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Math Help - The Probability of Ruin Matrix - What`s the formula?

  1. #1
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    The Probability of Ruin Matrix - What`s the formula?

    Hello everyone,

    I was not sure if this is an advanced topic, but since nobody has been able to answer me earlier I take my chances

    I found the following table in one of my books on finance and trading. The author does not mention where he got it and I do not believe he has made it himself. Still, I can`t find much info about it on the internet. Here goes:


    Profit/Loss Ratio - P/R
    Winning Percentage - % Win

    Please see the table below

    [html] % winner
    P/R 30% 40% 50% 60%
    __________________________________
    1:1 99 88 50 12
    2:1 74 14 2 0
    3:1 23 5 1 0
    4:1 14 5 1 0
    [/html]
    * Ruin is defined as a 50% drawdown from starting equity
    * The matrix assumes 100 trades executed for the same reason.

    I understand the table this way:

    Let`s say we have 40% winners/60% losers and a profit/loss ratio of 2:1. This gives us a 14% probability of ruin. That is, a 14% probability that all the 60 losing trades come successively.

    Could anyone please explain to me how this is calculated?

    I am making a sheet in excel where I want to experiment with different variables (initial account size in trading account, average size of winners/losers, different profit/loss ratios) and see how it affects the probability of ruin.

    Obviously, if the matrix above were to account for different account sizes, the average loser (in dollar) had to be adjusted so that the size of the total loss amounted to a 50% drawdown after 60 trades.

    Example:

    If we have a $5000 account, drawdown would occur if we had 60 losers in a row with an average loss of $41.67.

    With a $10,000 account, this would only lead to a drawdown of 25%. Thus, the average loss would have to be increased to $83.33 if we were to use the matrix.

    Also, I`m not sure if I understand how in the matrix the different profit/loss ratios affect the probability of ruin, since the loss is constant (1 dollar for example).

    I hope someone is able to follow my thoughts

    My understanding of probabilities is very weak and I`m not sure if I`m even communicating correctly what I want to know.

    Thanks very much in advance to anyone who has some clues or help to provide.

    Best regards,

    Trader
    Last edited by Trader; May 29th 2009 at 12:44 PM. Reason: Added content.
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  2. #2
    MHF Contributor

    Joined
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    Paris, France
    Posts
    1,174
    Quote Originally Posted by Trader View Post
    Hello everyone,

    I was not sure if this is an advanced topic, but since nobody has been able to answer me earlier I take my chances

    I found the following table in one of my books on finance and trading. The author does not mention where he got it and I do not believe he has made it himself. Still, I can`t find much info about it on the internet. Here goes:


    Profit/Loss Ratio - P/R
    Winning Percentage - % Win

    Please see the table below

    [html] % winner
    P/R 30% 40% 50% 60%
    __________________________________
    1:1 99 88 50 12
    2:1 74 14 2 0
    3:1 23 5 1 0
    4:1 14 5 1 0
    [/html]* Ruin is defined as a 50% drawdown from starting equity
    * The matrix assumes 100 trades executed for the same reason.

    I understand the table this way:

    Let`s say we have 40% winners/60% losers and a profit/loss ratio of 2:1. This gives us a 14% probability of ruin. That is, a 14% probability that all the 60 losing trades come successively.

    Could anyone please explain to me how this is calculated?
    Hi,

    Using google I found this book. I guess this is the one you're refering to?

    One thing is for sure: the starting equity must be given, otherwise it makes no sense. That makes me think the author did probably not get this table himself, indeed.

    I did a few tests and it seems that it should be between $15 and $20, but (oddly enough) the values in the matrix don't match exactly or even very closely for any initial account.

    Anyway, here's what the table should mean: (for instance, for the value "2:1, 60%", and assuming the initial equity is $20)
    Starting with an initial $20, we perform 100 trades successively, each of which can be a winner (with probability 60%), meaning that we win $2, or a loss (with probability 40%), meaning that we lose $1. During the sequence of trades, our account fluctuates, it may even become negative. The table tell that, with probability 14%, at some time we will have less than $10 in our account.

    If instead you start with $50, you would have to redo the whole table.

    I don't think there's a formula for the values of the table. They were certainly obtained by doing computer simulations. The idea is the following: you make a program that performs lots (thousands) of random sequences of 100 trades (each of which is a win with some given probability, like 60%), and you make it compute the proportion of sequences where ruin happens (i.e. at some time between 1 and 100, the equality goes below 50% of the initial value).
    I don't know if such simulations can be done with Excel. I did it with Scilab (a free program for numeric computations), but you could use any programming langage (or a programmable calculator).
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  3. #3
    Newbie
    Joined
    May 2009
    Posts
    2
    Hello Laurent,

    Thanks for writing

    You are correct about your guesses about the book title.

    What if we say that the initial account is $100 and the risk per trade is a constant $1 dollar? Would that change anything?

    Don`t you think it is possible to deduct a formula out of this matrix?

    I do however agree with you that it is very likely that the numbers are made from a simulation.

    Either way, I am interpreting the matrix wrong in my initial thread?

    It is not a 14% probability that we would get 60 losers in a row (I thought the way the author wrote made it sound like that), but a 14% probability that during the 100 trades we would experience drawdown (less than 50% of initial equity)?

    Thanks very much in advance Laurent.

    I`ll check out Scilab, if I understand anything of it

    All the best,

    Trader

    Quote Originally Posted by Laurent View Post
    Hi,

    Using google I found this book. I guess this is the one you're refering to?

    One thing is for sure: the starting equity must be given, otherwise it makes no sense. That makes me think the author did probably not get this table himself, indeed.

    I did a few tests and it seems that it should be between $15 and $20, but (oddly enough) the values in the matrix don't match exactly or even very closely for any initial account.

    Anyway, here's what the table should mean: (for instance, for the value "2:1, 60%", and assuming the initial equity is $20)
    Starting with an initial $20, we perform 100 trades successively, each of which can be a winner (with probability 60%), meaning that we win $2, or a loss (with probability 40%), meaning that we lose $1. During the sequence of trades, our account fluctuates, it may even become negative. The table tell that, with probability 14%, at some time we will have less than $10 in our account.

    If instead you start with $50, you would have to redo the whole table.

    I don't think there's a formula for the values of the table. They were certainly obtained by doing computer simulations. The idea is the following: you make a program that performs lots (thousands) of random sequences of 100 trades (each of which is a win with some given probability, like 60%), and you make it compute the proportion of sequences where ruin happens (i.e. at some time between 1 and 100, the equality goes below 50% of the initial value).
    I don't know if such simulations can be done with Excel. I did it with Scilab (a free program for numeric computations), but you could use any programming langage (or a programmable calculator).
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