Asset 1 has an expected return of 10% and a standard deviation of 20%.Asset 2 has an expected return of 15% and a standard deviation of 30%.The correlation between the two assets is less than 1.0.You form a portfolio by investing half of your money in asset 1 and half in asset 2.Which of the following best describes the expected return and standard deviation of your portfolio?
A)The expected return is 12.5% and the standard deviation is less than 25%.
B)The expected return is between 10% and 15% and the standard deviation is greater than 30%.
C)The expected return is 12.5% and the standard deviation is 25%.
D)The expected return is 12.5% and the standard deviation is greater than 25%.

Question

Quizplus · Accepted Answer

The expected return of the portfolio can be calculated as:
Expected Return of Portfolio = 0.5 x Expected Return of Asset 1 + 0.5 x Expected Return of Asset 2
= 0.5 x 10% + 0.5 x 15%
= 12.5%
The standard deviation of the portfolio can be calculated using the formula:
Standard Deviation of Portfolio = sqrt[(0.5 x Standard Deviation of Asset 1)^2 + (0.5 x Standard Deviation of Asset 2)^2 + 2 x Correlation x Standard Deviation of Asset 1 x Standard Deviation of Asset 2]
= sqrt[(0.5 x 20%)^2 + (0.5 x 30%)^2 + 2 x Correlation x 20% x 30%]
Since the correlation between the two assets is less than 1, the third term under the square root will be less than the sum of the other two terms, resulting in a standard deviation of the portfolio that is less than 25%. Therefore, the correct answer is A.

Asset 1 Has an Expected Return of 10% and a Standard