R-Multiple misleading ?

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christianh
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R-Multiple misleading ?

Post by christianh » Wed Jul 11, 2007 9:19 am

I would like to discuss a potential pitfall of the R-multiple concept.

The problem is, that having the R-multiple as a "fitness function" (i.e. the bigger the better) you are considering the "markets money" (i.e. money you have made in a still open trade) different to "your money" (i.e. money you have already locked in).

Consider the following example of a long trade:

- You enter at a price of 100 with a risk of 10. No additional stop loss than the initial one at 90.
- Over the next couple of days the price rises more or less in a straight way up to 200 (=10R) then it falls back to 150 and then goes back up to 250 (=15R) where you exit.

So you have made 15R. But during the trade you risked 11R (200 down to the stop at 90). That's very unrealistic in practical terms because your clients watching your NAV (that is the equity including the "markets money") see a drawdown from 200 to 150. So in theoretical terms the trade is a nice 15R trade but with unrealistic open trade risk.

So optimizing a trading model on that R-multiple can lead to un-tradeable (because of the drawdown/openrisk considerations) results.

IMO the only solution can be, to extend that R-multiple concept in that way that either the initial risk or the ongoing open risk, whichever is higher, are considered in the final R-multiple calculation.


I would appreciate any comment on that matter.

Christian

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Post by sluggo » Wed Jul 11, 2007 11:02 am

I agree that R-Multiples is not an extremely useful concept today, in the Year Of Our Lord 2007. It seems to be a hold-over from olden times, when people only analyzed one system trading one market. But those days are long gone; dead and buried. 21 years ago, in 1986, the Turtles traded two systems simultaneously, on a portfolio of more than 20 markets. And today, traders put on yet larger numbers of simultaneous trades.

In the modern era, with many simultaneous positions, it's not the individual trades that matter. It's their net sum, which is expressed in the equity curve. So I'm with you: let's deprecate obsolete measurements like R-Multiples, which study individual trades. Instead, let's concentrate on measurements of the equity curve (like: longest drawdown in months, Ulcer Index, R-Cubed, Kestner's K-Ratio, Robust Sharpe, etc.) which measure the net sum of all simultaneous positions.

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Post by jklatt » Wed Jul 11, 2007 3:42 pm

Hmmm....

One way to reduce the volatility is to shave off part of the position as risk gets too "high". Shave a little off at 110... 120... 130... etc. This will substantially reduce the drawdown experienced during the move from 200 to 150, but comes at the expense of overall return.

A good exercise is to look at Sugar during 2005 and early 2006. Lets say you got in at $10 sizing the position at 1% of equity based on an ATR of $0.10. You rode price up to about $20 and then got out at $17.

Overall return was 70%/units ($17 minus $10 divided by $0.10) with a drawdown of 30%/units ($20 minus $17 divided by $0.10).

Now fire up your simulator or Excel and calculate the daily return expresed in the prior day's ATR. Then cumulate each days return to produce an equity curve and measure the overall return and drawdown. You'll find that return goes down somewhat and drawdown goes down a lot. All you're really doing is monitoring the daily "risk" of the position and shaving off a bit as the position's risk increases (ATR rises).

I think the real question is just how important is open equity drawdown? It's easy to substantially lower open equity drawdown by doing what I described, but as a result you're sacrificing overall return. Maybe it's more important to work on trading psychology and/or aligning yourself with clients that understand that there are going to be big open equity drawdowns after big winning trades but over the long haul, it's a more "profitable" approach. I know it's a tough pill to swallow when you're caught up in MAR ratios and what not, but it's just how price/ATR tends to behave. Price rises, ATR expands, the position relative to the day of entry becomes more and more volatile as the trend matures producing larger and larger daily gains/drawdowns... but in the end being willing to experience the increased volatility will allow _closed equity_ to grow at a faster rate.

Cheers,

Jason

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Post by christianh » Thu Jul 12, 2007 12:09 am

Jason,

thank you for your thoughts. It should be clear for every serious trader how to handle ongoing open risk. The solution to convince customers to accept draw downs is not that easy. Consider a new customer who enters on a new equity high, which old customers have as open equity, and the open trades now give back too much of their profits, which old customers could maybe tolerate. So the game as a money manager is all about the risk/return numbers like Sharpe, Sortino, Volatility...

But that's off topic.

The question is the usability of the R-multiple in the case originally stated in my intro.

Christian

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Post by AFJ Garner » Thu Jul 12, 2007 2:09 am

I would agree that at the end of the day it is the overall equity curve which interests us most – the smoother the better and the easier to live with. I disagree that it is not important to carefully consider the make up of that curve - IE individual trades. By considering R Multiples you have another tool to help you understand the nature of the system you are trading, its quality, feel, raison d'etre.

Consider 2 versions of a Bollinger band breakout based on the same long term moving average and the same portfolio. One uses a 2 std dev band the other uses a 1 std band for entries, each uses the same MA as the exit.

The R Multiple profit distribution and profit contribution graphs give you a valuable insight into your individual trades and the way they combine to generate the equity curve - it helps you dig deeper into the curve and gain greater understanding of its composition.

The system using the wider bands will tend to have a higher win loss ratio (50/50 perhaps) while the narrower bands will have something more akin to 30/70. Some traders may find one or other system easier to trade on this basis.

By looking at the R Multiple graphs, the trader will notice how it is that both systems end up with similar profitability and similarly smooth equity curves (given suitable adjustment to position size to account for the width of the bands). Wider bands give R Multiples grouped in a fairly narrow range at the lower end of the scale (1 to 4), narrower bands tend to give trades with R Multiples spread more evenly across the spectrum (1 to 15+). Does it feel better to the trader to suffer 70% losing trades and make it all up on a minority of exciting whoppers or to make do with an equal proportion of losers and rather dull low R Multiple winners?

It is perhaps a personal matter – what information helps you to better understand the system you are trading? I find that R Multiples do help my understanding – I would feel very blind indeed if all I had were statistics to measure and illustrate the overall goodness of the combined equity curve and could not descend to the level of the individual trade.

That is coming close to the awful black boxes of the vendors. And who amongst us would seriously consider trading one of those?

Of course you must look under the hood and R Multiples are one of a series of tools to help you do that.

As to the pain of open equity give back – that is the nature of trend following – period. As has been pointed out, if you don’t like it, mitigate the effect by adopting profit taking. That is just what Jerry Parker says he does – not because he believes in it himself (he said in an interview that it makes him a little uneasy) but because he is managing money for others who, on balance, prefer it that way.

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Post by christianh » Thu Jul 12, 2007 2:35 am

AFJ Garner, I agree with you, but still the original question is the validity of a change to to the R-multiple calculation because of its shortcoming. I like the concept of R and have built trading models around it but...

"Wouldn't it be better to change the R-multiple calculation to take not only the initial risk but also the ongoing open risk (whichever is higher) into its calculation?" So the new formula would be:

R = Return / Max(Initial Risk, Max Open Risk in Trade)


IMO, this new formula is "better" than the original one. I would like to hear others comment on it (flaws in the formula,...).


Christian

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Post by AFJ Garner » Thu Jul 12, 2007 2:42 am

Christian
Just noticed you are an hour down the road from me - greetings from Klosters!

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Post by ecritt » Thu Jul 12, 2007 4:41 am

christianh wrote:AFJ Garner, I agree with you, but still the original question is the validity of a change to to the R-multiple calculation because of its shortcoming. I like the concept of R and have built trading models around it but...

"Wouldn't it be better to change the R-multiple calculation to take not only the initial risk but also the ongoing open risk (whichever is higher) into its calculation?" So the new formula would be:

R = Return / Max(Initial Risk, Max Open Risk in Trade)


IMO, this new formula is "better" than the original one. I would like to hear others comment on it (flaws in the formula,...).


Christian
This is a very good question; one I pondered for many months. I will add my thoughts and conclusions.

Both the initial risk and the max risk are individual data points among many other data points during the life of the trade. Also, depending upon your trading system you may have significantly different open profits as well as different probabilities of being stopped out corresponding to these two different data points.

I believe the argument that open equity is really closed equity (since client money will be coming in after substantial profits have been made) is valid in real life. It's not fair but this is a social science. Of course you can ignore if you don't have to cater to clients.

The way I handle this is to scale out of trades where risk has increased beyond some threshold. One could make the case that this is inferior behavior since I will make less money on a major trend in that trade. I would counter that I'm freeing up "risk units" to rotate over to new trades, improving my level of diversification and allowing me to use more heat at the portfolio level.

Regarding your question about initial risk vs. max risk:

R = Return / Max(Initial Risk, Max Open Risk in Trade)

I would run it both ways to see if the conclusions are similar. I would also investigate averaging or weighting the Actual Risk on each bar (when a new trade equity high is made) during the life of the trade. This would tell you what you really need to know. Problem is that it is very resource intensive to do so.

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Post by AFJ Garner » Thu Jul 12, 2007 10:02 am

Of course Eric, there is one very important way in which your trading on equities differs from TF on futures. Futures have a limited universe - one tends to like to maximise the gains from a given trend and therefore may be willing to suffer give back. After all, we have only 70 or 100 futures each of which trends rather irregularly.

Your universe of stocks at an all time high is (when times are good) so large that the parking lot gets full very quickly. You need to scale out to make room for new trades. And a benefit of scaling out of the oldest or perhaps the most profitable is that you make room for the new growth stocks on their way up. And scale down those which have perhaps plateaued. Thus you produce an outperformance of the S&P.

On another thread I gave some results of testing a simple momentum strategy of the MSCI World component stock indices. Without profit taking or scaling out. Returns similar to buy and hold but with a lesser and shorter DD and lower volatility. So, a static universe as with futures. You can only boost the returns with expensive borrowing.

Then I looked at testing those same indices plus a few others (bonds, currencies, commodities) on a rotational basis – keeping only the best 8 to 10 performers as at the month end and selling the others even though they may not have been at the end of their trend. Bingo – a return of 18% over 37 years with a max DD less than buy and hold (which had only produced around 10 to 11% from memory).

I digress from the original purpose of the thread. But scaling out (or exiting completely before the end of a trend) can work very well to improve performance on un-geared instruments.

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Post by AFJ Garner » Thu Jul 12, 2007 10:18 am

I ought to add that rotation/momentum produced a similar (18% CAGR) return even without the addition of commoditites, bonds currencies etc to the MSCI World components.

But those additions decreased the depth and length of the drawdowns by running for the harbour in times of equity storms.

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Post by ecritt » Sat Jul 14, 2007 2:26 pm

AFJ Garner wrote:Of course Eric, there is one very important way in which your trading on equities differs from TF on futures. Futures have a limited universe - one tends to like to maximise the gains from a given trend and therefore may be willing to suffer give back. After all, we have only 70 or 100 futures each of which trends rather irregularly.

Your universe of stocks at an all time high is (when times are good) so large that the parking lot gets full very quickly. You need to scale out to make room for new trades. And a benefit of scaling out of the oldest or perhaps the most profitable is that you make room for the new growth stocks on their way up. And scale down those which have perhaps plateaued. Thus you produce an outperformance of the S&P.
True for most, but it need not be so. Some very successful CTA's are using multiple settings applied to multiple systems (with negatively correlated risk drivers) across multiple time frames. I've also noticed that several CTA's are trading more than 150 markets including forwards & swaps and spreads too. Collectively they are managing thousands of individual equity curves. Each of these equity curves can be thought of as a security.

Right now I have 1,648 open stock positions with far less "independence" than CTA's have. You are right. What I do, I do out of necessity. But that doesn't mean a CTA will not benefit from the same approach. In fact, I believe this is what separates the great CTA's from the rest.

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Post by sluggo » Sat Jul 14, 2007 3:14 pm

ecritt wrote:Collectively they are managing thousands of individual equity curves. Each of these equity curves can be thought of as a security. ...... In fact, I believe this is what separates the great CTA's from the rest.
I imagine you mean "CPOs" and/or "Funds" rather than "CTAs". In order to trade thousands of Ralph Vincean Market Systems (what you call individual equity curves), at low enough leverage to produce an overall 10% CAGR with 10% MaxDD, after fees, and with at least one contract per Market System, the required account size exceeds fifty million dollars. That is fund territory, not managed account. Fund = CPO, managed account = CTA.

If a market system holds less than one contract then its contribution to the overall sum-of-all-equity-curves is probabilistic. Sometimes it matters (when SIGMA(ncars) rounds up) and other times it doesn't (when SIGMA doesn't.) When the action of a market system doesn't matter, it is not contributing it's measure of goodness (diversification, noncorrelation, anti-correlation) to the overall portfolio. You're robbing yourself of the potential benefits. This type of effect has been extensively studied by the Digital Signal Processing community and can be looked up on the Web using keywords "dither" and "sub-LSB resolution".

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Post by ecritt » Sun Jul 15, 2007 4:37 pm

sluggo wrote:I imagine you mean "CPOs" and/or "Funds" rather than "CTAs". In order to trade thousands of Ralph Vincean Market Systems (what you call individual equity curves), at low enough leverage to produce an overall 10% CAGR with 10% MaxDD, after fees, and with at least one contract per Market System, the required account size exceeds fifty million dollars. That is fund territory, not managed account. Fund = CPO, managed account = CTA.
Since you bring it up, yes there has been a significant push (by the firms I refer to as CTA's) towards funds and away from managed accounts. I think what you point out has a lot to do with it.

It's not as complicated as it sounds. With the proper programming thousands of equity curves can be aggregated into "virtual" positions that are only scaled up or down when the economics of doing so make sense.

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Post by AFJ Garner » Mon Jul 16, 2007 2:48 am

So, list of your top 5 CTAs Eric?

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Post by ecritt » Mon Jul 16, 2007 7:57 am

AFJ Garner wrote:So, list of your top 5 CTAs Eric?
Transtrend, Winton, Chesapeake, Lynx, Aspect.

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Post by AFJ Garner » Tue Jul 17, 2007 2:06 am

And what would your top choice of 5 more general hedge funds be?

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Post by ecritt » Tue Jul 17, 2007 10:26 am

AFJ Garner wrote:And what would your top choice of 5 more general hedge funds be?
I have no favorites from the typical hedge fund styles like merger arb, conv arb, rel val, distressed, event driven, or mkt neutral. I believe these are very crowded with managers that are all chasing the same finite alpha.

I've seen very little to be impressed with from the long/short equity category.

There are a few interesting long-bias or long-only equity programs out there. FUNDX and ACRNX both have long and successful track records. Rentec's institutional equities program is impressive. In the end we created our own.

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Post by ladadriver » Wed Jul 18, 2007 4:13 am

ecritt wrote:
sluggo wrote:I imagine you mean "CPOs" and/or "Funds" rather than "CTAs". In order to trade thousands of Ralph Vincean Market Systems (what you call individual equity curves), at low enough leverage to produce an overall 10% CAGR with 10% MaxDD, after fees, and with at least one contract per Market System, the required account size exceeds fifty million dollars. That is fund territory, not managed account. Fund = CPO, managed account = CTA.
Since you bring it up, yes there has been a significant push (by the firms I refer to as CTA's) towards funds and away from managed accounts. I think what you point out has a lot to do with it.

It's not as complicated as it sounds. With the proper programming thousands of equity curves can be aggregated into "virtual" positions that are only scaled up or down when the economics of doing so make sense.
Interesting thread.

Am I right to interpret your "aggregrate" curve idea as a shift from binary trading signals to a pseudo analogue position function? (Or have I concocted that idea via Sluggo's signal processing reference...)

Food for thought, albeit imaginary food given the size of my trading account.

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Post by AFJ Garner » Wed Jul 18, 2007 4:42 am

Let us try speaking a little plain English here for the likes of the ignorant and unwashed such as myself.

Outfits such as Transtrend trade 150 different products - more when you count intra and inter market spreads which are instruments in their own right. A spread has a direction - it trends, just like a single instrument; you can trend trade it.

Then there are multiple systems used. Different parameters of the same basic system, often.

None of this need actually be terribly complex in principal, although putting it all into effect must take some doing.

I do not believe it necessary to surround the topic in great complexity, great mystery. I do not believe that what any of these guys do is so sophisticated, so other worldly. Reading Transtrend's disclosure document re-enforces my instinct that these people are not supermen or Albert Einsteins.

Nor do I believe any of it takes great mathematical or statistical genius. Some CTAs like to clothe their product in big words of more than a couple of syllables and no doubt that's great for marketing. How many times in a prospectus have we seen reference to Nobel prize winners, obscure Russian physicists and the like.

Eric mentioned FUNDX. I am a great admirer of that outfit and their track record. I have read every column inch of their website and have tested out what they do – and “lo, it was goodâ€

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Post by sluggo » Wed Jul 18, 2007 6:42 pm

AFJ Garner wrote:I do not believe it necessary to surround the topic in great complexity, great mystery. I do not believe that what any of these guys do is so sophisticated, so other worldly. ... my instinct that these people are not supermen or Albert Einsteins.
You are going to love Chapter 11 of Ralph Vince's (newest book).

However it may be wise to remember that "most of these guys" is not the same as "all of these guys". Go visit 600 Route 25A, East Setauket, NY, 11733 USA for a reminder.

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