gr_markovitz.ipynb

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   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "dfCC = pd.read_csv('./procST4.csv')\n",
    "returnMat = dfCC.to_numpy()\n",
    "returnMat = returnMat[:,1:]\n",
    "returnMat = returnMat.T\n",
    "meanVecNP = returnMat.mean(axis=1)\n",
    "covMatrix = np.cov(returnMat,bias=True)\n",
    "from ipypb import irange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linalg as la\n",
    "\n",
    "\n",
    "def nearestPD(A):\n",
    "    B = (A + A.T) / 2\n",
    "    _, s, V = la.svd(B)\n",
    "    H = np.dot(V.T, np.dot(np.diag(s), V))\n",
    "    A2 = (B + H) / 2\n",
    "    A3 = (A2 + A2.T) / 2\n",
    "    if isPD(A3):\n",
    "        return A3\n",
    "    spacing = np.spacing(la.norm(A))\n",
    "    I = np.eye(A.shape[0])\n",
    "    k = 1\n",
    "    while not isPD(A3):\n",
    "        mineig = np.min(np.real(la.eigvals(A3)))\n",
    "        A3 += I * (-mineig * k**2 + spacing)\n",
    "        k += 1\n",
    "    return A3\n",
    "\n",
    "def isPD(B):\n",
    "    try:\n",
    "        _ = la.cholesky(B)\n",
    "        return True\n",
    "    except la.LinAlgError:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "--------------------------------------------\n",
      "Warning: your license will expire in 9 days\n",
      "--------------------------------------------\n",
      "\n",
      "Using license file c:\\gurobi\\gurobi.lic\n",
      "Academic license - for non-commercial use only - expires 2021-01-08\n"
     ]
    }
   ],
   "source": [
    "# Markovitz\n",
    "import matplotlib.pyplot as plt\n",
    "from gurobipy import GRB, Model\n",
    "\n",
    "m = Model(\"markovitzPortfolio\")\n",
    "meanVec = meanVecNP.tolist()\n",
    "covMatPSD = nearestPD(covMatrix).tolist()\n",
    "numAsset = len(meanVec)\n",
    "epsl = .01\n",
    "m = Model(\"portfolio\")\n",
    "m.setParam('OutputFlag', 0)\n",
    "x = m.addVars(numAsset,lb=0,ub=1, name=\"x\") # x_j_k\n",
    "m.setObjective(sum(covMatPSD[i][j]*x[i]*x[j] for i in range(numAsset) for j in range(numAsset)), GRB.MINIMIZE)\n",
    "m.addConstr(sum(x[i] for i in range(numAsset)) <= 1)\n",
    "m.addConstr(sum(x[i] for i in range(numAsset)) >= 1-epsl)\n",
    "m.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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   "source": [
    "# MinTarget = [i for i in range(5000,45000,100)]\n",
    "MinTarget = [i for i in range(15000,37000,100)]\n",
    "risk_data = np.zeros(len(MinTarget))\n",
    "ret_data = np.zeros(len(MinTarget))\n",
    "count_divers = np.zeros(len(MinTarget))\n",
    "dfExp = pd.DataFrame()\n",
    "for j in irange(len(MinTarget)):\n",
    "#     print(MinTarget[j])\n",
    "    m.addConstr(sum(x[i]*meanVec[i] for i in range(numAsset)) >= MinTarget[j],'BudgetConstr')\n",
    "    try:\n",
    "        m.optimize()\n",
    "        Invest = m.getAttr('x',x)\n",
    "        risk = m.objVal\n",
    "        m.remove(m.getConstrByName('BudgetConstr'))\n",
    "        m.update()\n",
    "        risk_data[j] = risk\n",
    "        investNP = np.array(Invest.values())\n",
    "        ret_data[j] = meanVecNP.T.dot(np.round(investNP,2))\n",
    "        count_divers[j] = np.sum(np.array(investNP) > .001, axis=0)\n",
    "        dfExp[str(MinTarget[j]) +\"_\"+ str(np.round(risk))] = np.round(investNP,3)\n",
    "    except:\n",
    "        break\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "fig = plt.figure()\n",
    "plt.rc('text', usetex=True)\n",
    "ax = fig.add_subplot(111)\n",
    "plt.plot(risk_data, ret_data, 'b-')\n",
    "plt.xlabel('SD(Risk)')\n",
    "plt.ylabel('Return')\n",
    "plt.grid()\n",
    "# plt.show()\n",
    "plt.savefig(\"dfMarkovitz_return_risk2.pdf\", bbox_inches = 'tight',pad_inches = 0)\n",
    "del m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "ret_data_bin = np.mean(np.stack( np.array_split(ret_data, 11), axis=0 ),axis=1)\n",
    "count_divers_bin = np.mean(np.stack( np.array_split(count_divers, 11), axis=0 ),axis=1)\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "plt.rc('text', usetex=True)\n",
    "plt.bar(ret_data_bin , count_divers_bin,8000)\n",
    "plt.xlabel('Return')\n",
    "plt.ylabel('Number of selected assets')\n",
    "# plt.show()\n",
    "plt.savefig(\"dfMarkovitz_diversity2.pdf\", bbox_inches = 'tight',pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfExp.to_csv(\"dfMarkovitz2.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "220"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ret_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "71.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "355/5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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