately.  It would be great if you could just flip a switch and convert a daily bar system to an intraday system and Look Inside Bar(LIB) is theoretically that switch.  Here I will prove that switch doesn’t always work.

Daily Bar System

  • Buy next bar at open of the day plus 20% of the 5 day average range
  • SellShort next at open of the day minus 20% of the 5 day average range
  • If long take a profit at one 5 day average range above entryPrice
  • If short take a profit at one 5 day average range below entryPrice
  • If long get out at a loss at 1/2 a 5 day average range below entryPrice
  • If short get out at a loss at 1/2 a 5 day average range above entry price
  • Allow only 1 long and 1 short entry per day
  • Get out at the end of the day

Simple Code for the System

value1 = .2 * average(Range,5);
value2 = value1 * 5;

Buy next bar at open of next bar + value1 stop;
sellShort next bar at open of next bar - value1 stop;

setProfitTarget(value2*bigPointValue);
setStopLoss(value2/2*bigPointValue);
setExitOnClose;
Simplified Daily Bar DayTrade System using ES.D Daily
Daily Bar Using 5 min Look Inside Bar

Looks great with just the one hiccup:  Bot @ 3846.75 and the Shorted @ 3834.75 and then took nearly 30 handles of profit.

Now let’s see what really happened.

What Really Happened – Bot – Shorted – Stopped Out

Intraday Code to Control Entry Time and Number of Longs and Shorts

Not an accurate representation so let’s take this really simple system and apply it to intraday data.  Approaching this from a logical perspective with limited knowledge about TradeStation you might come up with this seemingly valid solution.  Working on the long side first.

//First Attempt


if d <> d[1] then value1 = .2 * average(Range of data2,5);
value2 = value1 * 5;
if t > sess1startTime then buy next bar at opend(0) + value1 stop;
setProfitTarget(value2*bigPointValue);
setStopLoss(value2/2*bigPointValue);
setExitOnClose;
First Simple Attempt

This looks very similar to the daily bar system.  I cheated a little by using

if d <> d[1] then value1 = .2 * average(Range of data2,5);

Here I am only calculating the average once a day instead of on each 5 minute bar.  Makes things quicker.  Also I used

if t > sess1StartTime then buy next bar at openD(0) + value1 stop;

I did that because if you did this:

buy next bar at open of next bar + value1 stop;

You would get this:

Cannot Sneak a Peek with Data2

That should do it for the long side, right?

Didn’t work quite right!

So now we have to monitor when we can place a trade and monitor the number of long and short entries.

How does this look!

Correct Execution!

So here is the code.  You will notice the added complexity.  The important things to know is how to control when an entry is allowed and how to count the number of long and short entries.  I use the built-in keyword/function totalTrades to keep track of entries/exits and marketPosition to keep track of the type of entry.

Take a look at the code and you can see how the daily bar system is somewhat embedded in the code.  But remember you have to take into account that you are stepping through every 5 minute bar and things change from one bar to the next.

vars: buysToday(0),shortsToday(0),curTotTrades(0),mp(0),tradeZoneTime(False);


if d <> d[1] then 
begin
	curTotTrades = totalTrades;
 	value1 = .2 * average(Range of data2,5);
	value2 = value1 * 5;	
	buysToday = 0;
	shortsToday = 0;
	tradeZoneTime = False;
end;

mp = marketPosition;

if totalTrades > curTotTrades then
begin
	if mp <> mp[1] then 
	begin
		if mp[1] = 1 then buysToday = buysToday + 1;
		if mp[1] = -1 then shortsToday = shortsToday + 1;
	end;
	if mp[1] = -1 then print(d," ",t," ",mp," ",mp[1]," ",shortsToday);
	curTotTrades = totalTrades;
end;
if t > sess1StartTime and t < sess1EndTime then tradeZoneTime = True;

if tradeZoneTime and buysToday = 0 and mp <> 1 then 
	buy next bar at opend(0) + value1 stop;
	
if tradeZoneTime and  shortsToday = 0 and mp <> -1 then 
	sellShort next bar at opend(0) - value1 stop;

setProfitTarget(value2*bigPointValue);
setStopLoss(value2/2*bigPointValue);
setExitOnClose;
Proper Code to Replicate the Daily Bar System with Accuracy

Here’s a few trade examples to prove our code works.

Looks Right!

Okay the code worked but did the system?

Uh? NO!

Conclusion

If you need to know what occurred first – a high or a low in a move then you must use intraday data.  If you want to have multiple entries then of course your only alternative is intraday data.   This little bit of code can get you started converting your daily bar systems to intraday data and can be a framework to develop your own day trading/or swing systems.

Can I Prototype A Short Term System with Daily Data?

You can of course use Daily Bars for fast system prototyping.  When the daily bar system was tested with LIB turned on, it came close to the same results as the more accurately programmed intraday system.  So you can prototype to determine if a system has a chance.  Our core concept buyt a break out, short a break out, take profits and losses and have no overnight exposure sounds good theoretically.  And if you only allow 2 entries in opposite directions on a daily bar you can determine if there is something there.

A Dr. Jekyll and Mr. Hyde Scenario

While playing around with this I did some prototyping of a daily bar system and created this equity curve.  I mistakenly did not allow any losses – only took profits and re-entered long.

Wow! Awesome! Holy Grail Uncovered. Venalicius Cave!

Venalicius Cave!  Don’t take a loser you and will reap the benefits.  The chart says so – so its got to be true – I know right?

The same chart from a different perspective.

You Start and End at the Same Place. But What A Ride. Yikes!

Moral of the Story – always look at your detailed Equity Curve.  This curve is very close to a simple buy and hold strategy.   Maybe a little better.

Daily Bar Ratcheting Stop and Conditional Optimization

Happy New Year!  My First Post of 2021!

In this post I simply wanted to convert the intraday ratcheting stop mechanism that I previously posted into a daily bar mechanism.  Well that got me thinking of how many different values could be used as the amount to ratchet.  I came up with three:

I have had requests for the EasyLanguage in an ELD – so here it is – just click on the link and unZip.

RATCHETINGSTOPWSWITCH

Ratcheting Schemes

  • ATR of N days
  • Fixed $ Amount
  • Percentage of Standard Deviation of 20 Days

So this was going to be a great start to a post, because I was going to incorporate one of my favorite programming constructs : Switch-Case.  After doing the program I thought wouldn’t it be really cool to be able to optimize over each scheme the ratchet and trail multiplier as well as the values that might go into each scheme.

In scheme one I wanted to optimize the N days for the ATR calculation.  In scheme two I wanted to optimize the $ amount and the scheme three the percentage of a 20 day standard deviation.  I could do a stepwise optimization and run three independent optimizations – one for each scheme.  Why not just do one global optimization you might ask?  You could but it would be a waste of computer time and then you would have to sift through the results.  Huh?  Why?  Here is a typical optimization loop:

Scheme Ratchet Mult Trigger Mult Parameter 1
1 : ATR 1 1 ATR (2)
2 : $ Amt 1 1 ATR (2)
3 : % of Dev. Amt 1 1 ATR (2)
1 : ATR 2 1 ATR (2)
2 : $ Amt 2 1 ATR (2)

Notice when we switch schemes the Parameter 1 doesn’t make sense.  When we switch to $ Amt we want to use a $ Value as Parameter 1 and not ATR.  So we could do a bunch of optimizations across non sensical values, but that wouldn’t really make a lot of sense.  Why not do a conditional optimization?  In other words, optimize only across a certain parameter range based on which scheme is currently being used.  I knew there wasn’t an overlay available to use using standard EasyLanguage but I thought maybe OOP,  and there is an optimization API that is quite powerful.  The only problem is that it was very complicated and I don’t know if I could get it to work exactly the way I wanted.

EasyLanguage is almost a full blown programming language.  So should I not be able to distill this conditional optimization down to something that I could do with such a powerful programming language?  And the answer is yes and its not that complicated.  Well at least for me it wasn’t but for beginners probably.  But to become a successful programmer you have to step outside your comfort zones, so I am going to not only explain the Switch/Case construct (I have done this in earlier posts)  but incorporate some array stuff.

When performing conditional optimization there are really just a few things you have to predefine:

  1. Scheme Based Optimization Parameters
  2. Exact Same Number of Iterations for each Scheme [starting point and increment value]
  3. Complete Search Space
  4. Total Number of Iterations
  5. Staying inside the bounds of your Search Space

Here are the optimization range per scheme:

  • Scheme #1 – optimize number of days in ATR calculation – starting at 10 days and incrementing by 2 days
  • Scheme #2 – optimize $ amounts – starting at $250 and incrementing by $100
  • Scheme #3 – optimize percent of 20 Bar standard deviation – starting at 0,25 and incrementing by 0.25

I also wanted to optimize the ratchet and target multiplier.  Here is the base code for the daily bar ratcheting system with three different schemes.  Entries are based on penetration of 20 bar highest/lowest close.

inputs: 
ratchetMult(2),trailMult(2),
volBase(True),volCalcLen(20),
dollarBase(False),dollarAmt(250),
devBase(False),devAmt(0.25);


vars:longMult(0),shortMult(0);
vars:ratchetAmt(0),trailAmt(0);
vars:stb(0),sts(0),mp(0);
vars:lep(0),sep(0);



if volBase then 
begin
	ratchetAmt = avgTrueRange(volCalcLen) * ratchetMult;
	trailAmt = avgTrueRange(volCalcLen) * trailMult;
end;
if dollarBase then 
begin
	ratchetAmt =dollarAmt/bigPointValue * ratchetMult;
	trailAmt = dollarAmt/bigPointValue * trailMult;
end;
if devBase then 
begin
	ratchetAmt = stddev(c,20) * devAmt * ratchetMult;
	trailAmt = stddev(c,20) * devAmt * trailMult;
end;


if c crosses over highest(c[1],20) then buy next bar at open;
if c crosses under lowest(c[1],20) then sellshort next bar at open;

mp = marketPosition;
if mp <> 0 and mp[1] <> mp then
begin
	longMult = 0;
	shortMult = 0;
end;


If mp = 1 then lep = entryPrice;
If mp =-1 then sep = entryPrice;


// Okay initially you want a X point stop and then pull the stop up
// or down once price exceeds a multiple of Y points
// longMult keeps track of the number of Y point multiples of profit
// always key off of lep(LONG ENTRY POINT)
// notice how I used + 1 to determine profit
// and -  1 to determine stop level

If mp = 1 then 
Begin
	If h >= lep + (longMult + 1) * ratchetAmt then	longMult = longMult + 1;
	Sell("LongTrail") next bar at (lep + (longMult - 1) *  trailAmt) stop;
end;

If mp = -1 then 
Begin
	If l <= sep - (shortMult + 1) * ratchetAmt then	shortMult = shortMult + 1;
	buyToCover("ShortTrail") next bar (sep - (shortMult - 1) *  trailAmt) stop;
end;
Daily Bar Ratchet System

This code is fairly simple.  The intriguing inputs are:

  • volBase [True of False] and  volCalcLen [numeric Value]
  • dollarBase [True of False] and  dollarAmt [numeric Value]
  • devBase [True of False] and devAmt [numeric Value]

If volBase is true then you use the parameters that go along with that scheme.  The same goes for the other schemes.  So when you run this you would turn one scheme on at a time and set the parameters accordingly.  if I wanted to use dollarBase(True) then I would set the dollarAmt to a $ value.  The ratcheting mechanism is the same as it was in the prior post so I refer you back to that one for further explanation.

So this was a pretty straightforward strategy.  Let us plan out our optimization search space based on the different ranges for each scheme.  Since each scheme uses a different calculation we can’t simply optimize across all of the different ranges – one is days, and the other two are dollars and percentages.

Enumerate

We know how to make TradeStation loop based on the range of a value.  If you want to optimize from $250 to $1000 in steps of $250, you know this involves [$1000 – $250] / $250 + 1 or 3 + 1 or 4 interations.   Four loops will cover this entire search space.  Let’s examine the search space for each scheme:

  • ATR Scheme: start at 10 bars and end at 40 by steps of 2 or [40-10]/2 + 1 = 16
  • $ Amount Scheme: start at $250 and since we have to have 16 iterations [remember # of iterations have to be the same for each scheme] what can we do to use this information?  Well if we start $250 and step by $100 we cover the search space $250, $350, $450, $550…$1,750.  $250 + 15 x 250.  15 because $250 is iteration 1.
  • Percentage StdDev Scheme:  start at 0.25 and end at 0.25 + 15 x 0.25  = 4

So we enumerate 16 iterations to a different value.  The easiest way to do this is to create a map.  I know this seems to be getting hairy but it really isn’t.  The map will be defined as an array with 16 elements.  The array will be filled with the search space based on which scheme is currently being tested.  Take a look at this code where I show how to define an array of 16 elements and introduce my Switch/Case construct.

array: optVals[16](0);

switch(switchMode)
begin
	case 1:
		startPoint = 10; // vol based
		increment = 2;
	case 2:
		startPoint = 250/bigPointValue; // $ based
		increment = 100/bigPointValue;
	case 3:
		startPoint = 0.25; //standard dev
		increment = 0.25*minMove/priceScale;
	default:
		startPoint = 1;
		increment = 1;
end;

vars: cnt(0),loopCnt(0);
once 
begin
	for cnt = 1 to 16 
	begin
		optVals[cnt] = startPoint + (cnt-1) * increment;
	end;
end
Set Up Complete Search Space for all Three Schemes

This code creates a 16 element array, optVals, and assigns 0 to each element.  SwitchMode goes from 1 to 3.

  • if switchMode is 1: ATR scheme [case: 1] the startPoint is set to 10 and increment is set to 2
  • if switchMode is 2: $ Amt scheme [case: 2] the startPoint is set to $250 and increment is set to $100
  • if switchMode is 3: Percentage of StdDev [case: 3] the startPoint is set to 0.25 and the increment is set to 0.25

Once these two values are set the following 15 values can be spawned by the these two.  A for loop is great for populating our search space.  Notice I wrap this code with ONCE – remember ONCE  is only executed at the very beginning of each iteration or run.

once
begin
   for cnt = 1 to 16
   begin
     optVals[cnt] = startPoint + (cnt-1) * increment;
   end;
end

Based on startPoint and increment the entire search space is filled out.  Now all you have to do is extract this information stored in the array based on the iteration number.

Switch(switchMode) 
Begin
	Case 1:
		ratchetAmt = avgTrueRange(optVals[optLoops]) * ratchetMult;
		trailAmt = avgTrueRange(optVals[optLoops]) * trailMult;	
	Case 2:
		ratchetAmt =optVals[optLoops] * ratchetMult;
		trailAmt = optVals[optLoops] * trailMult;
	Case 3: 
		ratchetAmt =stddev(c,20) * optVals[optLoops] * ratchetMult;
		trailAmt = stddev(c,20) * optVals[optLoops] * trailMult;
	Default:
		ratchetAmt = avgTrueRange(optVals[optLoops]) * ratchetMult;
		trailAmt = avgTrueRange(optVals[optLoops]) * trailMult;
end;


if c crosses over highest(c[1],20) then buy next bar at open;
if c crosses under lowest(c[1],20) then sellshort next bar at open;

mp = marketPosition;
if mp <> 0 and mp[1] <> mp then
begin
	longMult = 0;
	shortMult = 0;
end;


If mp = 1 then lep = entryPrice;
If mp =-1 then sep = entryPrice;


// Okay initially you want a X point stop and then pull the stop up
// or down once price exceeds a multiple of Y points
// longMult keeps track of the number of Y point multiples of profit
// always key off of lep(LONG ENTRY POINT)
// notice how I used + 1 to determine profit
// and -  1 to determine stop level

If mp = 1 then 
Begin
	If h >= lep + (longMult + 1) * ratchetAmt then longMult = longMult + 1;
	Sell("LongTrail") next bar at (lep + (longMult - 1) *  trailAmt) stop;
end;

If mp = -1 then 
Begin
	If l <= sep - (shortMult + 1) * ratchetAmt then	shortMult = shortMult + 1;
	buyToCover("ShortTrail") next bar (sep - (shortMult - 1) *  trailAmt) stop;
end;
Extract Search Space Values and Rest of Code

Switch(switchMode)
Begin
Case 1:
  ratchetAmt = avgTrueRange(optVals[optLoops])ratchetMult;
  trailAmt = avgTrueRange(optVals[optLoops]) trailMult;
Case 2:
  ratchetAmt =optVals[optLoops] * ratchetMult;
  trailAmt = optVals[optLoops] * trailMult;
Case 3:
  ratchetAmt =stddev(c,20)optVals[optLoops]
ratchetMult;
  trailAmt = stddev(c,20) * optVals[optLoops] * trailMult;

Notice how the optVals are indexed by optLoops.  So the only variable that is optimized is the optLoops and it spans 1 through 16.  This is the power of enumerations – each number represents a different thing and this is how you can control which variables are optimized in terms of another optimized variable.   Here is my optimization specifications:

Opimization space

And here are the results:

Optimization Results

The best combination was scheme 1 [N-day ATR Calculation] using a 2 Mult Ratchet and 1 Mult Trail Trigger.  The best N-day was optVals[2] for this scheme.  What in the world is this value?  Well you will need to back engineer a little bit here.  The starting point for this scheme was 10 and the increment was 2 so if optVals[1] =10 then optVals[2] = 12 or ATR(12).    You can also print out a map of the search spaces.

vars: cnt(0),loopCnt(0);
once 
begin
	loopCnt = loopCnt + 1;
//	print(switchMode," : ",d," ",startPoint);
//	print("  ",loopCnt:2:0,"  --------------------");
	for cnt = 1 to 16 
	begin
		optVals[cnt] = startPoint + (cnt-1) * increment;
//		print(cnt," ",optVals[cnt]," ",cnt-1);
	end;
end;	
  Scheme 1
  --------------------
   1.00   10.00    0.00 10 days
   2.00   12.00    1.00
   3.00   14.00    2.00
   4.00   16.00    3.00
   5.00   18.00    4.00
   6.00   20.00    5.00
   7.00   22.00    6.00
   8.00   24.00    7.00
   9.00   26.00    8.00
  10.00   28.00    9.00
  11.00   30.00   10.00
  12.00   32.00   11.00
  13.00   34.00   12.00
  14.00   36.00   13.00
  15.00   38.00   14.00
  16.00   40.00   15.00
 
  Scheme2
  --------------------
   1.00    5.00    0.00 $ 250
   2.00    7.00    1.00 $ 350
   3.00    9.00    2.00 $ 400
   4.00   11.00    3.00 $ ---
   5.00   13.00    4.00
   6.00   15.00    5.00
   7.00   17.00    6.00
   8.00   19.00    7.00
   9.00   21.00    8.00
  10.00   23.00    9.00
  11.00   25.00   10.00
  12.00   27.00   11.00
  13.00   29.00   12.00
  14.00   31.00   13.00
  15.00   33.00   14.00
  16.00   35.00   15.00 $1750

  Scheme 3
  --------------------
   1.00    0.25    0.00 25 % stdDev
   2.00    0.50    1.00
   3.00    0.75    2.00
   4.00    1.00    3.00
   5.00    1.25    4.00
   6.00    1.50    5.00
   7.00    1.75    6.00
   8.00    2.00    7.00
   9.00    2.25    8.00
  10.00    2.50    9.00
  11.00    2.75   10.00
  12.00    3.00   11.00
  13.00    3.25   12.00
  14.00    3.50   13.00
  15.00    3.75   14.00
  16.00    4.00   15.00

This was a elaborate post so please email me with questions.  I wanted to demonstrate that we can accomplish very sophisticated things with just the pure and raw EasyLanguage which is a programming language itself.

Highly Illogical – Best Guess Doesn’t Match Reality

An ES Break-Out System with Unexpected Parameters

I was recently testing the idea of a short term VBO strategy on the ES utilizing very tight stops.  I wanted to see if using a tight ATR stop in concert with the entry day’s low (for buys) would cut down on losses after a break out.  In other words, if the break out doesn’t go as anticipated get out and wait for the next signal.  With the benefit of hindsight in writing this post, I certainly felt like my exit mechanism was what was going to make or break this system.  In turns out that all pre conceived notions should be thrown out when volatility enters the picture.

System Description

  • If 14 ADX < 20 get ready to trade
  • Buy 1 ATR above the midPoint of the past 4 closing prices
  • Place an initial stop at 1 ATR and a Profit Objective of 1 ATR
  • Trail the stop up to the prior day’s low if it is greater than entryPrice – 1 ATR initially, and then trail if a higher low is established
  • Wait 3 bars to Re-Enter after going flat – Reversals allowed

That’s it.  Basically wait for a trendless period and buy on the bulge and then get it out if it doesn’t materialize.  I knew I could improve the system by optimizing the parameters but I felt I was in the ball park.  My hypothesis was that the system would fail because of the tight stops.  I felt the ADX trigger was OK and the BO level would get in on a short burst.  Just from past experience I knew that using the prior day’s price extremes as a stop usually doesn’t fair that well.

Without commission the initial test was a loser: -$1K and -$20K draw down over the past ten years.  I thought I would test my hypothesis by optimizing a majority of the parameters:

  • ADX Len
  • ADX Trigger Value
  • ATR Len
  • ATR BO multiplier
  • ATR Multiplier for Trade Risk
  • ATR Multiplier for Profit Objective
  • Number of bars to trail the stop – used lowest lows for longs

Results

As you can probably figure, I  had to use the Genetic Optimizer to get the job done.  Over a billion different permutations.  In the end here is what the computer pushed out using the best set of parameters.

No Commission or Slippage – Genetic Optimized Parameter Selection

Optimization Report – The Best of the Best

Top Parameters – notice the Wide Stop Initially and the Trailing Stop Look-Back and also the Profit Multiplier – but what really sticks out is the ADX inputs

ADX – Does it Really Matter?

Take a look at the chart – the ADX is mostly in Trigger territory – does it really matter?

A Chart is Worth a 1000 Words

What does this chart tell us?

70% of Profit was made in last 40 trades

Was the parameter selection biased by the heightened level of volatility?  The system has performed on the parameter set very well over the past two or three years.  But should you use this parameter set going into the future – volatility will eventually settle down.

Now using my experience in trading I would have selected a different parameter set.   Here are my biased results going into the initial programming.  I would use a wider stop for sure, but I would have used the generic ADX values.

George’s More Common Sense Parameter Selection – wow big difference

I would have used 14 ADX Len with a 20 trigger and risk 1 to make 3 and use a wider trailing stop.  With trend neutral break out algorithms, it seems you have to be in the game all of the time.  The ADX was supposed to capture zones that predicated break out moves, but the ADX didn’t help out at all.  Wider stops helped but it was the ADX values that really changed the complexion of the system.  Also the number of bars to wait after going flat had a large impact as well.  During low volatility you can be somewhat picky with trades but when volatility increases you gots to be in the game. – no ADX filtering and no delay in re-Entry.  Surprise, surprise!

Alogorithm Code

Here is the code – some neat stuff here if you are just learning EL.  Notice how I anchor some of the indicator based variables by indexing them by barsSinceEntry.  Drop me a note if you see something wrong or want a little further explanation.

Inputs: adxLen(14),adxTrig(25),atrLen(10),atrBOMult(1),atrRiskMult(1),atrProfMult(2),midPtNumBar(3),posMovTrailNumBars(2),reEntryDelay(3);
vars: mp(0),trailLongStop(0),trailShortStop(0),BSE(999),entryBar(0),tradeRisk(0),tradeProf(0);
vars: BBO(0),SBO(0),ATR(0),totTrades(0);

mp = marketPosition;
totTrades = totalTrades;
BSE = barsSinceExit(1);
If totTrades <> totTrades[1] then BSE = 0;
If totalTrades = 0 then BSE = 99;


ATR = avgTrueRange(atrLen);

SBO = midPoint(c,midPtNumBar) - ATR * atrBOMult;
BBO = midPoint(c,midPtNumBar) + ATR * atrBOMult;

tradeRisk = ATR * atrRiskMult;
tradeProf = ATR * atrProfMult;

If mp <> 1 and adx(adxLen) < adxTrig and BSE > reEntryDelay and open of next bar < BBO then buy next bar at BBO stop;
If mp <>-1 and adx(adxLen) < adxTrig AND BSE > reEntryDelay AND open of next bar > SBO then sellshort next bar at SBO stop;

If mp = 1 and mp[1] <> 1 then
Begin
	trailLongStop = entryPrice - tradeRisk;
end;

If mp = -1 and mp[1] <> -1 then
Begin
	trailShortStop = entryPrice + tradeRisk;
end;
	
if mp = 1 then sell("L-init-loss") next bar at entryPrice - tradeRisk[barsSinceEntry] stop;
if mp = -1 then buyToCover("S-init-loss") next bar at entryPrice + tradeRisk[barsSinceEntry] stop;


if mp = 1 then 
begin
	sell("L-ATR-prof") next bar at entryPrice + tradeProf[barsSinceEntry] limit;
	trailLongStop = maxList(trailLongStop,lowest(l,posMovTrailNumBars));
	sell("L-TL-Stop") next bar at trailLongStop stop;
end; 
if mp =-1 then 
begin
	buyToCover("S-ATR-prof") next bar at entryPrice -tradeProf[barsSinceEntry] limit;
	trailShortStop = minList(trailShortStop,highest(h,posMovTrailNumBars));
//	print(d, " Short and trailStop is : ",trailShortStop);
	buyToCover("S-TL-Stop") next bar at trailShortStop stop;
end;

Converting A String Date To A Number – String Manipulation in EasyLanguage

EasyLanguage Includes a Powerful String Manipulation Library

I thought I would share this function.  I needed to convert a date string (not a number per se) like “20010115” or “2001/01/15” or “01/15/2001” or “2001-01-15” into a date that TradeStation would understand.  The function had to be flexible enough to accept the four different formats listed above.

String Functions

Most programming languages have functions that operate strictly on strings and so does EasyLanguage.  The most popular are:

  • Right String (rightStr) – returns N characters from the right side of the string.
  • Left String (leftStr) – returns N character starting from the left side of the string
  • Mid String (midStr) – returns the middle portion of a string starting at a specific place in the string and advance N characters
  • String Length (strLen) – returns the number of characters in the string
  • String To Number (strToNum) – converts the string to a numeric representation.  If the string has a character, this function will return 0
  • In String (inStr) – returns location of a sub string inside a larger string ( a substring can be just one character long)

Unpack the String

If the format is YYYYMMDD format then all you need to do is remove the dashes or slashes (if there are any) and then convert what is left over to a number.   But if the format is MM/DD/YYYY format then we are talking about a different animal.  So how can you determine if the date string is in this format?  First off you need to find out if the month/day/year separator is a slash or a dash.  This is how you do this:

whereIsAslash = inStr(dateString,”/”);
whereIsAdash = inStr(dateString,”-“);

If either is a non zero then you know there is a separator.  The next thing to do is locate the first “dash or slash” (the search character or string).  If it is located within the first four characters of the date string then you know its not a four digit year.  But, lets pretend the format is “12/14/2001” so if the first dash/slash is the 3rd character you can extract the month string by doing this:

firstSrchStrLoc = inStr(dateString,srchStr);
mnStr= leftStr(dateString,firstSrchStrLoc-1);

So if firstSrchStrLoc = 3 then we want to leftStr the date string and extract the first two characters and store them in mnStr.  We then store what’s left of the date string in tempStr by using rightStr:

strLength = strLen(dateString);

tempStr = rightStr(dateString,strLength-firstSrchStrLoc);

Here I pass dateString and the strLength-firstSrchStrLoc – so if the dateString is 10 characters long and the firstSrchStrLoc is 3, then we can create a tempstring by taking [10 -3  = 7 ] characters from right side of the string:

“12/14/2001” becomes “14/2001” – once that is done we can pull the first two characters from the tempStr and store those into the dyStr [day string.]  I do this by searching for the “/” and storing its location in srchStrLoc.  Once I have that location I can use that information and leftStr to get the value I need.   All that is left now is to use the srchStrLoc and the rightStr function.

srchStrLoc = inStr(tempStr,srchStr);
dyStr = leftStr(tempStr,srchStrLoc-1);
yrStr = rightStr(tempStr,strLen(tempStr)-srchStrLoc);

Now convert the strings to numbers and multiply their values accordingly.

DateSTrToYYYMMDD = strToNum(yrStr) X 10000-19000000 + strToNum(mnStr) X 100 + strToNum(dyStr)

To get the date into TS format I have to subtract 19000000 from the year.  Remember TS represents the date in YYYMMDD  format.

Now what do  you do if the date is in the right format but simply includes the dash or slash separators.  All you need to do here is loop through the string and copy all non dash or slash characters to a new string and then convert to a number.  Here is the loop:

        tempStr = "";
        iCnt = 1;
        While iCnt <= strLength
        Begin
            If midStr(dateString,iCnt,1) <> srchStr then
            	tempStr += midStr(dateString,iCnt,1);
            	iCnt+=1;
        end;
        tempDate = strToNum(tempStr);
        DateStrToYYYMMDD = tempDate-19000000;

Here I use midStr to step through each character in the string.  MidStr requires a string and the starting point and how many characters you want returned from the string.  Notice I step through the string with iCnt and only ask for 1 character at a time.  If the character is not a dash or slash I concatenate tempStr with the non dash/slash character.  At the end of the While loop I simply strToNum the string and subtract 19000000.  That’s it!  Remember EasyLanguage is basically a full blown programming language with a unique set of functions that relate directly to trading.

Here is the function and testFunc caller.

STRINGFUNCANDFUNCCALLER

 

Ratio Adjusted versus Point Adjusted Contracts in TradeStation Part 2

Thomas Stridsman quote from  his “Trading Systems That Work Book”

The benefits of the RAD contract also become evident when you want to put together a multimarket portfolio…For now we only state that the percentage based calculations do not take into consideration how many contracts you’re trading and, therefore, give each market an equal weighting in the portfolio.

The Stridsman Function I presented in the last post can be used to help normalize a portfolio of different markets.  Here is a two market portfolio (SP – 250price and JY -125Kprice contract sizes) on a PAD contract.

1-Contract SP and JY on PAD data

Here is the performance of the same portfolio on a RAD contract.

Equal rating of SP and JY on RAD data

 

The curve shapes are similar but look at the total profit and the nearly $125K draw down.  I was trying to replicate Thomas’ research so this data is from Jan. 1990 to Dec. 1999.  A time period where the price of the SP increased 3 FOLD!  Initially you would start trading 1 JY to 2 SP but by the time it was over you would be trading nearly 3 JY to 1 SP.  Had you traded at this allocation the PAD numbers would be nearly $240K in profit.  Now this change occurred through time so the percentage approach is applied continuously.  Also the RAD data allows for a somewhat “unrealistic” reinvestment or compounding mechanism.  Its unrealistic because you can’t trade a partial futures contract.  But it does give you a glimpse of the potential.  The PAD test does not show reinvestment of profit.  I have code for that if you want to research that a little bit more.  Remember everything is in terms of Dec. 31 1999 dollars.  That is another beauty of the RAD contract.

Another Stridsman Quote

Now, wait a minute, you say, those results are purely hypothetical.  How can I place all the trades in the same market at presumably the same point in time?  Well, you can’t, so that is a good and valid question; but let me ask you, can you place any of these trades for real, no matter, how you do it?  No, of course not.  They all represent foregone opportunities.  Isn’t it better then to at least place them hypothetically in today’s marketplace to get a feel for what might happen today, rather in a ten-year-old market situation to get a feel for how the situation was back then?  I think wall can agree that it is better to know what might happen today, rather than what happened ten years ago.

That is a very good point.  However, convenience and time is import and when developing an algorithm.  And most platforms, including my TS-18, are geared toward PAD data.  However TS-18 can look at the entire portfolio balance and all the market data for each market up to that point in time and can adjust/normalize based on portfolio and data metrics.  However, I will add a percentage module a little later, but I would definitely use the StridsmanFunc that I presented in the last post to validate/verify your algorithm in today’s market place if using TradeStation.

Email me if you want the ELD of the function.