FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
The VIX index is quoted as 24.0. Using the standard interpretation of VIX as an annualized volatility of S&P 500 returns over the next 30 days, and assuming 252 trading days per year and 21 trading days in the 30-day period with the square-root-of-time rule, what is the approximate one-month (21-trading-day) standard deviation of S&P 500 returns implied by VIX?
The implied one-month standard deviation is about 6.93%. Scale the annualized 24% by the square root of the time fraction, 21/252 = 1/12, giving 24% × 0.2887. Simply dividing by 12 would wrongly give 2.00%, since volatility scales with the square root of time.
- A2.00%
- B6.93%Correct
- C24.00%
- D1.51%
Explanation
One-month sd = 24% × sqrt(21/252) = 24% × sqrt(1/12) = 24% × 0.28868 = 6.93%. Dividing by 12 instead of its square root gives 2.00%, a common error. Using 24% ignores horizon scaling.
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