perplexed: Position Sizing

Discussions about Money Management and Risk Control.
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damian
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perplexed: Position Sizing

Post by damian » Thu May 22, 2003 12:00 pm

I didn't know what to call this thread.

Lets say I have a portfolio and one of the markets is Pencils. Using a fixed fractional position sizing method, each individual market tests well on single contract testing.

After a single market test using position sizing I observe that Pencils has a modest +ve sloping EC. However the last 6 months has been riddled with whipsaws. On the single file test, the position size decreased as teh DD grew (thanks to FF) and although the Pencil equity curve went into DD, the results over the full test are fine.

Now consider the situation where the remainder of the portfolio is doing very, very well up to date. In a portfolio test, our capital is growing very fast and position size is increasing. This means that the positions being taken in the Pencil market are also very large. So large that the string of losses over the last 6 months in the Pencil market have been large enough in $ terms to wipe out the modest profit made over the years leading up to the DD.

Now when you look at the performance of each market from the portfolio test, you find that Pencils are losing money overall.

A far simpler example:

- You trade CL and JY.
- your system started 3 years ago with only these markets.
- Both have been winners over the years.
- Position size is growing slowly.
- Then CL returns some huge wins.
- You get a signal to buy JY.
- the position size indicated is double that of the last JY trade.
- the large JY trade is a loser, so are the next 4, but position size for JY is still increasing as CL is a money machine, trade after trade it wins big.
- on a portfolio basis, no big deal that JY is losing.[1]
- but the recent strings of JY losses wipes out all the steady and respectable profit from the last 3 years of trading JY.
- suddenly JY looks like a bad market to trade, even though it has won consistently for the last few 3 years.

Why do I feel like I am going around in circles?

[1] is this line the key to my problem?

Part of me thinks that I should use individual market tests (with position sizing) when determining what markets trade well in a system. when I assess the portfolio results I should focus more on portfolio EC rather than performance of individual markets within the portfolio.

Thankyou for reading my long post.

Mark Johnson
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What to do, if anything, about a laggard mkt in a portfo

Post by Mark Johnson » Thu May 22, 2003 3:58 pm

Would you clarify this one point please?
Using a fixed fractional position sizing method, each individual market tests well on single contract testing.
It seems contradictory to me to use fixed fractional position sizing while doing single contract testing. Probably I've misunderstood! :oops:

thx, mj

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Post by Kiwi » Thu May 22, 2003 8:45 pm

Damian,

I think that you are falling into a trap that I did once on the Omega group in response to something that Chuck Lebeau posted. You are confusing the results of one run with the results of all possible runs for your portfolio that includes JY. In some possible sequences the loss will occur earlier, in some it will occur later. What bought this home to me was as follows:

Chuck said that when you had a drawdown you should not decrease the bet size. The reason he recommended this was that he demonstrated from a sequence of trades that when you reduced bet size you had an overall reduction in expectancy. The argument was posted to the Omega list where a better statistician illustrated the fallacy. His illustration also demonstrates, in passing, that your JY trade is only one of a range of statistically possible sequences and you need not worry about it.


> Fixed fractional has a negative expectancy? What do you
> mean?
Do you have
> any references? I don't believe this is true, but I've got
> an open mind.
>
> At XXX we use fixed fractional position sizing
> and believe it
> is the wisest choice -- as I believe you also concluded
> after your Monte
> Carlo testing.
>
>
> Regards,
> Aaron

----- Original Message -----

> Aaron,
>
> No references needed. Its a simple demonstration which I've
> borrowed from one of Chuck LeBeau's Traders Club Bulletins:
>
> "Here are the numbers: Risk is always 5% of current capital.
> (I'm going to round the numbers to two decimals.)
>
> Capital $ Risk W/L Account balance
> 100.0 5.00 L 95.00
> 95.00 4.75 L 90.25
> 90.25 4.51 L 85.74
> 85.74 4.29 L 81.45
> 81.45 4.07 L 77.38
>
> OK we are already tired of losing. Let's have five winners
> in a row and see if we can get our money back.
>
> Capital $ Risk W/L Account balance
> 77.38 3.87 W 81.25
> 81.25 4.06 W 85.31
> 85.31 4.27 W 89.58
> 89.58 4.48 W 94.06
> 94.06 4.70 W 98.76
>
> As you can see we had an equal number of winners and losers
> yet somehow we lost money. Perhaps it is because we had bad
> luck and got started in the wrong direction. Lets reverse
> the sequence of trades so that we start out on a winning
> streak instead of losing. Maybe that will help.
>
> Capital $ Risk W/L Account balance
> 100.00 5.00 W 105.00
> 105.00 5.25 W 110.25
> 110.25 5.51 W 115.76
> 115.76 5.79 W 121.55
> 121.55 6.08 W 127.63
>
> Looks good so far. Starting off with winners looks much
> better than starting with losses. But now we have five
> losers coming up.
>
> Capital $ Risk W/L Account balance
> 127.63 6.38 L 121.25
> 121.25 6.06 L 115.19
> 115.19 5.76 L 109.43
> 109.43 5.47 L 103.96
> 103.96 5.20 L 98.76
>
> Hmmm. It doesn't seem to matter if we start out with a
> string of winners or a string of losses. Somehow we wound up
> losing the same amount of money either way."
>
> The full bulletin is at:
>
> http://traderclub.com/discus/messages/1 ... ?SundayApr
> il3020001039pm
>
> I recommend Chuck's group for some interesting discussions
> although some of the members are a bit puerile. His
> bulletins are excellent material.
>
> So the problem is that if your system has marginal
> expectancy then fixed fractional will reduce it further.
> The other side of it makes up for this. On the positive
> side, because you reduce bet size in a losing streak you can
> start with a larger percentage bet for a given maximum
> drawdown. As you can see from my previous posting this not
> only gives you a higher return for a given maxDD but you
> also get a smaller maxDD at 2 Standard Deviations indicating
> a reduced risk of ruin.
>


Fixed fractional sizing does not have a negative expectation.

Chuck LeBeau has done a disservice to his readers. A system model that gets
exactly 5 wins and 5 losses and for every 10 trades and always gets exactly
5 wins and 5 losses is a poor model of a system. If you have ever traded a
strategy you'll recognize that a strategy can sometimes have a good run and
do 6 or 7 wins in a 10 trade set. And sometimes it'll have a bad set and
see only 3 or 4 wins in a 10 trade set.

A better model of a strategy is the binomial distribution. This is the
distribution of the number of times heads shows up when you flip a coin. We
assume each trade and each toss of the coin are independent. Chuck LeBeau
would have us believe that if we have tossed the coin 9 times (made 9
trades) and have gotten 5 heads (winners) and 4 tails (losers) then we will
automatically have a tail (loser) on the next flip (trade) -- might as well
skip the trade! That is not true. The next flip (trade) still has a 50/50
chance of turning up heads or tails (winner or loser for a strategy with a
50% chance of having a winner).

We won't necessarily have exactly 5 wins and 5 losses for every 10 trades.
If we flip a coin 10 times the most likely result is 5 heads and 5 tails,
but there is a chance of having anywhere from 0 heads and 10 tails all the
way up to 10 heads and 0 tails.

Now if we take Dennis' email where we bet 25% of the available capital each
trade, and start with $100, he showed that with 5 wins and 5 losses you
would end up with $72.42. But the full range of possibilities, with the
ending capital, and the chance of that possibility happening are:

0 wins, $5.63, 0.1%
1 win, $9.39, 1.0%
2 wins, $15.64, 4.4%
3 wins, $26.07, 11.7%
4 wins, $43.45, 20.5%
5 wins, $72.42, 24.6% (Dennis' example)
6 wins, $120.70, 20.5%
7 wins, $201.17, 11.7%
8 wins, $335.28, 4.4%
9 wins, $558.79, 1.0%
10 wins, $931.79, 0.1%


To get the expectation for this model of a strategy, we need to multply the
ending capital for each possibility by the chance of that possibility
occurring and then add across all possibilities. If you do this you'll find
that the strategy has a $100 expectation -- exactly what we started with!
Fixed fractional trading does not have a negative expectation. Nor does it
turn good systems into losing systems.

You might think intuitively -- "well my strategy has ups and downs and I'll
always be playing the largest size on the losers and then after the losers
I'll be playing smaller size when I have winners, so it makes sense that I
would lose money on a 50/50 system." I reply that the human brain is not
very good at intuiting probabilities. Each trade is independent. Whether
we previously had a winner or a loser and whether we just upped or reduced
the size, doesn't affect whether the next trade will be a winner or a loser.

Maybe it would be easier to think of it this way if you want to be
intuitive... Having 0 wins is just as likely as having 10 wins. With 0
wins we lose about $94. But with 10 wins we make a whopping $832! Average
these out and you are way ahead. Keep doing this with opposing pairs... 1
win loses less money than 9 wins gains. Etc. The positive expectation of
the five opposing pairs offsets the expected loss from exactly 5 wins.

I think backtesting and the proper use of the statistics gained in
backtesting are the most important thing in being a profitable trader and it
pains me to see Chuck LeBeau misleading people.


Regards,
Aaron
So I would ignore the interaction between money management scaling and the individual trade and recommend a process something like this:

1) Perform a basic test for inclusion in your portfolio based on single contract testing. This will determine if there is any reasonable profitability from your system on this contract (no one adds ES to a trend following portfolio). Note that you may get poor performance (low MAR and profit factor) but still include it for diversification if your 2nd and 3rd tests suggest that you should.

2) Test the portfolios with money management ... ignore single results like the impact of a losing trade at 4x original risk wiping out all prior profits.

3) Monte Carlo scramble the results (yes, its not right but it is the best we have) and determine a level of risk of ruin that is acceptable to you and thus your bet size.

At 2) and 3) you need to look at the poorly performing single contract markets and decide if they are likely to improve the Sharpe Ratio/g.c. Ratio/Lake Ratio of your returns. This is probably an art (someone else please correct me) and will likely result in you including some extras just because you don't really know how they will perform in future.

John

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Post by edward kim » Fri May 23, 2003 1:39 pm

Kiwi wrote:Chuck said that when you had a drawdown you should not decrease the bet size. The reason he recommended this was that he demonstrated from a sequence of trades that when you reduced bet size you had an overall reduction in expectancy. The argument was posted to the Omega list where a better statistician illustrated the fallacy. His illustration also demonstrates, in passing, that your JY trade is only one of a range of statistically possible sequences and you need not worry about it.
Hey John,

Does Chuck feel that the inverse is true - that if you have an drawup/increase in equity, you should not increase the bet size? If he does believe that is true, then bets get smaller as % of the account as the account grows.

If he believes that is not true, then at what point does someone start trading smaller if they lose a lot of money? Is there a statistical validation point where the sequence of trades is now becoming significant enough where he needs to pare down risk? For example, if someone has the following:

$100,000 account
2% risk
$2,000 tisk per trade fixed

After 25 losers in a row, he is now taking 50K / $2,000 = 4% risk per trade. If you can clarify Chuck's comments, it will give me a better understanding.

Thanks,

Edward

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Post by Mark Johnson » Fri May 23, 2003 2:21 pm

What Chuck said and when he said it and all other details, are contained within the original. It is located at http://traderclub.com/discus/messages/1 ... 20031022am

Here are a couple of plots I did at the time:

MODERATOR'S NOTE: Changed graphs to vertical format.
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Post by Kiwi » Fri May 23, 2003 4:21 pm

Oops I seem to have said more than needed :shock:

My main point was that when you look at one sequence of trades you have to realise that it is just one. A range of others could also have occurred (whether or not the distribution is normal and whether or not there is serial dependency) and you need to consider the possible distributions in your decisions.

Without going back to the original discussions in depth then Mark's diagrams do a nice job of illustrating how Chuck's idea impacts risk per trade.

Chuck wasnt advocating removing the increase in bet sizing and I seem to recall that most posters would have instituted a reduction at some point. What Chuck (seems to me) to have been illustrating is that much of probability (and thus trading) is counterintuitive unless you are trained and experienced in each new area. I am always amazed when something new catches me out. :wink:

John

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Monte Carlo

Post by gbos » Sat May 24, 2003 6:18 pm

8) If one knows the characteristics (profit/loss frequency and magnitude) of the trades generated from his system, then an easy way to examine the alternative paths that chance alone could realize is Monte Carlo simulation. Suppose that you know your system generates equal probable (this assumption can be relaxed) trades with profit-loss xi for every unit risked (xi positive for winners and negative for losers) .Then you can form a matrix with this payoff and run your Monte Carlo simulation. See the following excel xp spreadsheet.
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MoneyManagement.xls
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damian
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Post by damian » Sat May 24, 2003 10:41 pm

Mark,

regarding the apparent contradiction in the second post:

What I wrote was wrong. I chopped a whole heap out of the beginning of this post and the remaining first sentence was left doesn't make sense. I was not supposed to have the words "single contract". Sorry for the confusion. My silly mistake.

As for the remainder of the posts, I am still digesting. As I was thinking about this problem I did consider that Monte Carol would be associated. quite some time ago I tried to use the method (I think with some of Mark J's C+ code, in fact) but left it alone as I didn't understand the theory behind the concept well enough to understand the significance of the results.

Thankyou for the posts to date. I will return with more discussion after digestion.

damian

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Post by bloom » Sun May 25, 2003 12:59 am

gbos:

Thanks for the file!!!

damian
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Post by damian » Tue May 27, 2003 2:01 am

gbos,

Firstly, thankyou for the file.

Regarding forming a matrix of payoff data. Do you refer to the values that can be entered in col C for #trade1-20? This at first seemed obvious to me but the value 'Trades per trial' in D24 caused me to re-think.

What I am doing at the moment is assuming I have 100 trades where 75% have an average loss of -0.50

I populate 15 of the 20 cells in col C with -0.50. In the remaining 5 cells I attempt to describe the character of my 25% winning trades. This I find tough as over 100 trades I might have one 15R trade and one 8R trade. Although only one of each, they both make a big difference in a trend following approach. The remaining winning trades are concentrated between +1 and +5 (for example). With only 5 cells left in teh matrix with which to work, I have difficulty describing my winners.

My question is this: is my difficulty a function of a total misunderstanding of how to use the matrix of 20 trades?

regards
damian

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About the spreadsheet

Post by gbos » Tue May 27, 2003 6:55 am

A few explanations about the spreadsheet:

Yes, the payoffs that we know (by statistics) our system generates are entered in column C.
When we click on Monte Carlo button, vba code does the following:
It creates a trial of say 30 consecutive trades. Each trade of these is pooled randomly from the payoff matrix. It doesn’t matter if one particular payoff has been drawn previously in this particular trial, it can be redrawn with equal probability with the others.
The bankroll after each trade is

Bankroll (after trade) = Bankroll (before trade) + betting_fraction * Bankroll (before trade) *payoff

At the end of each trial (end of 30 trades) the program keeps the final bankroll.
The process is repeated for a few thousand more trials and the histograms and percentiles statistics of final bankroll are calculated.

A few key numbers are presented in the spreadsheet as
1. the average final bankroll at the end of each trial
2. the expectancy (on average how much we make for every dollar we bet given this payoff matrix)
3. Kelly betting fraction (the optimal fraction of our current bankroll that we must bet in order to maximize the geometric growth of our Bankroll)
Note that besides its optimality Kelly fraction has a few undesirable properties (for example large drawdown) and usually a lower betting fraction is used.

If the payoffs does not have the same probabilities of occurrence then there must be made a few changes in the vba code. For a problem of the kind that you described I changed a little the spreadsheet and added a column that you must enter the probabilities for occurrence of each payoff (see below). I also saved the spreadsheet in a format that previous excel versions can run.

Best Regards
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