Answer: -0.2

## Calculation of Kendall's τ Correlation Coefficient Kendall's τ measures the ordinal association between two variables. It is calculated as: τ = (number of concordant pairs - number of discordant pairs) / (total number of pairs) ### Step 1: List the data pairs - Year 1: (3, 8) - Year 2: (1, 5) - Year 3: (-4, 6) - Year 4: (5, 2) - Year 5: (2, 9) ### Step 2: Compare all pairs Total number of pairs = C(5,2) = 10 **Concordant pairs** (both variables move in same direction): - (3,8) vs (1,5): X decreases (3→1), Y decreases (8→5) → Concordant - (3,8) vs (-4,6): X decreases (3→-4), Y decreases (8→6) → Concordant - (3,8) vs (5,2): X increases (3→5), Y decreases (8→2) → Discordant - (3,8) vs (2,9): X decreases (3→2), Y increases (8→9) → Discordant - (1,5) vs (-4,6): X decreases (1→-4), Y increases (5→6) → Discordant - (1,5) vs (5,2): X increases (1→5), Y decreases (5→2) → Discordant - (1,5) vs (2,9): X increases (1→2), Y increases (5→9) → Concordant - (-4,6) vs (5,2): X increases (-4→5), Y decreases (6→2) → Discordant - (-4,6) vs (2,9): X increases (-4→2), Y increases (6→9) → Concordant - (5,2) vs (2,9): X decreases (5→2), Y increases (2→9) → Discordant ### Step 3: Count concordant and discordant pairs - Concordant pairs: 4 - Discordant pairs: 6 ### Step 4: Calculate τ τ = (4 - 6) / 10 = -2 / 10 = -0.2 Therefore, Kendall's τ correlation coefficient is **-0.2**, indicating a weak negative correlation between the returns of Asset X and Asset Y.

Author: Tanishq Prabhu