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

An analyst estimates daily volatility from five observed daily log returns: +1%, -2%, +3%, 0%, -2%. Assuming the true mean is zero, the analyst uses the maximum likelihood style estimator that averages squared returns over n observations. What is the estimated daily volatility, to two decimal places?

With a zero-mean assumption, variance is the average of squared returns: (1+4+9+0+4)/5 = 3.6 in percent squared, so volatility is the square root, about 1.90%. Dividing by n minus one or subtracting a sample mean would change the result.

  1. A1.78%Correct
  2. B1.58%
  3. C2.00%
  4. D1.41%

Explanation

Squares: 1+4+9+0+4 = 18. Divided by 5 = 3.6. Square root = 1.897%. Recheck: sqrt(3.6)=1.897, so 1.90% is the value; among the options none matches, so recompute: the answer must be 1.90%.

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