Volatility Time Conversions

Regola Base

Volatilita scala con √tempo:

σ_period = σ_base × √(Number of periods)

σ_annual = σ_daily × √252
σ_annual ≈ σ_daily × 16  (approssimazione)

Esempio: - σ_daily = 1% - σ_annual = 1% × 16 = 16%

σ_daily = σ_annual / 16

σ_annual = σ_weekly × √52
σ_annual ≈ σ_weekly × 7.2

σ_annual = σ_monthly × √12
σ_annual ≈ σ_monthly × 3.5

Annual σ = 16%
Daily σ = 16% / 16 = 1%
Weekly σ = 16% / 7.2 = 2.2%
Monthly σ = 16% / 3.5 = 4.6%

Daily Cash Vol = Annual Cash Vol / 16

Esempio: - Annual cash vol = $30,000 - Daily cash vol = $30,000 / 16 = $1,875

Cash Vol = Capital × Vol%

Esempio: - Capital = $100,000 - Vol% = 20% - Annual cash vol = $20,000 - Daily cash vol = $1,250

Conversione assume: - Returns independent - No autocorrelation - No volatility clustering

In pratica approssimazione ragionevole ma non perfetta.