Financial Risk Manager Part 1

The rank correlation coefficient (Spearman's rank correlation) is calculated using the formula:

$\hat{\rho}_s = 1 - \frac{6 \sum_{i=1}^{n} (R_{X_i} - R_{Y_i})^2}{n(n^2 - 1)}$

First, we need to rank the X and Y values separately:

Ranking X values (ascending order):

• -0.6 (smallest) → Rank 6
• -0.5 → Rank 5
• 0.5 → Rank 4
• 1.3 → Rank 3
• 3.1 → Rank 2
• 4.3 (largest) → Rank 1

Ranking Y values (ascending order):

• -5.4 (smallest) → Rank 6
• -2.3 → Rank 5
• 2.1 → Rank 4
• 2.5 → Rank 3
• 3.0 → Rank 2
• 6.5 (largest) → Rank 1

Now we calculate the squared differences between ranks:

Now plug into the formula:

$\hat{\rho}_s = 1 - \frac{6 \times 10}{6(6^2 - 1)} = 1 - \frac{60}{6 \times 35} = 1 - \frac{60}{210} = 1 - 0.2857 = 0.7143$

Therefore, the rank correlation coefficient is 0.7143, which corresponds to option D.