Beta (BETA)

Summary

Beta: the slope of a least-squares linear regression of one series' percentage returns (y, from inReal1) against another's (x, from inReal0) over a rolling window. Measures how much a security moves relative to a market index. Beta = 1 moves with the index; < 1 less volatile, > 1 more volatile.

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

outReal: line · zero · positive · negative

Formula

Per-bar returns: $x_i=(p^0_i-p^0_{i-1})/p^0_{i-1}$ from inReal0, $y_i=(p^1_i-p^1_{i-1})/p^1_{i-1}$ from inReal1. With $n$ =period over the window: $\beta = \dfrac{n\,S_{xy}-S_x S_y}{n\,S_{xx}-S_x^2}$ , where $S_{xx}=\sum x^2,\ S_{xy}=\sum xy,\ S_x=\sum x,\ S_y=\sum y$ .

Inputs

inReal0 — Series whose returns are the regression x (market/index)
inReal1 — Series whose returns are the regression y (security)

Outputs

outReal — Beta: regression slope of inReal1-returns on inReal0-returns

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	5	1–100000	Rolling window length (number of returns) for the regression sums

Properties

Numerical Stability: Start-Independent


☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Display Shift


☐ Can Output NaN or ±Inf
☐ Identity at Period 1
☐ Uses Transcendental
☐ Input Must Be Positive

Example

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

int n = 252;
double series0[252]; /* your data, oldest first */
double series1[252]; /* your data, oldest first */
double out[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_BETA( 0, n - 1, series0, series1, 5, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

let series0 = vec![0.0; 252]; // your data, oldest first
let series1 = vec![0.0; 252]; // your data, oldest first
let mut out = vec![0.0; 252];

let core = Core::new();
let range = core.beta(0, series0.len() - 1, &series0, &series1, 5, &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[] series0 = new double[252]; // your data, oldest first
double[] series1 = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.beta(0, series0.length - 1, series0, series1, 5, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

using System;
using TALib;

var series0 = new double[252]; // your data, oldest first
var series1 = new double[252]; // your data, oldest first
var outReal = new double[252];

var core = Core.Default;
OutRange r = core.Beta(0, series0.Length - 1, series0, series1, 5, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { beta } from 'ta-lib';

const series0 = new Float64Array(252); // your data, oldest first
const series1 = new Float64Array(252); // your data, oldest first

const { begIdx, values } = beta(series0, series1, { timePeriod: 5 });
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.4.0.

TA-Lib Definition: beta.c · beta.yaml

Native	File
C	`ta_BETA.c`
Rust	`beta.rs`
Java	`Core_BETA.java`
C#	`Core_BETA.cs`
TypeScript	`beta.ts`

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

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

Aliases

Beta coefficient