Financial Risk Manager Part 1

Explanation

The 95% confidence interval for the mean return is calculated using the formula:

CI = Mean return ± (t-critical × Standard error)

CI = Mean return ± (t-critical × Standard error)

Step 1: Identify the parameters

• Sample mean (μ) = 2.85% = 0.0285
• Sample standard deviation (σ) = 1.6% = 0.016
• Sample size (n) = 18
• Confidence level = 95%

Step 2: Determine degrees of freedom and critical t-value

• Degrees of freedom (df) = n - 1 = 18 - 1 = 17
• For a 95% confidence interval (two-tailed), we use α/2 = 0.025
• From the t-table: t₁₇,₀.₀₂₅ = 2.11

Step 3: Calculate standard error

Standard error = σ / √n = 0.016 / √18 = 0.016 / 4.2426 = 0.00377

Standard error = σ / √n = 0.016 / √18 = 0.016 / 4.2426 = 0.00377

Step 4: Calculate margin of error

Margin of error = t-critical × Standard error = 2.11 × 0.00377 = 0.00796

Margin of error = t-critical × Standard error = 2.11 × 0.00377 = 0.00796

Step 5: Calculate confidence interval

Lower bound = 0.0285 - 0.00796 = 0.02054
Upper bound = 0.0285 + 0.00796 = 0.03646

Lower bound = 0.0285 - 0.00796 = 0.02054
Upper bound = 0.0285 + 0.00796 = 0.03646

Therefore, the 95% confidence interval is [0.02054, 0.03646], which matches option D.

Key points:

• We use t-distribution because population variance is unknown
• Degrees of freedom = n - 1 = 17
• For 95% confidence interval, we use α/2 = 0.025 (two-tailed)
• The correct t-value from the table is 2.11