Kelly Formula [KF]

Summary:
This position sizing script risks a specified fraction of the account equity on each trade, it does so by using an approximate formula to determine the fixed fractional that maximizes the equity growth rate.

	 ' Assign the parameters to script variables.
	_defaultTradeRisk = defaultTradeRisk
	_defaultRiskRatio = defaultRiskRatio
	_minimumTrades = minimumTrades
	_enableExitSizing = enableExitSizing

	 ' Get the order type.
	Define typeOrder As Integer = OrderType(orderIndex)
	 ' Get the order symbol index.
	Define symbolIndex As Integer = OrderSymbolIndex(orderIndex)
	 ' If the order type is an entry order then calculate the position size.
	If (typeOrder = C_BUY Or _
		typeOrder = C_SELL_SHORT) Then
		Define kelly As Number
		 ' Use for the ratio between the average winning trade and the average losing trad.
		Define averageRatio As Number
		 ' Use for the average winning trade amount.
		Define averageWinningTrade As Number
		 ' Use for counting the winning trades.
		Define winningTrades As Integer
		 ' Use for the average losing trade amount.
		Define averageLosingTrade As Number
		 ' Use for counting the losing trades.
		Define losingTrades As Integer
		 ' Use for the probability of winning a trade.
		Define probabilityOfWinningTrade As Number
		 ' Use for the maximum trade loss, which defines the trade risk.
		Define tradeRisk As Number
		 ' Use for the P/L of the current trade.
		Define profitLoss As Number
		 ' Get the closed trades indexes.
		Define closedTrades() As Integer = TradeIndexList(C_CLOSED)
		 ' Iterate over all of the closed trades.
		For i As Integer = 0 To closedTrades.Length - 1
			 ' Get the P/L of the current closed trade.
			profitLoss = TradeProfitLoss(closedTrades(i))
			 ' Count the winning and losing trades, and sum their values.
			If (profitLoss > 0) Then
				winningTrades += 1
				averageWinningTrade += profitLoss
			Else
				losingTrades += 1
				averageLosingTrade += MathAbs(profitLoss)
				 ' Keep track of the largest loss.
				If (profitLoss < tradeRisk) Then
					tradeRisk = profitLoss
				End If
			End If
		Next
		 ' Calculate the kelly f value using historical information.
		If (winningTrades + losingTrades  > _minimumTrades) Then
			averageWinningTrade = averageWinningTrade / winningTrades
			averageLosingTrade = averageLosingTrade / losingTrades
			probabilityOfWinningTrade = winningTrades / (winningTrades + losingTrades)
			averageRatio = averageWinningTrade / averageLosingTrade
			kelly = ((averageRatio + 1) * probabilityOfWinningTrade - 1) / averageRatio
			OutputWriteLine(averageWinningTrade & " " & averageLosingTrade & " " & probabilityOfWinningTrade & " " & averageRatio & " " & kelly)
		Else
		 ' Assign the kelly f value from the user specified default value.
			kelly = _defaultRiskRatio / 100
			tradeRisk = -1 * _defaultTradeRisk		
		End If
		Return MathFloor((kelly * AccountEquity()) / MathAbs(tradeRisk))
	Else If (_enableExitSizing)
		 ' If the order type is an exit order then calculate the position size.
		Define openPositions() As Integer = PositionIndexList(C_OPEN)
		For i As Integer = 0 To openPositions.Length - 1
			If (PositionSymbolIndex(openPositions(i)) = symbolIndex) Then
				Return PositionQuantity(openPositions(i))
			End If
		Next
	End If