Scaling / 'Pyramiding'

Discussions about Money Management and Risk Control.
shakyamuni
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Scaling / 'Pyramiding'

Post by shakyamuni » Sat Feb 07, 2004 4:56 pm

I am currently fooling around and doing some brainstorming with my scaling/'pyramiding' algorithms to see if I can invite some additional value.


We might be able to engender a mutually beneficial discussion on the topic.
Last edited by shakyamuni on Sat Jan 08, 2005 6:09 pm, edited 1 time in total.

jankiraly
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Post by jankiraly » Sat Feb 07, 2004 6:59 pm

Another way to think about pyramiding (adding more size to an existing trade) is to consider each of the pyramid entries to be its own unique self-contained trading system. This lets you simulate and analyze them individually.

It could help you see whether you're putting on the first unit too soon. (if so then the standalone system containing the first entry, will be a poor performer or maybe even a loser.) It could help you see whether you're putting on the last unit too late (if so then the standalone system with the final entry will be poor).

Or perhaps you're not pyramiding far enough. You could find this out by creating another standalone system that enters even after the "last" pyramid entry, and seeing if its performance pleases you.

Some people like to have a nice orderly progression of frequencies. They arrange their pyramid schedule to get, for example
70% of trades with an initial entry, also get a first add-on (pyramided) entry
70% of trades with a first add-on, also get a second add-on
70% of trades with a second add-on, also get a third add-on
etc.

It's very easy to measure and adjust this (if you care about balanced percentages), when the individual entries are unique systems. Just count the #trades, a statistic that's readily available in all the test software packages I ever saw.

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The importance of Pyramiding

Post by brendo » Sat Feb 07, 2004 9:01 pm

Personally, I have found Pyramiding to be the most powerful part of my trading system, and it thus has added much greater value than to me than 'Entry' and certainly more value than early exit of losing trades.

I have used variations of the Pyramid procedure as described in the 'Original Turtle' rules in both short and long term trading systems and this has generally worked quite well for me.

Brendo

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Scaling

Post by ksberg » Sun Feb 08, 2004 1:50 am

Scaling, or adding additional units/positions makes an interesting study. As shakyamuni suggests, there are all sorts of "shapes" one could apply, and they have widely different characteristics.

I use the term "scaling in" when the total size of aggregate position is known in advance, and "scaling up" when sizing is applied successively. In that parlance, Turtle rules use "scaling up". The difference is probably academic, but becomes pronounced depending on HOW you scale, and WHEN you size.

For instance, original Turtle rules determined unit size on entry, and added successive units every 1/2 N. For Turtle, the HOW is by repeating units, the WHEN is to determine size on first entry.

We can change the HOW by modifying unit size on each position. If units are sized on first entry, but unit size is reduced on every added position what we have is an inverse pyramid. For example, if we repeat half the last unit, this might look like 8, 4, 2, 1.

Of course, we can make the WHEN of sizing dynamic, and alter position size as we're adding positions. For scaling in, this means we re-adjust distribution based on a net balance of existing and planned units. For scaling up, the unit size is also reduced, but not by as much. With volatility sizing, this generally means a reduction in strength, as volatility expands.

Another algorithm changes the HOW by adding when the profits of existing units can pay for an additional position. The sizing determination can be either first entry, or taken dynamically.

We can make both HOW and WHEN dynamic as well. That is, after the first entry, unit sizing and subsequent entries are continually adjusted by the sizing algorithm itself. This last one is pretty wild, and the behavior reminds me of non-linear dynamic systems: they can shoot the moon as easily as plow into the dirt, and are extremely sensitive to input (market) conditions.

I find that the effect of scaling also depends on choice of sizing algorithm, and how equity is determined:
  • Closed Equity
    Total Equity
    Core Equity
    Reduced Total Equity
    Reduced Core Equity
I've seen analysis that states results roughly scale depending on choice of equity model. However, these don't account for variations in HOW and WHEN scale and sizing are executed, as mentioned above. You can imagine how differently the results are between using Total Equity and dynamic sizing with inverse pyramiding to Closed Equity and sizing only up front, but repeating sized units.

In all cases, test these ideas thoroughly before rushing off to trade them. Equity, sizing and scaling are all closely related. Choices and combinations can have a huge impact on final results. Just make sure it's a positive impact :wink:

Cheers,

Kevin

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pyramids

Post by Neil » Tue Feb 10, 2004 5:44 pm

I have been using a modified turtle sytsem for a few months now with good effect. Playing the market's money.

1. As soon as a position shows a stopped in profit, risk a percentage of that profit, 25%? and add a further trade with 2ATR entry.

2. As that extra position moves into open profit the stop will come up, allowing more risk for another position up to the 25%.

3. As the stops on all of the positions come up, more stopped in profit can be risked. The shape of the pyramid evolves according to the nature of the trend.

4. The pyramid only stops once the core postion is finally stopped out.

A couple of issues have arisen about the trailing stop.

A very rapidly rising trend with an n day stop will not by definition be showing a stopped in profit until n days or more have elapsed. A 20 day stop is not pyramid friendly.

I have settled on using a 3xATR stop on the core position in order to stop in profits more rapidly. I then run a 2ATR stop behind the pyramid positions to let them contribute to profits even more rapidly, allowing more positions to be added.

More variations might include;

adding positions more aggressively early on and then being a little more cautious later on.

changing the types and tightness of stops. Variations in ATR multiple for example or parabolic stops.

Account size and the instrument being traded is going to dictate the effectiveness. A small account trading one-lot futures is going to be tied up by unit size. But equities and spread bets work very well :lol:

I haven't done any testing, but on a purely qualitative basis it seems clear that getting the pyramid going early is going to be bebeficial.

The nature of a system is going to change, in that those small trends could provide less profit to the system. The bulk, if not all of the profits are going to come from mega-trends that are milked for every last dollar.

Regards,

Neil

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Post by Sebastian » Tue Feb 10, 2004 6:48 pm

More variations might include;

adding positions more aggressively early on and then being a little more cautious later on.

changing the types and tightness of stops. Variations in ATR multiple for example or parabolic stops.

Neil, a couple of observations I've made that might be of use to you:

I put together a Turtle variant in Excel using EOD data where only one position could be added on any one day (regardless of the size of the move), and a separate one where multiple positions could be added on the same day if price moved through multiple 1/2N entry points.

The second system (builds positions more quickly) gets a bit better overall performance but also has larger drawdowns. Since the MAR ratio is just about the same for both of these systems, I opted for safety and only add one position per signal day. Your mileage may vary, so test for yourself.:)

The other thing I've noticed is that the ATR-based stops and N-day based stops measure different things. ATR stops are based on volatility but N-day based stops are a reflection of the actual trend in the security. I've noticed that ATR-based stops can get hit pretty frequently even when there is no change in the trend, which means you can get bounced out of exactly the kind of strong trend that the Turtle system is so successful at catching.

(Maybe c.f. can confirm/deny this.) My theory is that the two separate kinds of stops in the Original Turtle Rules were designed for two separate conditions: The ATR stop was designed to stop you out quickly with small losses on "fake-out breakouts" that didn't follow-through and the N-day stops were intended to keep you in solid trends for a long ride.

FWIW.


Luck,

Sebastian

Neil
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pyramids and stops

Post by Neil » Wed Feb 11, 2004 6:18 am

Sebastian,

I agree with you that an n day stop is certainly very good at trend following with the basic 4 entry turtle setup. My problem with it is that if you get lucky on a very strong trend, say a 6ATR move in 3 days, you cannot claim a profit for at least 20 days. This does not allow you to add any more risk. I am not adding turtle style units, just adding risk as a function of stopped in prifits.

Regarding the type of stop to be used, for me it must serve two purposes.

1. Keep away from the day to day fluctuations in price.

2. Move in the direction of the trend.

Day to day fluctuations are measured by ATR. If you take a multiple of ATR you can pretty much estimate the probability of being stopped out on a particular day. 1xATR is quite likely, 3x ATR is very unlikely. It is the daily lows which I am trying to avoid so I use a stop which is the highest low since entry, minus 3 ATR for long positions. I find that it keeps me in a trade for months at a time and yet stays close enough in to keep the profits coming. If you compare this to a 20 day stop, you get stopped out at pretty much the same point.

My thoughts on 2ATR entries come from a study I did on maximum adverse excursion. That being the maximum distance a position will move against you in terms of ATR before finally becoming profitable. If you look at a series of profitable trades the vast majority go profitable with less than 1.5 ATR excursion, the rest within 2 ATR. If a position goes further than 2ATR against you then the probability of winning diminishes rapidly. I have attached a chart below.

Does anyone have any thoughts on the risk profile to use. How about risking 100% of profit early on, say less than 1xrisk as profit, and then reducing to say 10% as the trend matures. Every trend has a finite lifetime, does anyone have any data on the longevity of trends? There would be no point adding to positions on a very mature trend if it is statistically unlikely to continue. Or would there?

Regards,

Neil
Attachments
Trading Log_29629_image001.gif
R on the x axis represents the profit as a multiple of initial risk.
Trading Log_29629_image001.gif (7.92 KiB) Viewed 24889 times

shakyamuni
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Post by shakyamuni » Wed Feb 11, 2004 11:54 am

Does anyone have any thoughts on the risk profile to use. How about risking 100% of profit early on, say less than 1xrisk as profit, and then reducing to say 10% as the trend matures. Every trend has a finite lifetime, does anyone have any data on the longevity of trends? There would be no point adding to positions on a very mature trend if it is statistically unlikely to continue. Or would there?
I find that the logevity of trends tends to depend on how you define a trend. It also depends on whether you define logevity in terms of time or price.
Last edited by shakyamuni on Sat Jan 08, 2005 6:10 pm, edited 1 time in total.

shakyamuni
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Post by shakyamuni » Wed Feb 11, 2004 12:00 pm

Another way to think about pyramiding (adding more size to an existing trade) is to consider each of the pyramid entries to be its own unique self-contained trading system. This lets you simulate and analyze them individually....It could help you see whether you're putting on the first unit too soon...It could help you see whether you're putting on the last unit too late...
Or perhaps you're not pyramiding far enough.
This is a very good idea!
Last edited by shakyamuni on Sat Jan 08, 2005 6:17 pm, edited 1 time in total.

Neil
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trend longevity

Post by Neil » Wed Feb 11, 2004 2:00 pm

Shakyamuni,

I would define trend longevity in terms of R multiples. R being the initial risk. This would standardise all trends as all entries are made with 2ATR stops. Life gets a little complicated with contract rollovers but I would view these as a continuation rather than a new trade. It would be interesting to see a histogram of completed trades. From this you could deduce the probability of a trend continuing and then construct a logical pyramid structure. Do you know if Veritrader can produce this data?

Regards,

Neil

shakyamuni
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Post by shakyamuni » Sat Feb 28, 2004 8:19 pm

Neil,

You may want to raise the issue with some of the boys from g.c..
Last edited by shakyamuni on Sat Jan 08, 2005 6:10 pm, edited 1 time in total.

Neil
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Trend longevity

Post by Neil » Sun Feb 29, 2004 5:11 am

Shakyamuni,

It seems that Veritrader does the job beautifully. The first page of the results shows a histogram and cumulative frequency chart of R-multiple distributions.

Using this to deduce the probability of the trend contininuing and how much further it might go, I've managed to produce a chart showing how much is a good idea to add. Interestingly it concludes that it is not worth pyramiding a position after 5R in your favour. The R-multiple I'm using is based on the first of the four turtle units. I've used 80% of Kelly's optimal f to calculate the position size. (as a percentage of stopped in profits on that position not account size. I only risk the market's money)

This isn't a simulation admittedly, I prefer to stick a trade or two on instead. I find account size much more interesting than VBA. :lol:

Regards,

Neil

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Post by Bernd » Sun Feb 29, 2004 8:25 am

:wink:
Last edited by Bernd on Fri Apr 18, 2008 11:10 pm, edited 1 time in total.

Neil
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pyramids

Post by Neil » Sun Feb 29, 2004 5:43 pm

"How will that distribution change, when I introduce pyramiding." (Is this, what you are doing Neil?)
I'm looking at the distribution of R-multiples to decide how much of my profits to risk to further positions and whether it is worth adding to a position at all. Positions added are additional to the four turtle positions.

From the distribution I have worked out that early on it is well worth risking a large proportion of profit (because of the probability of the trend continuing and how far it might continue) and after about 5R it is probably not profitable to add further risk.

This shapes my pyramid and enhances profitability in a most satisfactory way :D

Regards,

Neil

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Scaling in and scaling out

Post by Corn Elius » Fri Jun 18, 2004 1:14 pm

It seems to me that there are two distinctly different ways of handling a trend. One way is to buy a number of contracts at the beginning, then scale out of the contracts as the trend progresses, so that you have made all your money before the trend ends. Another way is to add contracts as the trade progresses so you can possibly make more money at the end. Have I got this right? And how does one get out of Example 1 and example 2. All at the same time when a stop is hit, or scaling out in some fashion?

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Post by Ted Annemann » Fri Jun 18, 2004 2:25 pm

Shoot, there's a lot more than two ways to do it! Imagine that all the different entries and exits (of fractional portions of your Overall Position) each represent their own little self contained "sub-system". The final macroscopic Trading System is nothing more than the linear superposition of all these little sub-systems. When you think of it this way, you immediately see that the sub-systems can have ANY relationship to each other (including NO relationship), that the mind of Man could possibly devise. There are far more than two possible relationships.

Get out a clean sheet of paper and brainstorm. You'll easily dream up a dozen or two dozen schemes. Take on more and more units as things get better and better. Take on more and more units as things get worse and worse. Peel off more and more units as things get better and better. Peel off more and more units as things get worse and worse. Take on (or peel off) more units as more and more time-in-trade accumulates. Arrange the numerical schedule of add-ons to be constant velocity (+1, +1, +1, +1, +1). Arrange the numerical schedule of add-ons to be increasing velocity (+1, +2, +3, +4). Arrange the numerical schedule of add-ons to be decreasing velocity (+4, +3, +2, +1). Arrange peel-offs to be constant velocity, or increasing velocity, or decreasing velocity.

It's an area that invites exploration. Explore! Cook up some ideas and try em out. See what works well and what works poorly. Go and do and learn.

shakyamuni
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Post by shakyamuni » Fri Jun 18, 2004 6:30 pm

You can also try the martingale strategy- it’s a surefire winner every time. Some traders claim it might be pretty risky, but that is neither here nor there.

The martingale works best if you have a very small bankroll to begin with.

Just throw down an initial bet of arbitrary size, then - as the position goes against you - double the size of your position every time you get a hunch that the market is about to turn and move in your favor.

Some traders claim that it might be dangerous to use a hunch-based trading system. Sometimes hunches work out fantastically- Victor Hugo had a hunch that Quasimodo would be a likeable character and that turned out pretty well.

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Post by DrHendricks » Mon Jun 21, 2004 3:44 pm

The martingale works best if you have a very small bankroll to begin with.
This certainly would have worked best for Barings if it had been the case for Nick Leeson.

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Post by shakyamuni » Mon Jun 21, 2004 11:20 pm

Good point Dr. H, it probably would have been good for Nick too.

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Scaling/Pyramiding

Post by Corn Elius » Thu Jun 24, 2004 11:07 am

Hi Ted. I agree that there are many different permutations, and that I should try them all for myself. Having said that, I can't realistically see me doing that. I'd like to understand what other people have tried and works, doesn't work - in general, as an approach. I'm a computer consultant by trade, and I talk to other people about tools, operating systems, editors, languages, platforms, I read magazines, etc. There just isn't enough time to try every thing yourself - at least for me. On this board I think the agregate experience is valuable.

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