Question

Mr. Lowe wants to add Third Corp. to his portfolio. His actual portfolio consists of First Corp and Second Corp with weights of 40% and 60% respectively. That portfolio has a  ? (rho) of .7.
When he adds Third Corp, he wants the portfolio to have 50% weight of Third Corp and the rest in First and Second Corp in their original weights. The portfolio of the 3 companies would have a  ?= -.25.

The following table has the financial data for the 3 companies.

Company	Average Return	Weight	?
First Corp	10%	40%	20.00
Second Corp	16%	60%	27.50
Third Corp	18%	50%	31.00

What is the expected return of the new portfolio with the 3 companies?

What is the standard deviation of new portfolio with the 3 companies?

Answer 1

Scenario after addition of Third Corp in the portfoio:

Company	Average Return, Ri	Weight, Wi	?i
First Corp	10%	20%	20.00%
Second Corp	16%	30%	27.50%
Third Corp	18%	50%	31.00%

The expected return of the new portfolio with the 3 companies

= 20% x 10% + 30% x 16% + 50% x 18%

= 15.80%

Variance of new portfolio with the 3 companies

= (20% x 20.00%)2 + (30% x 27.50%)2 + (50% x 31.00%)2 + 2 x (-0.25) x (20% x 20.00% x 30% x 27.50% + 30% x 27.50% x 50% x 31.00% + 50% x 31.00% x 20% x 20.00%)

= 0.0212875

Hence, the standard deviation of new portfolio with the 3 companies

= Variance1/2 = 0.02128751/2 = 14.59%