TradersCALM - Position Sizing Interview
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  This article was first published in the December 2000 edition of "The CALM Trader" newsletter.     The article has been reproduced here here to meet the favourite requests of TradersCALM site searchers (position sizing and risk of ruin).

"The Calm Trader" defines ‘being calm’, as the state of mind of being both self-assured and confident.
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This time we are fortunate to have an interview with a successful trader.

  This guy just keeps on winning.     He is very calm and thoughtful about his trading.
But most of us would be fairly confident and self-assured about our trading if we were making over 11% on total capital every month with very low maximum losses.

  He tells me his last losing month was over one year ago, and he has never been down more than 10% of total capital at any one time, on any one day since he started trading his current system.

  I have seen some of his weekly statements and he often makes more than 5% a week.     There are many traders who make more than this – but he keeps his profits.     And with limited and often tiny running losses, this is quite an impressive performance.

  He tells me he is just about to implement a modification to his system he has been researching and testing for the last 7 months using an average 22 years of data over 6 markets.     It promises to yield an extra 0.3% a month average return, but more important from his perspective, to reduce the occurrence of losses.     It uses a changed position sizing approach.     No change in the basic system concepts, just optimising the reward to risk ratios by adjusting relative position sizes in differing circumstances.

  The Calm Trader had to ask him what he meant by position-sizing and how he used it to improve his impressive reward to risk ratio.
 
The Editor comments:

It would be useful background preparation for this article for readers to re-read or refer to one of the archives.     The ‘Win Some, Lose Some’ article is now available on-line for your convenience.     It is not necessary to have read this article first to enjoy the interview, but I think you will find "Win Some, Lose Some" a useful preparation.     The article is in the Self Awareness sub-section of the archives.     Please give me access to the archives.
  When I read the interview, I needed no more excuse for writing an article on my favourite trading topic – learning.





 

The Calm Trader

What’s position-sizing all about then?
 

Keeps on Winning

Every trader does it.     Some do not know they are doing it.     Fewer still exploit the full potential for profit.
 

TCT

Yes, but what is it?
 

KOW

Position sizing can be defined as altering the trade size based on the perception, by the trader, of the likely success of the trade.
 

TCT

And every trader does this?
 

KOW

Yes.     At each possible opportunity to enter a market, don’t you decide whether to enter or not? Of course you do.     This is a decision, based on your perceptions of success (however defined) to take the trade, with say your normal size, or not to take the trade.

This is a position-sizing decision to use your normal size of shares or contracts or a use a position-size of zero based on your perceptions of success.
 

TCT

So every trader at some basic level uses position-sizing.

But surely there is more to it than that?
 

KOW

Yes.     I am using position sizing to maximise profits while minimising risk.
 

TCT

I’d like some of that.     Tell me more.
 

KOW

OK.     But it is simpler if we build up the ideas slowly.
 

TCT

Suits me.
 

KOW

There are just two main ideas to grasp.     Everything else can be considered refinements and application.

The two core concepts are:
  • coping with a series of losses,
  • determining expected results.
 

TCT

With you so far.
 

KOW

Well lets look at coping with losses first.     Like all simple ideas it takes less words to explain with an example or two.

We will say you are trading on the outcome of a coin being tossed.     It is a fair coin.     That is 50% of the time it comes up heads, 50% of the time tails.
 

TCT

That’s my kind of example.
 

KOW

You are trading on heads.
And I am very kind, I will pay you out twice your stake(trade) if you win, and keep your stake(trade) when you lose.
 

TCT

Those are my kind of odds.    
 

KOW

Yes, but you can still lose.
 

TCT

How?
 

KOW

Imagine your total capital was $100.     And you bet it all on the first toss of the coin.     And it came up tails.
 

TCT

But no-one would be so stupid to risk it all on one trade.
 

KOW

Right.     But that is the point.     How do you know what is the right position size – the optimal amount to trade each time? Wait, I’ll start to answer the question.     Not by giving you the optimal amount, but a way of determining a basis for the maximum amount to trade each time.
 

TCT

OK.
 

KOW

Let us assume you risk just $1 each trade.     You can stand 99 losses in a row and still have $1 of capital left.
 

TCT

But that is just not going to happen.
 

KOW

But it could.     Let us look at how likely a run of tails (bad news for you) is, for say, 3 tails in a row, 7 tails in a row.     You agree that a run of 3 or even 7 tails in a row is a reasonable possibility?
 

TCT

Yes, of course.     This will be interesting.

Probability of tail is 50%

 

 

Number of tails in a row

Percentage probability
of tails in a row (chance in 100)

 


Chance in 1,000

 

Chance in 10,000

 

1

50.0000000000

500.0000000000

5000.0000000000

 

2

25.0000000000

250.0000000000

2500.0000000000

 

3

12.5000000000

125.0000000000

1250.0000000000

 

4

6.2500000000

62.5000000000

625.0000000000

 

5

3.1250000000

31.2500000000

312.5000000000

 

6

1.5625000000

15.6250000000

156.2500000000

 

7

0.7812500000

7.8125000000

78.1250000000

 

8

0.3906250000

3.9062500000

39.0625000000

 

9

0.1953125000

1.9531250000

19.5312500000

 

10

0.0976562500

0.9765625000

9.7656250000

 

11

0.0488281250

0.4882812500

4.8828125000

 

12

0.0244140625

0.2441406250

2.4414062500

 

13

0.0122070313

0.1220703125

1.2207031250

 

14

0.0061035156

0.0610351563

0.6103515625

 

15

0.0030517578

0.0305175781

0.3051757813

 

99

2.E-28

2.E-27

2.E-26



 

TCT

See, I told you.     I have more chance of winning the State Lottery than getting 99 tails in a row with a fair coin.     And I don’t even buy a ticket in the lottery.
 

KOW

Very funny.     But look at the table for ten tails in a row.
 

TCT

Yep, as near, as well, 1 in a thousand chance.
 

KOW

That means that if you bet $10 a time, that would give you ten bets before you lost all your $100.     And the risk of ruin (that is losing all your money), betting $10 a time would be about 1 in a thousand.
 

TCT

What does that really mean?
 

KOW

If you were happy with a risk of ruin of 1 in a thousand, you could afford to bet up to 10$ a trade (coin toss).
 

TCT

OK, if I know I am happy with a 1 in a 1,000 risk of ruin, the coping with a series of losses idea tells me the maximum position size I should take should be $10.
 

KOW

In simple terms, yes.     If you are happy with a 1 in a thousand risk of ruin.

As you cannot win if you are not in the game, I like to stay in the game.     So maybe I would like only a 1 in 10,000 risk of ruin.     This means I have to be able to cope with 14 tails in a row not your 10.     So I could only afford to trade with a maximum position size of $7 each trade ($100/14).
 

TCT

Wait a bit.     Let me understand this.     I can use the acceptable level of risk of ruin idea to help me decide what maximum level of contracts or shares I can safely trade given my account size.
 

KOW

In simple terms yes.     But I don’t like that word ‘safely’ – there is still your risk of ruin – losing all your money.
 

TCT

OK.     I accept the rebuke.     I can see this idea is useful.     I can even see it may help me to be calmer.     What else is there to this position-sizing thing?
 

KOW

Well, do you remember expected results?
 

TCT

Yes, what’s that?
 

KOW

It is also simple.     Just simple multiplication and subtraction.

Remember the good odds I gave you for this fair coin? I pay out twice your stake(trade) if it comes up heads, and I keep your stake(trade) if the coin comes up tails.
 

TCT

Yes.
 

KOW

Well the expected result of a single trade with a position size of 1 are just the probability of winning (50%) times the amount of winnings (2) less the probability of losing (50%) times the amount lost (1).

That is +0.5 x 2 – 0.5 x 1.     This equals +1.0 – 0.5 = + 0.5.

In other words, for each $1 staked, the expected result is 50 cents profit.     So on the position size you chose before, of $10 a trade, an expected profit of $5 a trade.
 

TCT

I like it.
 

KOW

Yes a reasonably good, positive expected result.
 

TCT

So how does it impact position-sizing?
 

KOW

OK.     So which trading system would you prefer to trade?
  • (a) a 50% probability of winning with a 50 cent expected result or
  • (b) a 30% probability of winning with a $1.10 cent expected result?
 

TCT

No way am I falling into any trap here – my ignorance is too great.     I do not know enough to choose.
 

KOW

A good answer.     Let us look at a similar table of probabilities to the one we looked at before.     But this time with a biased coin with 30% odds of heads (winning for you), the odds of losing the coin toss being 70%.
 

TCT

OK.


Probability of tail is 70%

 

 

Number of tails in a row

Percentage probability
of tails in a row (chance in 100)

 


Chance in 1,000

 

Chance in 10,000

 

1

70.0000000000

700.0000000000

7000

 

2

49.0000000000

490.0000000000

4900

 

3

34.3000000000

343.0000000000

3430

 

4

24.0100000000

240.1000000000

2401

 

5

16.8070000000

168.0700000000

1680.7

 

6

11.7649000000

117.6490000000

1176.49

 

7

8.2354300000

82.3543000000

823.543

 

8

5.7648010000

57.6480100000

576.4801

 

9

4.0353607000

40.3536070000

403.53607

 

10

2.8247524900

28.2475249000

282.475249

 

19

0.1139889519

1.1398895185

11.39889519

 

20

0.0797922663

0.7979226630

7.97922663

 

25

0.0134106862

0.1341068620

1.34106862

 

26

0.0093874803

0.0938748034

0.938748034

 

50

0.0000017985

0.0000179847

0.000179847

 

99

5.E-14

5.E-13

4.62068E-12



 

KOW

If you still wanted a 1 in a 1,000 risk of ruin you could go for a $5 maximum based on 20 losers in a row.
 

TCT

I see, and you could go for, well a $3 maximum trade.     Based on $100 divided by 26 rounded down to $3 ?
 

KOW

You learn fast.     Now let us look at the expected profit per trade for the same risk of ruin.

For (a) you would bet $10 to get $5 expected profit a trade.

For (b) you would bet $5 to get $5.50 expected profit a trade.
 

TCT

So I should just prefer (b)?
 

KOW

(b) appears to be better for you – just wait a bit.

Now let us look at what I would get with my perception of acceptable risk of ruin.

For (a) I could bet a maximum of $7 to get $3.50 expected profit a trade.

For (b) I could bet a maximum of $3 to get $3.30 expected profit a trade.
 

TCT

So it can depend on perception of risk of ruin?
 

KOW

Yes, but I would prefer to generalise that to perception of risk.
 

TCT

I did notice you said (b) ‘appears’ to be better for me.
 

KOW

Yes, appearances can hide reality.     First even if 1 in a thousand is right for you in one market or time, is 1 in a thousand the right risk of ruin for you in this kind of trade at this time, for this allocation of capital? You may also have different views of risk than just risk of ruin.     I don’t think you are a machine or without emotions.     How would you cope with a run of 10 losses in a row?
 

TCT

Not too well, I suspect.
 

KOW

With (b) you only have 30% chance of winning each trade.     So the probability of having 10 losses in a row is significantly greater with (b) than it is with (a).     In fact you are about 29 times more likely to have 10 losers in a row with trading system (b) than you are with trading system (a).     As fear distorts your perceptions, usually to your detriment, this must be considered.

So taking into account human emotions, the expected profit may need to be substantially higher than the 10% better it is in the example above to compensate for the higher trader-emotional-response-risk of having a large number of losers in a row.

Also our coin tossing example was very simple.     In trading commodities, currencies, or shares or indexes etc., there are not two outcomes – win a fixed amount or lose a fixed amount.     There is a more of a continuum of possible wins and losses and a probability distribution for the various outcomes.

So the expected results are a little more work to derive.    
 

TCT

I like your concept of trader-emotional-response-risk.

But the core concepts of position-sizing are still useful despite all your caveats.
 

KOW

You’re right.     But use with care.     Think about the ideas and what they might mean for you.     Go slowly – there is no rush.     Understand the basics before moving on.     Build your house on good foundations.     Forgive me – keep calm!
 

TCT

OK, but I have a good memory.     You said you are not changing your trading systems, but adjusting your position sizes and this will give substantial benefits.
 

KOW

Yes.     To understand this just think about the two trades you were offered as alternatives: (a) and (b).     You wisely did not choose between them without knowing more.

But what if they were not alternatives for all your risk capital as you assumed.     You did not have to risk your maximum trade permitted by risk of ruin considerations (based on series of losses).     Nor indeed just choose one of the trading systems.     You could allocate say 50% risk capital to (a) and 50% of risk capital to (b).     You could place say $5 a trade on (a) and $2 a trade on system (b).

Now what do you think would happen to your expected results if you did this? You need to try it with real-life examples of two systems until you understand the way it works.

And what would happen to the combined series of losses if trading system (b) was typically only a winner when trading system (a) tended to lose? In the jargon there was a negative correlation of returns between the two systems returns.

I’ll answer that – by trading both systems together, when they have a negative correlation, your risk of ruin could fall, sometimes dramatically – or you could increase your maximum trade size for the same risk of ruin.

In other words your reward to risk ratio would be higher.     Doubling the ratio is not uncommon.     You make more for each unit of risk.     You are calmer.     I know that is music to your ears.     I have increased my reward risk ratio, perhaps on ten occasions over the last few years.     I cannot imagine trading with the reward to risk ratio I used originally.     Mind blowing.

It is what my recent research has been all about – finding the best sets of negative correlation between systems.     Then evaluating combinations of position-sizing to give new set of series of losses and to find the new risk of ruin.     Then performing enough research to build the same level of confidence that I enjoy at the moment.     My trading success is based partly on confidence, which in turn is based on research.     But I attribute most of my success to my principle of continuous improvement.
 

TCT

Yes, confidence is half our definition of calm.

And I feel your peace gives you the emotional balance to steadily improve.

Is this where understanding position-sizing really comes up with the goods?
 

KOW

Well thank you for those kind words.     Sensible use of position-sizing both for each system and across systems can really reduce risk or increase profits for the same risk.     I also use position sizing concepts to increase position size(s) as my risk capital grows and to reduce them as my account balance falls.

And all this obviously has benefits in emotional terms as well.     But I have been using some position-sizing concepts successfully for years.     Remember these are just my ideas – they can be wrong, they can be improved.

I also understand my perceptions of risk quite well.     I have made a long study of how probabilities of success vary with differing circumstances for my preferred markets, trading vehicles and trading strategy.     I have a reasonable amount of experience of evaluating different alternatives strategies based on the various probabilities.     But I still get surprised.     Surprised by things I have overlooked, misjudged or where I have just got the calculations wrong.

I try not to take anything for granted but revisit it all.     Just recently, one market circumstance I thought was clear-cut, well now I feel is nearly the opposite of what I documented.     I am still working out the implications and learning what changes I need to make to my systems.

Get the basic concepts understood and applied simply first.     Build on a firm foundation.

Get maximum loss in your trades under control.     This is classical money management – only partly related to position-sizing.
 

TCT

Good advice.     After I have digested all of this, and probably discussed it with friends, I will start to look at one of my old systems with renewed interest.     To see if it has any negative correlation with the one I use today.     I shall have to find my calculator!     Food for thought.     Thank you for sharing some of your ideas and your time.
 

KOW

My pleasure.

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