Re: Asset Allocation
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i don't see how diversifying can increase EV. i am pretty sure it can maintain or nearly maintain EV at less risk though.
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Alright math geek. The arithmetic mean would stay the same but the geometric mean can be raised using diversification. Thus the ending wealth will be increased.
If you have investment A that has a 20% return in even years and a 0% return in odd years, the arithmetic return is 10%. Then you have investment B that has a 0% return in even years and a 20% return in odd years, with the same arithmetic return is 10%. However, the correlation is -1 - completely uncorrelated.
The geometric average of investment A and investment B is 8.15%. However, a portfolio of 50% A and 50% B has a geometric average of 8.25%
After 4 years of investment A or investment B, $1 would grow to $1.44. 4 years of 50% A 50% B grows to $1.46.
Booyah!
-Ton
[/ QUOTE ]ummmmm no...
i could be wrong but i don't think i am. you are making some mistakes in your math. first of all investment A and B don't have the same EV. if you end on year 2N+1, the A portfolio is greater than the B portfolio. if you end on year 2N, then the portfolios are equal in value. (nottice invoking that this is an infinite series doesn't help your case, the holding period is finite, people's lives are finite)
furthermore, unless i doing the math wrong a half A half B portfolio really would be worth 1.44 after 4 years.
if i am wrong, i would honestly like you to point it out because i have an interest in this kind of math.
i think ultimately you are confusing the concept of expected value and you are using some 'fuzzy math' it appears.
also, 0 correlation means completely uncorrelated. and in fact these two investments are correlated, postively.
what's wrong with this?
invest 1 dollar in A and 1 dollar in B (50-50 allocation you mentioned).
YEAR 1
A is worth 1.2
B is worth 1
YEAR 2
A is worth 1.2
B is worth 1.2
Year 3
A is worth 1.44
B is worth 1.2
Year 4
A is worth 1.44
B is worth 1.44
so after 4 years, 44% return from A, 44% return from B, 44% return from .5A and .5B
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