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Is money management and position sizing really that important?

Money management and position sizing skills are regarded as ESSENTIALS for successful trading. This is shown by 'The Ralph Vincent Experiment'. Keep reading to find out why only 2 out of the 40 participants ended up with more money than when they started.

Van Tharp, on page 162 of his book 'Trade your way to financial freedom'(1999) states that position sizing is the key topic behind any Holy Grail trading system. He states its the difference between the ho-humm trading methodology and the world's best methodologies. Yet in his experience working with many traders he finds that few people even think about the topic.

Larry Williams a high profile well known trader says money management is his favorite subject. In his book, Day Trade Futures Online Larry says "Until you use a money management approach, you will be a two-bit speculator, making some money here, losing some there, but never making a big score....".

Also confirming what Van Tharp had discovered, Larry goes on to say that the truly shocking thing about money management is how few people want to hear about it or learn the correct formulas.

The Ralph Vincent Experiment

Ralph Vincent "The Ralph Vincent Experiment" in Lucas and Lebeau, Technical Traders Bulletin March 1992 pp1-2 completed an experiment with 40 Ph.D.s which shows the importance of money management. None of the 40 Ph.D.s knew about money management. They were asked to play a simple computer game whereby out of the 100 trials, 60% would produce a winning result and 40% losing. They were given $1,000 in play money and instructed to stake as much or as little as they wanted on each of the 100 trials. They would win or lose exactly what they risked per trial.

How do you think the results turned out?

Without applying any money management rules, even though they had a 60% win ratio, only 5% came out with more than their original starting balance. 38 of the participants lost money.

[Where have you seen that ratio before? (5% successful & 95% unsuccessful) Strange that it happens to be the same ratio of the general population of successful traders to unsuccessful ones over the longer term.]

If the participants had a knowledge of money management they could have capitalized on the 60% win/loss ratio and staked a constant amount on each trial and also not risking too much on one single trial. If they had used that strategy they would have ended up with more than the original $1,000 they started with.

The participants whom risked too much on any particular trial would have faced the following difficulty in trying to recover;

To recover from a 20% loss it takes a 25% gain
To recover from a 40% loss it takes a 66.7% gain
To recover from a 50% loss it takes a 100% gain
To recover from a 60% loss it takes a 150 % gain
To recover from a 75% loss it takes a 300% gain
To recover from a 90% loss it takes a 900% gain

What if a participant specifically risked a very small amount on each trial and kept that amount constant?

That participant would have made very little in addition to his original $1,000. However, at least he would still remain with a positive balance. ie risk $1 to gain $1 with a 60% chance of success. Notice we can apply our expectancy model that we learn't from analyzing a trading system. For a review on expectancy formula, click here.

Lets try the formula

APPT = Average Profit Per Trade that we can expect.(Expectancy)

APPT = (Probability of Win x Average win) - (Probability of loss x Average loss)

APPT = (60% x $1) - (40% x $1)

APPT = (.60) - (.40)

APPT = .20

APPT = 20 cents is our expected profit per $1 risked

What that means is that after the 100 trials, if we risked $1 per trial we would end up with a profit of $20,(100x20c) taking our closing balance to $1020.

But what if, instead of risking $1 per trial we risk $500 per trial? Will we not win the game because our expectancy formula says we will get back 20% of our dollars risked? So if we risk $500 per trial can we expect 100 trials x $100 = $10,000 profit + $1000 = $11,000 balance?

But wait, what if we take a bigger risk to make sure we really do win the game? Lets risk it all and hope we have string of winners to begin with. The maths for risking the whole $1,000 on each trial; We expect 100 trials x $200 ($1000x20%)= $20,000 profit + $1000 = $21,000 balance.

Surely we would have to win the game? Who cares about money management?

Lets check and see if these numbers are real?

We will now do a short version of the 100 trial. We will cut it down to show the first 10 trials. (Then multiply the result by ten).

Starting Balance $1,000
Trial 1 Win +$1000 $2,000
Trial 2 Win +$1000 $3,000
Trial 3 Win +$1000 $4,000
Trial 4 Win +$1000 $5,000
Trial 5 Loss -$1000 $4,000
Trial 6 Loss -$1000 $3,000
Trial 7 Win +$1000 $4,000
Trial 8 Win +$1000 $5,000
Trial 9 Loss -$1000 $4,000
Trial 10 Loss -$1000 $3,000

Total Profit +$2000

Imagine our trial continues like this over and over until we have reached our 100 trials. The figures are simply multiplied by ten to get us from 10 to 100 trials.

That means total profit +$2000 for ten trials x 10 = $20,000 + $1,000 starting balance = $21,000. This shows that we have now verified that the APPT expectancy formula is correct.

BUT WHY THEN DID 95% OF THE PARTICIPANTS END UP WITH LESS THAN THEIR STARTING $1000? The participants had a system (game) with a 60% Win rate and a win/loss size ratio of 1:1. What went wrong?
Lets find out;

Lets try our 10 trial again, but this time we will reverse the order of the trial outcomes. We will flip it upside down. We will use trial 10 as trial 1, trial 9 as trial 2, trial 8 as trial 3, etc Everything else will remain the same.

Our first participant whom risked his whole starting capital;

Starting Balance $1,000
Trial 1 Loss -$1000 $0
Trial 2 Loss -$ $0
Trial 3 Win +$ $0
Trial 4 Win +$ $0
Trial 5 Loss -$ $0
Trial 6 Loss -$ $0
Trial 7 Win +$ $0
Trial 8 Win +$ $0
Trial 9 Win +$ $0
Trial 10 Win +$ $0

Total Profit +$0

Well, our participant who got lucky the first time was unlucky this time. It only took him one trial to be completely washed up and unable to continue the game.

Ok, what about the other participant who was going to make $10,000 profit by risking half of his $1000 on each trial? His $500 per trial lasted for two trials after taking two consecutive losses of $500 each. He was washed up quickly too.

And what about another participant who was risking 30% of his starting capital? Lets see what would have happen;

Starting Balance $1,000
Trial 1 Loss -$300 $700
Trial 2 Loss -$300 $400
Trial 3 Win +$300 $700
Trial 4 Win +$300 $1,000
Trial 5 Loss -$300 $700
Trial 6 Loss -$300 $400
Trial 7 Win +$300 $700
Trial 8 Win +$300 $1,000
Trial 9 Win +$300 $1,300
Trial 10 Win +$300 $1,600

Total Profit +$600

That means total profit +$600 for ten trials x 10 = $6,000 + $1,000 starting balance = $7,000.

This participant was very fortunate that trials three and four were winners. Otherwise, he would have been out of the game too. (If trial three and seven were losers he would have been left with $100 to try and recover with). Also notice, his account balance was down by 60% on the two occasions. This participant is hanging on by the seat of his pants, relying heavily on winning trades coming through at critical times. If he were a trader he would have a hard task to make 150% profit from these low levels to get him back up to his original starting balance.

Remember our table;

To recover from a 20% loss it takes a 25% gain
To recover from a 40% loss it takes a 66.7% gain
To recover from a 50% loss it takes a 100% gain
To recover from a 60% loss it takes a 150 % gain
To recover from a 75% loss it takes a 300% gain
To recover from a 90% loss it takes a 900% gain

The participants in the experiment game did not have the luxury of a good win/loss size ratio. They were stuck with a 1:1 ratio, meaning that they could only win an amount they were willing to lose. So imagine the bad state a participant would be in if he had a few consecutive losses in a row that were not manageable amounts.

We can see the reason why 95% of the participants failed the game

No doubt they would have risked too much on any given trial. They could have had a string of seven or more losing trades that would have made it impossible for them to recover their initial starting balance? Or It could have been that some participants had only one, two, or three HUGE LOSSES that reduced their account down to extremely low levels.

Also, some participants probably tried to increase their stake size after one, two or three losses hoping that they could recover the loss. (Martingale strategy). Problems with martingale strategies develop when the streak of consecutive losses causes the risk / reward ratio to blow out of proportion. What happens when there is a streak of fifteen losses in a row? (Is it logical to risk losing $700 by trying to save $100?)

On the other hand if the participants had used Anti-martingale strategies, which means increasing the amounts they risked on each trial after winning streaks they would have done better.

The lesson's from the experiment with the 40 Ph.D.s is loud and clear.

1.Do not risk too much money on any one position due to unknown timing and length of losing streaks.

2.There is a correct (Optimum) amount of money to risk on each trial. (position size). This amount can be calculated dependent on the rules of the game /system.

In case you are wondering what was the correct answer to the position size in the above experiment. The optimum amount to achieve the maximum gain was for the participants to risk 20 percent of their new equity each time. The balance of their accounts would have grown to about $7,500.

For trading purposes risking 20% of your closing balance would be regarded as a very high risk strategy. Very poor money management. Lets look at the effect on our account should we start with a string of consecutive losses.

Our starting account balance $1,000

less 20% loss number1 -$200 $800
less 20% loss number2 -$160 $640
less 20% loss number3 -$128 $512
less 20% loss number4 -$102 $409
less 20% loss number5 -$82 $327
less 20% loss number6 -$65 $262
less 20% loss number7 -$52 $209

After a bad string of 7 losses our account is now down to $209. We now need to make 378.5% to recover. See how risking 20% of our account balance is way to much.

Risk between 1% to 3%

Jack Schwager's book Market Wizards (1989) day and trend follower Larry Hite says about money management;

"Never risk more than 1% of the total equity on any trade. By only risking 1%, I am indifferent to any individual trade."

The general consensus on money management is that a trader should limit his risk up to about 3% maximum on any one position.
Does this seem reasonable?

Let check it out with the above previous seven in a row loss.

Our starting account balance $10,000

less 3% loss number1 -$300 $9,700
less 3% loss number2 -$291 $9,409
less 3% loss number3 -$282 $9,127
less 3% loss number4 -$274 $8,853
less 3% loss number5 -$266 $8,587
less 3% loss number6 -$258 $8,329
less 3% loss number7 -$250 $8,079

After our bad string of 7 losses our account is now down to $8,079. We now need to make 23.8% to recover.

Using our maximum money management 3% risk rule shows a recovery from a shocking 7-in-a-row loss situation is very feasible. Only 23.8% to recover compared to our earlier example of 378.5% if we risked 20% of our balance per trade. See how good money management can protect us!

As you noticed, we had to increase our account size from $1,000 to $10,000 to make our stop loss sizes reasonable. This shows that the smaller your account the more difficult it will be to apply proper money management rules.

To Learn more indepth details about money management - specifically; position sizing methods go here

See also the article section dealing with money management here.

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