Question 1
Multiple Choice
Confidence Level
0%
An analyst records the following annual returns for a portfolio:
Year | Return (%) |
|---|---|
1 | 5% |
2 | 6% |
3 | 2% |
4 | 1% |
5 | 3% |
If the target return is 4%, the target downside deviation is closest to:
Explanation
Target downside deviation considers only returns below or equal to the target, and is calculated using:
σ _{d} = √ \frac{1}{n} \sum_{}^{} (B - X) ^{2}
Where:
B = 4% (target return)
X = returns less than or equal to 4%
n = 5 (total number of periods)
Step 1: Identify returns below or equal to 4%:
Year | Return (%) | Deviation (B − X) | Squared Deviation |
|---|---|---|---|
3 | 2% | 2% | 4 |
4 | 1% | 3% | 9 |
5 | 3% | 1% | 1 |
Sum of squared deviations = 4 + 9 + 1 = 14
Step 2: Plug into formula:
σ _{d} = √ \frac{14}{5} = 1.673