AuthorTopic: Proportions in Portfolio of two Assets
Duby
@2014-12-15 06:55:22
Hello,
Can you guys help me with the following:

E(R) for Fund A is 19 with Standard Devitation of 33
E(R) for Fund B is 8 with Standard Devitation of 13
The colleration between the two funds is .10.
If the investor requires a portfolio return of 12%, what should be the proportions for each fund? Actually how do you find w1 and w2, because the formula requiers the w1 and w2 figures?
paulhugan2k
@2015-01-16 00:14:57
With the basic formula for portfolios with 2 assets you can deduce a direct formula for w1 by replacing w2 = 1 - w1 as: w1 + w2 = 1

E(Rp) = w1*E(R1) + w2*E(R2)

Replacing: E(Rp) = w1*E(R1) + ( 1 - w1 )*E(R2)
-> 0.12 = w1*0.19 + ( 1 - w1 )*0.08
-> w1 = 0.364
-> w2 = 1 - w1, w2 = 0.636

Now, this is the formula to calculate weights in the point know as the global minimum-variance portfolio (the point where efficient frontier begins):

w1 = ( Variance2 - Cov1,2 ) / ( Variance1 + Variance2 - 2*Cov1,2 )

w2 = 1 - w1