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

Which statement best explains why continuously compounded returns are often used to model asset returns over multiple periods?

Continuously compounded returns are additive across periods, and when they are normally distributed, the resulting prices are lognormal and cannot be negative. This makes multi-period modeling tractable. They do not exceed holding period returns for gains, nor remove volatility effects.

  1. AThey are additive across periods and consistent with lognormal prices.Correct
  2. BThey always exceed the holding period return for the same price change.
  3. CThey eliminate the effect of volatility on terminal prices.

Explanation

Log returns sum across periods, and if they are normally distributed, prices are lognormal and stay positive. Log returns are actually lower than the holding period return for positive changes, and they do not remove volatility effects.

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