Rolling Sharpe Ratio (SHARPE)

Summary

The rolling Sharpe ratio: the mean return in excess of a risk-free rate, divided by the standard deviation of that excess return, over a trailing window. A drift-over-volatility measure of the series itself, scaled to a year. Above 0 the window's returns beat the risk-free rate on average; the larger the value, the more return per unit of volatility.

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 risk-free rate $R_f$, excess returns $d_i = r_i - R_f$ and annualization $A$, over the trailing $n$ returns:

$$\text{SHARPE} = \sqrt{A}\,\frac{\bar{d}}{\sigma_d}, \qquad \bar{d} = \frac{1}{n}\sum d_i, \qquad \sigma_d = \sqrt{\frac{1}{n-1}\sum (d_i - \bar{d})^2}$$

The result is $\pm\infty$ by the sign of $\bar{d}$ when every excess return in the window is equal, and NaN when they are also exactly 0.

Notes

• This is Sharpe's 1994 ex post ratio with a constant benchmark, over simple returns and the sample (n−1) standard deviation.
• A window whose returns are all equal has no spread: the result is +Inf or -Inf by the sign of the mean excess return, and NaN when that mean is exactly 0. With an annualization of 0 it is NaN there and 0 elsewhere.
• The risk-free rate 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 Sharpe ratio of the trailing window, or ±Inf or NaN where the window has no spread

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	20	2–100000	Number of returns in the window; one price more is read
optInRiskFreeRate	real	0	any real	Risk-free return per bar, subtracted from each return
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

C

#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_SHARPE( 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.sharpe(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.sharpe(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]);

C#

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.Sharpe(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 { sharpe } from 'ta-lib';

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

const { begIdx, values } = sharpe(series, {
  timePeriod: 20,
  riskFreeRate: 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: sharpe.c · sharpe.yaml

Native	File
C	ta_SHARPE.c
Rust	sharpe.rs
Java	Core_SHARPE.java
C#	Core_SHARPE.cs
TypeScript	sharpe.ts

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

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

Aliases

Sharpe Ratio, Reward-to-Variability Ratio, Rolling Sharpe

See Also

STDDEV · VAR · BETA · ROCP

References

• Sharpe, W. F. "The Sharpe Ratio." The Journal of Portfolio Management, 21(1), Fall 1994, 49-58.