Beta and Market-Relative Risk

Install and import#

bash

npm install fintech-algorithms

import { betaAndMarketRelativeRisk } from "fintech-algorithms/financial-mathematics-statistics-and-data-foundations/financial-risk-and-performance-statistics/beta-and-market-relative-risk";

Signature#

betaAndMarketRelativeRisk(input)

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

input

{
  "returns": [0.01, -0.02, 0.015, -0.01, 0.03],
  "benchmark": [0.008, -0.01, 0.012, -0.006, 0.02],
  "frequency": 252,
  "target": 0,
  "confidence": 0.8,
  "riskFree": 0.0001,
  "weights": [0.6, 0.4],
  "covarianceMatrix": [
    [0.04, 0.01],
    [0.01, 0.09]
  ]
}

Call#

betaAndMarketRelativeRisk(input)

Returns#

object with 2 fields: beta, marketVariance

{
  "beta": 1.5903307888040712,
  "marketVariance": 0.0001572
}

Diagrams#

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

Expected Shortfall — Basel Framework MAR33
Mutual Fund Performance — William F. Sharpe
Measures of Scale — NIST/SEMATECH e-Handbook
Historical-example decision