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I have only quickly checked the risk of ruin formula, and it does not look equivalent to my formula. In the formula (E5/E4) should stand for b and (E6/E4) for a. a and b seem to be inversed. Also the risk of ruin would be the complement 1 - P(a,b,k) of the probability of success given by the formula in post #44.

I would further suggest to format the percentages to allow two digitals after the separator.

The following 3 users say Thank You to Fat Tails for this post:

@Fat Tails (and others), why is Kelly the best or recommended method for this type of calculation? Is that based on popularity, or is there a mathematical reason to use Kelly over something (?) else?

Mike

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The following 2 users say Thank You to Big Mike for this post:

The Kelly formula is all about compounding returns.

If you have developed a betting (or trading) approach with a known edge (positive expectancy), then you want to know which fraction of your account you should bet to get maximum growth in the longer run.

The Kelly formula gives a mathematical answer to that question, as it calculates the optimal fraction - called optimal f - leading to maximum growth of your account. It is just mathematics. I am not interested in popularity, but in growing my account.

The Kelly formula is based on a number of assumptions, which limit its application in practice.

(1) It should only be applied if there is an edge or positive expectancy.
(2) It can only be applied to Bernoulli distributions, that is bets with two possible outcomes.
(3) It assumes that you can adjust the bet size in a continuous way

In my example I have selected a trading approach, which always leads to two possible outcomes, that is a win of 18.2 points or a loss of 11.8 points to comply with the condition (2).

The condition (3) is not respected for small accounts, but at least you get close to the optimal bet size by calculating the number of contracts, which best represent the risk adjusted optimal f.

The following 8 users say Thank You to Fat Tails for this post:

Thanks for modifying it, it now reflects the formula, which I have suggested. So at least it is something on that we can agree.

I think it is a very useful little tool. Because I like it, I would also suggest some further enhancements. I let you control your tool, so make a change request, although I could do it myself.

Actually the way the tool works is to enter all the input variables in the orange field and then play around with the Kelly factor, until the risk of ruin matches the acceptable risk. The actual risk involved is Optimal F multiplied with the Kelly factor.

Here are my suggestions:

-> Replace "risk aversion" with "Tolerated risk"
-> Replace Full/Half/ Quarter Kelly with "Kelly Factor"
-> Somehow highlite the "Kelly Factor", because that is the field that needs to be adjusted
-> Give instructions to the user somewhere: "Please adjust Kelly factor until risk of ruin matches tolerated risk"
-> Add an output line below the number of contracts to show the accepted loss per trade as the percentage of equity (Adjusted Optimal F = [Value], the value representing Optimal F * Kelly factor.

Thank you for your help. This spreadsheet is very simple. but it is a powerful tool for determining the optimum number of contracts in line with anybody's risk appetite.

The following 9 users say Thank You to Fat Tails for this post:

Stephen wrote: I was wondering if there is some term that proceeds 'ruin'.

If initially one has $100,000 and day trades, isn't there some percentage where there
is obviously a 'problem' or some sort. Bad method, or whatever.

If one started with $100,000 and now the trading account just went shy of $50,000, I'd
say something is dreadfully wrong, yet ruin is far away, or may never occur I suppose.

Sorry, there is apparently some confusion with my question. I thought there might be a term
I never heard of before that was not ruin, but indicated a trading method/system was almost
certainly...well... fatally flawed. I thought about a trading account at the instant it reached a point
of being down more than half. 50.01% down let's say. That figure is arbitrary of course.
Even being down more than 1/3 is not pretty.

You wrote that if one has $1,000,000 then is down 90% to $100,000, that is ruin if I say it is

OR

it is not ruin if I say it is not.

To me, ruin means that the trading account is too depleted to allow trading. I always thought
that anyway. There is no uncertainty about it. Otherwise what I consider ruin for my trading
account can change each day. Even each moment I guess.

What is someone started with $10,000,000 and is down 90%? I don't see how someone can
reach ruin if they're a millionaire, and have $1,000,000 in the bank.

- Stephen

The following user says Thank You to stephenszpak for this post:

If you are down 90% your trading approach may be flawed, or you have simply been unlucky. The calculation of risk of ruin supposes that your trading approach is not flawed, but that you have an edge.

Even if you have an edge, there is a small probability that you reach the drawdown equivalent to ruin. This is the risk of ruin.

The following 4 users say Thank You to Fat Tails for this post:

Looks like I am late to the party. Lots of other things going on at the moment so I didnt have too much time i could spend on futures.io (formerly BMT)...

Nice work, thanks.

As condition (2) is probably the most problematic regarding the practical usefulness of this formula for trading I thought about how it perhaps might be possible to mitigate that. If we would use the mean loss/win in order to come closer to condition (2) the formula would return bet sizes larger than the optimum due to compounding effects of variance in return not being accounted for. It should/may (theoretically) be possible to factor that in using standard deviations of the wins/losses.
But perhaps I'm only dreaming

Vvhg

Hic Rhodos, hic salta.

The following 4 users say Thank You to vvhg for this post: