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Account size when trading multiple instruments
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Account size when trading multiple instruments

  #11 (permalink)
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I think it is important to remember to be realistic. Too many traders think they can earn $500 a day on a $10,000 account. Can it be done? Sure. Will the majority of traders who try to do it succeed? No. $500 a day on $10,000 would be 125,000 return on 250 trading days from a 10,000 account. Insane.

I will think getting $500 on an $10,000 account trading leveraged instruments; futures, CFD is possible. But it will not be possible if you are trading $10,000 worth of stocks.

$10,000 allow you to intraday trade almost 20 contracts of ES and all you need is 2-3 ticks profit to get $500. The hard part is to be consistent in being profitable.

But on the other hand, I had heard a couple of traders who told me they used to be profitable when trading for a firm but when they leave the company and start trading on their own accounts, they seem to have problem being profitable. I am thinking if it has to do with account size.

What I believe is, with a large account, you are psychologically able to handle a larger stop and less likely to be fearful therefore allowing your profit to run.

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jonc View Post
I will think getting $500 on an $10,000 account trading leveraged instruments; futures, CFD is possible. But it will not be possible if you are trading $10,000 worth of stocks.

$10,000 allow you to intraday trade almost 20 contracts of ES and all you need is 2-3 ticks profit to get $500. The hard part is to be consistent in being profitable.

But on the other hand, I had heard a couple of traders who told me they used to be profitable when trading for a firm but when they leave the company and start trading on their own accounts, they seem to have problem being profitable. I am thinking if it has to do with account size.

What I believe is, with a large account, you are psychologically able to handle a larger stop and less likely to be fearful therefore allowing your profit to run.

20 contracts on a 10k account? That is insane to me.

Yes, trading someone elses money vs your own is very, very different. It's quite similar to the sim vs cash phenomenon. Anyone can make money on sim, it's pretty easy. Doing it on cash is hard. The difference: psychology for the most part.

Trading someone elses money can be a good fit for some traders.

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Ralph Vince book The Leverage Space Trading Model deals with optimal bet size for multiple trading instruments.
The 2% "rule" is rather pointless without some kind of edge estimation. Keep in mind the optimal kelly bet size for a 1:1 bet(10 point profit target / 10 point stop ) would be your edge itself. So if you really had a 5% edge on that trade then the optimal geometric growth for that bet would be 5% of the account.
I believe 2% was probably arrived at because it keeps someone with overall negative expected value per trade going long enough to run into some winning streaks with a large enough random return that gives the illusion of profitability.
Euan Sinclair's book Volatility Trading is probably worth the price for the money management section actually.

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jstnbrg View Post
The 2% rule is frequently mentioned on this forum, namely that you should not risk more than 2% of your account on a single trade. This implies a minimum account size of 50 times what you will risk on a single trade in a single instrument. My question is: What is the minimum account size if you are trading more than one instrument? Is there an equation that gives a "safe" account size? Clearly, if you're trading 2 instruments that are 100% correlated, have the same tic size and the same volatility, and you are the same way on both, your account should be twice as large. What if the correlation between the two instruments is 0? Will your "1 contract" account size suffice for both? What if you're trading 3 or 4 instruments simultaneously?

Heuristic Approach

The main problem is that correlations between instruments are changing. Even if you have carefully chosen your instruments to approach a zero correlation, you can be unlucky and find yourself with all your trades going against you at the same time.

So from a practical point of view you need two limits

- the 2% limit (I use 1%) per trade
- a second global limit (for example 5%) for the maximum risk that you are willing to accept

If you apply this rule you could put on 2 trades full size and 1 trade half size to comply with it. That said you are accepting a drawdown of 5% as a result of those trades.

Zero-Correlation also does not help to reduce the size of the maximum drawdown.

(1) If you select trades with an assumed positive correlation, there is no reduction in risk.

(2) If you select trades with an assumed negative correlation, the profit potential is also reduced.

(3) If you select trades that are assumed to be non-correlated, this is obviously the best choice, but let us look what it means. When putting on three non-correlated trades with a winning percentage of 50% each, the odds are

- 12.5% that all 3 are profitable trades
- 37.5% that 2 are profitable and 1 is a losing trade
- 37.5% that 1 is a profitable and 2 are losing trades
- 12.5% that all 3 are losing trades

So the assumed zero-correlation does not mean that the trades will partially cancel out, but the losses may well add up.


Mathematical Approach

The mathematical approach is based on the grounds that you will need to optimize the geometrical growth of your account. The related concepts of advanced money management have been pioneered by J.L. Kelly, Edward Thorpe (known for his book "Beat the Dealer"), Fred Gehm and Ralph Vince. So if you already own the book by Gehm, a likely addition would be one of the books of Ralph Vince. His work is based on optimal f, which is known for producing large draw-downs but the best longtime performance. It is not easy to understand and I have only read a small part of it (still on my reading list), so I am not trying to explain the details here.

I attach a paper summarizing some of the sources on money management.

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Account size when trading multiple instruments-martin-sewell-money-management.pdf  
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Fat Tails, thanks, this is exactly the type of response I was hoping for, short of a formula I could plug in to Excel. And I didn't expect to get that. Thank you very much for the clear explanation and the other resources.

If I'm understanding you correctly, trading non-correlated instruments will not reduce the size of a maximum draw down. It should, however, reduce the odds that it will happen. Using the same logic you employed above in (3),

When putting on three 100% correlated trades with a winning percentage of 50% each, the odds are

50% that all 3 are profitable trades
50% that all 3 are losing trades.

So the odds of all 3 being losers at the same time goes from 12.5% to 50% as correlation goes from 0 to 100%, in this "coin flip" scenario.

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jstnbrg View Post
Fat Tails, thanks, this is exactly the type of response I was hoping for, short of a formula I could plug in to Excel. And I didn't expect to get that. Thank you very much for the clear explanation and the other resources.

If I'm understanding you correctly, trading non-correlated instruments will not reduce the size of a maximum draw down. It should, however, reduce the odds that it will happen. Using the same logic you employed above in (3),

When putting on three 100% correlated trades with a winning percentage of 50% each, the odds are

50% that all 3 are profitable trades
50% that all 3 are losing trades.

So the odds of all 3 being losers at the same time goes from 12.5% to 50% as correlation goes from 0 to 100%, in this "coin flip" scenario.

Absolutely agree with you. The maximum drawdown of 3 non-correlated instruments will not be reduced, but the frequency of this happening is reduced.

So you can actually increase size, if you are willing to accept larger occasional drawdowns. I am sure that the Excel formula that you are looking for does exist. It will use variance and covariance of the P&L for the instruments traded. If you assume zero correlation you will get an exact formula depending on the trade expectancy and variance for each instrument only.

In practice this is will be difficult, as you may not assume zero correlation for any two instruments traded, but would need a backtest within the framework of your trading strategy that allows you to get an idea of correlation / covariance of the individual P&Ls.

Also I am not sure that the problem is a mathematical one. If you follow the approach of the Kelly formula / optimal f as described by Ralph Vince, this may produce larger drawdowns than one could stand emotionally.

Now, your original 2% rule is nothing scientific but just heuristic and ways below the optimum suggested by the Kelly criterion. Easy to extend that approach and assume that if you trade 3 weakly correlated instruments you will need

(a) in the worst case to triple your capital
(b) in the best case to continue with the same capital

The diversification will therefore require that you increase your trading capital by a value between 0% and 200%. What about selecting to increase the capital by 100%? Doubling your capital to trade three weakly correlated instruments? This means that the worst drawdown - for 3 trades put on simultaneously - will be 3%, but it will only happen occasionally.

I would use such a rule of thumb and in parallel study the approach of experts such as Ralph Vince and eventually fine-tune the money management afterwards.


Last edited by Fat Tails; January 2nd, 2011 at 02:01 PM.
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  #17 (permalink)
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Fat Tails View Post
Also I am not sure that the problem is a mathematical one. If you follow the approach of the Kelly formula / optimal f as described by Ralph Vince, this may produce larger drawdown than one could stand emotionally.

Thanks for saying this. It's worth repeating. Don't get so caught up in the perfect math model that you forget to consider what you will actually "allow" to unfold. So I'd say your math model, in that case, has to include a formula for your own personality so you can incorporate that into your trading

Mike

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Big Mike View Post
Don't get so caught up in the perfect math model that you forget to consider what you will actually "allow" to unfold. So I'd say your math model, in that case, has to include a formula for your own personality so you can incorporate that into your trading

Mike

I agree, plus trading results are backward looking only. You can't get too married to your simulation results or your live record. Fat Tails' screen name says it all. I wasn't trading during the flash crash, but if you were long eminis when that happened there's a good chance you could not have executed a stop at a price remotely near where you expected to. I have been present and trading in the pits during more than one black swan event, including standing outside the MMI (precursor to the Dow) pit on Black Monday 1987. I was too scared to trade that week, but I knew history was being made. Market makers like Bruce Williams were making markets $1000 wide on a one lot and getting tons of trades! (And he still lost six figures that day, as chronicled in "When Supertraders Meet Kryptonite"). I think Black Swan events will become more common now that market making is done by high frequency bots that turn themselves off when volatility gets too high. And some day, a terrorist is going to set off a nuke in a city. In the past, I've seriously considered owning way out of the money strangles against my position size as insurance, and I'm still thinking about it.

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Understanding the optimal bet size for a given edge does not detract from the ability to use a heuristic such as 2%.
Using only the heuristic though says absolutely nothing about the optimal bet size. Maybe 3% would be better, maybe 1% would be better, maybe the bet is not worth taking at all.
Taleb jargon is a pseudo intellectual way of stating the obvious IMO.

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dutchbookmaker View Post
Understanding the optimal bet size for a given edge does not detract from the ability to use a heuristic such as 2%.
Using only the heuristic though says absolutely nothing about the optimal bet size. Maybe 3% would be better, maybe 1% would be better, maybe the bet is not worth taking at all.
Taleb jargon is a pseudo intellectual way of stating the obvious IMO.

I'm a little lost here. Am I being criticized for using the phrase "Black Swan or for invoking the concept or both?

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