You put half of your money in a share portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of you money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The share and bond portfolio have a correlation 0.55. The standard deviation of the resulting portfolio will be ________.
A)more than 18% but less than 24%
B)equal to 18%
C)more than 12% but less than 18%
D)equal to 12%

Question

Quizplus · Accepted Answer

To find the standard deviation of the resulting portfolio, we need to use the formula:

σᵣ = sqrt(w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂)

where 
w₁ and w₂ are the weights of the share and bond portfolio respectively, 
σ₁ and σ₂ are the standard deviations of the share and bond portfolio respectively, 
ρ is the correlation between the two portfolios.

Here, w₁ = w₂ = 0.5 (since the money is equally divided), 
σ₁ = 24%, σ₂ = 12%, 
and ρ = 0.55.

Plugging in these values, we get:

σᵣ = sqrt(0.5²(24%)² + 0.5²(12%)² + 2(0.5)(0.5)(0.55)(24%)(12%))
   ≈ 16.64%

Therefore, the standard deviation of the resulting portfolio will be more than 12% but less than 18%. The closest answer choice is (C).

You Put Half of Your Money in a Share Portfolio