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

nigahiga

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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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tkhunny

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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?
 

nigahiga

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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?
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 :p
 

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tkhunny

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Well, okay, but why did we do that? It's a consistent, well-defined, recursive process.

\(\displaystyle 1.125^{n} = 1,000,000 \implies n = 117.2962683\)


Did we need to draw the tree?
 
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nigahiga

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Well, okay, but why did we do that? It's a consistent, well-defined, recursive process.

\(\displaystyle 1.125^{n} = 1,000,000\implies n = 117.2962683\)

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

tkhunny

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