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FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility

Using EWMA with lambda = 0.97, the prior-day variance of Asset A is 0.000400, of Asset B is 0.000900, and the prior-day covariance is 0.000240. Yesterday's returns were 1.0% for A and 2.0% for B. What is the updated correlation, to three decimals?

The updated correlation is 0.406. After updating both variances (0.000391 and 0.000885) and the covariance (0.0002388) with EWMA, dividing covariance by the product of the volatilities gives a value slightly above the prior 0.400.

  1. A0.400
  2. B0.406Correct
  3. C0.420
  4. D0.388

Explanation

Cov = 0.97(0.000240)+0.03(0.0002)=0.0002388. Var A = 0.000391; Var B = 0.000885. Volatility product = sqrt(0.000391*0.000885)=sqrt(3.46035e-7)=0.00058825. Correlation = 0.0002388/0.00058825 = 0.406. The 0.400 option is the stale prior correlation.

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