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 selfassured and confident.  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 selfassured 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 positionsizing 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 reread or refer to one of the archives. The ‘Win Some, Lose Some’ article is now available online 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 subsection 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 positionsizing 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 positionsizing decision to use your normal size of shares or contracts or a use a positionsize of zero based on your perceptions of success.  
TCT 
So every trader at some basic level uses positionsizing. 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:
 
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 noone 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 

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.E28 
2.E27 
2.E26 
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 positionsizing 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 positionsizing?  
KOW 
OK. So which trading system would you prefer to
trade?
 
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 

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.E14 
5.E13 
4.62068E12 
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 traderemotionalresponserisk 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 traderemotionalresponserisk. But the core concepts of positionsizing 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 reallife 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 positionsizing 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 positionsizing really comes up with the goods?  
KOW 
Well thank you for those kind words.
Sensible use of positionsizing 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 positionsizing 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 clearcut, 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 positionsizing.  
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. TradersCALM home page 