Financial Risk Manager Part 1

Explanation

To calculate the 99% confidence interval for the quarterly returns, we use the formula:

Standard error of the sample mean = $\frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}}$

Given:

• Sample size (n) = 121
• Standard deviation (σ) = 8% = 0.08
• Sample mean (x̄) = 1.5% = 0.015
• 99% confidence level

Step 1: Calculate standard error $SE = \frac{0.08}{\sqrt{121}} = \frac{0.08}{11} = 0.00727$

Step 2: Find critical z-value For 99% confidence interval, the critical z-value is 2.575

Step 3: Calculate margin of error $Margin\ of\ error = z \times SE = 2.575 \times 0.00727 = 0.0187$

Step 4: Calculate confidence interval $CI = x̄ \pm margin\ of\ error = 0.015 \pm 0.0187$ $Lower\ bound = 0.015 - 0.0187 = -0.0037 = -0.37\%$ $Upper\ bound = 0.015 + 0.0187 = 0.0337 = 3.37\%$

Therefore, the 99% confidence interval is approximately [-0.37%; 3.37%], which matches option A [-0.4%; 3.4%].