Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard deviation of returns of 20% and a risk-free asset with an interest rate of 4%; calculate the standard deviation of the returns on the resulting portfolio:
A) 8%
B) 10%
C) 20%
D) none of the above

Question

Quizplus · Accepted Answer

To calculate the standard deviation of the portfolio, we use the formula:
σp = sqrt(w1^2 x σ1^2 + w2^2 x σ2^2 + 2w1w2ρσ1σ2)
where:
- σp is the standard deviation of the portfolio
- w1 and w2 are the weights of the two assets (in this case, they are equal)
- σ1 and σ2 are the standard deviations of the two assets
- ρ is the correlation coefficient between the returns of the two assets (which is assumed to be zero in this case, since no correlation information is given)

Substituting the given values, we get:
σp = sqrt(0.5^2 x 0.20^2 + 0.5^2 x 0^2 + 2 x 0.5 x 0.5 x 0 x 0.20)
   = sqrt(0.01)
   = 0.1 or 10%

Therefore, the correct answer is B) 10%.

Suppose You Invest Equal Amounts in a Portfolio with an Expected