Statistics for finance · level 2
Annualising volatility
Returns scale with time; volatility scales with the square root of time. Memorise √252 ≈ 16 and √12 ≈ 3.5 and the conversion is one multiplication.
Worked example: Daily volatility 2%. Annualised volatility?
daily σ2%
√25215.87
annual σ31.75%
Step by step
- 1
Volatility scales with the root of time
σ_annual = σ_daily × √252
- 2
√252 ≈ 15.9 — call it 16
2 × 16 ≈ 32%
- 3
Exact
2 × 15.87 = 31.75%
- 4
Monthly instead
σ_monthly × √12 (≈ 3.46)
Daily volatility 2%. Annualised volatility? = 31.75
The theory behind it
Intuition
Volatility scales with the square root of time because independent shocks add in variance, not in standard deviation: σ_annual = σ_daily × √252.
Common pitfalls
- ×Multiplying daily volatility by 252.
- ×Annualising when returns are autocorrelated.
In the interview
Risk questions in investment cases.