Serenity Ratio

Definition

The Serenity Ratio is a risk-adjusted metric that combines return, drawdown, and volatility to assess the stability and sustainability of an investment. It provides a comprehensive measure of risk-adjusted efficiency.

Formula

$\text{Serenity Ratio}=\frac{R_p - R_f}{\text{Ulcer Index} \times \text{Pitfall}}$

Where:

• $R_p$ = Portfolio return
• $R_f$ = Risk-free rate
• Ulcer Index = Quadratic mean of the drawdowns (depth and duration of drawdowns)
• Pitfall = $\frac{\text{CDaR}}{\sigma_p}$, the extreme-risk penalty
• CDaR = Conditional Drawdown at Risk (the CVaR of the drawdown distribution)
• $\sigma_p$ = Standard deviation of portfolio returns