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

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• 02-08-2018, 06:57 PM
nigahiga
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
• 02-09-2018, 07:06 AM
tkhunny
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?
• 02-09-2018, 03:58 PM
nigahiga
Quote:

Originally Posted by tkhunny
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
• 02-09-2018, 05:34 PM
tkhunny
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?
• 02-09-2018, 05:55 PM
nigahiga
Quote:

Originally Posted by tkhunny
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.
• 02-09-2018, 11:21 PM
tkhunny
Quote:

Originally Posted by nigahiga
Wow, stumped. That's amazing... I need to study more.

Keep up the good work. Remember my signature. :-)