Explanation:
B: -0.2
Explanation of Kendall’s τ calculation:
Kendall’s τ (tau) is a rank-based correlation coefficient that counts concordant and discordant pairs.
Formula:
where:
Step 1: List the returns (no ties present)
Step 2: Classify all 10 pairs
Concordant pairs (both move in same direction):
Discordant pairs (move in opposite directions):
Step 3: Compute τ
This negative value indicates a weak negative ordinal association between the returns of asset X and asset Y.
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A portfolio manager is trying to determine the correlation between the return of two assets. Given the following data about the yearly returns of the stocks, he decides to calculate the Kendall's τ correlation coefficient for the returns of these assets.
| Year | Return of asset X | Return of asset Y |
|---|---|---|
| 1 | 3% | 8% |
| 2 | 1% | 5% |
| 3 | -4% | 6% |
| 4 | 5% | 2% |
| 5 | 2% | 9% |
Calculate Kendall's τ correlation coefficient for the returns of the two assets.
A
-0.1
B
-0.2
C
0
D
0.1