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Old 02-22-2007, 07:05 PM
almostbusto almostbusto is offline
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Join Date: Mar 2006
Location: unemployed
Posts: 1,262
Default Re: Asset Allocation

i don't see how diversifying can increase EV. i am pretty sure it can maintain or nearly maintain EV at less risk though.


let x,y have Ev=3
Ex=3
Ey=3
E(.5x)+E(.5y)= .5Ex+.5Ey=3

so it doesn't matter how you split up your money across x and y EV is the same. however variance MAY (in the real world, definitely) be reduced.

let varx=vary=4
Var(.5x + .5y)=.25varx+.25vary+.5cov(x,y)

if x and y are independent then cov(x,y)=0
if they are actually the same variable then cov(x,y)=cov(x,x)=varx and variance is maintained
if they are negatively correlated then cov is negative which is even better than them being independent.

so, there you go.

EDIT: i would also consider your portfolio to be conservative FWIW. you are very diversified and long term returns from bonds and reits (the reit part might be arguable, i am not sure) will be lower than a diversified portfolio consisting entirely of stocks.

personally i believe you can be totally diversified and still have all your assets in one class. this isn't true for all asset classes however.

finally, just to clarify if anything is unclear. if you only care about maximizing EV you would invest all your money into the one asset with the highest EV. if there are two asset choices that tie for highest EV (ie in the real world, the difference between the two asset's estimated EV is not statistically significant) then of course you would split up your money between the two.
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