R multiples & Expectency
R multiples & Expectency
With my recent discovery of automated calculation of R in my testing s/w I have started playing around with the concept a lot more.
I calculated the mathematical expectancy of a variant of PGO and got 0.59
The calculation I used is as follows:
1) I calculated Rmultiple on each trade being TradeProfit$/InitialRisk$
2) I defined buckets of 0.5R width
3) I counted the R's in each bucket. ie, frequency distribution.
4) I found the probability of a trade being in each bucket = bucket count/total trades
5) I multiplied probability and payoff for each bucket. [for the bucket value, ie, the payoff, I used the midpoint of the bucket]
6) I summed 5.
7) the result was 0.59
So for every 1R risked, the system expectancy is 0.59R. I am surprised that this is so low. What do you deem to be an minimum expectancy for a good system? (I will send the spreadsheet to anyone who is interested).
Perhaps someone could also point out if I have a misunderstanding of the concept and it's calculation.
cheers
damian
I calculated the mathematical expectancy of a variant of PGO and got 0.59
The calculation I used is as follows:
1) I calculated Rmultiple on each trade being TradeProfit$/InitialRisk$
2) I defined buckets of 0.5R width
3) I counted the R's in each bucket. ie, frequency distribution.
4) I found the probability of a trade being in each bucket = bucket count/total trades
5) I multiplied probability and payoff for each bucket. [for the bucket value, ie, the payoff, I used the midpoint of the bucket]
6) I summed 5.
7) the result was 0.59
So for every 1R risked, the system expectancy is 0.59R. I am surprised that this is so low. What do you deem to be an minimum expectancy for a good system? (I will send the spreadsheet to anyone who is interested).
Perhaps someone could also point out if I have a misunderstanding of the concept and it's calculation.
cheers
damian
Last edited by damian on Sun May 25, 2003 11:57 am, edited 1 time in total.

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You can see Microsoft Madness at work in damian's chart. When you tell Excel to fit a trendline to data whose Xcoordinates are dates, it "helpfully" converts them to Julian Dates before doing the calculations. Thus March 1, 1990 is transformed into the integer 32933.
Converting his exponential trendline to something traders are used to seeing, the Compound Annual Growth Rate is about 56%. Can't get more accurate than that since Excel only printed the exponent to two digits.
Converting his exponential trendline to something traders are used to seeing, the Compound Annual Growth Rate is about 56%. Can't get more accurate than that since Excel only printed the exponent to two digits.
R Multiple Calculation
Damian,
I think that everything was done right, although I didn't go over every detail of the calculations.
I have two posts on the topic "Analysis of Turtle System Test #14 (Original turtle system forum)" where I go over Rmultiples in detail.
As to your comment about PGO, the average expectancy is about 2x that of c.f.' turtle system test. The REAL measure is "yearly expectancy", which is the (average expectancy) * (number of trades/year).
Doug
I think that everything was done right, although I didn't go over every detail of the calculations.
I have two posts on the topic "Analysis of Turtle System Test #14 (Original turtle system forum)" where I go over Rmultiples in detail.
As to your comment about PGO, the average expectancy is about 2x that of c.f.' turtle system test. The REAL measure is "yearly expectancy", which is the (average expectancy) * (number of trades/year).
Doug
Eck, PGO is a simple trend follower along the lines of what I suggested to someone a few days ago. I think it may have come from Mark Johnson. In tradestation one interpretation of the code was:
I think you needed to exit on crossing back over the moving average. Another formula with colourful variables was expanded in
http://traderclub.com/discus/messages/1 ... #POST10002
MODERATOR'S NOTE: A separate thread on PGO was split from this topic:
viewtopic.php?t=282
Damian, In the interests of finding out what a reasonable expectancy might be I tried it on 3 markets from 1990 until today with a medium term trend follower (risk same in each case). The results were:
which is probably not surprising given how good a trend follower JY has been.
John
If C>Xaverage(c,89)+3*avgTruerange(10) then buy next bar market;
If C<Xaverage(c,89)3*avgTruerange(10) then sellshort next bar market;
Note that although close this is wrong ... the code below is correct as c.f. says and gives a slightly different result
I think you needed to exit on crossing back over the moving average. Another formula with colourful variables was expanded in
http://traderclub.com/discus/messages/1 ... #POST10002
MODERATOR'S NOTE: A separate thread on PGO was split from this topic:
viewtopic.php?t=282
Damian, In the interests of finding out what a reasonable expectancy might be I tried it on 3 markets from 1990 until today with a medium term trend follower (risk same in each case). The results were:
Code: Select all
Expectancy Trades Annual Return
JY 3.48 21 trades 5.6R pa
TY 0.27 83 trades 1.7R pa
LC 0.09 44 trades 0.3R pa
John
Last edited by Kiwi on Mon May 26, 2003 5:46 pm, edited 2 times in total.
To answer the original question, if a trendfollowers typical target is 40% winning trades, with av profit:av loss ratio of 2:1, then for each dollar risked in a trade, the expectancy is $0.20, i.e.
40% * $2 + 60% * ($1) = $0.20
I think your R is effectively the same as the above calculation, and I would therefore conclude that any expectancy of $0.20 per $1 risked per trade is a reasonable target.
In my stock trading systems, I find it difficult to hit this target consistently over many years.
Perhaps I should look at PGO more closely, or perhaps I should give up on stocks.
40% * $2 + 60% * ($1) = $0.20
I think your R is effectively the same as the above calculation, and I would therefore conclude that any expectancy of $0.20 per $1 risked per trade is a reasonable target.
In my stock trading systems, I find it difficult to hit this target consistently over many years.
Perhaps I should look at PGO more closely, or perhaps I should give up on stocks.
On R (and E):
PeterK 
Thankyou for the simple sanity check. Using it I find a result of 0.48 (prob win = 45%, avgwin/avgloss = 2.33). Like you I also do not see these results in real time LT trend following. (After 89 trades, I see avgwin/avgloss = 2.38, prob win = 33% giving E = 0.11).
doug
Using Yearly E, I calculated 28.06 on the PGO variant test. I am currently mulling my way through your referenced R posts. Thanks for pointing me to them.
John the Kiwi 
again, a good sanity check. I should have thought to do the same. Those three markets display a nice range of E (or did you calc R as labeled?).
On PGO:
Ed
feel free to start a PGO topic
c.f. (and others)
I was one of those people you suggested . Quite some time ago I contacted Mark and he pointed me at the key colour in the equation. I think he said it was green. Being a lazy dope, I still couldn't work it out (the geometry really threw me). I ended up getting someone elses help. It came as a real surprise that PGO was very similar in concept to one of my early system creations ("Directional Deviant") which I dismissed as it was "too easy to create, thus no good". PGO got me looking at Directional Deviant again and now that is what I trade. I use PGO as a benchmark system these days. I have several variants of PGO which are good clay to play with ideas.
PeterK 
Thankyou for the simple sanity check. Using it I find a result of 0.48 (prob win = 45%, avgwin/avgloss = 2.33). Like you I also do not see these results in real time LT trend following. (After 89 trades, I see avgwin/avgloss = 2.38, prob win = 33% giving E = 0.11).
doug
Using Yearly E, I calculated 28.06 on the PGO variant test. I am currently mulling my way through your referenced R posts. Thanks for pointing me to them.
John the Kiwi 
again, a good sanity check. I should have thought to do the same. Those three markets display a nice range of E (or did you calc R as labeled?).
On PGO:
Ed
feel free to start a PGO topic
c.f. (and others)
I was one of those people you suggested . Quite some time ago I contacted Mark and he pointed me at the key colour in the equation. I think he said it was green. Being a lazy dope, I still couldn't work it out (the geometry really threw me). I ended up getting someone elses help. It came as a real surprise that PGO was very similar in concept to one of my early system creations ("Directional Deviant") which I dismissed as it was "too easy to create, thus no good". PGO got me looking at Directional Deviant again and now that is what I trade. I use PGO as a benchmark system these days. I have several variants of PGO which are good clay to play with ideas.
Some infoeck wrote:Hey Damian,
I have no idea what PGO is. Do you think we need a thread for people like us who want to share information and ideas about this?
The difference between the entry point and the stop loss point multiplied by the number of lots is the starting risk or 1 R2, independent of how and in which units we measure the stop level, be it dollars, percents, volatility units or sixpacks. This definition of risk is not equal to the first definition  the risk may be many times the 1 R if the stops are not executed due to lack of discipline3, gaps against the position or unexpectedly high slippage. The profit, then, can be defined in units of risk per share or in multiples of R. In terms of multiples the basis rule of speculation will be formulated as: keep losses at the level of 1 R as long as possible and let profits reach many times R.
The expectancy in multiples of R will mean how much can we win or lose per unit of risk in an average trade. To calculate expectancy in terms of multiples of R we must place the results of our trades in a table with the following columns: Number of lots Profit or Loss Starting risk Multiple of R
The Profit or Loss must take into account broker commissions and slippage. Multiple of R is calculated by dividing the second column by the third. Then to calculate expectance it is enough to add up the values of the fourth column and divide by the number of trades. This method is also works with "intuitive" trading.
http://tssupport.com/knowledgebase/?act ... le&id=1506
http://tssupport.com/knowledgebase/?act ... le&id=1507
http://tssupport.com/knowledgebase/?act ... le&id=1505
Toni.