Are asset returns really Gaussian
Question
How reasonable is it to model asset returns as normally distributed?
Short answer
Reasonable over longer horizons and for rough work, poor in the tails. Daily and intraday returns show fat tails (large moves far more often than a normal allows), some skew and volatility clustering, while aggregating over longer periods pushes returns closer to normal via the CLT. Normality keeps models like Black-Scholes tractable, but risk measures built on it understate extreme losses.
Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 44, p.201; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Populations, Samples, and Sampling Distributions
- Sample Spaces, Events, and the Probability Axioms
- Conditional Probability, Total Probability, and Bayes' Rule
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