FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
An analyst uses an EWMA model with lambda = 0.94 to update the covariance between two assets. The prior-day covariance estimate is 0.00020. Yesterday's returns were 2.0% for Asset X and -1.0% for Asset Y. What is the updated covariance estimate?
The EWMA update is 0.94 times the prior covariance plus 0.06 times the product of returns, giving 0.000176.
- A0.000188Correct
- B0.000194
- C0.000182
- D0.000200
Explanation
EWMA covariance: new = 0.94(0.00020) + 0.06(0.02)(-0.01) = 0.000188 + 0.06(-0.0002) = 0.000188 - 0.000012 = 0.000176. Check: 0.94*0.00020 = 0.000188; the return product is -0.0002, times 0.06 = -0.000012; sum = 0.000176. This is not among the options, so the keyed value must be reconsidered: the correct result 0.000176 is absent.
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