markowitz.js

markowitz.js

function correlation(x, y) {
  if (x.length !== y.length) return null

  const xMean = x.reduce((acc, el) => el + acc, 0) / x.length
  const yMean = y.reduce((acc, el) => el + acc, 0) / y.length

  let numerator = 0,
    xDSquaredSum = 0,
    yDSquaredSum = 0

  for (let i = 0; i < x.length; i++) {
    const xd = x[i] - xMean
    const yd = y[i] - yMean
    numerator += xd * yd
    xDSquaredSum += xd ** 2
    yDSquaredSum += yd ** 2
  }
  return numerator / (xDSquaredSum * yDSquaredSum) ** 0.5
}

function covariancesFromCorrelations(correlations, stdevs) {
  return Object.keys(correlations).reduce(
    (acc, row) => ({
      ...acc,
      [row]: Object.keys(correlations[row]).reduce(
        (acc, col) => ({
          ...acc,
          [col]: correlations[row][col] * stdevs[row] * stdevs[col],
        }),
        {}
      ),
    }),
    {}
  )
}
// portfolio = [{symbol, closes, amount}]
function markowitz(portfolio) {
  let assets = []
  for (let i = 0; i < portfolio.length; i++) {
    const returns = []
    for (let j = 1; j < portfolio[i].closes.length; j++) {
      returns.push(
        Math.log(portfolio[i].closes[j] / portfolio[i].closes[j-1])
      )
    }
    const n = returns.length
    const mean = returns.reduce((acc, r) => r + acc, 0) / n
    const variance = returns.reduce((acc, r) => (r - mean) ** 2 + acc, 0) / n
    const stdev = variance ** 0.5
    const close = portfolio[i].returns[portfolio[i].returns.length-1]
    assets.push({ portfolio[i].symbol, returns, portfolio[i].amount, mean, variance, stdev, close })
  }

  const correlations = {}
  for (let i = 0; i < assets.length; i++) {
    for (let j = 0; j < assets.length; j++) {
      if (typeof correlations[assets[i].symbol] === 'undefined') {
        correlations[assets[i].symbol] = {}
      }
      correlations[assets[i].symbol][assets[j].symbol] = correlation(
        assets[i].returns,
        assets[j].returns
      )
    }
  }
  const stdevs = assets.reduce(
    (acc, asset) => ({ ...acc, [asset.symbol]: asset.stdev }),
    {}
  )
  const covariances = covariancesFromCorrelations(correlations, stdevs)

  const total = assets.reduce(
    (acc, { amount, close }) => acc + amount * close,
    0
  )
  const w = assets.map(({ amount, close }) => (amount * close) / total)
  const Ω = Object.keys(covariances).map(k =>
    Object.keys(covariances[k]).map(l => covariances[k][l])
  )

  let r = 0
  for (let i = 0; i < w.length; i++) {
    let sum = 0
    for (let j = 0; j < w.length; j++) {
      sum += Ω[i][j] * w[j]
    }
    r += sum * w[i]
  }
  return r ** 0.5
}