Sharpe Ratio Calculation

Formula Base

SR = (r - b) / s

SR = (Mean return - Risk-free rate) / Std Dev of returns

Strategia con: - Annual return = 10% - Risk-free rate = 2% - Volatility = 20%

SR = (10% - 2%) / 20% = 8% / 20% = 0.40

Realistic SR = Backtest SR × Discount Factor

Discount factors: - Out-of-sample bootstrap: 0.75 - Rolling window: 0.60 - In-sample only: 0.25

SR_annual = (Mean daily - Daily risk-free) / Std daily × √252

Shortcut (assumendo daily risk-free ≈ 0):

SR ≈ (Mean daily / Std daily) × √252 ≈ (Mean daily / Std daily) × 16

SE(SR) = √[(1 + 0.5 × SR²) / N_years]

Esempio (1 anno dati, SR = 0.5):

SE = √[(1 + 0.125) / 1] = √1.125 = 1.06

Enorme uncertainty! Serve multi-year track record.