CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
A stock's continuously compounded returns are 6% in the first year and -2% in the second year, with an initial price of 50. Assuming no dividends, the price at the end of year two is closest to:
Continuously compounded returns are additive over time, so the two-year return is 6% minus 2%, or 4%. The ending price is 50 × e^0.04, which is about 52.04. Treating the returns as simple rates or ignoring the sum gives wrong values.
- A50.00
- B52.04Correct
- C52.55
Explanation
Continuously compounded returns add across periods: 6% - 2% = 4%. Price = 50 × e^0.04 = 50 × 1.04081 = 52.04. The 52.55 value multiplies simple growth factors (1.06 × 0.98 would give 51.94, and 50 × e^0.06 × 1.02 style errors give higher figures), and 50.00 ignores growth.
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