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The two sides of probability


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The two sides of probability

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  #1 (permalink)
Bellheim Germany
 
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Hello,

in the thread
a few members pointed out that even in a 50:50 chance market you can make money if you "bet" in favor of a higher reward. Meaning something in the line of target 2 points versus stop 1 point.

Someone posted nice plots of account developments having 40:60 or 30:70 win loss relations.

I have a question wich bugs me every time I read something in that direction.
If you have an automated system which purely on a random basis opens a long or a short position with a 1:2 risk:reward relation. Isn't any attempt to increase the monetary outcome by adjusting the risk:reward relation automatically impacting your win loss trade count in a negative way? With a risk reward ration of 3:1 the market has to walkt 3 times the "distance" in the right direction. One could also say the the chance of hitting your stop is 3 times as high as hitting your target. The same should apply to a not randomly opened position but also on a position which is for example long on an ascending moving average. Still the smaller stop room affects your chance of hitting target before stop in a bad way.

I'm not doubting the scientific correctness of "just increase your risk reward ratio" but where is the practical use if you reduce the occurrence of a positive outcome by increasing the reward.

I'm lacking a the statistical background, some vocabulary and englisch is not my main language. I hope the message comes through and I don't sound harsh.

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  #3 (permalink)
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There is no way to overcome the obvious points you mentioned:

Option 1. If your higher win rate comes at the expense of taking a larger risk, this will eventually just average out to 50/50. But you you will still pay all your transaction costs, spread costs etc.

Option 2. If you try to fudge the equation the opposite way you will have similar results. If you use tighter stops and larger profit targets you will have a lower win rate, but the value of the win rate will be higher. All things random and even, this will still average out to 50/50. You will still end up losing because of transaction costs, spread costs, etc.

In terms of how you exploit any of this and make money...... If you can correctly gauge the volatility, you can apply one or the other strategies at the right time and come out ahead.

1. In low volatility periods. You won't see huge moves, so if you set your stop outside of the range the market is moving it will rarely get hit. Option 1 will beat a low volatility market using random entries.

2. In high volatility periods, the market will have as much of a chance of moving 5 ticks as 10 ticks for example. So in these periods you go with option 2. Again, using random entries, all other factors even, you can mathematically be profitable doing this.


I had an old journal on here that describes this type of system in more detail. But basically you are betting on long term volatility patterns, not direction.

Best of luck.

In the analytical world there is no such thing as art, there is only the science you know and the science you don't know. Characterizing the science you don't know as "art" is a fools game.
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  #4 (permalink)
Legendary Market Wizard
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I have a hard time believing any professional trader uses arbitrary r/r ratios in their trading. r/r is a byproduct of the system, not the foundation.

However, you are correct. When you change arbitrary r/r ratios you're also changing your winning %.

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  #5 (permalink)
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pema83 View Post
Hello,

in the thread
a few members pointed out that even in a 50:50 chance market you can make money if you "bet" in favor of a higher reward. Meaning something in the line of target 2 points versus stop 1 point.

Someone posted nice plots of account developments having 40:60 or 30:70 win loss relations.

In the post you refer to, the math is correct but the assumptions are not realistic and therefore do not work in the real world.

We all know that the farther out the target the less often the target will be reached. In the real world it is actually worse than that.

In the real world, especially for an intraday trader with finite daily trading time windows, not only will a farther out target be reached less often, but the percentage of time it is reached will continually degrade well below the percentage required to breakeven as the target is moved farther out.

The farther out the target the less the chance of reaching it often enough to breakeven. Eventually a target will have a nearly zero percent chance of getting reached because it is larger than the largest daily range over a given time span.

For example, setting aside slippage, commissions and the nature of how a market order is filled compared to a limit order (a big ask, I know!), the percentages of wins required to breakeven in a set-it-and-forget-it scenario are:

Risk:reward
1:1 50%
1:2 33%
1:3 25%

This is simple math.

In the real world, based on empirical evidence that I've kept over hundreds of trades, if I am only 50% successful reaching 1R over a series of trades, my success rate in reaching the farther targets look more like the following:

1:1 50%
1:2 25%
1:3 13%

As you can see, the farther the target, the more degraded the success percentage. All scenarios beyond 1:1 are losers. Add in slippage, commissions and the nature of how a market order is filled compared to how a limit order is filled and it gets worse.

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  #6 (permalink)
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1. The market is not a Gaussian probability cure, that is it does not have a bell shaped probability. It has a skewed curve with a fat tail. So as others have said your basic assumption is false.
2.How often a trade can happen is an issue on total returns. But if it is just a random system you need to look at what the average rotation is. Another way to look is ATR. Market ATR increases with the time for the bars. As others have said if you are inside of random movement and counting on a move outside of random you need luck.
3. In one of Van Tharp's books they used random entry with appropriate position sizing and stop loss. It made a little money. I have never seen an experiment with random entry and exit. What is that a double dart board system?
4. As others have said risk reward is only a part of the calculation. Going back to Van Tharp he has a very good suggestion. Compile the results (in R) for 100 trades and then do a histogram to see what your distribution looks like.
5. For us little people math is a tool, not a machine. It will help us craft a better trade but it will not guarantee it. Only Renaissance hedge fund has a math machine and they have never been able to build a second one.

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  #7 (permalink)
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system not using arbitrary r/r

1.89 R/R 66% win $223 expectancy/contract/trade

0 - .85 14%
.86 - 1.70 17%
1.71 - 2.56 11%
2.57 - 3.42 11%
3.43 - 4.28 7.5%
4.29 - 5.13 4.3%
5.14 - 6.00 1.1%

Same system entries but with arbitrary R/R ratios

1:1 66% win $95 expectancy
2:1 50% win $98 expectancy
3:1 41% win $109 expectancy
4:1 36% win $141 expectancy
5:1 26% win $78 expectancy
6:1 23% win $90 expectancy

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  #8 (permalink)
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Trailer Guy View Post
1. The market is not a Gaussian probability cure, that is it does not have a bell shaped probability. It has a skewed curve with a fat tail.

The market doesnt move in a straight line and thats why you model it using linear regression. Thats where you will find your perfectly shaped probability curve.

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  #9 (permalink)
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Massive l View Post
I have a hard time believing any professional trader uses arbitrary r/r ratios in their trading. r/r is a byproduct of the system, not the foundation.

However, you are correct. When you change arbitrary r/r ratios you're also changing your winning %.


Massive l View Post
system not using arbitrary r/r

1.89 R/R 66% win $223 expectancy/contract/trade

0 - .85 14%
.86 - 1.70 17%
1.71 - 2.56 11%
2.57 - 3.42 11%
3.43 - 4.28 7.5%
4.29 - 5.13 4.3%
5.14 - 6.00 1.1%

Same system entries but with arbitrary R/R ratios

1:1 66% win $95 expectancy
2:1 50% win $98 expectancy
3:1 41% win $109 expectancy
4:1 36% win $141 expectancy
5:1 26% win $78 expectancy
6:1 23% win $90 expectancy

@Massive l, I'm trying to understand your numbers here, because I think they tell an important story. But can you just explain explicitly what you mean? I think it's that your results would have been cut short if you had killed the trades at pre-set R multiples, which I think is often true, but I don't really quite understand the numbers themselves. Can you say more, please?

Bob.

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  #10 (permalink)
Legendary Market Wizard
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bobwest View Post
@Massive l, I'm trying to understand your numbers here, because I think they tell an important story. But can you just explain explicitly what you mean? I think it's that your results would have been cut short if you had killed the trades at pre-set R multiples, which I think is often true, but I don't really quite understand the numbers themselves. Can you say more, please?

Bob.

I have non-arbitrary r/r results with the % of total wins making up each r/r range. I didn't feel like writing the code to give me exact 2:1, 3:1, etc. as the auto range that was spit out would suffice.

The bottom numbers show arbitrary r/r results.

The results show that using arbitrary r/r limits your profits and is not my preferred method of system building.
If I get a wild hair later I'll go with other way with r/r by keeping my profit the same while increasing risk.

I do use a max stop loss (only hit once in the last 100 trades and it's not that big), but $ or tick amount in profits changes based on that day's volume, bar height, time.

You can also see that 4:1 produces the highest expectancy ($92 less than non-arbitrary though).
However, it only wins 36% of the time. For my mental health, I prefer to win at least 50% of the time so even with the highest expectancy I still would never trade something that won 36% of the time. Maybe another +10% I might consider it.

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  #11 (permalink)
Legendary Market Wizard
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Massive l View Post
system not using arbitrary r/r

1.89 R/R 66% win $223 expectancy/contract/trade

0 - .85 14%
.86 - 1.70 17%
1.71 - 2.56 11%
2.57 - 3.42 11%
3.43 - 4.28 7.5%
4.29 - 5.13 4.3%
5.14 - 6.00 1.1%

Same system entries but with arbitrary R/R ratios

1:1 66% win $95 expectancy
2:1 50% win $98 expectancy
3:1 41% win $109 expectancy
4:1 36% win $141 expectancy
5:1 26% win $78 expectancy
6:1 23% win $90 expectancy

doing this backwards now. 1:2 (reward to risk)

1:1 66% win $95 expectancy
1:2 61% win $167 expectancy
1:3 61% win $88 expectancy
1:4 69% win $125 expectancy
1:5 72% win $129 expectancy
1:6 73% win $110 expectancy

Higher winning percentage and higher expectancy with reward kept at 1 while increasing risk.
1:3 has the lowest expectancy. It had the same winning % as 1:2 but with larger losers, therefore lower expectancy. 1:4, 1:5, and 1:6 was wide enough where the stop didn't get hit and price came back for a winning trade, creating a higher win % and a higher expectancy. Also, because of the increased risk, this strategy had about 50 less trades as the duration of the trade was increased by increasing the stop. It took the market a longer amount of time to reach the stop.

The largest string of losers in a row even with 1:6 was 3 and a couple of 2 losers in a row as well. The average loss on 1:2 vs 2:1 was of course 2x the amount.

Looking at the numbers the strategy I am leaning towards with arbitrary r/r is 1:2. The average loser is 2x the amount as 2:1 but it's still not a number that would affect me psychologically. 1:2 actually only had 33 less trades than 2:1. The higher the risk, the longer the duration therefore less trades. 1:4 - 1:6 all were around 50.

In the same amount of time, 1:2 out performed 2:1 by 15% ROE because of the 170% increase in expectancy.
All arbitrary r/r strategies under-performed the non-arbitrary exit strategy by about 50% ROE.

EDIT

Now increasing both the reward (target) and increasing risk (stop) while keeping the ratio at 1:1

2x 1:1 68% win $161 expectancy 80 trades
3x 1:1 65% win $198 expectancy 66 trades
4x 1:1 53% win $49 expectancy 55 trades
don't think I need to do 5x...

Doubling and tripling the target and stop out-performed the 1:2 ratio on about the same amount of trades by 15% and 16% ROE respectively. Average risk was the same on 2x vs 1:2 ratio of course however tripling the target and stop increased average loser by 36%. For only a 1% gain in ROE, increasing target and stop is not worth the risk in this case.

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  #12 (permalink)
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, vaguely related

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