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Scaling in and scaling out...when the total is NOT the sum of its parts
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Scaling in and scaling out...when the total is NOT the sum of its parts

  #1 (permalink)
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Scaling in and scaling out...when the total is NOT the sum of its parts

Have you ever abandoned a strategy because it had untolerable drawdown?

When examining the potential profit additions and potential loss reductions with scaling, the possibilities are quite significant.

The following comes with some assumptions.

Assumption 1: Your profit targets and your loss limits are numerically large enough in size in order to justify scaling. For discretionary traders, this number will be much higher, because the burden of computation and execution becomes untenable for fast moving markets and small increments. For automated traders, as long as the increments are large enough to support the resoluation/granularity, then scaling may be beneficial. (i.e. it wouldn't do much good to scale out or in if your strategy has P/L on the order of 2 ticks, but the effects will become much more prolific and relevant if you have P/L on the order of 10, 50, 100 ticks, etc).

Assumption 2: Your strategy isn't perfect. If your strategy/system has a perfect profit curve, then scaling will not add any value. Obviously, there's no one that features such a strategy, so a healthy dose of reality shows us that as consistent and close to the mean as we'd like to be (with wins and losses, expectancy, etc), everyone's system features a degree of variance away from the mean. The greater the variance, the more scaling will add in your money management.

Assumption 3: You have enough capital to feature scaling money management. For a simple 1 lot/1 contract strategy, obviously you cannot scale. For a 2 lot/2 contract strategy, you have the option of scaling in or out (one but not the other). For a 3 lot/3 contract strategy, you have the option of both scaling in and out.

Here's how it works.

Similar to MFE/MAE, runup and drawdown analysis will show you that there are a number of trades where the outcome fixes itself. That is to say, at a certain amount of runup, the probability that the trade will result in a profit increases. As the drawdown increases, at some point, it becomes very unlikely that your trade will recover.

Again, this depends on the level of variation away from the mean. The reason we carry the increment of stop loss that we do, is because we've determined that level gives us the optimum chance of surviving drawdown, but not cutting a winner short. A small percentage of our wins, will be at or near our stop. A greater portion of our wins will experience some drawdown, but more toward the average drawdown. A small portion of our wins, will experience very little to no drawdown. Conversely, a small percentage of our losses, will experience no runup whatsoever (hopefully, if we've developed an edge, the number of these types of losses will be significantly less than the no drawdown wins we achieve). A small number of losses will approach very close to our profit target (but retrace). The majority of our losses will occur within a standard deviation of the average/mean runup.

Scaling out. Scaling out provides more impact that scaling in for a couple of 2nd order/indirect reasons.

The first reason is that by scaling out of trades that are most likely destined to end negative, is that we reduce drawdowns (if nothing else, this is beneficial by itself alone). Reducing drawdown enables us to put more of our captial to work and requires us to carry less drawdown reserve. Carrying less reserve means that we can compound quicker. Not to digress, but a strategy that features half the profit (but half the drawdown) of a strategy that features twice as much of each, will outperform the latter strategy. Why? Compounding and increasing positionsize will quickly overcome the other strategy that must carry a larger amount of capital in reserve.

The obvious impact of scaling out is also reduction of total loss. Scaling out will reduce your average loss value, thereby making your strategy more profitable.

Scaling in. Scaling in can be beneficial to a strategy, however, I find that in MOST cases, if your strategy doesn't feature a great number of outliers, or a large variance away from the mean (for winners) then scaling in usually isn't as beneficial as simply trading the maximum position allowed (while still obeying your capital management rules and carrying the appropriate level of drawdown reserve). Usually, scaling in will yield more profit. But it the profit incrase will not be proportional to the increase in positionsize. (that is to say, unless your strategy has a some really big winners, and a large variance of win sizes, scaling in by another contract/lot will not result in the same amount of profit as if you'd simply traded that available capital from the onset).

This requirement to hold capital in reserve is what makes scaling in less useful than scaling out. Scaling out requires that you carry no additional capital that's not working for you (or at the least, when you put that capital on the sideline, it's for a good reason, because it would have been working poorly for you).

Additionally, those traders that portfolio trade will also enjoy the benefits of scaling out in the sense that they can reallocate that capital to other, more profitable ventures (during that particular time).


Taking advantage of the real value of scaling. As covered briefly above, scaling out, should be used PRIMARLY as a tool to reduce drawdown. IF there happens to be an increase in profits (via a reduction in average loss) that's simply a convenient benefit.

This concept escapes a lot of traders. By trading 2 contracts instead of 1, you MAY actually reduce the netprofit/contract by scaling out. (that is to say, if you net $10k with 1 contract, you may end up only netting $18k with 2 contracts scaling out).

However, the reduction in drawdown, many times, can easily overcome the reduced netprofit/contract by the benefits of compounding.

In summary, you should do the analysis and determine if scaling money management will help you. It may not. But if you do, you should focus on second order analysis techniques that take into account trade compounding through increasing position sizing.

It's a difficult concept for most traders to understand that a strategy that features $30k in profits (but $5k/contract drawdown) will yield LESS overall profit, than a strategy that features $20k in profits (but $2500/contract drawdown).

Now, that comes with some assumptions.

Assumption 1) You're actually going to increase your positionsize.

Assumption 2) You're actually going to carry drawdown reserve.

Assumption 3) You're trading a discrete or incremental instrument like futures. The compounding effects for more granular instruments (like small share equities) the compounding effect is reduced.

Assumption 4) You're starting out with 1 contract (or actually 2 if you want to scale out). As your capital increases, it takes less and less profit to result in an increase in positionsize in contract number. I.e. a 20% trade profit for a single contract will not result in an increase in positionsize. But a 20% trade profit for a 50 contract account, will most certainly afford an increase in positionsize.

A case can be made for management strategies that forgoe drawdown reserve, once a minimum capital runup has been achieved.

In essence, if you determine the maximum drawdown for 1 contract of CL on your system is $4500. (you've done this through thorough monte carlo exercise and you're confident that a $4500 DD is less than 1% likely). Then you must carry an additional $4500 for every contract above and beyond the broker/exchange minimum for CL.

You may elect however, that once you double your intial equity, (and your positionsizes have increased) to forgoe the DD reserve and simply trade the maximum contracts permitted by your broker. This will mean that if you begin a drawdown period, rather than using reserve to weather the drawdown, you'll simply reduce your positionsizes on the way down.

This technique produces larger/amplified runups and drawdowns. You'll make more profit this way, but your equity curve will be less smooth and you'll experience more horrifying (and gratifying) swings.

IN THAT STYLE OF MONEY MANAGEMENT, the concept and effect of drawdown is muted or removed altogether.

In order to be totally thorough, a trader should consider all these primary and secondary effects in their trading plan before choosing, eliminating a particular system/strategy.

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."
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  #3 (permalink)
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RM99,

Thanks very much for a thoughtful and thorough post.

This is a topic that Iíve struggled with for a long time. Kaufman (Kaufman, Perry (2004) New Trading Systems and Methods (4th Edition) Ė John Wiley & Sons) has a chapter on this. Though, the chapter is very short and is not backed by any empirical analysis. It does provide a number ideas and compares them graphically. The other good explanation of the logic of this Iíve seen a presentation by Jeff Boccaccio at a London Traders and Investors Club meeting (Jeff Boccaccio's Trader Channel | Traders & Investors Club).

But, I havenít found any good research or references on the scaling or dynamic positions sizing problem. I suspect there is a lot of literature if one looked on using options to hedge (put / calls, etc), but not using position management with a outright position (e.g. spot FX, shares).

Iím not sure I fully understood your view here. Are you suggesting that if you deploy a scaling out position management strategy that you can trade a bigger position?

Scaling out is not recommended by Van Tharp (Tharp, Van K (2007) Trade your way to financial freedom (2nd Edition) Ė McGraw Hill Professional), as he correctly shows that you are holding all the possible risk at the start of the trade then not ďletting your winners runĒ as you are taking off position size as the position runs in your direction. Again, Van Tharpís views are not supported by empirical or researched evidence. Whilst I would recommend developing an understanding of Tharpís position what about the other side the coin? As you say, doesnít it depended on the payoff profile of the strategy a method of scaling out of a position may be preferable?

My rough and ready research into the topic is this:

1. Using scaling out for trend following strategy takes up the percentage of profitable trades (this is good thing for standard trend following systems usually arenít good with 30 Ė 40% winners) but takes down the profit per trade
2. Scaling into trend following strategies takes the % of profitable trades down

And what about scaling stops? For example, if you had a stop that is 3 * ATR, what about if we took 1/3 of the position off at 1 ATR to see if the position turned around. If the position moved against us 2 * ATR we could take off another 1/3. If the position moved 3 ATR then we take all the remaining position off. My thinking goes that it would allow for positions that move against us initially then take off in the desired direction. I call this idea graduated stops. Though, it is exactly that, just an idea (it might be a rubbish idea). I havenít done any significant testing on it.

One of the advantages of trading algorithmically is the adjusting position sizes on the fly is easy, with the right rules. But the trick is finding the right rules.

I do wonder if there isnít some basic math / modelling we can do to help us understand the topic further? And I mean keep it simple to illuminate the discussion. Iíve done some simple modelling of a basic trading outcome.

Iíve included here a calculation sheet that models some basic trades. That is:

1. Assume that $10,000 funded account
2. We risk 1% of that account per trade
3. Cell D5 is the number of trades
4. The percentage of winners is in column G (with the loser percentage being 1-column G)
5. Row 1 is the actual pay-off in dollars for each trade
6. Row 2 is the percentage increase in the winner pay-off above the stop loss payoff
7. Below is a surface plot of the outcomes

What we canít model here is the probably of ruin. As we increase the position size of the trade we must increase the probably of ruin. As Ralph Vince quotes in his book (The Mathematics of Money Management - 1992):

ďif you play a game with unlimited liability, you will go broke with a probability that approaches certainty as the length of the game approaches infinity.Ē

If we increase our position size then we increase our probably of ruin. However, I think your argument is that we also increase our probably of a winner as we are scaling out when the trade moves with us? From the spreadsheet we can see that if we increase our percentage of winners than we increase our probably of landing in a profitable zone. Which could lead one to assume you are right, if by increasing our percentage of winners, this is good. But also, as per Van Tharpís point, donít we reduce our payoff per winner if we scale out? Doesnít that drag us back towards the left hand side of the table in the spreadsheet as we are reducing the size of the difference between the winners and losers.

We probably need a Monte Carlo analysis to understand the risk of ruin as we increase the position size? Surely someone has done that previously making some basic assumptions with regards to size of account risked versus probably of ruin. (see link here if anyone has this software we can probably model it: Monte Carlo Analysis : Day Trading Strategies : Forex Trading Systems : Adaptrade Software)

Iíve probably raised as many questions as answers here; but I donít think this is a simple topic. And my thinking on the topic isnít as nearly as rounded as it needs to be by.

Let me summarise:

1. I initially thought that for trend following systems it would be good to scale into a position Ė thereby, accentuating the ďlarge winnerĒ skewness of the pay-off curve (a few very large winners). But to date, Iíve not worked out any method for doing this that increases profits.
2. I like you point about that scaling out can actually help Ė however, I do have in the back of my mind that Tharpís point that if we scale out we reduce the pay-offs of the really big winners
3. And finally, if you increase your position size what about the risk of ruin?

Thanks,

drolles

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RM99,
I totally disagree. I'm against scaling in or out. I explained it almost two ears ago. Mike does not like repetitions, so you can look for yourself.

Quoting 
Not to digress, but a strategy that features half the profit (but half the drawdown) of a strategy that features twice as much of each, will outperform the latter strategy

Not correct. Second strategy is exactly like first with two contracts.

Quoting 
It's a difficult concept for most traders to understand that a strategy that features $30k in profits (but $5k/contract drawdown) will yield LESS overall profit, than a strategy that features $20k in profits (but $2500/contract drawdown).

This is correct 20/2.5 > 30/5.

Baruch

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same strategy if different payoff structure?

Baruchs,

Thanks very much for the follow-up post.

Do you think you could cross-post the link for you postings on scaling. I’ve struggled to find posts on this. I’ve searched all your posts and found this one: https://futures.io/psychology-money-management/1024-effective-risk.html#post11640

Is that the one you refer to?

In that post, I do like your coin example. Where does it come from? Have you modelled that using a random number generator?

I take your point about the correlation of the payoffs. But I’m not sure I fully agree with the statement that you are trading the same strategy if you change the position management approach.

As per my comment in the previous post, from my research you change the shape of the payoffs if you start to scale-in or out. Therefore, is it still the same strategy?

Kind regards,

drolles


Last edited by drolles; April 10th, 2012 at 11:56 AM. Reason: changed wording
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Iíve just found this thread on risk of ruin (https://futures.io/psychology-money-management/15602-risk-ruin-7.html#post209771).

This is something we probably need to play into the discussion as well Ė the position sizing approach one using to for the strategy in question. It probably depends if you are trading Fixed Fraction, Optimal-f or Kelly (Iím not sure Iíve ever really understood the difference).

Good play Fat Trails on the posts on that thread. Very good.

Cheers,

drolles

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Quoting 
But Iím not sure I fully agree with the statement that you are trading the same strategy if you change the position management approach.

Exactly the opposite. For me scaling is like two or more different strategies, but they are not independent strategies. One end (entry or exit) are the same.
So you think its easier to invent several wining strategies at once, then only one?
https://futures.io/traders-hideout/501-some-thoughts-trading.html
https://futures.io/psychology-money-management/2197-most-important-piece-trading-2.html

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Understanding baruchs's position?


baruchs View Post
Its funny that in this "great" community no one tries to understand what trading is about.
The only responses you get is when you give some useless indicators or complete setups, but if you try to get people to think, no one is interested.

This cracks me up .

I wonder at the traffic here sometimes. I've also asked some basic questions and tried to get some debates going - e.g. end of trade draw downs, etc to no avail. Those threads that generate the most discussion to appear to be the threads with a set-up is shared.

But back to the topic at hand...


baruchs View Post
Exactly the opposite. For me scaling is like two or more different strategies

Ok, I see.

I've read through the threads you reference, thanks very much for those.

So I'm not sure after reading the threads I could understand your position correctly? Are you saying that scaling is good, but only where the strategy works? But you are also saying that one can trade a losing strategy combined with a winning strategy to smooth the profit curve?

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Quoting 
So I'm not sure after reading the threads I could understand your position correctly? Are you saying that scaling is good, but only where the strategy works? But you are also saying that one can trade a losing strategy combined with a winning strategy to smooth the profit curve?

I said several times scaling is bad!! Its trading blind folded. Test each exit (scaling out) or entry (in) for it self.
I give two examples for adding losing strategy. They are self explanatory.

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