How to find the minimum variance portfolio, 2 company's, 5 portfolios.

Question

Hi

 

i have found out the following

 

 

Weight in Kingsley Weight in Duvall ER SD

0.0%    100.0%  15.00     25.00
25.0%   75.0%   13.75     21.25

50.0%   50.0%   12.50     18.87
75.0%   25.0%   11.25     18.41
100.0% 0.0%     10.00     20.00

 

i would like to know the solution to the following below

 

Using the data in part (a) identify the minimum variance portfolio.
Explain the role of preferences in determining the optimum
portfolio

if anyone can help me thank you so much 

 

i would like 2 percentages for the 2 companys and 2 figures for the ERand SD, im fairly stuck on this, again thank you

 

Answer 1

A has ER of 15% with 25% std dev

B has ER 0f 10% with 20% STdev. We need to check if there is correlation

when we have 50%A and 50% B Var(A) = .25^2 = 5% and Var(B) - .20^2 or 4%.

The std of the Portfolio with equal weights is 18.87%. The Variance is thus

Var(portfolio) = 18.87^2 =3.56% = ((1/2)^2)Var(A) +((1/2)^2)Var(B) + 2 *((1/2)(1/2) Cov(AB) so 3.56% = (5%)/4 + (4%)/4 + COV (AB)/2

sooo 3.56%-2.25% = COV(AB)/2 so COV(AB) =2.62%.

The Covariance Matrix is

COV (AB) = .05 .0262

.0262 .04

The minimum variance portfolio weights are given by

w = Inverse(COV(AB) *Unit/ (Unit'Inverse(COV(AB)) Unit) where

Unit' = [ 1 1] and w' = [wa wb]

Inverse COV(AB = 30.45 -19.95

-19.95 38.06

this yields wa =36.7 and wb =63.3 this portfolio has a variance of 3.493% or std dev or 18.69% the expected return = 11.835%

If you want to plot this in excel create a table that start with the weight to A =0 ( and weight to B = 100. move the weight to A from 0 to 100% in 1% increments.

The E(r) is will be the weighted average of the 2 returns. the std dev = sqrt ((wa^2)..05 +((1-wa)^2).04) +2(wa(1-wa))*.0262)

You can create a scatterplot to graph the frontier