Question

1. An investor is evaluating a two-asset portfolio of the following securities: Stock Expected Return Expected Risk (?) Correlation (?) Google (U.S.) 18.60% 22.80% .60 Vodafone (U.K.) 16.00% 24.00%

a. If the two securities have a correlation of .60 what is the expected risk and return for a portfolio that is equally weighted?

b. If the two securities have a correlation of .60 what is the expected risk and return for a portfolio that is 70% Google and 30% Vodafone?

c. Which of the portfolios is preferable? On what basis?

Answer 1

	Expected Return	Expected Risk
Google	18.60%	22.80%
Vodafone	16%	24%

Correlation Coefficient between two is 0.60.

Expected return and Standard deviation of a portfolio with two stocks is calculated as follows:

a) w1 (Google) = 50%, w2 (Vodafone) = 50%

Expected return, using above formula = 50% * 18.6% + 50% * 16% = 17.30%

Standard Deviation of portfolio =

= 20.93%

(b) w1 (Google) = 70%, w2 (Vodafone) = 30%

Expected return, using above formula = 70% * 18.6% + 30% * 16% = 17.82%

Standard Deviation of portfolio =

= 21.08%

c. In order to assess, which portfolio is better, we should measure return earned per unit of risk taken.

=> For portfolio in (a), return per unit of risk = 17.3%/20.93% = 0.826

=> For portfolio in (b), return per unit of risk = 17.82%/21.08% = 0.845

Since portfolio in (b) offers more return per unit of risk, go for that. For same amount (unit of risk) taken, a rational investor would want to maximize his/her return.