lequant40

// When backtesting trading stategies with exchange traded funds (ETFs), it is most of the time necessary
// to extend these ETFs closing prices time series to have a longer history.

// When the underlying index of the ETF is available, one problem is to how to merge the index data 
// with the ETF data so that there is no price level discontinuity, but before, the first problem to solve
// is how to reconciliate potentially different dates between:
// - The underlying index calculation dates
// - Available trading dates for the other ETFs also used in the trading strategy

// Fictious example:

lequant40

/**
 * Compute the mean-variance minimum variance frontier, as a list of (portfolio volatility, portfolio return) pairs.
 * 
 * @param {Array.<number>} returns, the assets returns, e.g. [0.01, 0.05]
 * @param {Array.<Array.<number>>} covarianceMatrix, the covariance matrix of the assets, e.g. [[1, 0], [0, 1]]
 * @param {number} portfolios, the number of portfolios to compute on the mean-variance minimum variance frontier, e.g. 25
 *
 * @return {Array.<Array.<number>>}, the list of (portfolio volatility, portfolio return) pairs to be inserted into a Google Spreadsheet
 **/
function computeMinimumVarianceFrontier(returns, covarianceMatrix, portfolios) {

lequant40

function arithmeticReturns(assetsPrices) {
    var xhr = new XMLHttpRequest();
    var url = "https://api.portfoliooptimizer.io/v1/assets/returns"; 
    xhr.open("POST", url, true);
    xhr.setRequestHeader("Content-Type", "application/json");
    xhr.onreadystatechange = function () {
        if (this.readyState === XMLHttpRequest.DONE) {
            // Status 200 == all good
            if (this.status === 200) { 
                // Parse the response as JSON

lequant40

Public Sub GenerateRandomPortfolios()
    'Define the Portfolio Optimizer REST API endpoint to target
    Dim EndPoint As String
    EndPoint = "https://api.portfoliooptimizer.io/v1/portfolios/generation/random"

    ''Create the JSON body for the REST API request
    Dim Body As New Dictionary
        'The number of assets
        Body.Add "assets", 5
        

lequant40

// Dependencies
var fs = require('fs');
const axios = require('axios');
const { mean, std } = require('mathjs');


// Definition of the risk free returns, and of the indexes prices
// In sample period
var nbPeriods = 12 * 24; // months of returns data, until 30/12/2012
var rf = [0.67,0.70,0.71,0.68,0.69,0.64,0.63,0.63,0.64,0.63,0.61,0.61,0.62,0.63,0.63,0.63,0.62,0.62,0.60,0.60,0.58,0.57,0.57,0.52,0.50,0.49,0.47,0.45,0.45,0.45,0.45,0.43,0.42,0.39,0.36,0.32,0.31,0.32,0.33,0.30,0.30,0.29,0.26,0.26,0.22,0.24,0.27,0.25,0.24,0.24,0.24,0.24,0.25,0.25,0.25,0.25,0.24,0.25,0.26,0.25,0.24,0.28,0.28,0.32,0.34,0.34,0.35,0.37,0.38,0.41,0.45,0.45,0.47,0.47,0.46,0.46,0.46,0.44,0.44,0.43,0.43,0.43,0.43,0.40,0.40,0.40,0.41,0.41,0.41,0.41,0.42,0.42,0.40,0.41,0.41,0.41,0.41,0.41,0.42,0.42,0.39,0.41,0.42,0.41,0.41,0.41,0.41,0.42,0.41,0.42,0.41,0.40,0.40,0.41,0.40,0.39,0.35,0.34,0.36,0.36,0.36,0.37,0.36,0.36,0.37,0.38,0.38,0.40,0.38,0.40,0.42,0.42,0.45,0.46,0.46,0.46,0.45,0.46,0.49,0.50,0.49,0.50,0.49,0.47,0.39,0.39,0.34,0.31,0.29

lequant40

fetch('https://api.portfoliooptimizer.io/v1/portfolio/optimization/mean-variance-efficient',
      { 
        method: 'POST',
        headers: { 'Content-Type': 'application/json' },
        body: JSON.stringify({ assets: 13,
                               assetsReturns: [...],
                               assetsCovarianceMatrix: [[...], ...],
                               constraints: { 
                                              portfolioVolatility: 0.05/Math.sqrt(260),
                                              maximumAssetsWeights: [0.20,0.10,0.20,0.20,0.20,0.20,0.20,0.20,0.10,0.10,0.20,0.50,0.50],

lequant40

fetch('https://api.portfoliooptimizer.io/v1/factors/residualization',
      { 
        method: 'POST',
        headers: { 'Content-Type': 'application/json' },
        body: JSON.stringify({ factors: [{factorReturns: [...], factorResidualization: true 
                                          factorReturns: [...], 
                                         ...
                                         }]
                             })
      })

lequant40

fetch('https://api.portfoliooptimizer.io/v1/portfolio/optimization/hierarchical-clustering-based-risk-parity',
      { 
        method: 'POST',
        headers: { 'Content-Type': 'application/json' },
        body: JSON.stringify({ assets: 10,
                               assetsCovarianceMatrix: [[1.000647799, -0.003050479,  0.010033224, -0.010759689, -0.005036503, 0.008762563,  0.998201625, -0.001393196, -0.001254522, -0.009365991],
                                                       [-0.003050479,  1.009021349,  0.008613817,  0.007334478, -0.009492688, 0.013031817, -0.009420720, -0.015346223,  1.010520047,  1.013334849],
                                                       [0.010033224,  0.008613817,  1.000739363, -0.000637885,  0.001783293, 1.001574768,  0.006385368,  0.001922316,  0.012902050,  0.007997935],
                                                       [-0.010759689,  0.007334478, -0.000637885,  1.011854725,  0.005759976, 0.000905812, -0.011912269,  0.000461894,  0.012572661,  0.009621670

lequant40

fetch('https://api.portfoliooptimizer.io/v1/portfolio/optimization/hierarchical-risk-parity/clustering-based',
      { 
        method: 'POST',
        headers: { 'Content-Type': 'application/json' },
        body: JSON.stringify({ assets: 5,
                               assetsCovarianceMatrix: [[1,1,0,0,0],[1,1,0,0,0],[0,0,1,0,0],[0,0,0,1,1],[0,0,0,1,1]],
                               clusters: 3,
                               acrossClusterAllocationMethod: "equalWeighting",
                               withinClusterAllocationMethod: "equalWeighting",
                             })