What
we will attempt to do is build a Monte Carlo Simulation simulating 1000 runs of
500 trades each with multiple contracts, multiple profit targets, multiple stop
losses and multiple probabilities that each is hit/not hit. We will be all in on the initial purchase but
pyramid or “scale out” based on specific profit targets being hit.
First, determine
how many profit targets you are going to have.
Divide the total number of contracts you are trading by this number. For this example, assume that you have 3
contracts with 3 separate profit targets.
We will define these as profit targets #1, #2 and #3.
Second, determine
your initial “drop dead” stop loss. This
will be the amount of money you will lose per contract assuming that profit
target #1 is not hit. You would be “all
out” at this point.
Third, determine
your initial risk to reward ratio for each of your profit targets. For this example, we will assume the
following:
Profit Target #1: Initially risking 10
ticks for a Reward of 20 ticks (1:2 R/R Profile)
Profit Target #2: Initially risking 10
ticks for a Reward of 30 ticks (1:3 R/R Profile)
Profit Target #3: Initially risking 10
ticks for a Reward of 40 ticks (1:4 R/R Profile)
Fourth, determine
how you will scale out or move your stop loss up if and when Profit
Targets #1 and #2 are hit. For this
example, we will do the following:
Scale Out #1: If Profit Target #1 is
hit, we will exit the first contract then we will move the stop loss on the 2
remaining contracts to breakeven plus a tick.
Scale Out #2: If Profit Target #2 is
hit, then we will move the stop loss on the 1 remaining contract to Profit
Target #1.
Fifth, determine
the Winning Percentage (WP) for each of the individual scenarios that you could
have for your scale outs and profit targets.
In this example, we basically have 4 scenarios:
Scenario #1: Call this the “Worst Case
Scenario.” None of the profit targets
are hit and we are stopped out on all 3 contracts. Our loss is equal to 10 ticks times 3
contracts.
Scenario #2: Profit Target #1 is hit
on 1 contract, but we are stopped out on the remaining 2 contracts at breakeven
plus a tick (Scale Out #1). If Scenario
#2 occurs, then we will have 1 contract at a 1:2 R/R and 2 contracts at a
breakeven plus a tick for a total profit of 22 ticks.
Scenario #3: Profit Target #1 is hit
on 1 contract and Profit Target #2 is hit on 1 contract, but we are stopped out
on the remaining 1 contract at Profit Target #1 (Scale Out #2). If Scenario 3
occurs, then we will have 1 contract at a 20 Ticks, 1 contract at 30 ticks and
1 contract at 20 ticks.
Scenario #4: Call this the “Best Case
Scenario.” Profit Targets #1, #2 and #3
are all hit. If Scenario 4 occurs, then
we will have 1 contract at a 20 Ticks, 1 contract at 30 ticks and 1 contract at
40 ticks.
Assume
for a second that on any given trade, the Stop Loss and Profit Targets happen
the following percentage of the time.
Think of the table below as the average that, on a given trade, all 3
contracts would have reached the ultimate profit target or been stopped out:
|
Scenario
|
Probability
|
Total Profit/(Loss)
|
|
#1
|
50%
|
(30) ticks
|
|
#2
|
25%
|
+22 Ticks
|
|
#3
|
15%
|
+70 Ticks
|
|
#4
|
10%
|
+90 Ticks
|
Fifth, we will
also be using fixed risk money management strategies. If you recall, this is a type of money
management strategies that does 2 things:
1. It limits the risk on any one trade to
a fixed percentage of the account equal to the Account Value divided by your
Average Total Loss (across all contracts traded). For example, if you had an initial account
value of $10,000 and never wanted to risk more than 1%, then your fixed risk on
any one trade would be $100.
Essentially, you would have 100 capital units to begin with.
2. It allows the account to compound with
the same initial risk on each trade. If
your account grows to $20,000 after 100 trades and you still want to risk 1% of
your account, then you should be willing to risk $200 on the next trade.
One
problem that I ran into last time is that what happens when the account value
dips below a certain threshold where the individual trade risk is greater than
the fixed risk. To illustrate, take the
above example – we have a 1% fixed risk parameter on a $10,000 account. That means that no more than $100 could be
risked on a given trade. If the first
trade in the series is a loss, then our account is now at $9,900. Our fixed risk is then 1% or a maximum of $99
on the next trade. If our average loss
or individual trade risk is $100, then technically you can’t take the next
trade – you would have to risk $0. This
results in no additional trades being taken in the series. One way to fix this is to delineate between
the individual trade risk and the fixed risk and simply reduce the number of
contracts. I will show you how these two
work together below. Another way would
be to put a minimum contract specification in your simulation. This would specify that, no matter the fixed
risk on the next trade, you would always trade 1 contract.
Another
problem that was encountered last time is the situation where you reach an
unrealistic number of contracts traded.
In one instance, the simulation returned that we should trade 2,000
contracts on the next trade. This is
unrealistic for most retail traders. A
simple fix for the simulation is to place a limit on the number of contracts
traded.
Building Our Excel
Monte Carlo Simulator
The
first step is to create your input page and call it “INPUT” like this:
In
this example, we will be simulating 500 trades in the account and repeating
this 1000 times. We will assume that we
will trade the NQ futures contract with a tick value of $5 per tick. We will initially trade 3 contracts with a
risk per contract (Scenario #1 above) of 10 ticks. We never want to risk more than .5% of our
account on any given trade. Finally, we
assume that the Scenarios outlined above have the given winning percentages,
resulting in a gain/loss per contract outlined above.
Under
the 2nd tab, create a random number generator for each simulation
and call it “Rand”. We want a random
number between 0 and 1 that is rounded to 2 decimal places. You can generate a random number with these
parameters by entering the following:
=ROUND(Rand(),2)
The
2nd Tab then looks like this and is copied over 500 columns (trades
are illustrated in each column) and down 1000 rows (simulations are contained
in each row):
Under
the 3rd tab, we create another sheet that returns the profit or loss
from the random number generation. Call
the 3rd tab “Result”. We then
apply the following rules based on the winning percentages (“WP”) we entered
into the Input tab:
For
random numbers less than the WP contained in Scenario 1, return a 1 (this would
be a loss).
For
random numbers greater than the WP of Scenario 1 but less than the WP of (Scenario
1 + Scenario 2), return a 2.
For
random numbers greater than the WP of (Scenario 1 + Scenario 2) but less than
the WP of (Scenario 1 + Scenario 2 + Scenario 3), return a 3.
For
random numbers greater than the WP of (Scenario 1 + Scenario 2 + Scenario 3)
but less than the WP of (Scenario 1 + Scenario 2 + Scenario 3 + Scenario 4),
return a 4.
You
can do this by creating a nested “IF” function in Excel. For cell B2 in the “Results” tab enter the
following:
=IF(Rand!B2<Input!$C$17,1,IF(Rand!B2<(Input!$C$17+Input!$C$18),2,IF(Rand!B2<(Input!$C$17+Input!$C$18+Input!$C$19),3,4)))
Our
Results tab looks like this:
For
instance, in cell b2 under the Rand tab, it returned the random number 0.6 for
our first trade in our first simulation.
We judge this to mean that for trade 1 simulation 1, we achieved
Scenario 2. You can see in the picture
above, the Result tab returned a 2.
The
step will help us determine whether the trade was a win (by achieving either
Scenarios 2, 3 or 4) or a loss (by achieving Scenario 1).
For
the 4th Tab called WinLoss, enter the following formula in cell c2:
=IF(Result!B2=1,"L","W")
This
tells Excel that if the output in the Results tab is equal to 1, return “L” and
otherwise return a “W.” Your WinLoss tab
should look like this:
We
then want to calculate the maximum number of losers or “L” that we had in a
row. You can do this by creating a 5th
tab on your workbook and calling it WLStreak.
Three calculations are required.
In
cell c2 of WLStreak, enter the following:
=IF(WinLoss!C2="L",1,0)
This
tells Excel that if the outcome of the first trade in the first simulation was
a loss or an “L”, enter a 1 and otherwise enter a 0. Copy this formula down Column C of WLStreak.
In
cell d2 of WLStreak, enter the following:
=IF(WinLoss!D2="L",C2+1,0)
This
tells Excel that if the outcome of the second trade in the first simulation was
a loss or an “L”, add 1 to cell C2 and otherwise enter a 0. This little formula will calculate your
losses in a row and reset them if you have a win. Copy this over to the last trade and down to
the last simulation.
Finally,
in cell a2 of WLStreak, enter the following:
=MAX(C2:SH2)
This
tells Excel that, for the first simulation, what is the maximum number of
losses or “L” that you had in a row.
Cell C2 corresponds to the first trade in the first simulation and cell
SH2 corresponds to the last trade in the first simulation. Copy what you have in cell A2 down each row
for the 1000 simulations.
You
can see in the picture above that the 10th simulation had 17 losses
in a row (see cell A11).
Now
that we now the outcome of each simulation and trade, we need to construct a 6th
tab and call it AccountValue. We will apply
the fixed risk money rules we talked about and allow us to simulate how the account
grows and contracts.
The
AccountValue tab looks like this:
For
column C, reference the starting account value on the input page. This is where every simulation will start
out. In cell C2, I entered the following
formula and copied it down for each simulation:
=Input!$C$3
Next,
create a lookup table called “Scen” using the formula tab. This will be used to lookup the profit or
loss per contract on each trade. Recall
that a “1” in the far left column tells us to return Scenario 1.
Back
to the Account Value tab, for the first trade in the first simulation, enter
the following:
=VLOOKUP(Result!B2,Scen,6)*Input!$C$7+C2
This
tells Excel the following:
1. Lookup the result of the first trade in
the Results tab,
2. Go to the Scen table, find the corresponding
row based on the Result,
3. Return the 6th column over
which is the profit/loss per contract,
4. Multiply it by the number of contracts
we started with on the Input page
5. Add it to our starting account value
contained in cell c2.
Next,
create a second lookup table and call it NoCon or Number of Contracts. This is where our FRMM comes into play. Here is a picture of my NoCon:
Back
to the Account Value tab, for the second trade in the first simulation, enter
the following:
=VLOOKUP(D2*Input!$F$8/Input!$C$6,NoCon,2)*VLOOKUP(Result!C2,Scen,6)+D2
This
formula tells Excel the following:
1. Multiply the previous trade’s account
value by your fixed risk percentage on the Input
page.
2. Divide it by the points per
contract. This result is the maximum
number of contracts you can
trade on this trade.
3. Go to our NoCon table and lookup this
value, returning the number in the second
column. For example, if the result of
Step 2 is a 5, the maximum number of
contracts you could trade would be 3. If
Step 2 returns a 28, the maximum number
of contracts you could trade would be 27.
4. Multiply the numbers of contracts times
the resulting profit/loss per contract and add
it to the previous trades account value.
You
have now created a simulation of this system, scaling out at three different
profit targets. You can add tabs for
maximum drawdown, maximum losses and the ulcer index by following
the steps here.
Interpreting
the Results
One
simulation of the above gives the following results:
|
Ending Account Value
|
||
|
Minimum
|
42,590
|
|
|
Maximum
|
298,840
|
|
|
Average
|
127,341
|
|
|
Median
|
121,585
|
|
|
Mode
|
132,270
|
|
|
Standard Deviation
|
43,688
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
83,652
|
171,029
|
|
2-SD (95% Confidence)
|
39,964
|
214,717
|
|
Maximum Drawdown
|
||
|
Minimum
|
-5.86%
|
|
|
Maximum
|
-28.56%
|
|
|
Average
|
-12.26%
|
|
|
Median
|
-11.68%
|
|
|
Mode
|
-9.19%
|
|
|
Standard Deviation
|
3.43%
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
-8.83%
|
-15.69%
|
|
2-SD (95% Confidence)
|
-5.40%
|
-19.12%
|
|
Ulcer Index
|
||
|
Minimum
|
1.58%
|
|
|
Maximum
|
10.67%
|
|
|
Average
|
3.63%
|
|
|
Median
|
3.41%
|
|
|
Standard Deviation
|
1.16%
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
2.48%
|
4.79%
|
|
2-SD (95% Confidence)
|
1.32%
|
5.95%
|
|
Max Losing Streak
|
||
|
Minimum
|
4
|
|
|
Maximum
|
17
|
|
|
Average
|
8.22
|
|
|
Median
|
8.00
|
|
|
Standard Deviation
|
1.91
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
6.30
|
10.13
|
|
2-SD (95% Confidence)
|
4.39
|
12.05
|
This
gives a very nice, tradable system with an average ending account value of
around 127k, a drawdown of around 12%, UI of 3.63% and max losing streak of 8. The full report in PDF format can be found here.
The
better comparison is whether or not scaling out results in a higher ending
account value with a similar risk profile.
If we were to assume that you could get your 1:2 Risk/Reward on all 3
contracts, rather than scaling out, what would the results look like? Remember, we assumed we hit profit target #1
with all 3 contracts but held on for targets #2 and #3. Here are the results:
|
Ending Account Value
|
||
|
Minimum
|
89,550
|
|
|
Maximum
|
418,500
|
|
|
Average
|
240,823
|
|
|
Median
|
240,150
|
|
|
Mode
|
285,900
|
|
|
Standard Deviation
|
50,059
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
190,764
|
290,882
|
|
2-SD (95% Confidence)
|
140,705
|
340,941
|
|
Maximum Drawdown
|
||
|
Minimum
|
-4.65%
|
|
|
Maximum
|
-21.55%
|
|
|
Average
|
-9.74%
|
|
|
Median
|
-9.28%
|
|
|
Mode
|
-9.09%
|
|
|
Standard Deviation
|
2.55%
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
-7.20%
|
-12.29%
|
|
2-SD (95% Confidence)
|
-4.65%
|
-14.83%
|
|
Ulcer Index
|
||
|
Minimum
|
1.14%
|
|
|
Maximum
|
5.71%
|
|
|
Average
|
2.45%
|
|
|
Median
|
2.33%
|
|
|
Standard Deviation
|
0.65%
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
1.80%
|
3.09%
|
|
2-SD (95% Confidence)
|
1.16%
|
3.74%
|
|
Max Losing Streak
|
||
|
Minimum
|
5
|
|
|
Maximum
|
18
|
|
|
Average
|
8.19
|
|
|
Median
|
8.00
|
|
|
Standard Deviation
|
1.84
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
6.36
|
10.03
|
|
2-SD (95% Confidence)
|
4.52
|
11.87
|
This
looks a lot more promising, since the average account value is almost double
with a lower average drawdown and lower UI.
The full report
can be found here.
However,
what if we accepted more fixed dollar risk on each trade – instead of .5% of
the account, we increased it to 1%? The
table is below and the full report
can be found here.
|
Ending Account Value
|
||
|
Minimum
|
45,590
|
|
|
Maximum
|
456,000
|
|
|
Average
|
247,422
|
|
|
Median
|
247,015
|
|
|
Mode
|
147,150
|
|
|
Standard Deviation
|
53,386
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
194,036
|
300,808
|
|
2-SD (95% Confidence)
|
140,651
|
354,194
|
|
Maximum Drawdown
|
||
|
Minimum
|
-7.77%
|
|
|
Maximum
|
-51.69%
|
|
|
Average
|
-20.07%
|
|
|
Median
|
-18.78%
|
|
|
Mode
|
-15.04%
|
|
|
Standard Deviation
|
6.63%
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
-13.44%
|
-26.70%
|
|
2-SD (95% Confidence)
|
-6.81%
|
-33.34%
|
|
Ulcer Index
|
||
|
Minimum
|
1.78%
|
|
|
Maximum
|
25.14%
|
|
|
Average
|
5.40%
|
|
|
Median
|
4.77%
|
|
|
Standard Deviation
|
2.48%
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
2.92%
|
7.89%
|
|
2-SD (95% Confidence)
|
0.43%
|
10.37%
|
|
Max Losing Streak
|
||
|
Minimum
|
5
|
|
|
Maximum
|
18
|
|
|
Average
|
8.27
|
|
|
Median
|
8.00
|
|
|
Standard Deviation
|
1.84
|
|
|
Low
|
High
|
|
|
1-SD (68% Confidence)
|
6.43
|
10.11
|
|
2-SD (95% Confidence)
|
4.60
|
11.94
|
Here is the
full report if we can reduce our probability of Scenario 1 (all out stop
loss) to 40% and increase Scenario #2 to 35%.
Hope
this helps. Keep ya mind right.
