Sortino Ratio

The Sortino ratio was developed by Frank Sortino as a response to the Sharpe ratio's key flaw: penalizing upside volatility the same as downside volatility. In investing, you want volatility to the upside — it is only downside moves that cause financial and psychological harm.

**Formula:** Sortino = (Rp - T) / DD Where Rp is portfolio return, T is the target minimum acceptable return (MAR, often 0% or the risk-free rate), and DD is the downside deviation — the standard deviation of returns that fall below T.

**Downside deviation calculation:** 1. Identify all return periods where return < T (target) 2. Square the difference between each return and T 3. Average these squared differences 4. Take the square root Only negative-relative returns contribute to the denominator. Large positive returns do not inflate the denominator and reduce the ratio.

**Sortino vs. Sharpe in crypto:** Because Bitcoin and altcoins have positively skewed return distributions during bull markets (many moderate days, occasional massive gains), the Sortino ratio often looks significantly better than the Sharpe ratio for crypto assets. A coin that goes up 30% one month and down 5% the next has high Sharpe-penalizing volatility but excellent Sortino characteristics.

**Interpreting Sortino ratios:** - Below 1.0: Downside risk not justified by return - 1.0–2.0: Acceptable risk-adjusted performance - Above 2.0: Good downside-adjusted performance - Above 3.0: Excellent; rare and worth investigating for data quality

**When to prefer Sortino over Sharpe:** - Momentum strategies (frequent positive outliers) - Trend-following systems - Bull-market-only backtests - Any strategy where you suspect asymmetric return distribution

The Sortino ratio is particularly useful when evaluating DeFi yield strategies that have steady positive returns with occasional sharp downside events (smart contract exploits, depeg events), rather than symmetric volatility.