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

Using EWMA with λ = 0.94 for all terms, prior variances are 0.0001 for X (1% volatility) and 0.0004 for Y (2% volatility), and the prior covariance is 0.00012 (correlation 0.60). Today X returns +2% and Y returns -1%. What is the updated correlation, to two decimals?

The updated correlation is about 0.47. After the EWMA update, the variances are 0.000118 and 0.000382 and the covariance is 0.0001008. Dividing the covariance by the square root of the variance product gives roughly 0.47, down from 0.60, because today's returns moved in opposite directions.

  1. A0.47Correct
  2. B0.50
  3. C0.59
  4. D0.60

Explanation

Var X = 0.94×0.0001 + 0.06×0.0004 = 0.000118. Var Y = 0.94×0.0004 + 0.06×0.0001 = 0.000382. Cov = 0.94×0.00012 + 0.06×(-0.0002) = 0.0001008. Correlation = 0.0001008 / sqrt(0.000118×0.000382) = 0.0001008/0.0002123 ≈ 0.47. Dividing by the old volatilities (0.0002) gives 0.50, which is wrong because the variances also update.

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