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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A
0.001824
B
0.1824
C
0.228
D
0.00228
Explanation:
Explanation
This is a population variance calculation since we have data for the entire population (all 5 managers).
Step 1: Calculate the population mean (μ)
[ \mu = \frac{\sum X_i}{N} = \frac{0.24 + 0.26 + 0.30 + 0.18 + 0.20}{5} = \frac{1.18}{5} = 0.236 ]
Step 2: Calculate squared deviations from the mean
[ (0.24 - 0.236)^2 = (0.004)^2 = 0.000016 ] [ (0.26 - 0.236)^2 = (0.024)^2 = 0.000576 ] [ (0.30 - 0.236)^2 = (0.064)^2 = 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: Calculate population variance
[ \sigma^2 = \frac{\sum (X_i - \mu)^2}{N} = \frac{0.00912}{5} = 0.001824 ]
Key Points:
- This is population variance (divide by N = 5)
- For sample variance, we would divide by (n-1) = 4
- The result 0.001824 corresponds to option A
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