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FRM Part I · FRM Exam Part I · Exotic Options

Over five days, an asset has daily log returns of +1%, −2%, +1%, −1% and +1%. Realized variance for a variance swap is computed assuming a zero mean, by averaging the squared daily returns over n = 5 observations and annualizing with 252 days. Which is the annualized realized volatility, to two decimals?

Annualized realized volatility is 20.08%. The squared returns sum to 8, the average is 1.6, annualizing by 252 gives 403.2, and the square root is 20.08%. Dividing by four instead of five, or skipping annualization, gives the wrong figures.

  1. A20.08%Correct
  2. B22.45%
  3. C1.26%
  4. D44.90%

Explanation

Sum of squared returns = 1 + 4 + 1 + 1 + 1 = 8 (%²). Dividing by 5 gives a daily variance of 1.6, and multiplying by 252 gives 403.2. The square root is 20.08%. Dividing by n−1 = 4 gives 22.45%, the sample-variance mistake. Skipping annualization gives 1.26%. Multiplying the sum by 252 without averaging gives 44.90%.

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