What Is the Sortino Ratio?

The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative portfolio returns—downside deviation—instead of the total standard deviation of portfolio returns.

The Sortino ratio takes an asset or portfolio's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.

Formula and Calculation

The Sortino ratio is calculated as follows:

$$\text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_d}$$

Where:

• $R_p$ = Actual or expected portfolio return
• $R_f$ = Risk-free rate
• $\sigma_d$ = Standard deviation of the downside (downside deviation)

The key difference from the Sharpe ratio is that the Sortino ratio only considers downside volatility, which many investors consider more relevant since upside volatility is generally welcomed.

What the Sortino Ratio Can Tell You

The Sortino ratio is a useful way for investors, analysts, and portfolio managers to evaluate an investment's return for a given level of bad risk. Since this ratio uses only the downside deviation as its risk measure, it addresses the problem of using total risk, or standard deviation, which is important because upside volatility is beneficial to investors.

Interpreting the Sortino Ratio

Generally speaking, Sortino ratios can be interpreted as follows:

A higher Sortino ratio result is better. A Sortino ratio greater than 2.0 is considered good, and a ratio greater than 3.0 is considered excellent.

Negative Sortino Ratio

A negative Sortino ratio indicates that the investment's return is less than the risk-free rate. This suggests the investment is not providing adequate compensation for the risk taken.

Sortino Ratio vs. Sharpe Ratio

The Sortino ratio improves upon the Sharpe ratio by isolating downside or negative volatility from total volatility by dividing excess return by the downside deviation instead of the total standard deviation of a portfolio or asset.

The Sharpe ratio punishes the investment for good risk (upward price movements), which provides positive returns for investors. However, determining which ratio to use depends on whether the investor wants to focus on total or standard deviation, or just downside deviation.

Why Downside Deviation Matters

Many investors prefer the Sortino ratio because it only penalizes returns that fall below a target or required rate of return. This is more aligned with how most investors think about risk—they don't mind volatility when prices go up, only when they go down.

Use Cases for Trading Bots

When evaluating trading bots and algorithmic strategies, the Sortino ratio is particularly valuable because:

1. Asymmetric return profiles: Many trading strategies have non-normal return distributions
2. Drawdown focus: Traders typically care more about losses than gains
3. Better comparison: Strategies that limit downside risk will score higher

Calculating Downside Deviation

Downside deviation is calculated by:

1. Setting a minimum acceptable return (MAR), often the risk-free rate
2. Taking all returns below the MAR
3. Squaring the differences
4. Taking the square root of the average

$$\sigma_d = \sqrt{\frac{\sum_{t=1}^{n} \min(0, R_t - MAR)^2}{n}}$$

Example

Consider a trading bot with:

• Annual return: 18%
• Risk-free rate: 3%
• Standard deviation: 15%
• Downside deviation: 8%

Sharpe Ratio: $\frac{18\% - 3\%}{15\%} = 1.0$

Sortino Ratio: $\frac{18\% - 3\%}{8\%} = 1.875$

The higher Sortino ratio indicates that much of the bot's volatility was to the upside, making it more attractive than the Sharpe ratio suggests.

FAQs

What is a good Sortino ratio?

A Sortino ratio above 2.0 is generally considered good, while a ratio above 3.0 is considered excellent. However, the "good" threshold depends on the investment type and market conditions.

Is a higher Sortino ratio always better?

Generally, yes. A higher Sortino ratio indicates better risk-adjusted returns when considering only downside risk. However, extremely high ratios may indicate a limited sample size or unusual market conditions.

When should I use Sortino vs. Sharpe?

Use the Sortino ratio when evaluating investments with asymmetric return distributions or when you're primarily concerned about downside risk. The Sharpe ratio is more appropriate when volatility in both directions matters equally.

Related Topics

• Sharpe Ratio
• Calmar Ratio
• Maximum Drawdown
• CAGR