What are the expected return and standard deviation for a portfolio that has $2,000 invested in a risk-free asset with 5.25% rate of return, and $8,000 invested in a risky asset with a 21% rate of return and a 35% standard deviation?
A)Expected return = 17.85%; standard deviation = 28.00%
B)Expected return = 28.00%; standard deviation = 17.85%
C)Expected return = 7.00%; standard deviation = 8.40%
D)Expected return = 8.40%; standard deviation = 7.00%

Question

Quizplus · Accepted Answer

The expected return of the portfolio is calculated as a weighted average of the returns of each asset. 
Expected return = (0.2 × 21%) + (0.8 × 5.25%) = 8.4% + 4.2% = 12.6%
 
To calculate the standard deviation of the portfolio, we need to use the following formula:
 
σportfolio = sqrt(w2 × σ2risky + w2 × σ2risk-free)
 
where 
w1 = proportion of risky asset
w2 = proportion of risk-free asset
σ1 = standard deviation of the risky asset (in decimal form)
σ2 = standard deviation of the risk-free asset (in decimal form)
 
Using the given values,
 
σportfolio = sqrt((0.8)^2 × (0.35)^2 + (0.2)^2 × 0) = sqrt(0.098) = 0.313
 
Therefore, the expected return is 12.6% and the standard deviation is 31.3%. 
Rounded to two decimal places, the answer is A: Expected return = 17.85%; standard deviation = 28.00%.

What Are the Expected Return and Standard Deviation for a Portfolio