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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A stock follows geometric Brownian motion with expected return μ = 12% per year and volatility σ = 20% per year (continuous compounding). What is the expected continuously compounded return per year, ie the mean of ln(S_T/S_0)/T?

The expected continuously compounded return equals μ minus half the variance: 12% − 0.5×(0.20)² = 10%. The 12% figure is the expected arithmetic rate of return, not the mean of the log return, because of the Ito convexity adjustment.

  1. A12%
  2. B10%Correct
  3. C14%
  4. D8%

Explanation

The mean of the continuously compounded return is μ − σ²/2 = 0.12 − 0.04/2 = 0.12 − 0.02 = 0.10. Using 12% ignores the Ito adjustment; 14% adds the adjustment with the wrong sign.

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