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CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns

An analyst simulates a stock's price over one year using continuously compounded returns that are normally distributed with a mean of 8% and a standard deviation of 20%. The current price is 50. A random standard normal draw of 0.5 is generated. The simulated end-of-year price is closest to:

The simulated price is about 59.86, which is closest to 60.80. The continuously compounded return is 8% plus 20% times 0.5, which is 18%. Multiplying the starting price of 50 by e raised to 0.18 gives roughly 59.86.

  1. A55.26
  2. B58.09Correct
  3. C60.80

Explanation

Return = 0.08 + 0.20 x 0.5 = 0.18. Price = 50 x e^0.18 = 50 x 1.19722 = 59.86. This is closest to 60.80, not 58.09. Check the distractors: 50 x 1.18 = 59.00 is the simple-return error; 50 x e^0.08 x ... is not used. So the key is 60.80? Closest to 59.86 is 58.09 (diff 1.77) versus 60.80 (diff 0.94), so 60.80.

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