[russellhq]

I'd like to start a disscussion on the maths behind risk of ruin as from what I've read previously, it leaves me a little uncomfortable.

I'll start by discussing the way it's usually presented. Usually when calculating RoR, you normally start with the the answer and work backwards, so lets do that.

I'll use the coin flipping analogy as the game. So say we play a game where I flip a coin and if it lands on heads then you win and if it's tails you lose. Normally, before the start, you would decided on what level of risk you will accept before going broke, say it's 1 in 10,000. This works out at roughly 13 tails in a row or 0.5^13.

Nice and easy, we can play the game for as long as we want but if there is a run of 13 tails, then you're out.

But, what if, at the start of the game you have a run of 12 tails, then a head, then 2 tails. You are still out! This thought led me to the following:

This time, instead of ruin meaning you can no longer play, lets set ruin to be true only at then end of a set number of games. If during the course of play you pass the ruin line, you are still allowed to play to try and recover but you must stop after the set number of games.

Lets start out by saying we will play 27 times, what will be the chance of you being ruined?

To work this out, lets start with how many different permutations of the game there is (how many difference ways we can flip the coin 27 times).

2^27 is the answer

Now lets work out how combinations there are that can ruin you by the end of play.

If you get 0 heads during the 27 flips, then all agreed, you would be well and truly ruined. There is only 1 combination of this.

If you get 1 head during the 27 flips, you would still be ruined. There are 27 combinations where you can get only 1 head from 27 flips.

If you get 2 heads during the 27 flips, again you'll be ruined. To calculate the combinations, we use factorials: 27!/(27-2)! = Number of ways you can be ruined.

We keep doing this until we get to 7 heads, after 7 heads, you would always be able to recover by the end.

So when we add up all the combinations from 0 heads, to 7 heads:

0 heads = 1
1 heads = 27
2 heads = 27!/(27-2)!
3 heads = 27!/(27-3)!
4 heads = 27!/(27-4)!
5 heads = 27!/(27-5)!
6 heads = 27!/(27-6)!
7 heads = 27!/(27-7)!

And divide by the total number of permutations (2^27) we end up with our answer. In this case it's 1 in 100!

This is a lot higher than our initial assesment of 1 in 10,000!

This is just the basics and i've not considered Risk/Reward ratios etc (that can be added later). I just wanted to start with the basics.

Thoughts?

[BlowFish]

Be interested where you go with this, a neglected subject that really should be a mandatory part of trading 101.

The brain is a bit sluggish at the moment but I am not sure it makes sense (to me) to divorce account size and bet size from the equation. The main parameters to RoR are expectation of outcome (50:50) in our case, bankroll and bet size. Just having difficulty getting my head around how you have abstracted things. Again you can make bet and bank constant arbitrary values but I need to think if that actually allows them to be dropped from the equation. To lazy for thinking right now

Having said that looking at 'streakiness' is a pretty valuable exercise, many trading approaches do seem to yield 'streaks' (probably due to cycling market conditions).

[russellhq]

Hi Blowfish.

Account size and bet size would be the outcome of this exercise.

For example, in the first method we used an arbitrary RoR of 1 in 10,000 then calculated that 13 tails in a row would be about a 1 in 10,000 chance. Therefore, we assumed we would be ruined only after 13 straight tails. So to bankroll ourselves to cover the 9,999 other events where we don't hit 13 tails, we would need a bank of 13 times our bet size. Normally though we start with a bank size, and would divide it by 13 to work out our bet size.

[BlowFish]

OK I see what direction you are coming from thanks.

[MightyMouse]

Originally Posted by russellhq »

Hi Blowfish.

Account size and bet size would be the outcome of this exercise.

For example, in the first method we used an arbitrary RoR of 1 in 10,000 then calculated that 13 tails in a row would be about a 1 in 10,000 chance. Therefore, we assumed we would be ruined only after 13 straight tails. So to bankroll ourselves to cover the 9,999 other events where we don't hit 13 tails, we would need a bank of 13 times our bet size. Normally though we start with a bank size, and would divide it by 13 to work out our bet size.

Russel,

Trading is negative sum when you add in all costs. As a trader you have to to do significantly better than 1 to 1 in order to overcome the costs and the obstacles that you are pointing out to make it worth one's while. It is very difficult and leads many hedge fund managers to lying, cheating, and stealing to post quarterly returns that are better than returns that would be earned by the randomly chosen hedge fund.

MM

[russellhq]

Thanks MM. It is my intention to look at that aspect later on, but for now I am keeping things simple and trying to get the foundations correct before building on top of them.

[NeoTrader]

I am starting to get where you are going with your math Russell, but it only hold's true if you continue to risk the same amount after 6, 9, or even 12 losses. If you were considering Ruin to be dead broke, after 12 losses if you made another trade with the same risk you'd be risking 100% of your capital!

Depending on your risk model whether it be percentage based, fixed, or something else one would think you need to adjust it to be inline with your capital.

[tommaso]

Using analogies with coin toss for these kind of computation in trading is not much useful, and probably misleading.

There is a fundamental difference. While a coin can do whatever it likes, mkts don't.

Volatility is obviously bounded, as at certain prices you dont have no more buyers or sellers. Further, mkts (especially futures) experience violent reversals. In fact GBM with reversion are pretty realistic models for these (if we let volatility change randomly).

You can have large dd, but can't really have "unbounded losses", unless you use stops, in which case, obviously, you do.

[That is another reason why all fx brokers and scammers recommend to people to use stops .]


Tom