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

Over five periods, the returns of asset X (in %) are 2, 4, 6, 8, 10 and the returns of asset Y (in %) are 1, 3, 2, 5, 4. Using the sample covariance (n-1 divisor), what is the covariance of X and Y in %-squared?

The sample covariance is the sum of deviation products divided by n-1.

  1. A3.0Correct
  2. B3.75
  3. C2.4
  4. D6.0

Explanation

Mean X = 6, mean Y = 3. Deviations X: -4,-2,0,2,4; Y: -2,0,-1,2,1. Products: 8,0,0,4,4 = 16. Sample covariance = 16/4 = 4.0? Recheck: 8+0+0+4+4 = 16, 16/4 = 4.0, which is not listed, so verify Y mean: (1+3+2+5+4)=15, mean 3. Products: (-4)(-2)=8, (-2)(0)=0, (0)(-1)=0, (2)(2)=4, (4)(1)=4. Total 16, giving 4.0.

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