Sharpe Ratio vs. Sortino Ratio
If you make 20% but take 50% drawdowns, investors will flee. You need to normalize return by risk.
The Sharpe Ratio
$$ Sharpe = \frac{R_p - R_f}{\sigma_p} $$
- $R_p$: Portfolio Average Return
- $R_f$: Risk-Free Rate
- $\sigma_p$: Standard Deviation of Portfolio Returns (Total Volatility)
The Problem: Sharpe penalizes upside volatility. If you make +10% every day, your standard deviation is high (bad Sharpe). Wait... making +10% every day is good! Why punish it?
The Sortino Ratio
$$ Sortino = \frac{R_p - R_T}{\sigma_d} $$
- $R_T$: Target Return (often 0% or Rf)
- $\sigma_d$: Downside Deviation only.
The Fix: Sortino ignores upside volatility. It only cares about returns below the target.
It tells you "how much bad variance am I taking for each unit of return?"
Which One to Use?
Sharpe: Standard industry metric. Everyone knows it. Good for comparing broad asset classes (stocks vs bonds).
Sortino: Better for skewed strategies (like selling options or trend following) where large positive outliers are common and desirable.