# Risk and Money Management

#### Apple Forex

##### New member
Hello all!

I currently trade currencies in Forex Market, and I somewhat understand the concept of being a winner long term, but I want to actually see how the numbers can run statistically. Formulas on how it should be calculated would be nice! (I should of paid attention in my statistics class in college )

Here is the data:

I am only willing to risk 1% to 5% of my equity in my account for each trade that I make. For example, let's say I deposit 100000 US Dollars and I risk 1% (1000 USD) per trade, which sums up to be 100 trades.

I have a probability range of 30-40% of winning a trade.

The only way I see winning down in the long run, is if I can extend my risk/reward ratio.

How far can I go with my risk/reward without compromising my equity? Say for example, I am willing to risk 1 dollar to win 3 dollars on a trade, but the trade only has a 30% chance of winning at that ratio. Would it be wise to have a risk/reward at 1 dollar for 2? I know for a fact I will be a loser in the long run if I run it 1 for 1.

Considering that my percentage of having a winning trade is between 30-40%. What is my risk/reward threshold and range? What is the probability of me losing all my equity if I lose ALL my trades?

What is my optimal (or sweet spot) I should wager for each trade for me to win in the long run? Depending on the trade, I can take an aggressive (5%) or conservative(1%) approach.

I can grasp the concept, but I can't seem to grasp the numbers. I would love to know how to properly calculate this! Let me know what you guys think.

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#### springfan25

##### New member
im not quite sure how to put this but it sounds like you're really asking for financial advice rather than maths help.

#### Apple Forex

##### New member
im not quite sure how to put this but it sounds like you're really asking for financial advice rather than maths help.
Actually, it is pure mathematical. If I word the data differently, it might be able to help simplify such a confusing question.

Let's say, we go to the casino and they offer a game called coin flip. Instead of the traditional 50/50 probability, you have a 30% chance of winning and the house has the 70% edge. However, every independent event of you winning gives you 3 times of what you initially bet.

So say you come with 100 dollars and wager 1 dollar per coin flip to win 3 dollars. Would this result in you being a long term winner? Or would I have to win a wager of 1 dollar to win 4 dollars instead? Will the house stack all your money away with these payoffs? Now, I know sequence will ALWAYS be random but I'd like to know how to calculate the possible risk of losing it all. I also know that being paid even (1 to 1) money on these odds will ultimately make you a loser. But if my risk/reward changes, it would make a significant difference on risk.

However, I want to know how to properly calculate these probabilities and possible risks using the proper mathematical formulas so I can get a general idea on my risk and money management strategy. My math isn't that strong, and I'm sure there are plenty of math geniuses here.

Let me know what you guys think!

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#### Plato

##### Well-known member
MHB Math Helper
Let's say, we go to the casino and they offer a game called coin flip. Instead of the traditional 50/50 probability, you have a 30% chance of winning and the house has the 70% edge. However, every independent event of you winning gives you 3 times of what you initially bet.

So say you come with 100 dollars and wager 1 dollar per coin flip to win 3 dollars. Would this result in you being a long term winner? Or would I have to win a wager of 1 dollar to win 4 dollars instead? Will the house stack all your money away with these payoffs? Now, I know sequence will ALWAYS be random but I'd like to know how to calculate the possible risk of losing it all. I also know that being paid even (1 to 1) money on these odds will ultimately make you a loser. But if my risk/reward changes, it would make a significant difference on risk.
If you have expectation of winning with a probability of 0.3 on independent trials and you have 100 tries then on average you should win 30 times. So in your example you spend \$100 to win \$90 on average.

If there is a probability of $$\displaystyle p$$ of success on each of $$\displaystyle N$$ independent trials then the expected number of successes is $$\displaystyle p\cdot N$$.

Is that anywhere near to a correct understanding of what you are asking?

#### Apple Forex

##### New member
If you have expectation of winning with a probability of 0.3 on independent trials and you have 100 tries then on average you should win 30 times. So in your example you spend \$100 to win \$90 on average.

If there is a probability of $$\displaystyle p$$ of success on each of $$\displaystyle N$$ independent trials then the expected number of successes is $$\displaystyle p\cdot N$$.

Is that anywhere near to a correct understanding of what you are asking?
Yes. This helped me see it quite a bit. However, when calculating the probability of losing all trades, how would one do that when sequences are random? Given an infinite amount of trials, if we were to graph winnings with the variable of time, would this have positive outcome? Meaning would we see it progressively rising as time progresses?

Thanks for the help!

#### Plato

##### Well-known member
MHB Math Helper
Yes. This helped me see it quite a bit. However, when calculating the probability of losing all trades, how would one do that when sequences are random? Given an infinite amount of trials, if we were to graph winnings with the variable of time, would this have positive outcome? Meaning would we see it progressively rising as time progresses?
I was addressing only the case you gave: we go to the casino and they offer a game called coin flip. Instead of the traditional 50/50 probability, you have a 30% chance of winning and the house has the 70% edge. However, every independent event of you winning gives you 3 times of what you initially bet..

These are known as Bernoulli distributions.
It is important to note that the number of trial is finite never infinite; the trials are independent so order does not matter; and the process in indeed random.

#### Apple Forex

##### New member
I was addressing only the case you gave: we go to the casino and they offer a game called coin flip. Instead of the traditional 50/50 probability, you have a 30% chance of winning and the house has the 70% edge. However, every independent event of you winning gives you 3 times of what you initially bet..

These are known as Bernoulli distributions.
It is important to note that the number of trial is finite never infinite; the trials are independent so order does not matter; and the process in indeed random.
Thanks!

Also, a few things. Although the sequences are random, I have been trying to calculate probability of losing all 100 trades.

Is it a simple calculation as this? Or am I missing something?

Does Pn = Probability of losing all 100?

When I do, I come up with 3.23 X 10-16

EDIT: n=100 and p=.7 (% of losing)

#### Jameson

$p = 0.3$, $n=100$
$P[W=100]=0.3^{100}$
$p=0.7$, $n=100$
$P[L=100]=0.7^{100}$