Metrics & Evaluation Interactive

Sharpe Ratio

Measure risk-adjusted returns. Compare strategies by how much return you get per unit of risk taken.

📊 The Sharpe Ratio Formula

Sharpe = (R_p - R_f) / σ_p

R_p = Portfolio/strategy return
R_f = Risk-free rate
σ_p = Portfolio volatility (std dev)

Interpretation

• > 1.0 = Excellent (hedge fund territory)
• 0.5 - 1.0 = Good
• 0 - 0.5 = Acceptable
• < 0 = Underperforming risk-free

Strategy Parameters

-5 30

5 40

0 10

📊 Result

0.27

Sharpe Ratio

Acceptable

Excess return: 4.0% ÷ Volatility: 15%

Simulated Cumulative Returns (36 months)

Higher Sharpe = smoother path to the same return. Volatility creates bumpy ride.

Strategy Comparison

Conservative

Return 6%

Volatility 8%

Sharpe 0.25

Balanced

Return 10%

Volatility 15%

Sharpe 0.40

Aggressive

Return 15%

Volatility 25%

Sharpe 0.44

Your Strategy

Return 8%

Volatility 15%

Sharpe 0.27

Note: Aggressive strategy has highest return but worst Sharpe. Risk-adjusted, Conservative may be better!

🏀 Sports Betting Applications

Evaluating Betting Strategies

→ Compare ROI vs variance across strategies
→ High-volume low-edge vs low-volume high-edge
→ Parlay strategies have high vol, often low Sharpe

House Perspective

→ Evaluate pricing strategy risk-adjusted performance
→ Higher Sharpe = more consistent profits
→ Guide reserve requirements based on volatility

📈 Related Metrics

Sharpe Ratio

(R - Rf) / σ

Return over risk-free, per unit total risk

Information Ratio

(R - Rb) / TE

Return over benchmark, per unit tracking error

Sortino Ratio

(R - Rf) / σ_down

Only penalizes downside volatility

R Code Equivalent

# Calculate Sharpe Ratio
sharpe_ratio <- function(returns, rf_rate = 0.04) { 
  excess_return <- mean(returns) - rf_rate / 12  # Monthly
  vol <- sd(returns)
  
  # Annualize
  sharpe <- (excess_return * 12) / (vol * sqrt(12))
  return(sharpe)
}

# Compare strategies
compare_strategies <- function(returns_list, names, rf = 0.04) { 
  results <- data.frame(
    strategy = names,
    return = sapply(returns_list, function(r) mean(r) * 12 * 100),
    vol = sapply(returns_list, function(r) sd(r) * sqrt(12) * 100),
    sharpe = sapply(returns_list, sharpe_ratio, rf_rate = rf)
  )
  return(results[order(-results$sharpe), ])
}

# Example
returns <- rnorm(36, mean = 0.006666666666666666, sd = 0.04330127018922194)
cat(sprintf("Sharpe: %.2f\n", sharpe_ratio(returns, 0.04)))

✅ Key Takeaways

• Sharpe = excess return per unit of risk
• > 1.0 is excellent, > 0.5 is good
• Compare strategies fairly across risk levels

• High return with high vol may have low Sharpe
• Useful for betting strategy evaluation
• Annualize using √time for volatility