MCOSDemo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Thanks for your interest in MCOS. This notebook has everything you will need to test and run the MCOS library. \n",
    "# For full information on how to use this library, please visit https://github.com/enjine-com/mcos\n",
    "# \n",
    "# \n",
    "# Prior to running this notebook, please install the MOCS library, and matlabplot\n",
    "# \n",
    "# pip install mcos\n",
    "# pip install matplotlib\n",
    "# \n",
    "# Thanks!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.935829159725291e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 199\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.17802254182672e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 288\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.770334384199979e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7834145341129084e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 9.23441914213521e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.004135256789751e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 199\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.282091827221918e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.688039265467279e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 271\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.2571444461333827e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.1825991248832847e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.035795186181785e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 288\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 9.065252731639316e-07\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.640780414025886e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.5692963472348879e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 306\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.912533604282528e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3877444987996316e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 288\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.013288198978665e-06\n",
      "            Iterations: 20\n",
      "            Function evaluations: 361\n",
      "            Gradient evaluations: 20\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.100567935944074e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 253\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.5271397045225668e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.92169538585846e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.586726288084685e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.0053089597725794e-06\n",
      "            Iterations: 19\n",
      "            Function evaluations: 343\n",
      "            Gradient evaluations: 19\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.5788442029438012e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.9568023071295216e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.6333876303005746e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.733067248924277e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.6934700404993017e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3093221896844374e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 181\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.489614716941771e-06\n",
      "            Iterations: 23\n",
      "            Function evaluations: 415\n",
      "            Gradient evaluations: 23\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.408569518125235e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.454500087730761e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.479808670949916e-06\n",
      "            Iterations: 20\n",
      "            Function evaluations: 361\n",
      "            Gradient evaluations: 20\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.122303999864589e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 162\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 5.33301119197541e-06\n",
      "            Iterations: 18\n",
      "            Function evaluations: 325\n",
      "            Gradient evaluations: 18\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.414754742787125e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.4371052759527093e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.4151213161693e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.6445438840301788e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.1867290842303913e-05\n",
      "            Iterations: 9\n",
      "            Function evaluations: 162\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.8561422342593665e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.6551582879571428e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 199\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.281230614718278e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.122844778441177e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 145\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.389034138240225e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 378\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3137872791201899e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 271\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.1235974670292335e-06\n",
      "            Iterations: 26\n",
      "            Function evaluations: 468\n",
      "            Gradient evaluations: 26\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0226932153789695e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.673726385559913e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.411447608802544e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 253\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.068871095294656e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "                 mean     stdev\n",
      "optimizer                      \n",
      "HRP          0.058970  0.044667\n",
      "markowitz    0.012565  0.018755\n",
      "NCO         -0.743738  1.778158\n",
      "Risk Parity -0.004552  0.009997\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='optimizer'>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from mcos import optimizer\n",
    "from mcos import observation_simulator\n",
    "from mcos import mcos\n",
    "from mcos.error_estimator import ExpectedOutcomeErrorEstimator, SharpeRatioErrorEstimator, \\\n",
    "    VarianceErrorEstimator\n",
    "from mcos.covariance_transformer import DeNoiserCovarianceTransformer, AbstractCovarianceTransformer\n",
    "from mcos.observation_simulator import AbstractObservationSimulator, MuCovLedoitWolfObservationSimulator, \\\n",
    "MuCovObservationSimulator\n",
    "from pypfopt.expected_returns import mean_historical_return\n",
    "from pypfopt.risk_models import sample_cov\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "#------------ Demo code for 20 American stocks------------------#\n",
    "\n",
    "# Mean Error Estimator\n",
    "\n",
    "# Create dataframe of price history to use for expected returns and covariance\n",
    "def prices_df() -> pd.DataFrame:\n",
    "    tickers = ['goog','baba', 'amzn', 'wmt', 'glpi', 'bac', 'uaa', 'shld', 'jpm', 'sbux', 'amd', 'aapl','bby',\n",
    "              'ge', 'rrc', 'ma','fb']\n",
    "    total_df = pd.DataFrame()\n",
    "    for id in tickers:\n",
    "        temp = pd.read_csv(id + '.us.txt', parse_dates=True, index_col='Date')\n",
    "        temp = pd.DataFrame(temp['Close']).rename(columns={\"Close\":id})\n",
    "        if total_df.empty:\n",
    "            total_df = temp\n",
    "        else:\n",
    "            total_df = total_df.join(temp)\n",
    "\n",
    "    return total_df\n",
    "\n",
    "# Choose the number of simulations to run\n",
    "num_sims = 50\n",
    "\n",
    "# Select the optimizers that you would like to compare\n",
    "op = [optimizer.HRPOptimizer(), optimizer.MarkowitzOptimizer(),optimizer.NCOOptimizer(), optimizer.RiskParityOptimizer()]\n",
    "\n",
    "# select the metric to use for comparison\n",
    "ee = ExpectedOutcomeErrorEstimator()\n",
    "\n",
    "# select your optional covariance transformer\n",
    "cov_trans = DeNoiserCovarianceTransformer()\n",
    "\n",
    "# convert price history to expected returns and covariance matrix\n",
    "mu = mean_historical_return(prices_df()).values\n",
    "cov = sample_cov(prices_df()).values\n",
    "\n",
    "# select your observational simulator\n",
    "obs_sim = MuCovObservationSimulator(mu, cov, num_sims)\n",
    "\n",
    "# Run the simulation\n",
    "results = mcos.simulate_optimizations(obs_sim, num_sims, op, ee, [cov_trans])\n",
    "print(results)\n",
    "results.plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.3375352935814835e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0361793228024204e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 252\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0646631464333731e-05\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.9294174363476366e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 6.178068385056679e-06\n",
      "            Iterations: 18\n",
      "            Function evaluations: 324\n",
      "            Gradient evaluations: 18\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.126557617757225e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.452717082321038e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.882165506771853e-07\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.8586299085365404e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.5319852272296897e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 199\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.550112481137265e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 163\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.5810554691998365e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.873764787353544e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.810420938502751e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 162\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 6.570523255587217e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 162\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.9038035841399696e-06\n",
      "            Iterations: 22\n",
      "            Function evaluations: 396\n",
      "            Gradient evaluations: 22\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3976488653470707e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.891564561513054e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 378\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.9401064891226872e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 288\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.3714242933060647e-06\n",
      "            Iterations: 23\n",
      "            Function evaluations: 415\n",
      "            Gradient evaluations: 23\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.6757489711591402e-06\n",
      "            Iterations: 18\n",
      "            Function evaluations: 325\n",
      "            Gradient evaluations: 18\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.559958443735306e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.926622247860263e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.840788370323323e-06\n",
      "            Iterations: 19\n",
      "            Function evaluations: 342\n",
      "            Gradient evaluations: 19\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.1546450022346843e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.44436746603227e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 198\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.260108861243044e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 271\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 5.128043526332647e-06\n",
      "            Iterations: 20\n",
      "            Function evaluations: 361\n",
      "            Gradient evaluations: 20\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.431318382185088e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.2679967872521298e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.35220910701749e-06\n",
      "            Iterations: 18\n",
      "            Function evaluations: 325\n",
      "            Gradient evaluations: 18\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.4765542897820532e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 5.1483772327511794e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 162\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8173254706506816e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 199\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.661117182260747e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 378\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.3732572251389787e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.507163988863355e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.824754418312118e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 162\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.6935784903318925e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.953568762629516e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.5570567976115514e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 378\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.559134436999065e-06\n",
      "            Iterations: 19\n",
      "            Function evaluations: 343\n",
      "            Gradient evaluations: 19\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.17059100901346e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 270\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.6235338456573393e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 253\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7109512666841426e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 199\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 0.00010009080020868962\n",
      "            Iterations: 17\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.6801778554129033e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.1522824911067107e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.073681694821609e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.7308138899172702e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "                 mean     stdev\n",
      "optimizer                      \n",
      "HRP          0.004648  0.001758\n",
      "markowitz    0.003394  0.001656\n",
      "NCO          1.011754  5.840285\n",
      "Risk Parity  0.000205  0.000111\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='optimizer'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Variance Error Estimator\n",
    "\n",
    "ee = VarianceErrorEstimator()\n",
    "results = mcos.simulate_optimizations(obs_sim, num_sims, op, ee, [cov_trans])\n",
    "print(results)\n",
    "results.plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.371857981078186e-06\n",
      "            Iterations: 27\n",
      "            Function evaluations: 486\n",
      "            Gradient evaluations: 27\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.1808098633103656e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 6.052847959380596e-06\n",
      "            Iterations: 18\n",
      "            Function evaluations: 325\n",
      "            Gradient evaluations: 18\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.2578583193020806e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.110847455490961e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.098174114694625e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 163\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.6485196865101163e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3825592903692662e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.991953597404679e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7162254904819132e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.8071349801984078e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.484629559196907e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.281736562319916e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.053138867815481e-06\n",
      "            Iterations: 24\n",
      "            Function evaluations: 432\n",
      "            Gradient evaluations: 24\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.144276266959487e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 306\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.92919953945634e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.8945903678921058e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.7035750729459734e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.0295668409192075e-06\n",
      "            Iterations: 18\n",
      "            Function evaluations: 325\n",
      "            Gradient evaluations: 18\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.4493619553379843e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 199\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.4088588204782535e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 288\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.550588865285366e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8399900657085723e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 271\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.4411641767259387e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8606012508241145e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 271\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0250208548630298e-05\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.7383347482061402e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 289\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.05989716889573e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.761032575309597e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 270\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.894100677906346e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 7.170236235421168e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 162\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.72885760196268e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.458882344094614e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 288\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.472270949341823e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.180009516671765e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.3111542143176836e-06\n",
      "            Iterations: 21\n",
      "            Function evaluations: 379\n",
      "            Gradient evaluations: 21\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.03447934815218e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.6063096431131304e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 271\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 7.718197634670615e-06\n",
      "            Iterations: 23\n",
      "            Function evaluations: 415\n",
      "            Gradient evaluations: 23\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.5352056385524514e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 253\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.214480416045394e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3029181315727729e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0538408102290536e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 198\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8874004336798216e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 306\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.152368101556508e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 145\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.9583143771974666e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 288\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7790103488770847e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 216\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.192732351560864e-06\n",
      "            Iterations: 18\n",
      "            Function evaluations: 325\n",
      "            Gradient evaluations: 18\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.3566246449153155e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 217\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.545090560436528e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 235\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.925905830128423e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 234\n",
      "            Gradient evaluations: 13\n",
      "                 mean     stdev\n",
      "optimizer                      \n",
      "HRP          0.704248  0.496550\n",
      "markowitz    0.350061  0.406126\n",
      "NCO         -0.867598  0.973037\n",
      "Risk Parity -0.265089  0.700969\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='optimizer'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sharpe Error Estimator\n",
    "\n",
    "ee = SharpeRatioErrorEstimator()\n",
    "results = mcos.simulate_optimizations(obs_sim, num_sims, op, ee, [cov_trans])\n",
    "print(results)\n",
    "results.plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.053385634238388e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.177546011669533e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.811987203291039e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 408\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.6855761952612587e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.085462706839911e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.1657827867740458e-05\n",
      "            Iterations: 12\n",
      "            Function evaluations: 613\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.501423027259906e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.392604523292602e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.9152163513065876e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8278260425207033e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.279656880641038e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 765\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 9.346635768818108e-07\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7198223355479008e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7193804628891297e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.7226223948663285e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.0170352678450915e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4811793439399159e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4189201297550875e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 459\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8440407486158673e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 510\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.570633076906245e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.2704628732438804e-05\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.2317543340671015e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4584216357631897e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.651128629009167e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.9929695673081748e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4968414227787635e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.5222981044298302e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 817\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4687579636788377e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.6911573725051005e-05\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8898363588782314e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.2089848693553566e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0868035413501064e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.1412947769025738e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.243336014865712e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.366370697191966e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3171223950180586e-05\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7885233506275912e-05\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8021053829307271e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 715\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.9010970207779505e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8034497567424274e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.638280834068127e-07\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.981775872843936e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 663\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8867025472739316e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8924790087129235e-06\n",
      "            Iterations: 24\n",
      "            Function evaluations: 1225\n",
      "            Gradient evaluations: 24\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 6.753242545583726e-07\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.6332426419054346e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.825540047953578e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0030957043370506e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.301889779422934e-05\n",
      "            Iterations: 14\n",
      "            Function evaluations: 714\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.1217673367307077e-05\n",
      "            Iterations: 14\n",
      "            Function evaluations: 714\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "                 mean      stdev\n",
      "optimizer                       \n",
      "HRP          0.005856   0.022261\n",
      "markowitz    0.080595   0.093575\n",
      "NCO          4.305494  36.632870\n",
      "Risk Parity  0.003929   0.018000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='optimizer'>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#------------ Demo code for 50 Chinese stocks------------------#\n",
    "\n",
    "# Mean Error Estimator\n",
    "\n",
    "# Create dataframe of price history to use for expected returns and covariance\n",
    "def prices_df() -> pd.DataFrame:\n",
    "    total_df = pd.read_csv(\"stocks_close.csv\",index_col=0)\n",
    "    return total_df\n",
    "\n",
    "# Choose the number of simulations to run\n",
    "num_sims = 50\n",
    "\n",
    "# Select the optimizers that you would like to compare\n",
    "op = [optimizer.HRPOptimizer(), optimizer.MarkowitzOptimizer(),optimizer.NCOOptimizer(), optimizer.RiskParityOptimizer()]\n",
    "\n",
    "# select the metric to use for comparison\n",
    "ee = ExpectedOutcomeErrorEstimator()\n",
    "#ee = SharpeRatioErrorEstimator()\n",
    "\n",
    "# select your optional covariance transformer\n",
    "cov_trans = DeNoiserCovarianceTransformer()\n",
    "\n",
    "# convert price history to expected returns and covariance matrix\n",
    "mu = mean_historical_return(prices_df()).values\n",
    "cov = sample_cov(prices_df()).values\n",
    "\n",
    "# select your observational simulator\n",
    "obs_sim = MuCovObservationSimulator(mu, cov, num_sims)\n",
    "\n",
    "# Run the simulation\n",
    "results = mcos.simulate_optimizations(obs_sim, num_sims, op, ee, [cov_trans])\n",
    "print(results)\n",
    "results.plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 6.952689499377261e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.52073071174064e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 459\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.5030649160597277e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.01558723393566e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.1887668120796194e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 715\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.072321325027989e-06\n",
      "            Iterations: 5\n",
      "            Function evaluations: 256\n",
      "            Gradient evaluations: 5\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.7711196624055712e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 459\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.6759882483020654e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0857329807789874e-05\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7707460331121913e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.1493255300709483e-06\n",
      "            Iterations: 17\n",
      "            Function evaluations: 867\n",
      "            Gradient evaluations: 17\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.849089973829966e-05\n",
      "            Iterations: 13\n",
      "            Function evaluations: 664\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0191870658804065e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 6.854985150976126e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3407963054425164e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.342903658867441e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.031109145964734e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.626528595121461e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 561\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0524502849946214e-06\n",
      "            Iterations: 5\n",
      "            Function evaluations: 255\n",
      "            Gradient evaluations: 5\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4351244388976827e-06\n",
      "            Iterations: 16\n",
      "            Function evaluations: 816\n",
      "            Gradient evaluations: 16\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.06615914842452e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8458402791975392e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.815131896505211e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.236318554325357e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0104950596928607e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.4588406583830266e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 766\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.055451612307458e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.246105092085402e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.1445731042070357e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 613\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.115330975377328e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0282475941870913e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 613\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3269946499500558e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 459\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3496566698451127e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.1148745019679212e-05\n",
      "            Iterations: 11\n",
      "            Function evaluations: 561\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8526461213224826e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0759993793924586e-05\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.739970201574043e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3780710618648316e-05\n",
      "            Iterations: 10\n",
      "            Function evaluations: 510\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 9.535665948671492e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0040870175412484e-05\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.297054194394764e-06\n",
      "            Iterations: 15\n",
      "            Function evaluations: 766\n",
      "            Gradient evaluations: 15\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.1903537394801752e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.344415998622122e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.236033968519165e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 7.196372469611893e-07\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 5.519950021022894e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.553993051769471e-07\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.9925408774167575e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 510\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.617158072703348e-07\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8416062018292171e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "                  mean      stdev\n",
      "optimizer                        \n",
      "HRP           0.001452   0.000257\n",
      "markowitz     0.010401   0.008391\n",
      "NCO          17.789596  70.664771\n",
      "Risk Parity   0.000257   0.000215\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='optimizer'>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Variance Error Estimator\n",
    "\n",
    "ee = VarianceErrorEstimator()\n",
    "results = mcos.simulate_optimizations(obs_sim, num_sims, op, ee, [cov_trans])\n",
    "print(results)\n",
    "results.plot.bar()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7724947797965462e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.2045228885582499e-05\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.122288137011796e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7124478725173924e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.59534984743711e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 510\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3143124043856894e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 306\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.0918974847661426e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.316857785988417e-05\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.072664128890502e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8940622907669193e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.8405337118159567e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.128211257304991e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7459396877469725e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 4.32699239833922e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.5557472088640269e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 459\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0364943363490813e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.626742734104214e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3504077049269124e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 408\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.130873141550035e-06\n",
      "            Iterations: 13\n",
      "            Function evaluations: 664\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.795865874518976e-06\n",
      "            Iterations: 12\n",
      "            Function evaluations: 613\n",
      "            Gradient evaluations: 12\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.899194929297024e-07\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.130113584897958e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 306\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.114420239858154e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3886933431671774e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4287685252179948e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.000681485906713e-05\n",
      "            Iterations: 9\n",
      "            Function evaluations: 459\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.8052403304980433e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 9.319476098287174e-07\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.071023165823107e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.2916730343966397e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 408\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.0227905748840581e-05\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8398180121082502e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.661293375503408e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.3048145526280604e-06\n",
      "            Iterations: 14\n",
      "            Function evaluations: 715\n",
      "            Gradient evaluations: 14\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.2332453306285005e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 459\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.7109879868131242e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.4526261842535712e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.800931425771835e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.074048714038331e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.628415755159725e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.42772863880323e-06\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.8121070694008517e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.722734929510368e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 8.831052859061397e-07\n",
      "            Iterations: 8\n",
      "            Function evaluations: 409\n",
      "            Gradient evaluations: 8\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.4080274196352e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 358\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.715857770666272e-06\n",
      "            Iterations: 6\n",
      "            Function evaluations: 307\n",
      "            Gradient evaluations: 6\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.6741976096575404e-06\n",
      "            Iterations: 11\n",
      "            Function evaluations: 562\n",
      "            Gradient evaluations: 11\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.302159220232317e-06\n",
      "            Iterations: 10\n",
      "            Function evaluations: 511\n",
      "            Gradient evaluations: 10\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 2.3303280861539076e-06\n",
      "            Iterations: 9\n",
      "            Function evaluations: 460\n",
      "            Gradient evaluations: 9\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.742113600938618e-05\n",
      "            Iterations: 13\n",
      "            Function evaluations: 664\n",
      "            Gradient evaluations: 13\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 1.564533452053536e-06\n",
      "            Iterations: 7\n",
      "            Function evaluations: 357\n",
      "            Gradient evaluations: 7\n",
      "                 mean     stdev\n",
      "optimizer                      \n",
      "HRP          0.223237  0.583484\n",
      "markowitz    0.810495  0.790587\n",
      "NCO         -0.543953  2.758543\n",
      "Risk Parity  0.287643  0.950699\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='optimizer'>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sharpe Error Estimator\n",
    "\n",
    "ee = SharpeRatioErrorEstimator()\n",
    "results = mcos.simulate_optimizations(obs_sim, num_sims, op, ee, [cov_trans])\n",
    "print(results)\n",
    "results.plot.bar()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}