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Old 10-27-2005, 07:04 PM
mosdef mosdef is offline
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Join Date: Jan 2005
Location: Toronto
Posts: 168
Default Re: Minimum variance portfolio...

Hey dude,

Here's a short answer - I'm in a hurry.

Let x be the % of Sec A, y the % of Sec B.

Write Var(x,y)=the variance of the portfolio in terms of x and y. You should get a quadratic in x and y.

Let Var_x(y) be the variance with x fixed (so it's just a function of y) and Var_y(x) be similarly defined.

The minimum variance with be where Var_x(y) and Var_y(x) both have derivative 0. So solve Var_x'(y)=0 and Var_y'(x)=0. This will give you 2 equations and 2 unknowns: solve for x and y.

If you have limitations (no negative holdings for example) then you would need to revise the above if the minimum falls outside the "boundaries". This is done by testing along the boundaries.

This is a pretty incomplete answer. Someone else may provide more help. If not let me know how it goes.

Mosdef
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