Excel MonteCarlo Simulation of Money Management Strategy #1: Fixed-Risk Money Management

Most of the strategy simulations I have reviewed up to this point have not applied any money management rules.  No matter the account size, I have continued to trade 1 contract (assuming we trade futures).  If the account doubled in the simulation, we continued to trade one contract.  If the account had a 50% drawdown, we continued to trade one contract.

For this simulation, I am going to use a fixed risk money management (“FRMM”) strategy. Fixed risk money management limits each trade to a predefined, or fixed, dollar risk. Initially, the fixed dollar risk per trade can be calculated by dividing the starting account by the number of units of money you wish to begin trading with.

FRMM = Account Balance / Number of Units of Money

As the account expands and contracts, the fixed risk strategy will adjust accordingly.

Previously, we were only concerned with Risk to Reward Ratio (as defined by the system’s Average Win divided by the systems Average Loss), Winning Percentage (the percentage of profitable trades) and starting account balance (your starting equity).

However, for the FRMM we need to introduce the following variables:

1.  Individual Trade Risk (“ITR”) – this is the amount of money that we are risking on a given trade.  For example, if through back testing you find that the average loss on a trade is $200, then the Individual Trade Risk is $200.  This may vary based on different signals that the system gives you.  For long entries you may have an ITR of $300 and for short entries an ITR of $200.  The ITR is solely a function of the individual signals of your trading system

2.  Fixed Dollar Risk (“FDR”) -  this is the maximum amount of money that you are willing to lose on any one trade.  Generally, this is based on your current account balance.  If you start with a $20,000 account, the maximum you may be willing to lose on a given trade may be $500. 

3.  Number of Contracts (“NOC”) – this is the FDR divided by the ITR rounded down to the nearest integer.  For an ITR of $200 and an FDR of $500, then the NOC to trade is $500/$200 = 2.5 rounded down to 2.

4.  Capital Units – This is our starting account value divided by our Fixed Dollar Risk.

Example System Parameters

For this simulation, I will use the following parameters:

Average Win:                             $300

Average Loss:                             $100

Starting Account Size:              $20,000

Winning Percentage:                40%

ITR:                                               $100 (Average Loss)

FDR:                                              $300

Using the FRMM principles discussed above, we define our Initial Trade Risk (“ITR”) as our average loss.  This may not always be the case but when back testing a strategy, it is a good number to start with.  I have initially set the fixed dollar risk at $300.  Based on our starting account balance of $20,000, this gives around 66.66 Initial Units of Capital to start with. 

Building Our Spreadsheet

So we still use our Rand() function to determine if the current trade is a win or a loss:

= if(Rand()<=Winning Percentage, Average Win + Prior Account Balance , Average Loss + Prior Account Balance)

However, because we are not using a single contract on each trade, we need to change what the Average Win and Average Loss amounts will be.  This requires us to determine how many contracts we want to trade based on our prior account balance.

Number of Contracts = Available Capital / Fixed Units / Trade Risk

Therefore, the Average Win for a given trade will be:

= (RoundDown(Prior Account Balance / Initial Capital Units / Initial Trade Risk)) * Average Win

The Average Loss for a given trade will be:

= (RoundDown(Prior Account Balance / Initial Capital Units / Initial Trade Risk)) * Average Loss

These formulas tell us how many contracts to trade based on our most recent account balance. 

For example, for Trade No. 1 and Simulation No. 1 above, our prior account balance is 20,000.  The number of contracts is determined by:

=   FDR/ITR

=   Account Value / Units of Money / ITR

=   20,000 / 66.66 Units of Money / 100 Trade Risk

=   3 contracts

Since Excel randomly returned a value greater than .4, it was counted as a loss.  So 3 contracts * -100 average loss now gives us a new account value after one trade of $19,700.

But what happens as our account grows?

After 137 trades (see the top row in the table above), our account value has grown to $117,200.  How many contracts do we trade on the next trade to implement our Fixed Risk Money Management strategy?  For the 138^th trade:

=  117,200/66.66/100

=  17.58 contracts rounded down to 17 contracts

Since Excel randomly determined that our 138^th trade was a win:

=  17 Contracts * $300 Average Win

=  $5,100

The $5,100 was added to $117,200 giving us a new account balance of $122,300.

For the 137^th trade we were never risking more than 1/66^th of our account.  This was as true on our first trade as it was on our 137^th trade.

Interpreting the Results of Fixed Risk Money Management Strategy

Now we can look at our results in through the lenses of ending account value, maximum drawdown and Ulcer Index.

Using the parameters described above and running 1000 simulations of 500 trades, we get the following results:

Ending Account Value
Minimum	139,500
Maximum	14,265,400
Average	1,540,864
Median	1,218,300
Mode	603,000
Standard Deviation	1,210,294
	Low	High
1-SD (68% Confidence)	330,571	2,751,158
2-SD (95% Confidence)	-879,723	3,961,452
Maximum Drawdown
Minimum	-9.69%
Maximum	-37.37%
Average	-16.77%
Median	-16.12%
Mode	-14.29%
Standard Deviation	3.96%
	Low	High
1-SD (68% Confidence)	-12.81%	-20.73%
2-SD (95% Confidence)	-8.85%	-24.68%
Ulcer Index
Minimum	2.71%
Maximum	10.63%
Average	4.67%
Median	4.47%
Standard Deviation	1.06%
	Low	High
1-SD (68% Confidence)	3.60%	5.73%
2-SD (95% Confidence)	2.54%	6.80%

All of the numbers are substantially larger than what we had with our single contract simulation.  Let’s compare Ending Account Value and Maximum Drawdown:

Ending Account Value
	FRMM	Single Contract
Minimum	139,500	32,800
Maximum	14,265,400	64,800
Average	1,540,864	49,793
Median	1,218,300	49,600
Mode	603,000	49,200
Standard Deviation	1,210,294	4,387

Maximum Drawdown
	FRMM	Single Contract
Minimum	-9.69%	-1.97%
Maximum	-37.37%	-13.81%
Average	-16.77%	-4.35%
Median	-16.12%	-4.14%
Mode	-14.29%	-3.45%
Standard Deviation	3.96%	1.42%

A few things to note:

1.  It is a way to compound your account.  We started with the same amount but ended up with a vastly larger account balance using FRMM.  This is a result of adding contracts as our account size grew.  We didn’t do this with the single contract simulation.

2.  Your drawdown will be much larger with FRMM.  The biggest difference is the maximum drawdown.  With FRMM, your average drawdown was 4 times that of a single contract.  The standard deviation was also 4 times larger.  With bigger wins come bigger losses.

3.  The Simulation doesn’t consider Margin Requirements or Limit the Number of Contracts Traded.  FRMM ignores the fact that, sometimes, it is impossible to trade the required number of contracts required of it.  Can you put on a 100 lot trade?  It is possible in some markets but not all.  Our biggest winner in FRMM traded more than 2,000 contracts.  This is likely impossible for even the largest retail traders.  But don’t ignore the real effects that FRMM can have.  One way to limit this is to say that, once you reach a specified number of contracts, you won’t trade any more contracts.

4.  In Reality, You Can Also Increase or Decrease the Fixed Dollar Risk as You Continue to Trade.  One adjustment you can make as your account grows is to increase the fixed dollar risk after a certain number of trades.  You can also increase the number of units of money to reduce your risk of ruin.

Changing Parameters

Below I change some of the parameters to see what effect it has.

What if we had a 1.5 R/R Ratio (Avg Win of 150 and Avg Loss of 100), a 40% WP, $20k Account, ITR of $100 and FDR of $200 (therefore, we never risk more than 1/100^th or 1% of our Account on a given trade)?

Ending Account Value
Minimum	11,550
Maximum	44,800
Average	19,977
Median	19,100
Mode	18,900
Standard Deviation	3,866
	Low	High
1-SD (68% Confidence)	16,112	23,843
2-SD (95% Confidence)	12,246	27,708
Maximum Drawdown
Minimum	-7.47%
Maximum	-44.67%
Average	-20.48%
Median	-19.43%
Mode	-25.00%
Standard Deviation	6.66%
	Low	High
1-SD (68% Confidence)	-13.81%	-27.14%
2-SD (95% Confidence)	-7.15%	-33.81%
Ulcer Index
Minimum	2.70%
Maximum	27.74%
Average	11.14%
Median	10.39%
Standard Deviation	4.72%
	Low	High
1-SD (68% Confidence)	6.41%	15.86%
2-SD (95% Confidence)	1.69%	20.58%

What if we had the same scenario above, but increased our Avg Win to 200 giving us a R/R ratio of 2:1?

Ending Account Value
Minimum	18,500
Maximum	102,500
Average	45,464
Median	43,600
Mode	40,500
Standard Deviation	13,372
	Low	High
1-SD (68% Confidence)	32,092	58,836
2-SD (95% Confidence)	18,719	72,209
Maximum Drawdown
Minimum	-6.26%
Maximum	-36.90%
Average	-13.61%
Median	-12.93%
Mode	-12.50%
Standard Deviation	3.76%
	Low	High
1-SD (68% Confidence)	-9.85%	-17.37%
2-SD (95% Confidence)	-6.09%	-21.12%
Ulcer Index
Minimum	2.03%
Maximum	21.70%
Average	4.92%
Median	4.51%
Standard Deviation	1.90%
	Low	High
1-SD (68% Confidence)	3.02%	6.82%
2-SD (95% Confidence)	1.12%	8.73%