It tells you that in 95% of the scenarios your results will be between x1 and x2 $.
I have been using a similar toy in excel. It will not do exactly what you want but you can take some ideas from it. You can change the code for example a little to include 100 equiprobable trades instead of 20 trades with corresponding probabilities.
Anyway the code is this (I could attach the spreadsheet but some people may feel uneasy to download a spreadsheet with code in it, though they could disable macros for the first time and inspect the code then enable macros again.)
Code:
'***********************************
'* Sort the numbers *
'***********************************
Sub Sort(n As Variant, arr() As Double)
Dim Temp As Double
Dim i As Long
Dim j As Long
For j = 2 To n
Temp = arr(j)
For i = j - 1 To 1 Step -1
If (arr(i) <= Temp) Then GoTo 10
arr(i + 1) = arr(i)
Next i
i = 0
10 arr(i + 1) = Temp
Next j
End Sub
'*********************************************
'* Construct Historgram Distribution *
'*********************************************
Sub Hist(n As Variant, M As Long, start As Double, Right As Double, arr() As Double)
Dim i As Long, j As Long, Find As Long
Dim Length As Double
ReDim breaks(M) As Single
ReDim freq(M) As Single
For i = 1 To M
freq(i) = 0
Next i
Length = (Right - start) / M
For i = 1 To M
breaks(i) = start + Length * i
Next i
For i = 1 To n
If (arr(i) <= breaks(1)) Then freq(1) = freq(1) + 1
If (arr(i) >= breaks(M - 1)) Then freq(M) = freq(M) + 1
For j = 2 To M - 1
If (arr(i) > breaks(j - 1) And arr(i) <= breaks(j)) Then freq(j) = freq(j) + 1
Next j
Next i
For i = 1 To M
Cells(i + 1, 9) = breaks(i)
Cells(i + 1, 10) = freq(i)
Next i
End Sub
'*******************************************************
' Simulate iteration trials with k trades each *
'*******************************************************
Sub MonteCarlo()
Dim Iteration As Long
Iteration = Cells(23, 4) 'number of trials
ReDim TP(Iteration) As Double 'bankroll at the end of each trial
Dim k As Long
k = Cells(24, 4) 'number of trades at each trial
initbankroll = Cells(25, 4) 'starting bankroll
sbankroll = 0 'average bankroll at the end of each trial
lnsbankrol = 0 'average ln bankroll at the end of each trial
Dim pay(20) 'trade payoff
Dim prob(20) 'payoff's probability of occurence
Dim cprob(20) 'cummulative probability of payoffs
cprob(0) = 0
SUMmaxdrawdown = 0
For ct1 = 1 To 20
pay(ct1) = Cells(ct1 + 2, 3)
prob(ct1) = Cells(ct1 + 2, 4)
cprob(ct1) = cprob(ct1 - 1) + prob(ct1)
Next ct1
'check if probability sum is 100%
If cprob(20) < 0.999 Or cprob(20) > 1.001 Then
MsgBox "Payoff Probabilities must sum 100%"
Exit Sub
End If
'kelly f .1% precission
For ct2 = 0.001 To 1 Step 0.001
ss = 0
For ct1 = 1 To 20
ss = ss + prob(ct1) * Log(1 + ct2 * pay(ct1))
Next ct1
If ss > maxss Then
ff = ct2
maxss = ss
End If
Next ct2
'growth rates
For ct2 = 1 To 20
nflag = 0
ss = 0
For ct1 = 1 To 20
If ct2 * ff / 10 * pay(ct1) > -1 Then
ss = ss + prob(ct1) * Log(1 + ct2 * ff / 10 * pay(ct1))
Else
nflag = 1
End If
Next ct1
Cells(ct2 + 2, 17) = ff / 10 * ct2
If nflag = 0 Then
Cells(ct2 + 2, 18) = ss
Else
Cells(ct2 + 2, 18) = ""
End If
Next ct2
' expectancy and variance
For ct1 = 1 To 20
s1 = s1 + prob(ct1) * pay(ct1)
s2 = s2 + prob(ct1) * (pay(ct1)) ^ 2
Next ct1
If Cells(26, 4) = "" Then
f = ff
Else
f = Cells(26, 4) 'betting fraction
End If
variance = s2 - s1 ^ 2
'trials loop
For ct1 = 1 To Iteration
bankroll = initbankroll 'bankroll at the begining of each trial
maxeq = initbankroll 'maxDD statistics
mineq = initbankroll
maxdrawdown = 0
' trades loop
For ct2 = 1 To k
randnum = Rnd
trade = 1 'witch trade payoff will be used
start:
If randnum <= cprob(trade) Then
bankroll = bankroll + f * bankroll * pay(trade)
GoTo estart:
End If
trade = trade + 1
GoTo start:
estart:
If bankroll > maxeq Then
drawdown = (maxeq - mineq) / maxeq
If drawdown > maxdrawdown Then maxdrawdown = drawdown
maxeq = bankroll
mineq = bankroll
End If
If bankroll < mineq Then
mineq = bankroll
End If
Next ct2
drawdown = (maxeq - mineq) / maxeq
If drawdown > maxdrawdown Then maxdrawdown = drawdown
SUMmaxdrawdown = SUMmaxdrawdown + maxdrawdown
sbankroll = sbankroll + bankroll
lnsbankroll = lnsbankroll + Log(bankroll / initbankroll)
TP(ct1) = bankroll
Next ct1
Call Sort(Iteration, TP)
Call Hist(Iteration, 40, TP(1), TP(Iteration), TP)
For i = 1 To 20
Cells(i + 3, 6) = 1 - (0.05 * i)
Cells(i + 3, 7) = TP(Int(Iteration / 20 * i))
Next i
Cells(3, 6) = "Close to 100%"
Cells(13, 6) = "50%"
Cells(23, 6) = "Close to 0%"
Cells(3, 7) = TP(1)
Cells(24, 7) = lnsbankroll / Iteration / k 'Growth Rate
Cells(25, 7) = sbankroll / Iteration 'average bankroll
Cells(26, 7) = s1 'expectancy
Cells(27, 7) = variance ' variance
Cells(28, 7) = ff 'kelly f
Cells(29, 7) = SUMmaxdrawdown / Iteration
End Sub