Scaling a 10% annual vol to a four-year horizon

Question

Annual log returns on an asset have volatility $10\%$ (independent across years). What is the volatility of its four-year log return?

Short answer

$20\%$ . Variances of independent log returns add, so four-year variance is $4 \times 0.1^2$ and volatility is $0.1\sqrt4 = 0.2$ .

Adapted from Crack, Heard on the Street, Q3.2, p.33; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Reading the Implied Vol Surface — Moneyness, Term Structure, and Quoting Conventions
Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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