Rolling Sortino Ratio (SORTINO)

Summary

The rolling Sortino ratio: the mean return in excess of a minimum acceptable return (MAR), divided by the downside deviation, over a trailing window, scaled to a year. It is the Sharpe ratio with upside volatility taken out of the denominator: only returns below the MAR count as risk. Above 0 the window's returns beat the MAR on average; the larger the value, the more return per unit of downside.

Chart

Chart metadata i

Drawn on the price pane over the close as a line; below it, a separate indicator pane with a zero line showing outReal as a solid line.

Metadata flags used: outReal: line, positive, negative

Reference data (CSV) · Chart (SVG)

Formula

With simple returns $r_i = (x_i - x_{i-1}) / x_{i-1}$ , per-bar minimum acceptable return $\text{MAR}$ , excess returns $d_i = r_i - \text{MAR}$ and annualization $A$ , over the trailing $n$ returns:

\text{SORTINO} = \sqrt{A}\,\frac{\bar{d}}{DD}, \qquad \bar{d} = \frac{1}{n}\sum d_i, \qquad DD = \sqrt{\frac{1}{n}\sum \min(d_i, 0)^2}

The result is $+\infty$ when no return in the window is below the MAR, and NaN when every return equals it.

Notes

The downside deviation divides by the full window n: a return above the MAR counts in n and adds zero to the sum. This is the definition of Sortino and Price (1994) and the divisor of Bacon's worked example; dividing by n−1, or by the number of returns below the MAR, gives a different value.
The mean is arithmetic, not compounded.
A window with no return below the MAR has no downside: the result is +Inf, and NaN when every return equals the MAR. In a rising market this is common. With an annualization of 0 it is NaN there and 0 elsewhere.
The MAR is per bar, in the same unit as the returns. For an annual rate R, pass (1+R)^(1/A) − 1, where A is the annualization; it is not de-annualized for you.
An annualization of 1 gives the raw per-bar ratio.
A zero price leaves no return to measure from it: the return of the bar after it counts as 0.

Inputs

inReal — The price series; its returns are computed internally

Outputs

outReal — Annualized Sortino ratio of the trailing window, or +Inf or NaN where the window has no return below the MAR

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	20	2–100000	Number of returns in the window; one price more is read
`optInMAR`	real	0	any real	Minimum acceptable return per bar; returns below it are the downside
`optInAnnualization`	real	252	≥ 0	Bars per year; the per-bar ratio is multiplied by its square root

Properties

Numerical Stability: Start-Independent


☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
✅ Can Output NaN or ±Inf i
☐ Identity at Period 1
☐ Display Shift
☐ Uses Transcendental
☐ Input Must Be Positive

Example

#include <stdio.h>
#include <ta_libc.h>

int n = 252;
double series[252]; /* your data, oldest first */
double out[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_SORTINO( 0, n - 1, series, 20, 0.0, 252.0, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

let series = vec![0.0; 252]; // your data, oldest first
let mut out = vec![0.0; 252];

let core = Core::new();
let range = core.sortino(0, series.len() - 1, &series, 20, 0.0, 252.0, &mut out)?;
println!("{} values from bar {}; last out = {}", range.count, range.beg_idx, out[range.count - 1]);

Java

import io.github.talib.Core;
import io.github.talib.OutRange;

double[] series = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.sortino(0, series.length - 1, series, 20, 0.0, 252.0, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

using System;
using TALib;

var series = new double[252]; // your data, oldest first
var outReal = new double[252];

var core = Core.Default;
OutRange r = core.Sortino(0, series.Length - 1, series, 20, 0.0, 252.0, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { sortino } from 'ta-lib';

const series = new Float64Array(252); // your data, oldest first

const { begIdx, values } = sortino(series, {
  timePeriod: 20,
  mar: 0,
  annualization: 252,
});
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.8.4.

TA-Lib Definition: sortino.c · sortino.yaml

Native	File
C	`ta_SORTINO.c`
Rust	`sortino.rs`
Java	`Core_SORTINO.java`
C#	`Core_SORTINO.cs`
TypeScript	`sortino.ts`

Python: talib.SORTINO, see ta-lib-python.

TA-Lib is also available for R and more using a wrapper.

Aliases

Sortino Ratio, Rolling Sortino, Downside Risk-Adjusted Return

References

Sortino, F. A. and Price, L. N. "Performance Measurement in a Downside Risk Framework." The Journal of Investing, 3(3), Fall 1994, 59-64.
Bacon, C. R. Practical Portfolio Performance Measurement and Attribution, 2nd ed. Wiley, 2008.