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Math Help - investment problem

  1. #1
    Newbie
    Joined
    Oct 2011
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    2

    investment problem

    you have two dependent investments
    investment A 20a .7
    investment B 20b .3
    a=how much you invest in A
    b=how much you invest in B
    both investments pay 20 times your money
    investment A will succed .7 and if it fails investment B succeds
    so,
    Investment A .7
    Investment B .3

    If you did this experiment an infinite number of times your expected value is
    E=.7(20a)+.3(20b)
    E= 14a+6b
    so,
    All your money should go with A even if A only succeded 51% of the time.

    but say I gave you 100$
    and I said this experiment will only be run one time.
    it would not be very smart to invest it all in A for there is a .3 chance you will go broke. (you don't want that to happen)
    So how would you invest your money? and why?

    what about if i ran the experiment 2 times or 3 or 4

    thanks
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  2. #2
    Junior Member
    Joined
    Sep 2011
    Posts
    58

    Re: investment problem

    Your payoffs for the investment are huge so you can guarantee a no loss investment if you put $95 In A and 5 in B and worst case scenario is that A fails and therefore B succeeds so you get your $100 back. If you were risk adverse you might just take the guaranteed profit by putting more than $5 in B. For example, if you split is 90-10 you can't possibly lose under your assumptions.

    To maximize profits you would still put it all in A but your point is that you have no minimized your losses. You can guarantee to walk away with 1000 by splitting 50-50 into A and B because no matter what happens one investment pays off 20*50 and thus you've turned your 100 into 1000.

    (I am assuming that you meant if A fails then B succeeds and if B fails then A succeeds)
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  3. #3
    Newbie
    Joined
    Oct 2011
    Posts
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    Re: investment problem

    so assuming the experiment is run once 50/50 is best.
    so it does not matter the probabilities of success and failer, all that matters is that if one fails the other succeeds. so even if the prob are .95 for A and .05 for B 50/50 is your best bet since it minimizes your loss.
    so 50/50 would still be best no matter what the prob are right?
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