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

An analyst simulates the price of a non-dividend-paying stock over one year using a single step: S1 = S0 × exp[(μ − 0.5σ²)T + σ√T·Z]. Given S0 = 100, μ = 8%, σ = 20%, T = 1, and a random draw Z = 0.50, the simulated price is closest to:

The simulated price is about 117.36. The drift is 0.08 minus half the variance, or 0.06, and the shock is 0.20 times 0.50, or 0.10. The exponent of 0.16 gives a growth factor of about 1.1735 applied to 100.

  1. A105.13
  2. B111.63Correct
  3. C117.36

Explanation

Drift = 0.08 − 0.5(0.04) = 0.06. Shock = 0.20 × 0.50 = 0.10. Exponent = 0.16. exp(0.16) = 1.1735, so S1 = 117.35. Option 105.13 uses a drift only of 0.05 (wrong), and 111.63 omits... check: 100×exp(0.11)=111.63 arises from using drift 0.01; the correct value is 117.35.

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