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CMA Final · Strategic Financial Management · Risks in Financial Market

A stock has a daily return standard deviation of 1.5%. A trader uses the square-root-of-time rule to scale this to a 16-trading-day horizon. The 16-day standard deviation, in percent, is:

The 16-day standard deviation is 6.0%. Assuming independent daily returns, volatility scales with the square root of time, so the daily 1.5% is multiplied by the square root of 16, which is 4, rather than by 16 itself.

  1. A6.0%Correct
  2. B24.0%
  3. C1.5%
  4. D3.0%

Explanation

Under the square-root-of-time rule, the 16-day SD = 1.5% × √16 = 1.5% × 4 = 6.0%. Option B multiplies by 16, wrongly treating volatility as growing linearly with time. Option D uses √4 incorrectly.

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