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Thread: Minimum days until expected values reach $1,000,000?

  1. #1
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    Minimum days until expected values reach $1,000,000?

    Given the left page scenario, what is the minimum number of days until the expected value rebalances to $1,000,000?
    The diagram on the right demonstrates pictorially how expected values are calculated per day iteration
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    Awesome problem. There is much to consider, here. Why don't you share with us some of what you have considered?

    Thought Question: with a .5 + .25 * 2 + .25 * (1/2) = .5 + .5 + .125 = 1.125 daily expected portfolio growth, are we SURE to get anywhere?
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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    Quote Originally Posted by tkhunny View Post
    Awesome problem. There is much to consider, here. Why don't you share with us some of what you have considered?

    Thought Question: with a .5 + .25 * 2 + .25 * (1/2) = .5 + .5 + .125 = 1.125 daily expected portfolio growth, are we SURE to get anywhere?
    Hey! I believe I have solved it. I calculated the expected values at the first three consecutive days, and derived a sequence formula for the nth expected value. Then I set it equal to 1,000,000 and voila! I got around n≈117.29 which rounds up to 118 days.

    Confirmation or flat-out rejection of my proposed solution would be appreciated
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    Well, okay, but why did we do that? It's a consistent, well-defined, recursive process.

    [tex]1.125^{n} = 1,000,000 \implies n = 117.2962683[/tex]


    Did we need to draw the tree?
    Last edited by mmm4444bot; 02-10-2018 at 03:27 AM. Reason: LaTex fix
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  5. #5
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    Quote Originally Posted by tkhunny View Post
    Well, okay, but why did we do that? It's a consistent, well-defined, recursive process.

    [tex]1.125^{n} = 1,000,000\implies n = 117.2962683[/tex]

    Did we need to draw the tree?
    Wow, stumped. That's amazing... I need to study more.

  6. #6
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    Quote Originally Posted by nigahiga View Post
    Wow, stumped. That's amazing... I need to study more.
    Keep up the good work. Remember my signature.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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