Sortino Ratio

Mean return minus the per-period target, divided by target downside deviation. Downside deviation is the square root of the average squared shortfall across all n observations, including zeros above target.

When to use: Use when shortfalls below a chosen target are the relevant risk. Match the target and returns to the same frequency.

Calculator

Formula

\text{Sortino} = \frac{\overline R-R_f}{\sqrt{\frac{1}{n}\sum_{i=1}^{n}\min(0,R_i-R_f)^2}}

Variables

Symbol	Name	Description	Unit
Sortino	Sortino Ratio	Excess return per unit of downside volatility	integer
Returns	Periodic Returns	Sequence of periodic returns as decimals (e.g. 0.05 for 5%)	%
Rf	Risk-Free Rate	Per-period risk-free rate as a decimal (use the same period as the returns)	%

Real-Life Examples

Example 1: Mixed Returns

Returns: 10%, −5%, 8%, −3%, 12%, 4%. Rf = 3%.

Given

Returns = [0.1, -0.05, 0.08, -0.03, 0.12, 0.04]Rf = 3.0000%

Step-by-Step

1.Mean periodic return = 0.0433333333333; target/risk-free rate = 0.03

2.Sum of squared shortfalls = 0.01; divisor = 6

3.Denominator = √(0.01 / 6) ≈ 0.0408248290464

4.Ratio = (0.0433333333333 − 0.03) / denominator (before rounding)

5.Sortino ≈ 0.326599

Result:0.33

For these inputs, Sortino Ratio is 0.326599 under the stated payment, compounding and accounting assumptions.

Frequently Asked Questions

All n observations. Above-target returns contribute zero, but still count in n. This is target downside deviation, not a sample standard deviation with divisor n−1.

One nonzero shortfall produces a positive denominator. If no return is below target, the denominator is zero and the ratio has no finite value.

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Sharpe Ratio