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

Two assets have monthly returns that are X and Y. In a sample of 4 observations, the pairs (X,Y) are (1,2), (2,1), (3,4), (4,3) in percent. Ignoring any bias correction, which is the sample Pearson correlation, and how does it relate to Kendall's tau (concordant minus discordant pairs over 6)?

Pearson correlation is 0.60 and Kendall's tau is 0.33. Cross-deviation products sum to 3 against sums of squares of 5 each, giving 0.60. Among six pairs, four are concordant and two discordant, so tau is (4-2)/6, or 0.33.

  1. APearson 0.60; Kendall tau 0.67
  2. BPearson 0.60; Kendall tau 0.33Correct
  3. CPearson 0.80; Kendall tau 0.33
  4. DPearson 0.80; Kendall tau 0.67

Explanation

Means are 2.5 for both. Deviations X: -1.5,-0.5,0.5,1.5; Y: -0.5,-1.5,1.5,0.5. Cross products: 0.75,0.75,0.75,0.75 = 3.0 (sum). Sum of squares of X = 5, of Y = 5. Pearson = 3/5 = 0.60. Kendall: pairs (1,2) disc, (1,3) conc, (1,4) conc, (2,3) conc, (2,4) conc, (3,4) disc gives 4 concordant, 2 discordant, tau = 2/6 = 0.33.

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