FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
Two return series have the following ranks over five periods. Series A ranks: 1, 2, 3, 4, 5. Series B ranks over the same periods: 2, 1, 4, 3, 5. Using the formula rho_s = 1 - 6*sum(d^2)/(n(n^2-1)), what is the Spearman rank correlation?
The Spearman rank correlation is 0.80. The squared rank differences sum to 4, so rho equals 1 minus 6 times 4 divided by 5 times 24, which is 1 minus 0.2, or 0.80.
- A0.60
- B0.80
- C0.90Correct
- D0.70
Explanation
Rank differences are -1, 1, -1, 1, 0, so squared differences sum to 4. rho = 1 - 6*4/(5*24) = 1 - 24/120 = 0.80. Check: 24/120 = 0.2, so 0.80. The 0.90 option is wrong, so recompute: the answer is 0.80.
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