Financial Risk Manager Part 1

Explanation

Kendall's tau (τ) is a measure of rank correlation that assesses the strength and direction of the relationship between two variables. The formula for Kendall's tau is:

$\tau = \frac{(n_c - n_d)}{\frac{n(n - 1)}{2}}$

Where:

• $n_c$ = number of concordant pairs
• $n_d$ = number of discordant pairs
• $n$ = number of observations

Given data:

• Time period: 2012 to 2016 (5 years)
• Number of observations (n) = 5
• Concordant pairs (n_c) = 2
• Discordant pairs (n_d) = 8

Calculation:

First, calculate the total number of possible pairs: $\frac{n(n-1)}{2} = \frac{5 \times 4}{2} = 10$

Now apply the Kendall's tau formula: $\tau = \frac{(2 - 8)}{10} = \frac{-6}{10} = -0.6$

Interpretation:

• A τ value of -0.6 indicates a moderately strong negative correlation
• This means that when one asset's rank increases, the other asset's rank tends to decrease
• The negative sign indicates an inverse relationship between the two assets

Therefore, the closest value to the Kendall τ is -0.6.