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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TTanishq

0.001824

0.1824

0.228

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