# Optimising Risk/Reward Values



## beachlife (20 June 2010)

Hi All
I recently saw the coin toss spiel and it got me thinking.  They were saying a share can eventually go up or down so the probability is 50:50 and if your reward/risk is 1:1 then you will break even in the long run (ignoring costs), so the way to become profitable is to change your reward/risk to 2:1.  50% of the trades will make 2 units profit and 50% will lose 1 unit so overall you will be profitable - so they say.

The problem I have with this is that they failed to mention that the probability of a 1 unit move is different to the probablity of a 2 unit move, so its more complex than what they were saying.  The bigger the reward, the less chance of hitting it.  So a 2:1 system could still have a low expectancy.

So this got me thinking about trying to find an optimal reward/risk relationship but its been a long time since I did probability at school so the maths has got me stumped.

Can anyone help with the formula for working this out.  As I see it the higher the reward/risk ratio, the smaller the chance of a successfull trade.  There must be a mathematically optimal value for reward/risk which would lead to an optimal target/stop criteria.

Thanks


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## GumbyLearner (20 June 2010)

Play 2 up on Anzac Day


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## akkopower (20 June 2010)

beachlife said:


> Hi All
> I recently saw the coin toss spiel and it got me thinking.  They were saying a share can eventually go up or down so the probability is 50:50 and if your reward/risk is 1:1 then you will break even in the long run (ignoring costs), so the way to become profitable is to change your reward/risk to 2:1.  50% of the trades will make 2 units profit and 50% will lose 1 unit so overall you will be profitable - so they say.
> 
> The problem I have with this is that they failed to mention that the probability of a 1 unit move is different to the probablity of a 2 unit move, so its more complex than what they were saying.  The bigger the reward, the less chance of hitting it.  So a 2:1 system could still have a low expectancy.
> ...




From what I can understand by what u have written there is no such formula, the expression will always change depending on what situation u r trying to model.

what do u mean by optimal risk reward?
optimal risk reward for me would be to get given a free ticket into the lotto, no risk but might win a mill. 

Or i guess zero risk infinity reward


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## beachlife (20 June 2010)

What I am trying to figure out is the probability of success to then work out the best expectancy.

eg reward/risk  -   probability of win   -      Expectancy
       1:1          -            50%           -             0
       2:1          -            ??              -             ??
       3:1          -            ??              -             ??

ie the probability of a 10 point move up vs a 10 point move down is 50:50
   the probability of a 20 point move up vs a 10 point move down is ??
   the probability of a 30 point move up vs a 10 point move down is ??

Perhaps in a random sample it will always be 0.

I've always tried to have reward/risk around 2:1 but end up with low % wins so not profitable so wondering if better to reduce the target price and get higher % wins for better overall expectancy (profits).


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## weird (20 June 2010)

beachlife said:


> Hi All
> I recently saw the coin toss spiel and it got me thinking.  They were saying a share can eventually go up or down so the probability is 50:50 and if your reward/risk is 1:1 then you will break even in the long run (ignoring costs), so the way to become profitable is to change your reward/risk to 2:1.  50% of the trades will make 2 units profit and 50% will lose 1 unit so overall you will be profitable - so they say.
> 
> The problem I have with this is that they failed to mention that the probability of a 1 unit move is different to the probablity of a 2 unit move, so its more complex than what they were saying.  The bigger the reward, the less chance of hitting it.  So a 2:1 system could still have a low expectancy.
> ...




include brokerage. Although I would not personally spend too much time on this exercise.


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## akkopower (20 June 2010)

huh?

I thought a sp was not purely random, so if u are a good trader u will have a +ve expectancy, b/c u can find the good trades. 

But if the sp changes were normally distributed yr expectation would be 0.

The only way to see would be to write some code and use it on real data or talk to someone who already has.

lets say for example a sp has resistance at 1.2 and support at 1.0.

The sp just fell from 1.2 to 1 and moved up to 1.05. take a bet, set a stop loss at 1.025 and set a take win (or whatever its called) at 1.175. If u win >1/6th of the time u are going to be in the $$$.

is this what u are after?

ie the probability of a 10 point move up vs a 10 point move down is >50:50 if u want to win
the probability of a 20 point move up vs a 10 point move down is > 1:2 if u want to win
the probability of a 30 point move up vs a 10 point move down is > 1:3 if u want to win

or

eg reward/risk - probability of win - Expectancy
1:1 - 50% - 0
2:2 - 33% - 0
3:3 - 25% - 0


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## Space Invader101 (20 June 2010)

beachlife said:


> Hi All
> I recently saw the coin toss spiel and it got me thinking.  They were saying a share can eventually go up or down so the probability is 50:50 and if your reward/risk is 1:1 then you will break even in the long run (ignoring costs)
> Thanks




You're kidding me, right.  People move the market, not some randomized system.  People aren't random.  They either make rational or emotional irrational decisions.

Next you'll be telling us your tests have found the holy grail of moving averages.


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## tech/a (20 June 2010)

> People aren't random. They either make rational or emotional irrational decisions.




*CLASSIC!!*


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## Space Invader101 (20 June 2010)

beachlife what type of investment (shares,futures,FX etc) and time frame are you referring to?  This sounds like something from the book: A random walk down wall street.  The writer is bias in favour of fundemental analysis and insists that technical analysis is random nonsense.

For trend trading, I don't believe in setting targets and limiting my profits.  Perhaps profit targets might be useful for volitile short-term trading.


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## beachlife (20 June 2010)

Space Invader101 said:


> You're kidding me, right.




No I'm not.  Thats exactly what was being said in a sales pitch by someone else - not me.  It just got me thinking.

In my own trading (end of day, 3-10 day time frame) I find that I rarely hit a 2:1 target and most often either get stoppped out for a loss or break even.  The wins at around 1:1 barely cover fees.  So was just thinking about lowering the profit target (as there is more chance of hitting a lower target), to raise the win : loss ratio and was trying to find a way to find the best target.

So which is better trying to get 2:1 and better than 30% success or aim for 1:1 and aim for better than 50% succes.  Maybe the best mix is somewhere in the middle.

Unfortunately there is no holy grail MA which is why I am trying to work on expectancy and money management.


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## Space Invader101 (20 June 2010)

beachlife said:


> No I'm not.  Thats exactly what was being said in a sales pitch by someone else - not me.  It just got me thinking.



By who?


beachlife said:


> In my own trading (end of day, 3-10 day time frame) I find that I rarely hit a 2:1 target and most often either get stoppped out for a loss or break even.  The wins at around 1:1 barely cover fees.  So was just thinking about lowering the profit target (as there is more chance of hitting a lower target), to raise the win : loss ratio and was trying to find a way to find the best target.
> 
> So which is better trying to get 2:1 and better than 30% success or aim for 1:1 and aim for better than 50% succes.  Maybe the best mix is somewhere in the middle.




The best thing to do is go through your past trades and find out.  Might be some work, but you'll get the answers your looking for.  You might also want to take into account the overall market direction: bullish or bearish.


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## Synergy (20 June 2010)

It feels to me like you're getting the horse and the cart around the wrong way here.

You're trying to optimise something that changes as a result of something more fundamental to the trading. The win rate of a system can't just be dialed in. You need to change other parameters to change it.

For me, the importance of win rate is purely emotional. Emotional comfort knowing that on average i'll win 45% of the time. Sure, if i made an improvement to my system that meant the win rate was 50% I'd be happy. But I'd be fairly happy if the improvement meant a win rate of 40% too.

The relationship you're trying to find will be specific to your system/trading, and probably can't be varied by a huge amount anyway. It's not likely that you could just trade to get 70% wins at the flick of a switch.

I would spend some time thinking about why the way you're trading is, or could be profitable. Then vary things directly related to that reason. The W:L and R:R will just play themselves out.


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## pixel (21 June 2010)

Space Invader101 said:


> beachlife what type of investment (shares,futures,FX etc) and time frame are you referring to?  This sounds like something from the book: A random walk down wall street.  The writer is bias in favour of fundemental analysis and insists that technical analysis is random nonsense.
> 
> For trend trading, I don't believe in setting targets and limiting my profits.  Perhaps profit targets might be useful for volitile short-term trading.




Ahh, the wonders of a closed mind! Technical Analysis can make people independent from spruikers of funnymental opinion; therefore, it has to be declared random nonsense: How else can "advisers" who change their recommendations more frequently than their socks, keep victims who pay for the random nonsense they spout on a daily basis? 

If sp movements were indeed random and subject to daily 50:50 for up and down (what about those sideways moves though?) then we might well give up and call it gambling. Fact is: You can follow technical strategies that give you an edge better than 50:50 risk/reward. It's not a one-size-fits-all, and it depends on the stock itself, its current direction (trending up, down, or moving sideways), as well as historic behaviour - something I call each share's DNA.
If I find, a stock has a 3:1 chance of doing one thing over the other(s), following that chance consistently will give me an overall profit of about 50%. It does, however, require the discipline of sticking to one's strategy and stopping out if the 1-in-4 chance does come about and bites my trade in the bum.

btw, I totally agree with spaceinvader's statement about profit targets. I too use a target only for calculating the risk/reward and position size at the start of a trade: Upside likely 30c above my entry, stop level 10c below it, results in an initial, theoretical RRR of 3:1. It also tells me, how many shares I can buy if I want to limit my potential loss to $xxx. But if the sp rises by only 20c and then turns, I'm not going to hang around till it hits my initial stop; that would mean I've lost 10c; I keep updating my stop level day by day - or for short-term trades by the minute! And if it keeps going, I'm not limiting my profit by accepting 30c, only to watch it continue to rise by 50c or $1...

*"Trading is all about probabilities."*


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## Boggo (21 June 2010)

pixel said:


> How else can "advisers" who change their recommendations more frequently than their socks, keep victims who pay for the random nonsense they spout on a daily basis?
> *"Trading is all about probabilities."*




Exactly pixel, have a look at BP from both the charts and from what is happening in reality, then have a read below of what the "advisers" are saying.

http://www.reuters.com/article/idUSTRE65H4A920100618


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## tech/a (21 June 2010)

There is an answer to the question.

Look to

(1) Increase Positive expectancy.
(2) Increase Winners over losers.
(3) Increase frequency.

You can do this with software which will test your ideas if you have the skill to code your method/s.
OR
Working through your past trades and future trades (Pretty hopeless in getting something with statistical significance.

This is what we should all be striving for in our trading.

I liken it to a retail business.(For simplicity).

(1) I may be able to mark up my product 300% or more and sell a few units a year and be nicely profitable. (Long term trader)
(2) But I may also be able to sell my product with a 20% mark up and sell 1000s of units a year and be very nicely profitable.(Short term Trader)

Each is profitable and 1 maybe better for one trader to another.


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## Space Invader101 (21 June 2010)

tech/a said:


> You can do this with software which will test your ideas if you have the skill to code your method/s.
> OR
> Working through your past trades and future trades (Pretty hopeless in getting something with statistical significance.




Mostly correct tech/a except regarding past trades having hopless statistical significance.  It's not what a piece of software would have done, but what you did and even more importantly what you're going to do that decides your financial fate.

If a trader using Metastock uses something as simple as a moving average cross to back test, that doesn't tell the trader everything like where the overall market is at, company anouncments, the financial health of the business invested in and how different sectors are performing.

I use different software now, but when I programmed Meta Stock in my earlier years, it agrees with everything.  It's not human and obeys its instructions.

Some of its bullish signals such as a stock spiraling downwards, it will calculate simply because the criteria temporarily agreed when in the real world I would have said "NO WAY!" to its buy signal.

Really, it's propably best to test both past trades and software backtesting to have more information to work with.


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## beachlife (21 June 2010)

My trading is based on technical entries, using a 1.2 atr stop, 2.4x atr target and a trailing stop using cfd's on the top 20.

My results are that the initial direction was often correct, but more often than not the direction would reverse and my trailing stop would be hit.  The overall result is no profits.  

So I started thinking about setting a lower target which would make my exits higher than my trailing stop and would also raise the expectancy, but where to set it is what I am trying to figure out.

All I know is that 2x atr was too high and rarely got filled.

I have also tried the no target approach in the past and that was just as bad.  Makes sense if I rarely hit 2x atr then not much chance of getting more by having no target.

In terms of technical entires I have tried trend following but found that once the trend was confirmed it was nealry over, hence rarely hitting target.

Have also tried to get in ealrier using a fairly low ma turn and patterns only to find that many were just short retracements and stops were hit early.

Cant seem to find the balance of reliable entry criteria with realistic targets.


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## tech/a (21 June 2010)

Space Invader101 said:


> Mostly correct tech/a except regarding past trades having hopless statistical significance.  It's not what a piece of software would have done, but what you did and even more importantly what you're going to do that decides your financial fate.




Statistical significance---I doubt any trader would have 1000 or so trades which will be a large enough data set to return any statistically significant result from which to extract a trading blue print.



> If a trader using Metastock uses something as simple as a moving average cross to back test, that doesn't tell the trader everything like where the overall market is at, company anouncments, the financial health of the business invested in and how different sectors are performing.




If your building a trading system it doesnt have to. You dont have to know everything.(What is everything?)



> I use different software now, but when I programmed Meta Stock in my earlier years, it agrees with everything.  It's not human and obeys its instructions.




Common with all software--however it disagrees when a condition is false.



> Some of its bullish signals such as a stock spiraling downwards, it will calculate simply because the criteria temporarily agreed when in the real world I would have said "NO WAY!" to its buy signal.




You are making a discretionary call the Software is making a conditional call---both correct.



> Really, it's propably best to test both past trades and software backtesting to have more information to work with.




Forward and backtest yes of course.


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## skc (21 June 2010)

beachlife said:


> What I am trying to figure out is the probability of success to then work out the best expectancy.
> 
> eg reward/risk  -   probability of win   -      Expectancy
> 1:1          -            50%           -             0
> ...




Even if share prices are normal random distribution it doesn't imply that the mean is 0. Look at historically the mean is probably closer to 10-12% each year.

What you are not taking into account of is the 600 other factors about share price movement.

What is the probability of 10pt move down vs 10pt move up *in what circumstances?*

After surprise rates announcements by RBA?
On a Wednesday?
After double bottom on a chart?
When the depth of market is showing 600 asks just above market price?
When RSI is 80 and overbought?
When my dog just licked my toe?

You need to observe the market first, develop hypothesis on what might be happening, test your theory THEN work out what is the probability on your profit equation.

The win% and win/loss ratio is a result of all that, not the starting point. Whoever is selling you the training isn't explaining that very well.


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## Sir Osisofliver (22 June 2010)

beachlife said:


> Hi All
> I recently saw the coin toss spiel and it got me thinking.  They were saying a share can eventually go up or down so the probability is 50:50 and if your reward/risk is 1:1 then you will break even in the long run (ignoring costs), so the way to become profitable is to change your reward/risk to 2:1.  50% of the trades will make 2 units profit and 50% will lose 1 unit so overall you will be profitable - so they say.
> 
> The problem I have with this is that they failed to mention that the probability of a 1 unit move is different to the probablity of a 2 unit move, so its more complex than what they were saying.  The bigger the reward, the less chance of hitting it.  So a 2:1 system could still have a low expectancy.
> ...




*Slaps Brain*  Who quoted this rubbish to you?

The 50:50 stuff is garbage. This dates back to Bachelier (Sp?) who attempted to model the risk of a share by the use of standard deviation and variance. IE  Take a share price chart and draw a moving average, the amount of variance from the mean and the frequency of that variance (giving you a bell curve and a standard deviation) provides a proxy for risk.

This model is however assumes that there is no relationship between price events, the 50:50 stuff you mentioned. How bizarre that there is no correlation between one day and the next in a share price to match all the other correlations that exist between shares and other factors.

If this model of assessing risk was accurate, you would be able to predict how frequently a particular event would occur.  How about the '87 stock market crash.  What do you think the probability is that such an event _could_ occur. The probability is 1x10 to the power of 50.  That is a farking big number. Or to put it another way that is 29 standard deviations, so far out of the bell curve and so far out of the realm of probability as to be virtually impossible.  Yet it's already happened.  This model of assessing risk is *broken* because it takes no notice of pre-existing correlation.

The market is a chaotic model - not a neat aggregate mathmatical expression

Cheers

Sir O


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## adt100 (22 June 2010)

To '87 you can add at least 5 other cases since then that would have been considered statistically insignificant (ie so unlikely to occur that could be ignored)......................................Each one could have blown you up if you had ignored.

A much brighter man than me has often said is shareprice is random than how do we get trends?.............................A quick took at most charts suggests trend of some description.


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## Space Invader101 (22 June 2010)

Beachlife, what CFD providers do you use?  Not CMC markets?  Their education is full of &$@#.  They give you hit and miss strategies with ideally selected examples.

CFD providers automatically take the oppisite side of a trade when you trade.  So if you lose, they profit.

I like CMC's trading software.  I don't like their education.  Every time they send me education emails, I just delete them.


It might not be your money management system that's failing you, but the chart time frame being used.  Longer time frames filters out market 'noise' and makes trends more visible.


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## Sir Osisofliver (22 June 2010)

adt100 said:


> To '87 you can add at least 5 other cases since then that would have been considered statistically insignificant (ie so unlikely to occur that could be ignored)......................................Each one could have blown you up if you had ignored.




In fact there have been more than five occurances - so why do we get this myth perpetuated?

Because 85% of the time the standard deviation version of risk works. So 85% of the time the Brokers and Salespeople get to make hay whilst the sun shines and get to say things like black swan events when it all goes pear shaped with no consequences to themselves. 







> A much brighter man than me has often said if shareprice is random than how do we get trends?.............................A quick took at most charts suggests trend of some description.




Agreed


Cheers

Sir O


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## patchau (13 July 2010)

I have recently downloaded a free Metastock addon called Visual Strategy  Trader  (VST).
It has been interesting to test out some trading strategies on ASX stocks  & ETF’s by applying a system then changing the parameters and instantly viewing  the results.
My Metastock coding skills are limited but so far all has gone well. I will attach some charts and if anyone is interested can  post any ASX chart with a breakout (Turtle) system applied and parameters of your choice eg. 21/7 ,  15/5.


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