Financial Risk Manager Part 1
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At a certain investment firm, each of the firm's 5 managers is tasked with overseeing a project. During a given one-year period, the managers reported the following individual returns from their projects: [24%, 26%, 30%, 18%, 20%]. Calculate the population variance of these returns.
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NNikitesh
A
0.1824%
B
18.24%
C
22.8%
D
0.228%
Explanation:
The correct answer is A (0.1824%).
Explanation:
Since the data represents the entire population of 5 managers (not a sample), we use the population variance formula:
σ² = Σ(Xᵢ - μ)² / N
Where:
- Xᵢ are the individual returns
- μ is the population mean
- N = 5 (population size)
Step 1: Calculate the mean (μ) μ = (0.24 + 0.26 + 0.30 + 0.18 + 0.20) / 5 = 1.18 / 5 = 0.236
Step 2: Calculate squared deviations from the mean (0.24 - 0.236)² = 0.004² = 0.000016 (0.26 - 0.236)² = 0.024² = 0.000576 (0.30 - 0.236)² = 0.064² = 0.004096 (0.18 - 0.236)² = (-0.056)² = 0.003136 (0.20 - 0.236)² = (-0.036)² = 0.001296
Step 3: Sum the squared deviations 0.000016 + 0.000576 + 0.004096 + 0.003136 + 0.001296 = 0.00912
Step 4: Divide by N (population size) σ² = 0.00912 / 5 = 0.001824
Step 5: Convert to percentage 0.001824 = 0.1824%
Key Points:
- Population variance divides by N (5)
- Sample variance would divide by (n-1) = 4
- The result is a variance of 0.1824%, not 18.24% (which would be off by a factor of 100)
- Options C and D are incorrect as they don't match the calculated value
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