Final answer:
The correct answer is option d. 16.23%.
Step-by-step explanation:
To find the standard deviation of the combined portfolio, we need to use the formula for the standard deviation of a portfolio:
σp = √(w12σ12 + w22σ22 + 2w1w2ρσ1σ2)
Where:
- σp is the standard deviation of the combined portfolio
- w1 and w2 are the weights of the investments (proportions of the total assets)
- σ1 and σ2 are the standard deviations of the investments
- ρ is the correlation coefficient between the investments
In this case, Mary has invested $9,600 in the Metro Doughnut Company and the remainder ($12,000 - $9,600 = $2,400) in the Safe Bond Fund. The weights are therefore 0.8 and 0.2 respectively. From the information given, we know that the correlation between the two investments is positive and the Safe Bond Fund explains 4% of the returns for the Metro Doughnut Company, which means ρ = 0.04. The standard deviation of the Metro Doughnut Company is 20% and the Safe Bond Fund has a standard deviation of 596.
Plugging in the values into the formula:
σp = √((0.8)2(20)2 + (0.2)2(596)2 + 2(0.8)(0.2)(0.04)(20)(596))
σp = √(256 + 14208 + 1913.6) ≈ 144.4415 ≈ 14.44%
Therefore, the standard deviation of the combined portfolio is approximately 14.44%.
The closest answer choice is Option d. 16.23%.