An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 5% and she puts 30% in a Treasury bill that pays 5%.Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively.
A) 10.0%, 6.7%
B) 12.0%, 22.4%
C) 12.0%, 15.7%
D) 10.0%, 35.0%

Question

Quizplus · Accepted Answer

To find the portfolio's expected rate of return, we use the weighted average of the expected returns of each asset.

Expected portfolio return = (0.70 x 15%) + (0.30 x 5%) = 10.5%

To find the portfolio's standard deviation, we need to calculate the variance of the portfolio first.

Variance of portfolio = (0.70^2 x 5%) + (0.30^2 x 0%) + 2(0.70 x 0.30 x 0%) 
= 0.245%

Standard deviation of portfolio = √0.245% = 15.7%

Therefore, the answer is C.

An Investor Invests 70% of Her Wealth in a Risky