Regularized-Portfolio-Optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regularized Portfolio Optimization\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "200\n"
     ]
    }
   ],
   "source": [
    "file = np.loadtxt(open(\"XReturns.csv\"), delimiter=\",\")\n",
    "X = file\n",
    "\n",
    "# X is a 200x48 matrix, 200 time steps and 48 assets\n",
    "# we will select the optimal wight of each asset to minimize the Risk (volatility) of the Portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First 120 steps will be use for training and the rest (80) for testing\n",
    "XTrain = X[0:120,:]\n",
    "XTest = X[120:200,:]\n",
    "\n",
    "XTrain = XTrain.transpose()\n",
    "XTest = XTest.transpose()\n",
    "\n",
    "# Clculating Covariance matrices\n",
    "# [we get 48x48 matrices, each value represents the covariance of one asset against one other]\n",
    "Cov_Train = np.cov(XTrain)\n",
    "Cov_Test = np.cov(XTest)\n",
    "\n",
    "p = 48\n",
    "vol_Test = np.zeros((1000,1))\n",
    "lambdas = np.zeros((1000,1))\n",
    "cont = 0\n",
    "\n",
    "for i in np.arange(0,10,.01):\n",
    "    inv_Cov_Train = np.linalg.inv(Cov_Train+i*np.identity(p)) # Recuerda que i es lambda\n",
    "    z = np.sum(inv_Cov_Train)\n",
    "    w = np.sum(inv_Cov_Train,axis=1)/z\n",
    "    vol_Test[cont] = w.transpose().dot(Cov_Test).dot(w)\n",
    "    lambdas[cont] = i # Solamente acumula los lambdas\n",
    "    cont = cont+1   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot0 = plt.figure(0,figsize=(6,4), dpi=100)\n",
    "plt.title('Minimizing Lambda')\n",
    "plt.plot(lambdas,vol_Test,'g' )\n",
    "plt.xlabel('Lambda')\n",
    "plt.ylabel('Volatility')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Asset        Weight\n",
      "  1    0.08560365061709004\n",
      "  2    0.08331023240359364\n",
      "  3    0.031796112328329205\n",
      "  4    0.07296784046159457\n",
      "  5    0.03205825783721221\n",
      "  6    -0.03597741154015003\n",
      "  7    0.021044899510456554\n",
      "  8    0.035785571690846604\n",
      "  9    0.0331428467714681\n",
      "  10    0.03735531674851317\n",
      "  11    -0.05941369177466519\n",
      "  12    0.013921378427290526\n",
      "  13    0.04738029238266714\n",
      "  14    -0.0017349643943913922\n",
      "  15    0.12866887160981372\n",
      "  16    0.07888605844652258\n",
      "  17    -0.008661595241488136\n",
      "  18    -0.07232286631003469\n",
      "  19    0.02581595941345284\n",
      "  20    0.0526897008068009\n",
      "  21    -0.0015984373044144937\n",
      "  22    0.013275408250489352\n",
      "  23    -0.013558299496167605\n",
      "  24    0.003933000430081748\n",
      "  25    0.018738001656508768\n",
      "  26    -0.00767061714154138\n",
      "  27    -0.047417476971620375\n",
      "  28    -0.03568406797529227\n",
      "  29    0.015067902204976143\n",
      "  30    0.008665114568755952\n",
      "  31    0.1225823126535635\n",
      "  32    0.0506742067357646\n",
      "  33    0.0879152591177243\n",
      "  34    0.01923453638547372\n",
      "  35    -0.019810132668349127\n",
      "  36    -0.029300100788065407\n",
      "  37    -0.07184415494724758\n",
      "  38    0.03770824901874184\n",
      "  39    0.02413486290800696\n",
      "  40    -0.0003073189567349962\n",
      "  41    -0.006143055563952045\n",
      "  42    -0.014222947979436594\n",
      "  43    0.003790135173510404\n",
      "  44    0.004026392525149226\n",
      "  45    0.05234990716480214\n",
      "  46    0.064035546006342\n",
      "  47    0.050691189701590526\n",
      "  48    0.06841812509641851\n"
     ]
    }
   ],
   "source": [
    "# Computing the value of lambda that minimizes volatility, from graph we can see is around 3\n",
    "min_vol = np.where(vol_Test == min(vol_Test))\n",
    "lambda_min = lambdas[min_vol]\n",
    "\n",
    "# Computing weights of 48 assets with minimizing lambda\n",
    "inv_Cov_Train = np.linalg.inv(Cov_Train+lambda_min*np.identity(p))\n",
    "z = np.sum(inv_Cov_Train)\n",
    "w = np.sum(inv_Cov_Train,axis=1)/z\n",
    "\n",
    "# Weight of every asset, remember that negative weights means shorting\n",
    "print(\"Asset        Weight\")\n",
    "for i in range(48):\n",
    "    print(\" \",i+1,\"  \",w[i])\n"
   ]
  },
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