> ## Documentation Index
> Fetch the complete documentation index at: https://kalpi.ai/docs/llms.txt
> Use this file to discover all available pages before exploring further.
# Sortino Ratio
> Evaluate risk-adjusted returns by isolating and penalizing only harmful downside volatility.
The **Sortino Ratio** is an advanced evolution of the Sharpe Ratio. While both metrics measure risk-adjusted returns, they define "risk" in completely different ways.
The Sharpe Ratio penalizes a strategy for *all* volatility. If your portfolio suddenly spikes upward by 20% in a single day, the Sharpe Ratio drops because the asset's standard deviation increased. However, institutional investors do not fear upside volatility—they only fear downside risk.
The Sortino Ratio solves this by only penalizing your score for **downside volatility** (returns that fall below your minimum acceptable target).
## The Mathematical Formula
The Sortino Ratio is calculated by dividing the portfolio's excess return by its downside deviation:
$\text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_d}$
**Where:**
* $R_p$ = The expected or historical return of the portfolio.
* $R_f$ = The risk-free rate of return (or minimum acceptable return).
* $\sigma_d$ = The standard deviation of the *negative* asset returns.
## Interpreting the Score
Because it ignores upside volatility, the Sortino Ratio is an exceptional metric for evaluating highly aggressive growth portfolios or trend-following systems that experience massive, sudden surges in profit.
The strategy is exposing your capital to an unacceptable amount of downside risk relative to the returns it generates.
Solid downside protection. The portfolio is generating decent excess returns without suffering massive structural breaks.
Institutional-grade risk management. The strategy captures strong upside beta while tightly capping and controlling capital drawdowns.