>What is a Sharpe Ratio?_
The Sharpe ratio measures risk-adjusted returns. It tells you how much excess return you receive for the extra volatility of holding a risky asset.
Sharpe Ratio = (Return - Risk Free Rate) / Volatility
In our game, we assume risk-free rate = 0 for simplicity
>True vs Sample Sharpe_
Understanding the difference is key to mastering this game:
TRUE SHARPE (Population Parameter)
The "true" Sharpe is the parameter we use to generate the returns. It's like the actual skill of a trader - constant but unknown.
SAMPLE SHARPE (Observed)
The "sample" Sharpe is calculated from the actual returns you see. Due to randomness, it usually differs from the true value.
>How Returns Are Generated_
We use Arithmetic Brownian Motion to generate realistic financial returns:
1. Start with a target "true" Sharpe ratio (-3 to 3)
2. Convert to annual drift and volatility
3. Generate 504 daily returns (2 trading years)
4. Each day: Return = drift + volatility × random_noise
Technical: We use Box-Muller transform for normally distributed noise
>Concrete Example_
Scenario: True Sharpe = 2.0 (Excellent strategy)
• Annual volatility: 20% (randomly chosen)
• Annual drift: 2.0 × 20% = 40%
• Daily drift: 40% / 252 ≈ 0.16%
• Daily volatility: 20% / √252 ≈ 1.26%
After generating 504 days of returns:
• Calculated mean return: 38.5% (close to 40%)
• Calculated volatility: 21.2% (close to 20%)
• Sample Sharpe: 38.5% / 21.2% = 1.82
True Sharpe: 2.0 → Sample Sharpe: 1.82
The difference is due to random variation in finite samples
>Why This Matters_
In TRUE mode: You're estimating the underlying parameter - like guessing a trader's actual skill level.
In SAMPLE mode: You're calculating from observed data - like evaluating past performance.
Real traders face this constantly: Is good performance skill (high true Sharpe) or just luck (sample Sharpe > true Sharpe)?
>Tips for Better Guessing_
• Sample Sharpe has more variation with volatile returns
• Over 2 years, sample usually converges toward true
• Extreme sample values (near ±3) often indicate lower true values
• Look at the consistency of returns, not just the average