FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A non-dividend-paying stock has μ = 9% and σ = 30% per annum. Over a 4-year horizon, what is the standard deviation of the continuously compounded return (ln(S_T/S_0)) under BSM assumptions?
The standard deviation is σ√T = 30% × √4 = 60%. Volatility scales with the square root of time, not linearly, because variance of the log return grows proportionally to the horizon under geometric Brownian motion.
- A30%
- B60%Correct
- C120%
- D7.5%
Explanation
The variance of ln(S_T/S_0) is σ²T = 0.09 × 4 = 0.36, so the standard deviation is 0.60 or 60%. Option A ignores the horizon. Option C multiplies σ by T instead of √T. Option D divides σ by T.
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