Explanation:
To calculate the interquartile range (IQR), we need to find the difference between the third quartile (Q3) and the first quartile (Q1).
Step 1: Arrange the data in ascending order The Sharpe ratios are already sorted: 0.2, 0.6, 0.7, 0.9, 1.0, 1.4, 1.6
Step 2: Find the position of Q1 (25th percentile) For n = 7 observations: Position of Q1 = (n + 1) × 0.25 = 8 × 0.25 = 2 So Q1 is the 2nd observation: 0.6
Step 3: Find the position of Q3 (75th percentile) Position of Q3 = (n + 1) × 0.75 = 8 × 0.75 = 6 So Q3 is the 6th observation: 1.4
Step 4: Calculate IQR IQR = Q3 - Q1 = 1.4 - 0.6 = 0.8
Step 5: Match with options The IQR of 0.8 corresponds to option B.
Verification:
Therefore, the interquartile range of the Sharpe ratios is closest to 0.8.
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An analyst gathers the following data on the Sharpe ratios of seven portfolios:
| Portfolio | Sharpe Ratio |
|---|---|
| 1 | 0.2 |
| 2 | 0.6 |
| 3 | 0.7 |
| 4 | 0.9 |
| 5 | 1.0 |
| 6 | 1.4 |
| 7 | 1.6 |
The interquartile range of the Sharpe ratios is closest to:
A
0.6.
B
0.8.
C
1.4.