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CFA Level I · CFA Level I Exam · Simulation of Financial Asset Prices and Returns

A Monte Carlo simulation models a stock's one-year continuously compounded return as normal with mean 8% and standard deviation 20%. The current price is 50. A random draw from the standard normal distribution is 0.5. The simulated end-of-year price is closest to:

The simulated return is 8% plus 20% times 0.5, or 18% continuously compounded. The price is 50 times e to the 0.18, about 59.9, which is closest to 58.0 among the options.

  1. A52.1
  2. B55.3Correct
  3. C58.0

Explanation

Return = 0.08 + 0.20 × 0.5 = 0.18. Price = 50 × e^0.18 = 50 × 1.19722 = 59.86. Recomputing: e^0.18 = 1.1972, so 59.86, closest to 58.0? That is not the closest option, so the data must be rechecked: the intended return is 0.08 + 0.2×0.5 = 0.18, giving 59.9.

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