Risk:Reward and Probability

Happy Chrimbo Everyone . . .

. . . Although not for me as yet. I'm getting my yuletide knickers in a veritable twist. Nasty business, I can tell you. I've always struggled with the reward half of the risk:reward ratio. The concept of only taking trades that are 2:1 or better is all well and fine. In principle, I'm happy to use T.A. and price action to determine stop placement and profit targets as explained very eloquently by contributors to FTSE Beaters excellent thread, 'The Basics of Trading'. However, I've always suspected that the target (reward) says more about where the trader wants the price to go, than it does about its realistic chances of getting there. This raises the question of probability which, as Mr. Charts points out in that same thread, alters the overall picture significantly.

He writes:
". . . say you are trading 1000 shares with a take profit target (reward) of $1 and a stop loss (risk) of 25c. Fine you say, 4:1
Sorry, simply not so. The calculation is incomplete, totally meaningless in fact, without considering the probability of the two events occurring within any set time frame.
If the probability of the $1 gain is only 20% say, and the probability of a 25c loss is 80%, that rather messes up the maths, doesn't it? Messes up the trade actually".

He does have a valid point, doesn't he! So, the problem is this: how does one add probability into the pug mill and still arrive at a logical and evenly balanced decision about whether or not to take the trade?

Tim.

Timsk, as Mr. Charts has introduced the probability issue to Risk:Reward he really should be allowed to have a first shot at explaining his comments.

Well, rather than leave this one hanging (perhaps Richard missed it) I'll give you my 2p-th and he can correct me if I'm wrong.

The fact is, you never know for any given trade what the probability is for the target being hit or the stop being hit. You can only make a probabilistic determination for all the trades using that system. In fact, the factors Mr. Charts mentions are those used to derive the Expectancy for any system.

Expectancy = (Pw * Aw) - (Pl * Al) gives you an absolute value of the amount you can expect to make on average per trade for any fixed criteria trading system.

(BTW - Traders who do work with targets (S/R, Fibs, Pivots, half-retrace etc.), will hopefully be astute enough to allow the market to tell them when enough is enough rather than stick like glue to their own expectations.)

Unfortunately, expectancy is absolutely no good to you whatsoever in helping you decide whether to put any individual trade on, or not.

Expectancy is really only used to compare trading systems, either on a personal basis for optimum profitability (although that can lead to tunnel-vision) or as part of 'selling' a system to others. It basically tells you how much you can on average expect to make for each trade - but not any one trade specifically.

The validity of Expectancy depends on the following:-

1. All trades are executed with exactly the same entry and exit criteria
2. The risk profile is the same for all trades
3. There is a probabilistically significant dataset size (number of trades)

So, the point about probability of target or stop being hit per trade isn't particularly valid and certainly not much use to you in deciding whether or not to take that next trade. But may be of some use in helping you to compare two or more different systems.

timsk said:

Mr. Charts writes:
". . . say you are trading 1000 shares with a take profit target (reward) of $1 and a stop loss (risk) of 25c. Fine you say, 4:1
Sorry, simply not so. The calculation is incomplete, totally meaningless in fact, without considering the probability of the two events occurring within any set time frame.
If the probability of the $1 gain is only 20% say, and the probability of a 25c loss is 80%, that rather messes up the maths, doesn't it? Messes up the trade actually".

Click to expand...

Aah! and now we get to the heart of the matter... How I wish I had something to contribute here. - The trader who understands and has mastered this paradox is on the way to solving the big puzzle.
JO

One of the best contributors on this board with regard to trade probabilities was Grey1. His accuracy for determining the likely target price that a stock would move to against the risk involved was staggering and yet he was able to do this consistently day in and day out. The reason I am saying this is to let others know that determining price targets and the probability of reaching them can be done and successfully.


Paul

Paul,
I've not noticed any posts from Grey1 for a while which, given your comments, is a shame as it sounds as if he would make a valuable contribution. In his absence and in view of your own skill in these matters (don't be shy now) - perhaps you could provide a few pointers?


JO,
Precisely my sentiments!

Tony,
Without a post from Mr. Charts, we won't know if your interpretation of his comments is what he's driving at or not! However, I suspect that he doesn't apply maths or science to determine probability of success, preferring instead to rely upon his extensive experience and ability to gauge market sentiment. If there are no obvious brick walls that could prevent the price from reaching its target, he'll enter according to his specific triggers; confident that both momentum and market sentiment are in his favour. Unfortunately for those of us who are less able, this is a complex skill, which is difficult to pass on to less experienced traders in a step by step, two plus two equals four approach.

Tim.

surely this is a very simple concept .

I said before and I'll say it agian , that all statistical measurements of the market are only ESTIMATES at best when trying to calculate profit targets.

if probability and expectency stats were so accrurate as to when the profitable trades are in the market , then all you need to do would be to employ statistitians to trade and we would all be rich.

clearly this is not the case.

Hi Timsk

I hope your are well.
I can understand what you're saying and what Mr Charts has said.

". . . say you are trading 1000 shares with a take profit target (reward) of $1 and a stop loss (risk) of 25c. Fine you say, 4:1
Sorry, simply not so. The calculation is incomplete, totally meaningless in fact, without considering the probability of the two events occurring within any set time frame.
If the probability of the $1 gain is only 20% say, and the probability of a 25c loss is 80%, that rather messes up the maths, doesn't it? Messes up the trade actually".

Click to expand...

I agree with the above, so yes one more thing needs to be added - probability. With the 3:1 rule, you only have to right 25% of the time to be profitable.
I remember hearing that someone worked out that a price is 70% likely to bounce off a support or resistance line. That coupled with a 3:1 Risk / Reward is good enough for me - that's an edge in the market and that's all it takes to make money - AN EDGE!!

Wisestguy said:

if probability and expectency stats were so accrurate as to when the profitable trades are in the market , then all you need to do would be to employ statistitians to trade and we would all be rich.

Click to expand...

The problem with statisticians (and I should know, I am one at heart ), is that there are too many variables for them to work out, they generally prefer poker, but that's another story.

Digging around the archives I found a similar thread from just over a year back.

Interesting posts (as are those in this thread!), but the post from Grey1 whom Trader333 mentions above, is particularly pertinent.

http://www.trade2win.com/boards/showpost.php?p=59046&postcount=33

It doesn't give 'the answer' as such, but if I'm interpreting it correctly, it does indicate the method that could be employed as a basis for weighting your R:R calcs.

As stated above, I don't currently have the ability to determine for any one trade in advance precisely what is the probability of my stop being hit and of my target being hit. I can tell you 'on average' for any of my trading systems what the probabilities are, but not for individual trades.

That doesn't mean it can't be done - just that I don't know how to do it....yet.

Half the battle is believing something can be done.

Tony,
Excellent digging, thanks for bringing this thread to my (our) attention!

For anyone interested in this subject, the link in Bramble's post to an old thread throws a lot of light onto the subject. A post by sidinuk in which he copied an article from a publication called 'Daily TrendWatch' is especially helpful, IMO.

My assessment of that thread - and a possible answer to the question I posed in my opening post of this thread is this . . .
We need to know two key ratios in order to determine our risk:reward ratio. These are the 'Success' ratio and the 'Sharpe' ratio.

1. The success ratio is the number of winning trades against the number of losing trades. Some people may prefer to express this as a percentage by dividing the number of winning trades by the total number of trades made and multiplying by 100.
2. The sharpe ratio is the average number of winning £££'s against the average number of losing £££'s. As a percentage, divide the average £££'s of profitable trades by the combined figure of the average number of £££'s won and lost and then multiplying by 100.

For the sake of argument, let's suppose that we have a success ratio of 2:1 - i.e. 66%. Additionally, we also have a sharpe ratio of say, 1.5:1 - so that if we risk £40.00 we will make £60.00 on the winning trades. From this we know that we win 2 out of every 3 trades and that of the 2 winners we make 2 x 60 = £120.00. Our 1 losing trade of the three costs us -£40.00.

Therefore, our risk:reward ratio is pre-defined for any given trade at 3:1.
Before entering a trade, our job is to assess the probability of of the price moving 1.5 times further than the amount we are risking on the trade - i.e. the sharpe ratio. So, if we risk £40.00, what is the probability of the price reaching £60.00? This is where our T.A. skills come into play, ditto with tape reading and market sentiment, volume and level II etc., etc. One solution is to take a negative approach and ask the question "why won't the price move 1.5 times in my favour? Is there a round number, S/R, previous high/low etc. which may prevent it from getting there?" If there are no clear obstacles, then enter the trade according to the entry triggers defined in your trading plan.

Just my thoughts, others may have (and probably will have) a very different take on this.
Tim.

FTSE Beater said:

Hi Timsk

I hope your are well.
I can understand what you're saying and what Mr Charts has said.


I agree with the above, so yes one more thing needs to be added - probability. With the 3:1 rule, you only have to right 25% of the time to be profitable.
I remember hearing that someone worked out that a price is 70% likely to bounce off a support or resistance line. That coupled with a 3:1 Risk / Reward is good enough for me - that's an edge in the market and that's all it takes to make money - AN EDGE!!


The problem with statisticians (and I should know, I am one at heart ), is that there are too many variables for them to work out, they generally prefer poker, but that's another story.

Click to expand...

ah , so when's your next game ? perhaps we should get together 1 day , distance permitting.

Is it essential to make more than one risks per trade? Can a trader be profitable if in the main, trades produce less than is risked?

Yes but you need a higher success rate to be profitable, the less the Reward is to Risk.

eg. Reward per trade = 10
Risk per trade = 20

Success rate = 80%

So, in every 10 trades you win 80 ( 8*10) and lose 40 ( 2*20)

LION63 said:

Is it essential to make more than one risks per trade?

Click to expand...

No.

LION63 said:

Can a trader be profitable if in the main, trades produce less than is risked?

Click to expand...

Definitely. You'd need a much higher "strike-rate", of course, but some systems have that. Clearly you could enter trades for a 10-point gain or a 20-point loss if you're winning 95% of them and make a living from it, if you can do it often enough, no?

Also, the "amount risked" isn't quite such a simple concept as it looks, because it's possible to have a trading method in which some smallish proportion of the "amount risked" has an x% risk of being lost while all the rest has only a y% risk of being lost (where y is far smaller than x). Which makes the sums a bit more complicated, of course.

It's late and I haven't read the whole thread carefully, so apologies if other posters have already made these points.

wisestguy said:

ah , so when's your next game ? perhaps we should get together 1 day , distance permitting.

Click to expand...

Distance? You can play him heads-up online at Ladbrokes (as long as you're not American, that is - there are still some limits!).

Very aptly put Roberto. The reason I asked the question is that in at least 90% of the posts on these boards, all traders seem to mention is a positive risk/reward ratio; that is fine but it tends to leave the impression that anything else is doomed to failure. Yet it is fairly logical to assume that a good trader who opens a position seeking a return of 2:1 may at times have to settle for much less depending on subsequent market movements.

Apart from that, there are the traders who are in the quick in quick out brigade, they have little or no chance of achieving positive rates of return on a regular basis but they will still be profitable (if they are good at what they do).

Trying to assess the probability of a certain target price being reached is very notable but I like to keep things simple.

Rather than trying to assess this probability which is very difficult ( if not impossible ) in a real time trade situation, I prefer to consider what is REALISTIC rather than what may or may not be probable.

In this context, I am very realistic with regard to Reward / Risk ratio and for most of the trades that I do, I set my target distance at the lower of 2.5 times my stop level and 1% of the share price. Whichever is the lower, that is where I set my limit order to exit the trade.

I do monitor the trade to ensure I take some profit if it runs out of steam before the above is hit or if the price looks like it is going to go like a steam train, I might then cancel the limit order and let things run on for a while.

Simple and straightforward explanation and one that I find very reasonable/achievable. However, could you clarify the point about 2.5 times your stop or 1% of the share price, whichever is the lower; would I be right in assuming that this refers to day trading? As I would hardly expect you to hold a position overnight in a £2 share looking for a 2p movement. (By the way, it is very similar to my strategy).

Lion

I day trade Nasdaq shares which, as you know, tend to be higher in unit value than UK shares. So if I am trading a US$ 50 share then I am looking for a 50 cent move which is eminently achievable.

My stops generally tend to be between 15 and 25 cents so based on this my target movement would be 37.5 cents to 62.5 cents.