Financial Risk Manager Part 1

Explanation

The correct answer is C (2,725). Here's the detailed calculation:

Step 1: Sort the Data The profits in ascending order are: $2,600, $2,700, $2,800, $3,800, $4,300, $9,900

Step 2: Assign Percentiles Using the method where we anchor the first observation at 0% and the last at 100%, with equally spaced in-between values:

• 0% - $2,600
• 20% - $2,700
• 40% - $2,800
• 60% - $3,800
• 80% - $4,300
• 100% - $9,900

Step 3: Locate the 25% Quantile The 25% quantile falls between the 20% and 40% points, which correspond to $2,700 and $2,800 respectively.

Step 4: Linear Interpolation

• The difference between 40% and 20% is 20 percentage points
• The difference between the corresponding values is $2,800 - $2,700 = $100
• The 25% quantile is 5 percentage points above the 20% point (25% - 20% = 5%)
• Proportion of the interval: 5% / 20% = 0.25
• Value at 25% = $2,700 + (0.25 × $100) = $2,700 + $25 = $2,725

Therefore, the 25% quantile of the profits is $2,725.