@railpath/finance-toolkit/dist/risk/calculateBeta.js

Production-ready finance library for portfolio construction, risk analytics, quantitative metrics, and ML-based regime detection

"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.calculateBeta = calculateBeta;
const BetaOptionsSchema_1 = require("../schemas/BetaOptionsSchema");
const BetaResultSchema_1 = require("../schemas/BetaResultSchema");
/**
 * Calculate Beta (β)
 *
 * β = Cov(asset, benchmark) / Var(benchmark)
 *
 * Measures systematic risk relative to market/benchmark.
 * β = 1: moves with market
 * β > 1: more volatile than market
 * β < 1: less volatile than market
 *
 * @param options - Asset returns and benchmark returns
 * @returns Beta, covariance, variance, correlation
 */
function calculateBeta(options) {
    const { assetReturns, benchmarkReturns } = BetaOptionsSchema_1.BetaOptionsSchema.parse(options);
    if (assetReturns.length !== benchmarkReturns.length) {
        throw new Error('Asset and benchmark returns must have same length');
    }
    const n = assetReturns.length;
    // Mean returns
    const assetMean = assetReturns.reduce((sum, r) => sum + r, 0) / n;
    const benchmarkMean = benchmarkReturns.reduce((sum, r) => sum + r, 0) / n;
    // Covariance
    let covariance = 0;
    for (let i = 0; i < n; i++) {
        covariance +=
            (assetReturns[i] - assetMean) * (benchmarkReturns[i] - benchmarkMean);
    }
    covariance /= n - 1; // Sample covariance
    // Benchmark variance
    let benchmarkVariance = 0;
    for (let i = 0; i < n; i++) {
        benchmarkVariance += Math.pow(benchmarkReturns[i] - benchmarkMean, 2);
    }
    benchmarkVariance /= n - 1; // Sample variance
    // Beta
    const beta = benchmarkVariance !== 0 ? covariance / benchmarkVariance : 0;
    // Asset standard deviation (for correlation)
    let assetVariance = 0;
    for (let i = 0; i < n; i++) {
        assetVariance += Math.pow(assetReturns[i] - assetMean, 2);
    }
    assetVariance /= n - 1;
    const assetStdDev = Math.sqrt(assetVariance);
    const benchmarkStdDev = Math.sqrt(benchmarkVariance);
    // Correlation
    const correlation = assetStdDev !== 0 && benchmarkStdDev !== 0
        ? covariance / (assetStdDev * benchmarkStdDev)
        : 0;
    return BetaResultSchema_1.BetaResultSchema.parse({
        beta,
        covariance,
        benchmarkVariance,
        correlation,
    });
}