### Wednesday, September 13, 2006

## Stick it up your R's

The portolio gained 1.0 percent today. I can’t recall when I first heard the term “R” but I do recall my initial reaction. It was a bit like what one’s reaction would be if your uncle Buck tried to “debunk” Einstein’s Special Theory of Relativity. You’d just smile and nod.

R is a measure of trading performance that tries to gauge one’s return relative to the amount of risk one takes. Specifically, R is how much you risk you assume on any given trade. Typically, R is defined as a percentage of one’s trading capital. So if you risk 1 percent of your capital on a trade and make a profit equal to 2 percent of your capital, you’ve made 2R.

But does this concept even make sense? Let’s ignore the rather unfortunate terminology (outside of trading, R has a very specific statistical meaning, that of a statistical coefficient). Let’s also ignore the fact that R has absolutely nothing to do with what financial economists would regard as risk: beta. Let’s just ask a simple question: does knowing “how many R’s one’s made over the course of a year” even tell you whether the person is making or losing money?

Consider the following example: Suppose Jim makes 1000 trades over the course of a year and risks 10 percent of his capital on each trade (R=10%). Naturally, Jim’s trading capital goes up or down depending on whether his last trade was profitable. Suppose that 520 trades turn out to be profitable and Jim earns 10% (1R) on each trade and 480 trades turn out to be unprofitable and Jim loses 10% (1R) on all those trades. Jim’s total R for the year is 520*R minus 480*R = 40R, which seems to imply he made a whopping 400 percent. Wow! Good job Jim! You’re almost as good as Trader Mike

But wait, what’s Jim’s actual cumulative percentage return? Well, that’s simple to calculate: it’s (1.1^520) times (0.9^480) = 0.36. So in reality, Jim has lost about 74 percent of his capital during the year. Oops, stick with that day job, Jim! Intuitively, the reason we get such divergent results is because it makes no sense to add up R's because if you lose 10 percent on a trade, you need

R is a measure of trading performance that tries to gauge one’s return relative to the amount of risk one takes. Specifically, R is how much you risk you assume on any given trade. Typically, R is defined as a percentage of one’s trading capital. So if you risk 1 percent of your capital on a trade and make a profit equal to 2 percent of your capital, you’ve made 2R.

But does this concept even make sense? Let’s ignore the rather unfortunate terminology (outside of trading, R has a very specific statistical meaning, that of a statistical coefficient). Let’s also ignore the fact that R has absolutely nothing to do with what financial economists would regard as risk: beta. Let’s just ask a simple question: does knowing “how many R’s one’s made over the course of a year” even tell you whether the person is making or losing money?

Consider the following example: Suppose Jim makes 1000 trades over the course of a year and risks 10 percent of his capital on each trade (R=10%). Naturally, Jim’s trading capital goes up or down depending on whether his last trade was profitable. Suppose that 520 trades turn out to be profitable and Jim earns 10% (1R) on each trade and 480 trades turn out to be unprofitable and Jim loses 10% (1R) on all those trades. Jim’s total R for the year is 520*R minus 480*R = 40R, which seems to imply he made a whopping 400 percent. Wow! Good job Jim! You’re almost as good as Trader Mike

But wait, what’s Jim’s actual cumulative percentage return? Well, that’s simple to calculate: it’s (1.1^520) times (0.9^480) = 0.36. So in reality, Jim has lost about 74 percent of his capital during the year. Oops, stick with that day job, Jim! Intuitively, the reason we get such divergent results is because it makes no sense to add up R's because if you lose 10 percent on a trade, you need

*more*than 10 percent just to get back to break even.
Comments:

Replace 10% with $1000. Does it then answer ? So it would seem that the problem is your use of 'R' (initial risk). I'd wager that most traders who are posting 'R' values that cause the whining are keeping their $'s risk per trade fairly consistent on a given day/week/month.

If anyone recalls from Market Wizards, there was the disucssion of how tracking performance in terms of percentage could paint a contradictory picture. The Market Wizard (I forget who) commented that he had seen many money managers who had good looking records in terms of percentages, but due to cash in flows and outflows had a net loss of money. So, will the same crowd now argue that calculation of percentage is a useless metric ?

'R', not unlike a hammer, is a tool... it's the correct solution to some problems but damn it just sucks at cleaning plate glass windows (both 'R' and hammers are poor choices in tools for that task).

- MikeB

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Amen Brother!!

:)

I understand if people aren't comfortable talking about their actual numbers, that's their choice.

But the educational component unfortunately goes out the window.

Just my opinion....

:)

I understand if people aren't comfortable talking about their actual numbers, that's their choice.

But the educational component unfortunately goes out the window.

Just my opinion....

I've been wanting to stay out of the R vs. actual numbers debate for a long time mainly because I didn't really know if this R-stuff was a widely adopted industry-wide measure.

But when I first encountered this R-measure, quite honestly I was confused and didn't get a full grasp as to whether the trade was a great success or not.

However, with the way you've just described it, I can certainly see how it can distort the numbers and I can certainly see why there is such division about this topic.

Thanks for giving me a clearer view of the "con" side of the topic.

But, I'm with Linda...I can certainly understand if people aren't comfortable talking about real numbers.

Just my 2 cents...

But when I first encountered this R-measure, quite honestly I was confused and didn't get a full grasp as to whether the trade was a great success or not.

However, with the way you've just described it, I can certainly see how it can distort the numbers and I can certainly see why there is such division about this topic.

Thanks for giving me a clearer view of the "con" side of the topic.

But, I'm with Linda...I can certainly understand if people aren't comfortable talking about real numbers.

Just my 2 cents...

I'm so sorry to see this anti-R sentiment in yet another blog that I enjoy. The misconceptions about R-based tracking are rampant. Of course adding and subtracting percentages, rather than multiplying them, makes no sense! I don't know anyone that claims you can derive their % equity increase from their R profit.

I'll be the first to admit that R has its limitations and pitfalls, but the anti-R crowd does not offer an alternative that gives me the benefits that my R tracking gives me. I can assure Linda and everyone else that it hase nothing to do with hiding my level of income from my readers.

Cumulative R doesn't tell you much, alone. Average R, or Expectancy, is an important number, though. Here's why: Your example Jim's expectancy is dismal, at 0.04... but at least it is positive. That means, he is trading well enough that he _can_ statistically make a long-term profit.

But, he's never going to show a profit risking 10% per trade. The reason is (as you pointed out), Jim has to win 11.5% or so to make up for a 10% loss. His expectancy and win rate are too low to cover that difference.

With a positive expectancy, though, we know that a risk amount exists that makes him money (ignoring transaction costs for now). For example, if Jim had traded with 1% risk, he would be up almost 42% for the year, even after that sad trading performance. You only need to make 1.02% to cover a 1% loss.

If we weren't tracking Jim's expectancy, and we saw him losing money hand over fist, what alternative tools would we have to know if his trades were theoretically profitable or not? Play around on a spreadsheet? Trial and error? I would love to have a better alternative to expectancy... but until I hear about one, I won't be abandoning it.

I'll be the first to admit that R has its limitations and pitfalls, but the anti-R crowd does not offer an alternative that gives me the benefits that my R tracking gives me. I can assure Linda and everyone else that it hase nothing to do with hiding my level of income from my readers.

Cumulative R doesn't tell you much, alone. Average R, or Expectancy, is an important number, though. Here's why: Your example Jim's expectancy is dismal, at 0.04... but at least it is positive. That means, he is trading well enough that he _can_ statistically make a long-term profit.

But, he's never going to show a profit risking 10% per trade. The reason is (as you pointed out), Jim has to win 11.5% or so to make up for a 10% loss. His expectancy and win rate are too low to cover that difference.

With a positive expectancy, though, we know that a risk amount exists that makes him money (ignoring transaction costs for now). For example, if Jim had traded with 1% risk, he would be up almost 42% for the year, even after that sad trading performance. You only need to make 1.02% to cover a 1% loss.

If we weren't tracking Jim's expectancy, and we saw him losing money hand over fist, what alternative tools would we have to know if his trades were theoretically profitable or not? Play around on a spreadsheet? Trial and error? I would love to have a better alternative to expectancy... but until I hear about one, I won't be abandoning it.

Hey where the F where y'all when all the F, err R preachers where slamm'n me for crapping about the value of posting R values to the readers of their own blogs :) You know... very few of Mike's readers even understood what I was trying to communicate and I gave up trying... haha. Well get ready for the R troops cause they will be all over dis one. Thanks for posting Real numbers Coach!

As you clearly showed using R is pretty dumb. Why don't people just use percentage returns?

If they only took R's at Best Buy...

If they only took R's at Best Buy...

Ditto to what Richard said. I see you pointed to my 100R post. Note that also gave average R, expectancy, and actual percentage gain. I did that for a reason. No way would I say R is the be-all, end-all of measuring performance. But it is, in my opinion, a great tool. However, a trader would be a fool not to track actual percentages and dollar results as well.

I'm also at a loss how anybody can argue that it's a bad thing to define your risk and then measure your results beased on a risk-to-reward ratio.

Glenn, don't give up, don't ever give up.

I'm also at a loss how anybody can argue that it's a bad thing to define your risk and then measure your results beased on a risk-to-reward ratio.

Glenn, don't give up, don't ever give up.

I see your post as an explanation of why R isn't a good way to measure compounded returns, but that's not the point of R. R is about system design and measuring expectancy, and comparing that expectancy across systems. It also is used as a variable by serious systems designers when backtested.

Financial economists should probably stick beta up their arse. I believe a better measurement than alpha and beta can be described by maximum drawdown, length of maximum drawdown, and total return.

I posted on the subject here.

http://www.billakanodoodahs.com/?p=13

Financial economists should probably stick beta up their arse. I believe a better measurement than alpha and beta can be described by maximum drawdown, length of maximum drawdown, and total return.

I posted on the subject here.

http://www.billakanodoodahs.com/?p=13

*Let’s just ask a simple question: does knowing “how many R’s one’s made over the course of a year” even tell you whether the person is making or losing money?*

Replace 10% with $1000. Does it then answer ? So it would seem that the problem is your use of 'R' (initial risk). I'd wager that most traders who are posting 'R' values that cause the whining are keeping their $'s risk per trade fairly consistent on a given day/week/month.

If anyone recalls from Market Wizards, there was the disucssion of how tracking performance in terms of percentage could paint a contradictory picture. The Market Wizard (I forget who) commented that he had seen many money managers who had good looking records in terms of percentages, but due to cash in flows and outflows had a net loss of money. So, will the same crowd now argue that calculation of percentage is a useless metric ?

'R', not unlike a hammer, is a tool... it's the correct solution to some problems but damn it just sucks at cleaning plate glass windows (both 'R' and hammers are poor choices in tools for that task).

- MikeB

I will not use any type of measurement unless it is absolutely perfect and insulated from any critisism from any source. :)

If you want to see how one real life a result viewed from the perspective of R compares to actual dollar gain, check out my rather dismal results over my begginer attempts at trading:

http://stockdaytrading.blogspot.com/2006/09/risk-units-vs-dollars.html

http://stockdaytrading.blogspot.com/2006/09/risk-units-vs-dollars.html

Okay, I thought about this more... I understand nodoodah's point about using R for system design. If I was designing a system, and say looking to implement some sort of Kelly bet-size, I'd want to know details about R.

But in this case, wouldn't the distribution of results be more useful? I'm picturing a histogram with the profit/loss along the x-axis binned (in say intervals of 0.1R).

But in this case, wouldn't the distribution of results be more useful? I'm picturing a histogram with the profit/loss along the x-axis binned (in say intervals of 0.1R).

Real risk is a function of the underlying company's fundamentals -not percent of your portfolio in play or percent returns. It's also a function of opportunity cost, which can be weighed by drawdown and time under water.

In my opinion, those who don't post their actual numbers are the ones who aren't confident enough about their abilities as a trader. If you're confident about your abilities, then why hide the numbers? You put your life out there in your blog, but you're scared of posting numbers because it's "none of the reader's business"?? How does that make sense? My only conclusion is that they're not confident enough to do it...

Mike, stop being a wuss and post your real numbers. No one cares about how many Rs you make in a year.

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