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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

Two assets have returns X and Y. A risk manager observes the following ranks for five paired observations (rank of X, rank of Y): (1,2), (2,1), (3,3), (4,5), (5,4). 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 equals 1 minus 0.20. This measures monotonic association using ranks rather than raw values.

  1. A0.60
  2. B0.80
  3. C0.90Correct
  4. D1.00

Explanation

Rank differences d are -1, 1, 0, -1, 1, so the sum of d squared is 4. Spearman = 1 - 6*4/(5*(25-1)) = 1 - 24/120 = 0.80. Check: 6*4=24, n(n^2-1)=5*24=120, so 0.80. The 0.90 option is wrong because it would imply a sum of squared differences of 2.

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