Explanation:
86. Solution: C
The following table provides the ranking of pairs with respect to X.
| Year | X | Y | X Rank | Y Rank |
|---|---|---|---|---|
| 2013 | -20.0% | 40.0% | 1 | 5 |
| 2012 | -10.0% | 20.0% | 2 | 4 |
| Year | X | Y | X Rank | Y Rank |
|---|---|---|---|---|
| 2010 | 5.0% | -10.0% | 3 | 1 |
| 2014 | 30.0% | 15.0% | 4 | 3 |
| 2011 | 50.0% | -5.0% | 5 | 2 |
There are two concordant pairs and eight discordant pairs shown as follows:
Concordant Pairs:
{(3,1),(4,3)}; {(3,1),(5,2)}
Discordant Pairs:
{(1,5),(2,4)}; {(1,5),(3,1)}; {(1,5),(4,3)}; {(1,5),(5,2)}; {(2,4),(3,1)}; {(2,4),(4,3)}; {(2,4),(5,2)}; {(4,3),(5,2)}
Thus, the Kendall τ correlation coefficient is -0.6.
Ultimate access to all questions.
A risk manager gathers five years of historical returns to calculate the Kendall τ correlation coefficient for stocks X and Y. The stock returns for X and Y from 2010 to 2014 are as follows:
| Year | X | Y |
|---|---|---|
| 2010 | 5.0% | -10.0% |
| 2011 | 50.0% | -5.0% |
| 2012 | -10.0% | 20.0% |
| 2013 | -20.0% | 40.0% |
| 2014 | 30.0% | 15.0% |
What is the Kendall τ correlation coefficient for the stock returns of X and Y?
A
-0.3
B
-0.2
C
-0.6
D
0.4
