Sortino Ratio Formula and Comparison to Sharpe
Sortino Ratio = (Portfolio Return - Minimum Acceptable Return) / Downside Deviation. The minimum acceptable return (MAR) is commonly set to 0% (any loss is unacceptable) or to the risk-free rate. Downside deviation = the standard deviation of returns that fall below the MAR, calculated by squaring only negative deviations (ignoring positive deviations), averaging them, and taking the square root. Unlike the Sharpe Ratio, which divides by total standard deviation (penalizing both upside and downside variance), the Sortino Ratio denominates only by downside variance.
A strategy that earns consistent small gains punctuated by occasional large gains will have a higher Sortino Ratio than Sharpe Ratio because its return distribution is positively skewed — the high upside volatility (good) inflates total standard deviation (penalizing the Sharpe) but does not inflate downside deviation (leaving the Sortino unaffected). Conversely, an options-selling strategy that generates consistent small income but has occasional catastrophic drawdowns will have a much lower Sortino than Sharpe — the tail risk is precisely what the Sortino penalizes most harshly.
Sortino Ratio calculation:
Returns: [+8%, +5%, -12%, +6%, +9%, -3%, +7%]
MAR = 0%
Negative returns only: [-12%, -3%]
Downside Deviation = √(average of [-12%², -3%²])
= √((0.0144 + 0.0009) / 2)
= √0.00765 = 8.75%
Annual Portfolio Return = 20%
Sortino = 20% / 8.75% = 2.29