FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
Ranks of five paired observations of two assets' monthly returns are: Asset A ranks 1,2,3,4,5 and Asset B ranks 2,1,4,3,5 for the same months. What is the Spearman rank correlation?
The Spearman rank correlation is 0.80. The squared rank differences sum to 4, so the statistic is 1 minus 6 times 4 divided by 5 times 24, which is 1 minus 0.20.
- A0.60
- B0.80
- C0.90Correct
- D1.00
Explanation
Rank differences are -1, 1, -1, 1, 0, so squared differences sum to 4. Spearman = 1 - 6 x 4 / (5 x (25 - 1)) = 1 - 24/120 = 0.80. Check: 24/120 = 0.20, giving 0.80, so the correct choice is 0.80.
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