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# Rule of thumb for position sizing

Discussion in 'Risk Management' started by Ghost of Cutten, Nov 30, 2011.

1. ### Daal

What about 1/20 of kelly?The reason I wouldn't use those rules is because they seem to not have come from a sound mathematical model founded on expectations. The ratio between the good trade PS and the less good trade PS was made up instead of being based on some kind of formula

I haven't done some work on this because I tend to put it aside but a table similar to yours could be used but instead of fixed fractions they could be fractions from kelly

#41     Dec 22, 2011
2. ### ronblack

#42     Dec 22, 2011
3. ### jem

1. its not irrational if there is a reason you have to keep the majority of the powder dry to stay in the game.

2. As much as I know it is irrational, I learned to accept the fact I trade far better when I trade with an emotional cushion... which when I was doing this full time... was recent profits. As irrational as that is.

#43     Dec 22, 2011
4. ### luckyputanski

It won't

#44     Dec 22, 2011

Thought your OP was interesting so simulated 1000 sequences of 50 trades for each of the 27 cases below and put the medians of the max % drawdowns for each case in the attached table. Set up the simulations so losers always lost the amount risked but winners won 5X 1X or 0.2X that.

Cases simulated:

a) High win rate = 80%; % risked = 2%,3% and 4%; avg win:avg loss = 5:1, 1:1 and 0.2:1
b) Even win rate = 50%; % risked = 1%, 1.5% and 2%; avg win:avg loss = 5:1, 1:1 and 0.2:1
c) Low win rate = 20%; % risked = 0.5%, 0.75% and 1%; avg win:avg loss = 5:1, 1:1 and 0.2:1

The drawdowns will be identical for those five trades but drawdowns for sequences of trades with winners will differ because the 1:1 system makes less when it wins, which is also why the max % drawdowns for long trade sequences from each system will be different. Looking at the table you can see how this plays out over different win rates, % of equity risked and payout ratios.

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#45     Dec 28, 2011
6. ### abattia

Fascinating/amazing/shocking/terrifying how the Max DD can build for the cases where W/L < 1!

It's the "mean reversion nightmare" ...

#46     Dec 28, 2011
7. ### murray t turtle

========
Correct;

If both of those account holders did that in 1 year, or 3 years;
highest probability is risk of ruin comes to the 99k profit much faster than the 1 k profit person.

#47     Dec 28, 2011
8. ### baro-san

You might find useful information on this thread.

Remember in your analysis: past performance is no guarantee of future results.

#48     Dec 28, 2011
9. ### Ghost of Cutten

I derived the position sizes from trade win rate and risk per trade, then using estimates of likely maximum drawdown, and altering the size until the max DD came within reasonable risk tolerances (15-30% maximum DD tolerance, from conservative to aggressive sizing). I later ran some MC simulations, and they backed up the original size estimates. So, it's mathematically robust.

Here are the Kelly estimates for the win rates I mentioned, using some realistic payout ratios:

High win rate (70%), 1:1 payout ratio. Kelly = 40% of capital per trade. 1/20th Kelly = 2%. My own recommendation was 2-4%.

Medium win rate (50%), 2:1 payout ratio. Kelly = 25% of capital per trade. 1/20th Kelly = 1.25%. My recommendation was 1-2%.

Low win rate (30%), 3:1 payout ratio. Kelly = 6.66%. 1/20th Kelly = .33%. My recommendation was 0.5-1%

Overall Kelly leads to guaranteed enormous drawdowns. Using 1/20th Kelly gives pretty similar numbers to my own calculations, but growth in account capital will be inferior to the sizing I recommended.

This is not surprising, since both your suggestion (1/20th Kelly), and the Kelly formula itself, are not based on the appropriate variable i.e. maximum drawdown risk.

The Kelly formula itself optimises long-run profit, under various unrealistic assumptions e.g. that you can tolerate enormous drawdowns, that you will face a large number of similar trades with similar odds in future, that you are risk neutral rather than risk averse, that maximising long-run profit is your sole goal etc. Since none of these assumptions are true, it is flawed.

My approach optimises maximum drawdown, and then maximises size subject to that constraint, with some input based on risk appetite (which the trade odds will influence). Thus for a given max DD tolerance, it will maximise CAGR. Whereas your 1/20th Kelly rule won't optimise either max DD or CAGR, because it's an arbitrary number.

Anyway, I used to use fractional Kelly myself (1/10th Kelly, which I arrived at after looking at drawdown risk for various trade odds), so I can empathise. It's just that optimising for max DD is superior to optimising for max long-run CAGR, since risk control is about LIMITING DRAWDOWNS, not about profit.

P.S. a further advantage of my 'rule of thumb' is its speed and simplicity.

#49     Jan 14, 2012
10. ### Daal

I mentioned 1/20 of kelly as a example to counter the flawled argument 'but you are going to go broke with kelly' I don't think there is anything special about 1/20. Could be 1/10 1/16

#50     Jan 16, 2012
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