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FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology

Five paired observations of two assets' returns have the following ranks: asset A ranks 1,2,3,4,5 and asset B ranks 2,1,4,3,5 respectively. Using the Spearman formula 1 - 6*sum(d^2)/(n(n^2-1)), what is the Spearman rank correlation?

The Spearman rank correlation is 0.80. The rank differences are plus or minus one for four pairs and zero for one, so the sum of squared differences is 4. Applying one minus six times four divided by five times twenty-four gives one minus 0.20, or 0.80.

  1. A0.60
  2. B0.80
  3. C0.90Correct
  4. D0.40

Explanation

Rank differences are -1, 1, -1, 1, 0, so d^2 sums to 4. Spearman = 1 - 6*4/(5*24) = 1 - 24/120 = 0.80. Wait check: 5*(25-1)=120, 24/120=0.20, giving 0.80. The 0.90 figure would result from using sum d^2 = 2, a miscount.

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