examples/RankAndSPO.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "sys.path.insert(0, os.path.abspath('..'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import cvxportfolio as cp\n",
    "\n",
    "plotdir='../../portfolio/plots/'\n",
    "datadir='../data/' \n",
    "\n",
    "sigmas=pd.read_csv(datadir+'sigmas.csv.gz',index_col=0,parse_dates=[0]).iloc[:,:-1]\n",
    "returns=pd.read_csv(datadir+'returns.csv.gz',index_col=0,parse_dates=[0])\n",
    "volumes=pd.read_csv(datadir+'volumes.csv.gz',index_col=0,parse_dates=[0]).iloc[:,:-1]\n",
    "\n",
    "w_b = pd.Series(index=returns.columns, data=1)\n",
    "w_b.USDOLLAR = 0.\n",
    "w_b/=sum(w_b)\n",
    "\n",
    "start_t=\"2012-01-01\"\n",
    "end_t=\"2016-12-31\"\n",
    "\n",
    "simulated_tcost = cp.TcostModel(half_spread=0.0005/2., nonlin_coeff=1., sigma=sigmas, volume=volumes)\n",
    "simulated_hcost = cp.HcostModel(borrow_costs=0.0001)\n",
    "simulator = cp.MarketSimulator(returns, costs=[simulated_tcost, simulated_hcost],\n",
    "                               market_volumes=volumes, cash_key='USDOLLAR')\n",
    "\n",
    "return_estimate=pd.read_csv(datadir+'return_estimate.csv.gz',index_col=0,parse_dates=[0]).dropna()\n",
    "volume_estimate=pd.read_csv(datadir+'volume_estimate.csv.gz',index_col=0,parse_dates=[0]).dropna()\n",
    "sigma_estimate=pd.read_csv(datadir+'sigma_estimate.csv.gz',index_col=0,parse_dates=[0]).dropna()\n",
    "\n",
    "optimization_tcost = cp.TcostModel(half_spread=0.0005/2., nonlin_coeff=1., \n",
    "                                sigma=sigma_estimate, volume=volume_estimate)\n",
    "optimization_hcost=cp.HcostModel(borrow_costs=0.0001)\n",
    "\n",
    "exposures = pd.read_csv(datadir+'exposures.csv.gz',index_col=[0,1],parse_dates=[0]).dropna()\n",
    "factor_sigma = pd.read_csv(datadir+'factor_sigma.csv.gz',index_col=[0,1],parse_dates=[0]).dropna()\n",
    "idyo_vars = pd.read_csv(datadir+'idyo_vars.csv.gz',index_col=0,parse_dates=[0]).dropna()\n",
    "risk_model = cp.FactorModelSigma(exposures, factor_sigma, idyo_vars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of periods                              1258\n",
      "Initial timestamp               2012-01-03 00:00:00\n",
      "Final timestamp                 2016-12-30 00:00:00\n",
      "Portfolio return (%)                         16.990\n",
      "Excess return (%)                            16.881\n",
      "Excess risk (%)                              13.909\n",
      "Sharpe ratio                                  1.214\n",
      "Max. drawdown                                14.616\n",
      "Turnover (%)                                252.000\n",
      "Average policy time (sec)                     0.002\n",
      "Average simulator time (sec)                  0.006\n"
     ]
    }
   ],
   "source": [
    "rank_and_long_short = cp.RankAndLongShort(return_forecast=return_estimate, \n",
    "                                       num_short = 10, num_long = 10, target_turnover = .01)\n",
    "result_rank = simulator.run_backtest(1E8*w_b,start_time=start_t,end_time=end_t,policy=rank_and_long_short)\n",
    "\n",
    "result_rank.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Cannot broadcast dimensions  (60, 432) (432,)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [16]\u001b[0m, in \u001b[0;36m<cell line: 3>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m spo \u001b[38;5;241m=\u001b[39m cp\u001b[38;5;241m.\u001b[39mSinglePeriodOpt(return_estimate, [\u001b[38;5;241m10.\u001b[39m\u001b[38;5;241m*\u001b[39mrisk_model,\u001b[38;5;241m7\u001b[39m\u001b[38;5;241m*\u001b[39moptimization_tcost,\u001b[38;5;241m10.\u001b[39m\u001b[38;5;241m*\u001b[39moptimization_hcost],\n\u001b[1;32m      2\u001b[0m                          [cp\u001b[38;5;241m.\u001b[39mLeverageLimit(\u001b[38;5;241m3\u001b[39m)])\n\u001b[0;32m----> 3\u001b[0m result_spo \u001b[38;5;241m=\u001b[39m \u001b[43msimulator\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_backtest\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1E8\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mw_b\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstart_time\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mstart_t\u001b[49m\u001b[43m,\u001b[49m\u001b[43mend_time\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mend_t\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpolicy\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mspo\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      5\u001b[0m result_spo\u001b[38;5;241m.\u001b[39msummary()\n",
      "File \u001b[0;32m~/repos/cvxportfolio2023/cvxportfolio/simulator.py:116\u001b[0m, in \u001b[0;36mMarketSimulator.run_backtest\u001b[0;34m(self, initial_portfolio, start_time, end_time, policy, loglevel)\u001b[0m\n\u001b[1;32m    114\u001b[0m start \u001b[38;5;241m=\u001b[39m time\u001b[38;5;241m.\u001b[39mtime()\n\u001b[1;32m    115\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 116\u001b[0m     u \u001b[38;5;241m=\u001b[39m \u001b[43mpolicy\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_trades\u001b[49m\u001b[43m(\u001b[49m\u001b[43mh\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    117\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m cvx\u001b[38;5;241m.\u001b[39mSolverError:\n\u001b[1;32m    118\u001b[0m     logging\u001b[38;5;241m.\u001b[39mwarning(\n\u001b[1;32m    119\u001b[0m         \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mSolver failed on timestamp \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m. Default to no trades.\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;241m%\u001b[39m t)\n",
      "File \u001b[0;32m~/repos/cvxportfolio2023/cvxportfolio/policies.py:266\u001b[0m, in \u001b[0;36mSinglePeriodOpt.get_trades\u001b[0;34m(self, portfolio, t)\u001b[0m\n\u001b[1;32m    263\u001b[0m costs, constraints \u001b[38;5;241m=\u001b[39m [], []\n\u001b[1;32m    265\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m cost \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcosts:\n\u001b[0;32m--> 266\u001b[0m     cost_expr, const_expr \u001b[38;5;241m=\u001b[39m \u001b[43mcost\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mweight_expr\u001b[49m\u001b[43m(\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwplus\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mz\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    267\u001b[0m     costs\u001b[38;5;241m.\u001b[39mappend(cost_expr)\n\u001b[1;32m    268\u001b[0m     constraints \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m const_expr\n",
      "File \u001b[0;32m~/repos/cvxportfolio2023/cvxportfolio/risks.py:58\u001b[0m, in \u001b[0;36mBaseRiskModel.weight_expr\u001b[0;34m(self, t, w_plus, z, value)\u001b[0m\n\u001b[1;32m     57\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mweight_expr\u001b[39m(\u001b[38;5;28mself\u001b[39m, t, w_plus, z, value):\n\u001b[0;32m---> 58\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mexpression \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_estimate\u001b[49m\u001b[43m(\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mw_plus\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mw_bench\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mz\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     59\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mgamma \u001b[38;5;241m*\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mexpression, []\n",
      "File \u001b[0;32m~/repos/cvxportfolio2023/cvxportfolio/risks.py:158\u001b[0m, in \u001b[0;36mFactorModelSigma._estimate\u001b[0;34m(self, t, wplus, z, value)\u001b[0m\n\u001b[1;32m    157\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_estimate\u001b[39m(\u001b[38;5;28mself\u001b[39m, t, wplus, z, value):\n\u001b[0;32m--> 158\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mexpression \u001b[38;5;241m=\u001b[39m cvx\u001b[38;5;241m.\u001b[39msum_squares(\u001b[43mcvx\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmultiply\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    159\u001b[0m \u001b[43m        \u001b[49m\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msqrt\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvalues_in_time\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43midiosync\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwplus\u001b[49m\u001b[43m)\u001b[49m) \u001b[38;5;241m+\u001b[39m \\\n\u001b[1;32m    160\u001b[0m         cvx\u001b[38;5;241m.\u001b[39mquad_form((wplus\u001b[38;5;241m.\u001b[39mT \u001b[38;5;241m*\u001b[39m values_in_time(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mexposures, t)\u001b[38;5;241m.\u001b[39mvalues\u001b[38;5;241m.\u001b[39mT)\u001b[38;5;241m.\u001b[39mT,\n\u001b[1;32m    161\u001b[0m                       values_in_time(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfactor_Sigma, t)\u001b[38;5;241m.\u001b[39mvalues)\n\u001b[1;32m    162\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mexpression\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/affine/binary_operators.py:241\u001b[0m, in \u001b[0;36mmultiply.__init__\u001b[0;34m(self, lh_expr, rh_expr)\u001b[0m\n\u001b[1;32m    239\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;28mself\u001b[39m, lh_expr, rh_expr) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    240\u001b[0m     lh_expr, rh_expr \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbroadcast(lh_expr, rh_expr)\n\u001b[0;32m--> 241\u001b[0m     \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mmultiply\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__init__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mlh_expr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrh_expr\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/affine/binary_operators.py:50\u001b[0m, in \u001b[0;36mBinaryOperator.__init__\u001b[0;34m(self, lh_exp, rh_exp)\u001b[0m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;28mself\u001b[39m, lh_exp, rh_exp) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m---> 50\u001b[0m     \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mBinaryOperator\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__init__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mlh_exp\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mrh_exp\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/atom.py:51\u001b[0m, in \u001b[0;36mAtom.__init__\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39margs \u001b[38;5;241m=\u001b[39m [Atom\u001b[38;5;241m.\u001b[39mcast_to_const(arg) \u001b[38;5;28;01mfor\u001b[39;00m arg \u001b[38;5;129;01min\u001b[39;00m args]\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mvalidate_arguments()\n\u001b[0;32m---> 51\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_shape \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshape_from_args\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     52\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_shape) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m     53\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAtoms must be at most 2D.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/affine/binary_operators.py:278\u001b[0m, in \u001b[0;36mmultiply.shape_from_args\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    275\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mshape_from_args\u001b[39m(\u001b[38;5;28mself\u001b[39m) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m Tuple[\u001b[38;5;28mint\u001b[39m, \u001b[38;5;241m.\u001b[39m\u001b[38;5;241m.\u001b[39m\u001b[38;5;241m.\u001b[39m]:\n\u001b[1;32m    276\u001b[0m     \u001b[38;5;124;03m\"\"\"The sum of the argument dimensions - 1.\u001b[39;00m\n\u001b[1;32m    277\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 278\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mu\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshape\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msum_shapes\u001b[49m\u001b[43m(\u001b[49m\u001b[43m[\u001b[49m\u001b[43marg\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshape\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43marg\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/utilities/shape.py:48\u001b[0m, in \u001b[0;36msum_shapes\u001b[0;34m(shapes)\u001b[0m\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m t \u001b[38;5;129;01min\u001b[39;00m shapes[\u001b[38;5;241m1\u001b[39m:]:\n\u001b[1;32m     46\u001b[0m     \u001b[38;5;66;03m# Only allow broadcasting for 0D arrays or summation of scalars.\u001b[39;00m\n\u001b[1;32m     47\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m shape \u001b[38;5;241m!=\u001b[39m t \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(squeezed(shape)) \u001b[38;5;241m!=\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(squeezed(t)) \u001b[38;5;241m!=\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[0;32m---> 48\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\n\u001b[1;32m     49\u001b[0m             \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mCannot broadcast dimensions \u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m+\u001b[39m\n\u001b[1;32m     50\u001b[0m             \u001b[38;5;28mlen\u001b[39m(shapes)\u001b[38;5;241m*\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m \u001b[38;5;28mtuple\u001b[39m(shapes))\n\u001b[1;32m     52\u001b[0m     longer \u001b[38;5;241m=\u001b[39m shape \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(shape) \u001b[38;5;241m>\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(t) \u001b[38;5;28;01melse\u001b[39;00m t\n\u001b[1;32m     53\u001b[0m     shorter \u001b[38;5;241m=\u001b[39m shape \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(shape) \u001b[38;5;241m<\u001b[39m \u001b[38;5;28mlen\u001b[39m(t) \u001b[38;5;28;01melse\u001b[39;00m t\n",
      "\u001b[0;31mValueError\u001b[0m: Cannot broadcast dimensions  (60, 432) (432,)"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/utilities/shape.py\u001b[0m(48)\u001b[0;36msum_shapes\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m     46 \u001b[0;31m        \u001b[0;31m# Only allow broadcasting for 0D arrays or summation of scalars.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     47 \u001b[0;31m        \u001b[0;32mif\u001b[0m \u001b[0mshape\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msqueezed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msqueezed\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m---> 48 \u001b[0;31m            raise ValueError(\n",
      "\u001b[0m\u001b[0;32m     49 \u001b[0;31m                \u001b[0;34m\"Cannot broadcast dimensions \"\u001b[0m \u001b[0;34m+\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     50 \u001b[0;31m                len(shapes)*\" %s\" % tuple(shapes))\n",
      "\u001b[0m\n",
      "ipdb> u\n",
      "> \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/affine/binary_operators.py\u001b[0m(278)\u001b[0;36mshape_from_args\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m    276 \u001b[0;31m        \"\"\"The sum of the argument dimensions - 1.\n",
      "\u001b[0m\u001b[0;32m    277 \u001b[0;31m        \"\"\"\n",
      "\u001b[0m\u001b[0;32m--> 278 \u001b[0;31m        \u001b[0;32mreturn\u001b[0m \u001b[0mu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum_shapes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    279 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    280 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0mis_psd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mbool\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n",
      "ipdb> u\n",
      "> \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/atom.py\u001b[0m(51)\u001b[0;36m__init__\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m     49 \u001b[0;31m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mAtom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcast_to_const\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marg\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     50 \u001b[0;31m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalidate_arguments\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m---> 51 \u001b[0;31m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_shape\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape_from_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     52 \u001b[0;31m        \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_shape\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     53 \u001b[0;31m            \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Atoms must be at most 2D.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n",
      "ipdb> u\n",
      "> \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/affine/binary_operators.py\u001b[0m(50)\u001b[0;36m__init__\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m     48 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     49 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlh_exp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrh_exp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m---> 50 \u001b[0;31m        \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mBinaryOperator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlh_exp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrh_exp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     51 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     52 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n",
      "ipdb> u\n",
      "> \u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/cvxpy/atoms/affine/binary_operators.py\u001b[0m(241)\u001b[0;36m__init__\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m    239 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlh_expr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrh_expr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    240 \u001b[0;31m        \u001b[0mlh_expr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrh_expr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbroadcast\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlh_expr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrh_expr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m--> 241 \u001b[0;31m        \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlh_expr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrh_expr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    242 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    243 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0mis_atom_log_log_convex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mbool\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n",
      "ipdb> u\n",
      "> \u001b[0;32m/Users/enzo/repos/cvxportfolio2023/cvxportfolio/risks.py\u001b[0m(158)\u001b[0;36m_estimate\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m    156 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    157 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0m_estimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwplus\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m--> 158 \u001b[0;31m        self.expression = cvx.sum_squares(cvx.multiply(\n",
      "\u001b[0m\u001b[0;32m    159 \u001b[0;31m            np.sqrt(values_in_time(self.idiosync, t)), wplus)) + \\\n",
      "\u001b[0m\u001b[0;32m    160 \u001b[0;31m            cvx.quad_form((wplus.T * values_in_time(self.exposures, t).values.T).T,\n",
      "\u001b[0m\n",
      "ipdb> u\n",
      "> \u001b[0;32m/Users/enzo/repos/cvxportfolio2023/cvxportfolio/risks.py\u001b[0m(58)\u001b[0;36mweight_expr\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m     56 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     57 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0mweight_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw_plus\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m---> 58 \u001b[0;31m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpression\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_estimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw_plus\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mw_bench\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     59 \u001b[0;31m        \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     60 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n",
      "ipdb> u\n",
      "> \u001b[0;32m/Users/enzo/repos/cvxportfolio2023/cvxportfolio/policies.py\u001b[0m(266)\u001b[0;36mget_trades\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m    264 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    265 \u001b[0;31m        \u001b[0;32mfor\u001b[0m \u001b[0mcost\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcosts\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m--> 266 \u001b[0;31m            \u001b[0mcost_expr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconst_expr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcost\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mweight_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwplus\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    267 \u001b[0;31m            \u001b[0mcosts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcost_expr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    268 \u001b[0;31m            \u001b[0mconstraints\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mconst_expr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n",
      "ipdb> d\n",
      "> \u001b[0;32m/Users/enzo/repos/cvxportfolio2023/cvxportfolio/risks.py\u001b[0m(58)\u001b[0;36mweight_expr\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m     56 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     57 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0mweight_expr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw_plus\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m---> 58 \u001b[0;31m        \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpression\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_estimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw_plus\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mw_bench\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     59 \u001b[0;31m        \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgamma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m     60 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\n",
      "ipdb> d\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> \u001b[0;32m/Users/enzo/repos/cvxportfolio2023/cvxportfolio/risks.py\u001b[0m(158)\u001b[0;36m_estimate\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m    156 \u001b[0;31m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m    157 \u001b[0;31m    \u001b[0;32mdef\u001b[0m \u001b[0m_estimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwplus\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0m\u001b[0;32m--> 158 \u001b[0;31m        self.expression = cvx.sum_squares(cvx.multiply(\n",
      "\u001b[0m\u001b[0;32m    159 \u001b[0;31m            np.sqrt(values_in_time(self.idiosync, t)), wplus)) + \\\n",
      "\u001b[0m\u001b[0;32m    160 \u001b[0;31m            cvx.quad_form((wplus.T * values_in_time(self.exposures, t).values.T).T,\n",
      "\u001b[0m\n",
      "ipdb> values_in_time(self.idiosync, t)\n",
      "                 MMM       ABT       ACN      ATVI      ADBE       AAP  \\\n",
      "2012-01-01  0.000061  0.000041  0.000126  0.000171  0.000273  0.000166   \n",
      "2012-02-01  0.000060  0.000041  0.000129  0.000168  0.000267  0.000161   \n",
      "2012-03-01  0.000058  0.000041  0.000130  0.000155  0.000262  0.000163   \n",
      "2012-04-01  0.000055  0.000040  0.000130  0.000156  0.000261  0.000162   \n",
      "2012-05-01  0.000053  0.000040  0.000128  0.000147  0.000256  0.000156   \n",
      "2012-06-01  0.000053  0.000040  0.000125  0.000152  0.000252  0.000193   \n",
      "2012-07-01  0.000050  0.000040  0.000117  0.000155  0.000238  0.000193   \n",
      "2012-08-01  0.000050  0.000037  0.000116  0.000159  0.000236  0.000202   \n",
      "2012-09-01  0.000049  0.000037  0.000116  0.000159  0.000238  0.000203   \n",
      "2012-10-01  0.000051  0.000039  0.000119  0.000158  0.000160  0.000207   \n",
      "2012-11-01  0.000046  0.000046  0.000117  0.000156  0.000125  0.000205   \n",
      "2012-12-01  0.000046  0.000047  0.000115  0.000154  0.000122  0.000230   \n",
      "2013-01-01  0.000044  0.000047  0.000102  0.000154  0.000122  0.000228   \n",
      "2013-02-01  0.000042  0.000051  0.000102  0.000155  0.000121  0.000227   \n",
      "2013-03-01  0.000041  0.000051  0.000102  0.000164  0.000118  0.000230   \n",
      "2013-04-01  0.000039  0.000053  0.000097  0.000164  0.000114  0.000235   \n",
      "2013-05-01  0.000041  0.000054  0.000097  0.000163  0.000113  0.000237   \n",
      "2013-06-01  0.000041  0.000059  0.000094  0.000175  0.000114  0.000211   \n",
      "2013-07-01  0.000041  0.000061  0.000110  0.000179  0.000119  0.000206   \n",
      "2013-08-01  0.000036  0.000064  0.000110  0.000231  0.000119  0.000202   \n",
      "2013-09-01  0.000034  0.000063  0.000104  0.000225  0.000114  0.000194   \n",
      "2013-10-01  0.000032  0.000065  0.000102  0.000222  0.000118  0.000196   \n",
      "2013-11-01  0.000026  0.000068  0.000097  0.000221  0.000114  0.000243   \n",
      "2013-12-01  0.000025  0.000069  0.000098  0.000215  0.000113  0.000237   \n",
      "2014-01-01  0.000031  0.000070  0.000099  0.000215  0.000141  0.000244   \n",
      "2014-02-01  0.000032  0.000071  0.000095  0.000210  0.000142  0.000249   \n",
      "2014-03-01  0.000033  0.000072  0.000095  0.000248  0.000146  0.000255   \n",
      "2014-04-01  0.000033  0.000071  0.000098  0.000246  0.000142  0.000253   \n",
      "2014-05-01  0.000034  0.000073  0.000098  0.000243  0.000144  0.000255   \n",
      "2014-06-01  0.000034  0.000073  0.000098  0.000249  0.000143  0.000219   \n",
      "2014-07-01  0.000033  0.000074  0.000095  0.000248  0.000153  0.000212   \n",
      "2014-08-01  0.000032  0.000080  0.000095  0.000239  0.000150  0.000182   \n",
      "2014-09-01  0.000032  0.000081  0.000094  0.000234  0.000147  0.000193   \n",
      "2014-10-01  0.000031  0.000081  0.000082  0.000235  0.000142  0.000191   \n",
      "2014-11-01  0.000033  0.000073  0.000082  0.000239  0.000144  0.000197   \n",
      "2014-12-01  0.000033  0.000070  0.000081  0.000249  0.000144  0.000171   \n",
      "2015-01-01  0.000034  0.000069  0.000080  0.000251  0.000157  0.000172   \n",
      "2015-02-01  0.000033  0.000067  0.000079  0.000258  0.000158  0.000174   \n",
      "2015-03-01  0.000033  0.000067  0.000077  0.000247  0.000158  0.000178   \n",
      "2015-04-01  0.000033  0.000064  0.000083  0.000246  0.000160  0.000178   \n",
      "2015-05-01  0.000032  0.000063  0.000082  0.000219  0.000157  0.000184   \n",
      "2015-06-01  0.000031  0.000057  0.000081  0.000211  0.000155  0.000192   \n",
      "2015-07-01  0.000031  0.000055  0.000063  0.000213  0.000148  0.000185   \n",
      "2015-08-01  0.000033  0.000054  0.000062  0.000173  0.000149  0.000185   \n",
      "2015-09-01  0.000035  0.000057  0.000062  0.000181  0.000152  0.000204   \n",
      "2015-10-01  0.000035  0.000056  0.000060  0.000185  0.000147  0.000221   \n",
      "2015-11-01  0.000035  0.000054  0.000060  0.000183  0.000152  0.000176   \n",
      "2015-12-01  0.000035  0.000053  0.000059  0.000192  0.000149  0.000211   \n",
      "2016-01-01  0.000039  0.000053  0.000055  0.000192  0.000122  0.000215   \n",
      "2016-02-01  0.000042  0.000062  0.000056  0.000198  0.000128  0.000220   \n",
      "2016-03-01  0.000043  0.000068  0.000057  0.000180  0.000128  0.000200   \n",
      "2016-04-01  0.000043  0.000068  0.000060  0.000187  0.000130  0.000203   \n",
      "2016-05-01  0.000044  0.000078  0.000058  0.000192  0.000128  0.000203   \n",
      "2016-06-01  0.000044  0.000078  0.000057  0.000188  0.000125  0.000207   \n",
      "2016-07-01  0.000045  0.000077  0.000056  0.000193  0.000120  0.000208   \n",
      "2016-08-01  0.000046  0.000073  0.000058  0.000202  0.000120  0.000207   \n",
      "2016-09-01  0.000046  0.000073  0.000058  0.000204  0.000119  0.000202   \n",
      "2016-10-01  0.000046  0.000074  0.000063  0.000201  0.000120  0.000204   \n",
      "2016-11-01  0.000043  0.000077  0.000064  0.000200  0.000118  0.000206   \n",
      "2016-12-01  0.000045  0.000084  0.000071  0.000193  0.000115  0.000251   \n",
      "\n",
      "                 AES       AET       AFL       AMG  ...       WYN      WYNN  \\\n",
      "2012-01-01  0.000164  0.000165  0.000123  0.000134  ...  0.000159  0.000307   \n",
      "2012-02-01  0.000162  0.000160  0.000124  0.000133  ...  0.000144  0.000293   \n",
      "2012-03-01  0.000156  0.000163  0.000121  0.000116  ...  0.000145  0.000306   \n",
      "2012-04-01  0.000150  0.000163  0.000123  0.000113  ...  0.000142  0.000302   \n",
      "2012-05-01  0.000147  0.000173  0.000122  0.000108  ...  0.000137  0.000299   \n",
      "2012-06-01  0.000128  0.000175  0.000116  0.000108  ...  0.000133  0.000295   \n",
      "2012-07-01  0.000126  0.000173  0.000112  0.000107  ...  0.000132  0.000293   \n",
      "2012-08-01  0.000115  0.000171  0.000111  0.000094  ...  0.000118  0.000291   \n",
      "2012-09-01  0.000116  0.000177  0.000107  0.000092  ...  0.000116  0.000287   \n",
      "2012-10-01  0.000115  0.000177  0.000107  0.000089  ...  0.000113  0.000283   \n",
      "2012-11-01  0.000116  0.000179  0.000104  0.000086  ...  0.000112  0.000273   \n",
      "2012-12-01  0.000117  0.000178  0.000103  0.000089  ...  0.000111  0.000266   \n",
      "2013-01-01  0.000113  0.000180  0.000103  0.000084  ...  0.000112  0.000265   \n",
      "2013-02-01  0.000115  0.000184  0.000107  0.000076  ...  0.000108  0.000256   \n",
      "2013-03-01  0.000115  0.000149  0.000110  0.000073  ...  0.000102  0.000250   \n",
      "2013-04-01  0.000113  0.000146  0.000107  0.000070  ...  0.000097  0.000235   \n",
      "2013-05-01  0.000113  0.000144  0.000109  0.000066  ...  0.000102  0.000235   \n",
      "2013-06-01  0.000113  0.000144  0.000097  0.000065  ...  0.000106  0.000235   \n",
      "2013-07-01  0.000114  0.000141  0.000097  0.000066  ...  0.000105  0.000235   \n",
      "2013-08-01  0.000113  0.000152  0.000095  0.000064  ...  0.000103  0.000228   \n",
      "2013-09-01  0.000104  0.000154  0.000093  0.000059  ...  0.000095  0.000226   \n",
      "2013-10-01  0.000101  0.000152  0.000087  0.000056  ...  0.000093  0.000205   \n",
      "2013-11-01  0.000095  0.000150  0.000083  0.000052  ...  0.000087  0.000179   \n",
      "2013-12-01  0.000097  0.000151  0.000084  0.000053  ...  0.000087  0.000168   \n",
      "2014-01-01  0.000102  0.000150  0.000082  0.000052  ...  0.000085  0.000165   \n",
      "2014-02-01  0.000099  0.000151  0.000078  0.000050  ...  0.000085  0.000177   \n",
      "2014-03-01  0.000100  0.000152  0.000078  0.000058  ...  0.000082  0.000153   \n",
      "2014-04-01  0.000103  0.000140  0.000076  0.000064  ...  0.000081  0.000147   \n",
      "2014-05-01  0.000101  0.000134  0.000067  0.000075  ...  0.000082  0.000163   \n",
      "2014-06-01  0.000100  0.000124  0.000065  0.000076  ...  0.000081  0.000176   \n",
      "2014-07-01  0.000100  0.000113  0.000062  0.000078  ...  0.000081  0.000181   \n",
      "2014-08-01  0.000097  0.000109  0.000064  0.000075  ...  0.000076  0.000178   \n",
      "2014-09-01  0.000091  0.000111  0.000064  0.000080  ...  0.000080  0.000181   \n",
      "2014-10-01  0.000091  0.000110  0.000064  0.000079  ...  0.000077  0.000188   \n",
      "2014-11-01  0.000097  0.000103  0.000063  0.000077  ...  0.000081  0.000180   \n",
      "2014-12-01  0.000100  0.000102  0.000062  0.000078  ...  0.000081  0.000184   \n",
      "2015-01-01  0.000107  0.000102  0.000062  0.000082  ...  0.000077  0.000197   \n",
      "2015-02-01  0.000108  0.000094  0.000057  0.000087  ...  0.000076  0.000208   \n",
      "2015-03-01  0.000111  0.000095  0.000052  0.000088  ...  0.000079  0.000220   \n",
      "2015-04-01  0.000108  0.000093  0.000047  0.000086  ...  0.000078  0.000227   \n",
      "2015-05-01  0.000105  0.000093  0.000041  0.000085  ...  0.000077  0.000294   \n",
      "2015-06-01  0.000103  0.000089  0.000041  0.000085  ...  0.000073  0.000298   \n",
      "2015-07-01  0.000105  0.000091  0.000040  0.000081  ...  0.000072  0.000312   \n",
      "2015-08-01  0.000110  0.000093  0.000039  0.000077  ...  0.000071  0.000333   \n",
      "2015-09-01  0.000114  0.000096  0.000038  0.000079  ...  0.000071  0.000355   \n",
      "2015-10-01  0.000117  0.000099  0.000038  0.000081  ...  0.000071  0.000371   \n",
      "2015-11-01  0.000122  0.000099  0.000036  0.000084  ...  0.000087  0.000362   \n",
      "2015-12-01  0.000132  0.000107  0.000036  0.000085  ...  0.000087  0.000371   \n",
      "2016-01-01  0.000130  0.000108  0.000037  0.000097  ...  0.000086  0.000393   \n",
      "2016-02-01  0.000141  0.000117  0.000039  0.000103  ...  0.000087  0.000392   \n",
      "2016-03-01  0.000147  0.000120  0.000041  0.000103  ...  0.000082  0.000495   \n",
      "2016-04-01  0.000151  0.000125  0.000042  0.000101  ...  0.000087  0.000510   \n",
      "2016-05-01  0.000152  0.000119  0.000041  0.000093  ...  0.000101  0.000524   \n",
      "2016-06-01  0.000153  0.000120  0.000040  0.000093  ...  0.000102  0.000542   \n",
      "2016-07-01  0.000158  0.000118  0.000040  0.000092  ...  0.000104  0.000589   \n",
      "2016-08-01  0.000159  0.000113  0.000035  0.000094  ...  0.000115  0.000603   \n",
      "2016-09-01  0.000160  0.000113  0.000035  0.000092  ...  0.000113  0.000602   \n",
      "2016-10-01  0.000161  0.000113  0.000034  0.000096  ...  0.000113  0.000606   \n",
      "2016-11-01  0.000156  0.000111  0.000034  0.000101  ...  0.000117  0.000598   \n",
      "2016-12-01  0.000155  0.000128  0.000035  0.000108  ...  0.000117  0.000577   \n",
      "\n",
      "                 XEL       XRX      XLNX      YHOO       YUM       ZBH  \\\n",
      "2012-01-01  0.000028  0.000151  0.000114  0.000265  0.000086  0.000124   \n",
      "2012-02-01  0.000028  0.000167  0.000110  0.000270  0.000087  0.000119   \n",
      "2012-03-01  0.000028  0.000168  0.000107  0.000276  0.000085  0.000118   \n",
      "2012-04-01  0.000029  0.000162  0.000105  0.000272  0.000082  0.000109   \n",
      "2012-05-01  0.000028  0.000142  0.000108  0.000262  0.000085  0.000110   \n",
      "2012-06-01  0.000029  0.000143  0.000105  0.000262  0.000086  0.000110   \n",
      "2012-07-01  0.000029  0.000145  0.000104  0.000259  0.000096  0.000111   \n",
      "2012-08-01  0.000028  0.000153  0.000102  0.000249  0.000098  0.000113   \n",
      "2012-09-01  0.000028  0.000151  0.000102  0.000259  0.000099  0.000110   \n",
      "2012-10-01  0.000028  0.000148  0.000100  0.000260  0.000102  0.000107   \n",
      "2012-11-01  0.000028  0.000155  0.000097  0.000259  0.000118  0.000097   \n",
      "2012-12-01  0.000028  0.000156  0.000099  0.000253  0.000138  0.000096   \n",
      "2013-01-01  0.000028  0.000155  0.000095  0.000250  0.000142  0.000095   \n",
      "2013-02-01  0.000028  0.000148  0.000095  0.000250  0.000145  0.000081   \n",
      "2013-03-01  0.000027  0.000149  0.000096  0.000246  0.000150  0.000080   \n",
      "2013-04-01  0.000029  0.000147  0.000087  0.000244  0.000150  0.000081   \n",
      "2013-05-01  0.000030  0.000147  0.000079  0.000244  0.000160  0.000072   \n",
      "2013-06-01  0.000030  0.000150  0.000080  0.000233  0.000161  0.000071   \n",
      "2013-07-01  0.000026  0.000152  0.000081  0.000236  0.000162  0.000069   \n",
      "2013-08-01  0.000026  0.000150  0.000087  0.000249  0.000162  0.000070   \n",
      "2013-09-01  0.000025  0.000148  0.000086  0.000230  0.000157  0.000070   \n",
      "2013-10-01  0.000025  0.000147  0.000081  0.000213  0.000152  0.000069   \n",
      "2013-11-01  0.000022  0.000161  0.000079  0.000189  0.000157  0.000070   \n",
      "2013-12-01  0.000022  0.000164  0.000082  0.000185  0.000163  0.000063   \n",
      "2014-01-01  0.000021  0.000164  0.000079  0.000178  0.000164  0.000060   \n",
      "2014-02-01  0.000020  0.000157  0.000079  0.000193  0.000167  0.000060   \n",
      "2014-03-01  0.000020  0.000153  0.000082  0.000189  0.000177  0.000060   \n",
      "2014-04-01  0.000020  0.000152  0.000081  0.000196  0.000179  0.000060   \n",
      "2014-05-01  0.000021  0.000157  0.000090  0.000195  0.000174  0.000085   \n",
      "2014-06-01  0.000019  0.000150  0.000090  0.000189  0.000171  0.000084   \n",
      "2014-07-01  0.000019  0.000151  0.000089  0.000198  0.000161  0.000082   \n",
      "2014-08-01  0.000020  0.000141  0.000119  0.000196  0.000164  0.000082   \n",
      "2014-09-01  0.000021  0.000140  0.000116  0.000199  0.000163  0.000083   \n",
      "2014-10-01  0.000021  0.000138  0.000119  0.000201  0.000162  0.000083   \n",
      "2014-11-01  0.000022  0.000147  0.000126  0.000194  0.000146  0.000083   \n",
      "2014-12-01  0.000022  0.000146  0.000121  0.000202  0.000127  0.000085   \n",
      "2015-01-01  0.000022  0.000144  0.000123  0.000201  0.000131  0.000086   \n",
      "2015-02-01  0.000022  0.000139  0.000134  0.000206  0.000127  0.000090   \n",
      "2015-03-01  0.000020  0.000141  0.000135  0.000204  0.000125  0.000089   \n",
      "2015-04-01  0.000021  0.000142  0.000140  0.000207  0.000125  0.000089   \n",
      "2015-05-01  0.000019  0.000148  0.000136  0.000207  0.000116  0.000090   \n",
      "2015-06-01  0.000018  0.000146  0.000134  0.000220  0.000126  0.000090   \n",
      "2015-07-01  0.000018  0.000142  0.000133  0.000221  0.000121  0.000090   \n",
      "2015-08-01  0.000018  0.000148  0.000128  0.000201  0.000121  0.000085   \n",
      "2015-09-01  0.000018  0.000147  0.000128  0.000205  0.000133  0.000088   \n",
      "2015-10-01  0.000018  0.000145  0.000130  0.000208  0.000135  0.000084   \n",
      "2015-11-01  0.000019  0.000139  0.000134  0.000207  0.000203  0.000092   \n",
      "2015-12-01  0.000018  0.000145  0.000131  0.000206  0.000206  0.000093   \n",
      "2016-01-01  0.000019  0.000147  0.000129  0.000215  0.000205  0.000094   \n",
      "2016-02-01  0.000023  0.000140  0.000142  0.000208  0.000209  0.000098   \n",
      "2016-03-01  0.000025  0.000145  0.000151  0.000236  0.000199  0.000100   \n",
      "2016-04-01  0.000025  0.000148  0.000153  0.000236  0.000202  0.000101   \n",
      "2016-05-01  0.000025  0.000175  0.000150  0.000232  0.000200  0.000076   \n",
      "2016-06-01  0.000026  0.000174  0.000151  0.000242  0.000200  0.000075   \n",
      "2016-07-01  0.000027  0.000174  0.000151  0.000230  0.000201  0.000076   \n",
      "2016-08-01  0.000027  0.000175  0.000120  0.000222  0.000193  0.000078   \n",
      "2016-09-01  0.000025  0.000175  0.000118  0.000228  0.000193  0.000078   \n",
      "2016-10-01  0.000025  0.000173  0.000115  0.000215  0.000193  0.000077   \n",
      "2016-11-01  0.000024  0.000162  0.000108  0.000210  0.000197  0.000113   \n",
      "2016-12-01  0.000025  0.000167  0.000110  0.000202  0.000196  0.000117   \n",
      "\n",
      "                ZION      USDOLLAR  \n",
      "2012-01-01  0.000193  1.948000e-11  \n",
      "2012-02-01  0.000177  1.928000e-11  \n",
      "2012-03-01  0.000177  1.913000e-11  \n",
      "2012-04-01  0.000185  1.804000e-11  \n",
      "2012-05-01  0.000179  1.655000e-11  \n",
      "2012-06-01  0.000170  1.542000e-11  \n",
      "2012-07-01  0.000164  1.489000e-11  \n",
      "2012-08-01  0.000146  1.404000e-11  \n",
      "2012-09-01  0.000145  1.314000e-11  \n",
      "2012-10-01  0.000138  1.230000e-11  \n",
      "2012-11-01  0.000137  1.202000e-11  \n",
      "2012-12-01  0.000135  1.120000e-11  \n",
      "2013-01-01  0.000133  1.033000e-11  \n",
      "2013-02-01  0.000136  9.159000e-12  \n",
      "2013-03-01  0.000133  8.723000e-12  \n",
      "2013-04-01  0.000133  8.541000e-12  \n",
      "2013-05-01  0.000129  8.525000e-12  \n",
      "2013-06-01  0.000129  8.557000e-12  \n",
      "2013-07-01  0.000128  8.648000e-12  \n",
      "2013-08-01  0.000123  8.552000e-12  \n",
      "2013-09-01  0.000116  8.690000e-12  \n",
      "2013-10-01  0.000112  8.668000e-12  \n",
      "2013-11-01  0.000112  8.763000e-12  \n",
      "2013-12-01  0.000112  9.034000e-12  \n",
      "2014-01-01  0.000109  9.274000e-12  \n",
      "2014-02-01  0.000098  9.389000e-12  \n",
      "2014-03-01  0.000100  8.974000e-12  \n",
      "2014-04-01  0.000093  8.749000e-12  \n",
      "2014-05-01  0.000092  8.273000e-12  \n",
      "2014-06-01  0.000088  7.781000e-12  \n",
      "2014-07-01  0.000086  7.319000e-12  \n",
      "2014-08-01  0.000089  6.722000e-12  \n",
      "2014-09-01  0.000085  6.068000e-12  \n",
      "2014-10-01  0.000083  5.373000e-12  \n",
      "2014-11-01  0.000079  4.582000e-12  \n",
      "2014-12-01  0.000077  4.091000e-12  \n",
      "2015-01-01  0.000077  3.824000e-12  \n",
      "2015-02-01  0.000078  3.550000e-12  \n",
      "2015-03-01  0.000080  3.005000e-12  \n",
      "2015-04-01  0.000080  2.606000e-12  \n",
      "2015-05-01  0.000077  2.426000e-12  \n",
      "2015-06-01  0.000076  2.320000e-12  \n",
      "2015-07-01  0.000080  2.178000e-12  \n",
      "2015-08-01  0.000081  2.185000e-12  \n",
      "2015-09-01  0.000078  2.401000e-12  \n",
      "2015-10-01  0.000076  2.450000e-12  \n",
      "2015-11-01  0.000066  2.300000e-12  \n",
      "2015-12-01  0.000064  3.053000e-12  \n",
      "2016-01-01  0.000064  6.248000e-12  \n",
      "2016-02-01  0.000064  9.981000e-12  \n",
      "2016-03-01  0.000062  1.568000e-11  \n",
      "2016-04-01  0.000055  2.151000e-11  \n",
      "2016-05-01  0.000053  2.494000e-11  \n",
      "2016-06-01  0.000053  2.970000e-11  \n",
      "2016-07-01  0.000054  3.399000e-11  \n",
      "2016-08-01  0.000057  3.966000e-11  \n",
      "2016-09-01  0.000058  4.599000e-11  \n",
      "2016-10-01  0.000059  5.170000e-11  \n",
      "2016-11-01  0.000060  5.830000e-11  \n",
      "2016-12-01  0.000062  7.122000e-11  \n",
      "\n",
      "[60 rows x 432 columns]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ipdb> t\n",
      "Timestamp('2012-01-03 00:00:00')\n",
      "ipdb> q\n"
     ]
    }
   ],
   "source": [
    "spo = cp.SinglePeriodOpt(return_estimate, [10.*risk_model,7*optimization_tcost,10.*optimization_hcost],\n",
    "                         [cp.LeverageLimit(3)])\n",
    "result_spo = simulator.run_backtest(1E8*w_b, start_time=start_t,end_time=end_t, policy=spo)\n",
    "\n",
    "result_spo.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Automatic pdb calling has been turned ON\n"
     ]
    }
   ],
   "source": [
    "exposures.loc[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x115ecb2e8>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/fmbtfvT4hWOYdWkOIhKUxK5UqGnPXdmOw2nYW1LJTa99R63T8L/rJwLwxrJc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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1190b9438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_rank.v.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11d8a5d68>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LdeT4yIdncWcYpvpE9dyfOj9832557k5wIsxzz/aSU/PBAgQ0qHbTcy8r5euIe26t2+hq\nctAF0Q8f36Ia0p16ygzDJIeo4q4GstbrtJgx7qo0qIZ57lkptrn28nVWz73gjblX03N/+CzgvlPj\nH8+gsTH3jhXeHE4Wd4ZpDqKKu+rur29vesoqLDNqz/h2RG1QBWQvVU9OvRN28QvLpLSQT7UaVAt5\n4N374x/LQmPF/ZJNvE88DsswTHPw+Ux3vpDzT5RQ4q5E9a27gLkve7dZuwwYMR741uPx7UhFjLkD\nQKbN67mrfUJTITMAhJNBY2Sz2Jb5IQQw77Vo20agsWEZ81WGxZ1hmgM948Us4atTEnfHc39oUnkY\nZtVCoLVvZXZE7cQEyLj7B9oDhCzinusA3rxd9skxx3S1ee9BmtZrsLFARBhPNTrJS4VkGKbno4dZ\ngkY3Ug6eLUtFZ9ZzldlRalCN4Mcun2Ps64i2HiZ69jfAS1d4j6ni+qKAMknNrbW/tVAKSBvbiiKw\nckG4nRHhBlWGYaqPLoj5AM+9tE038uKDiNqgat3XEV9dl9ZoI8hF8dz96uLYHjZClD9gukHCxJ09\nd4ZpCjziHuS5q+2NbUbu4k37y/SqzI44YZmyfR15XPCmu8wzwDZ5l9kyZvxCUlZ7BLBsdmwz/Ygk\n7kQ0gYg+IKKZRHSeZf0AIvoHEb1NRNOJqLI8HhZ3hmkO9HTGoJi7UvdCl7cTT+8h7jB0gJuHHpdS\ng2oFfiylgDkvA89epB3PMsC2LTav0B9s+v+n7DrxPmCX04GdTpae/0dPlh/jyz+NbzuiDdaRBnAV\ngEMBbA3gBCIyhz85C8AMIcQ4APsCuIyIQirRW3pjsbgzTHPg8dwjluzVhTCddUdbAmQmSyVE7cQE\nuPVlFJQCln1sP55aD2hZNZbCh3pIytMD1fH6xxwEHHYZ0GcYrJqobxuTKI+zXQHMFELMEkJ0Abgb\ngFn1XgDoR0QEoC+AZQCClbrdMmo5x9wZpjmIKu5CoCReehpiOgusN8b9nK1Q3JWoR/H8zQcIUXnO\nvf6QMHPorWEZ7X/X+/SY6ZExCoJFJYq4jwDwqfZ5nrNM50oAWwFYAGAagO8LIcoeY0R0JhFNJaKp\nK1evLj8Te+4M0xx4wjJBnrsAWvvL2S5NE1JZbyil0pi7OkZLhFTKjOG5Z9osmqR516bn3r5MDi2o\ne/Aez12XREPMOwJGq6pQ+KvVoHoIgLcAbAhgBwBXElF/cyMhxPVCiPFCiPH9+w8oPwqLe89g+Vxg\n9vONtoJJMnHCMiqHvUOr467SB9XQeN313KPkyZueezFfrkkfPqEdW+/EBOAf35dDC85+zt3GE3MP\n8Nz/e324fTGJIu7zAWykfR7pLNM5FcADQjITwGwAWwYe1VYBjcW9Z3DFjsDfvtpoK5gkU+hyY9hh\nYRk1dNy1X3KXK3E/7E9yuvt3K7NDedWVeO7FfHlYZvlcd95sUF2zWE51Ec9F9NxrQJROTK8BGENE\nm0CK+vEAvm5sMxfAAQCeJ6L1AWwBYFbwYW3izjH3HgE/hJkwinkp2u2d4dkytnFBVVGtPuvFH2Db\nc3hHZ6KMPWr13AMGHTHDMir8pA+fl/eLuYeb011CxV0IkSeiswE8CSAN4CYhxHQimuSsvxbAhQBu\nIaJpkGafK4RYGnxgS8syiwbDNAeFLkfclwbnuQN2r7qsHG6FKHGN4rmboZ9iURby8qNUz90RdxVf\n13ukeh5slmyZGhLpCgohHgPwmLHsWm1+AYCD452awzIM07QUcq63HNRDVfh57lUakU1l4FQr5q5j\nlh9QQu7x3LUH2/QH3fneZl0ZjTP+Ddywv34i/20DaFwPVVvMvZKayEzjiDJyDNP8CCFrv+j3gwrL\nACGeu5Yto2PWOq8UJbiRYu4xwzLmEH62tgX9wfbIOe78gI28222stTe0Dog1nJ6ved0+QqVwg2rP\nJzCWyqwzvH03cOtE4K073WWFLimWqUz4fWLzqlPV9twjxNzbjAw+W4Oqjhlz1/crnd+nMdl8kOyr\ndfzPtgF7nBVsawQaWFvGIu7mwLhMsnnhj422gEkCqnb7Si2JTtVwz/QKz5Yxs1SAKoZlYnjuEy72\nfhaFaOJu9n7VIxC6564/sMz/WffUs73hCcVQCjhwMjDhd/62WGhcyV+b564X+GeSj14hj1l3UaEL\nvRG0mHfEvTUkz13roapTNXF3zh0l5l5WXx3Btvt67rq4ayGpjXYD5rwg58t6w+ribnTY2ukkoP+G\n/nb4kCzPfelH9TeDYZjuobxbPU5e6JKearZXcA9VNVLREVe6HZbMY3UHFZaJ4rnb4txB7QV+4q57\n7urNYfH7rrADlrcV7QGXaXMzcQ6cXJGwA0mLuS/9sP52MN2gDsm6TPIpiXsWeOce4M/byfrs6awU\nqtDCYSS90w13chdVKxVSiWuUmLutm39Qpo9fWEYvP/DG34DfbwbMnuLdJshz1+3oRtJCA0diEkC2\nD5Bb4y5a9VnjzGHis/42jbaASQLKU6WUzAjJdwC9BklxT7eEZ8vY5qsVlsnHiLlbxT3IczfquSvM\nrL/2peXtiUExd7nA/7wRaaznnmkFBm7sLsu1A13t/vswCcG58aKOcM80N7owqUbDztVa8a8A71Mf\nQFr3UqsVltnze3Jqa7QNYrMD5DQXoEd+A4HYsv66jEKJQZ57lWisuKezQJ8h8nPbQDldu6xhJjER\nKORR+rFGrdPNNDelkrdF1+MuOtkyIHtvdO8BnKml4mJ3OfhCWb4gbmXFLQ6V0641/tv4xdxt+3SG\nibvfSSoPyzS2QTXd4l4g1WhgjnzOJIu1Wh3+sG7lzLqBR9w1j1v9vgPjxtq6JHWKU4IdFEnwi7k/\ncEb5tmWee0hYpgr13Rvruacy7lO93wZyyuKebPQ3KxZ3BvCKe0YT91TGEfcAz10Py3iO2eDGetWg\na4qyjll+IIiymHvEsEw3HniN99xVS7uqtRD0GsQ0Hv3hy+LOACjFFETR6YDjkM5Kka4kLNNolPjq\nNeZN/Dx3G2Geew0yzxrbiSnd4ib89xokp9ygmmzadc+dY+4MvA2ivddzl3esDPfcPWEZz0GraGAM\ndj4VGDvBbRTtDBohySfmbiM05t5MDaooAumMmzakxD3Hnnui0T13zpZhAFeYnv4lMOdFd3n75866\nEI+cNM/fXFZvDv8zsMUEby/RdCvwzX8AQ7fybmuOxBRE1FTI0ltAnWLuRDSBiD4goplEdJ7PNvsS\n0VtENJ2Ipti28SCMsAx77j2D1YvktP8I9twZiZ/X2dI7gucOJDIs09LHnR9zELDJl8u3ScUIy3Qa\n4Z3+xjDU6hrGTdkMIPSRQ0RpAFcBOAhycOzXiOgRIcQMbZuBAK4GMEEIMZeIhoWeWQiZB6tef0qe\nO4t7opn/BjBwFNDSj2PujMRP3CkFmQrpI9qBjYUNblDVS/KW3lYNe+OEZdYud+e/+Q9go12MYzn/\nrxL39TaT00Gjo1hrJUrMfVcAM4UQs6QNdDeAiQBmaNt8HXIM1bkAIIRYHH5YJ89dxdyzvaUnH9Q6\nzTSeNUuAwZvJ0drZc2cAf3Hf4ivA0pnh4m7rxKSy5xrFgBHSgelaBXz5p/ZtSqGUCAEQ1VP2gF/b\n3wLUMdS4szucCAzeFBi1Rzy7NaKEZUYA+FT7PM9ZpjMWwCAieo6IXieik20HIqIziWgqEU3N53JO\ng6oTlsm0SoHnsExymTwAmD9VvmVl2thzZxws4r3XD4Gxh4Rky6j9jLDMpvsBo3arso0VoDzyvk4g\nwnxIxfHcAVmyd+8f2deZ8XsiYOM9u9X2UK0G1QyAnQEcBuAQAL8korHmRkKI64UQ44UQ4zOZtOO5\nO2GZdFbGuTgsk3yyvWQ+M4s7A9gHtj9wspxGibmbnvuo3atlWXXwGzgkTiokEO3/qlZNHUQLy8wH\noI8JNdJZpjMPwOdCiDUA1hDRfwCMA+Bf5lEYYZm08tw5WyaR6JXuKCU993YuFcEgWLyDPPeycI3p\nySeEkuB203MPegjolTWrRBTP/TUAY4hoEyJqAXA8gEeMbR4GsBcRZYioN4DdALwXfFijQTXTKlvX\n2XNPJnoxpFTGyXTiVEgGIeIekAr57G/kVDl4fdd3puH5GHXFT3Djeu5BsfnSgCd19NyFEHkiOhvA\nkwDSAG4SQkwnoknO+muFEO8R0RMA3gFQBHCjEOLdkAM7MXcVlmmRJYDX9Zj7c5fIdMOvJmwIO4+4\np+VfaIobs04QlPUSFJZ58XI5VU7C+NNkT/Wtj6qufZVSKunrCG53Y+5B25U89+r1K410JCHEYwAe\nM5Zda3y+FMClkc9cCsvonnsfWft4XWTWFODWI9zPu38HGDKmcfaY6KPAR6kZwqw76PfB+tsBi6a5\nn4PuE9WBUWlAKgVse3RtbKwEJeZ+YRkl1tUIy/RyquJuVL32hgbXlsl6PfeWdThb5oU/eT9fOd5b\ngbHRFDTPndIs7oyLfh98ewrwS734X4TaMrb650lCeejbH+9drjz6aoRlBm8KnDkFOOQ38e3zocH1\n3I3yoNk+boPqq9cB93yzMbbVm8XvA7OeLV9u1qNoFF1rgEs3dT+LAos746Lug51PkV6sHlpQ90lH\nQI2WQs5/XSPZ4ityqjoWffknwHlaVrjy6COHZULkdsMd6t6gWiMcz33gKPkxnXUaVNcAKxcAj/8M\nmPFQcr/4anKbT4yx1g2WHzweXPVOsdrok9a1uvbiPnlA+dsMk0xEAeg9BDj88vJ1lAI+mwb8bpTs\n0GSjmNDf+OGXAz941y1FQOStehnbc4+4XZVooOdelBfnm48C+58P9BnqdmJ69wF3uwuHuIPcNiP5\nLn8Rr2Ue+RefAHcdDzx8Vvi2ZmGkTiXuNa4F8szk2h6fqQ6iGFCCQEtrXOKTQJfUsEymBRi4kXeZ\n/v+oN5TIMff6ym0DPXfIUMygjWX3XiL5hCx0lldQ+/zjxthXDy4a6t+IXKihuKtrvPSj4O0+eAJ4\n7x/eZV1rItbpNhAi2gMrSSPyMOGIor/A6WL4uLXmoLc9J/Fo/0/Jc3dkdIMdgneN+hCoEg0Wd8Mj\nVK88ZgW1a79UH3uSRr4T+OgZ4Ib9gVyV67ioeH5Y9+a7jgOe/Ll3WdeaysIyz/4GuGhYeEc1Fvee\nRSHnX/ZW91ZXznPnZz3nzic1LGPD47ln3WU/mw0cda19n9K+65rnrqNiW6a4r6vkO4GXrgDmvw7M\neLi6x+5wqtRFqUVt0rUa0QY+NnjjNufcAY1rADfU9jQ6VgJtA+zr/ATt1onufFLDMjZ0cdd/O70H\nl+tZ2b7rlOduXAzlub95e/1tSRJ9nB56hS5g+HZyftq91T2HKkHq96MMoqvCmLs+1mYQLO5ePn4W\nWL2k0Vb407Eivrjr9NQ3NTOzJewteJ0Ky5heY53/+YZjK7gEyKwhQJbUVTHqNRGqKMehoxviPv60\nysIyLO7xEQK47UjgD5snVwQ7lgNtA31WaoLXa7DPNgn9v8IoKxUQIu51Hl0qWZ771keWD2XVKISo\nfpzbxC9LJuuEp/KdbqZQtQuqKc+9pW+8/U56CNjz7PjiPm+qG3P99L8hG/fQH3st0O+RBW8Cd50A\nXLlr4+yxEeS5ezriVTJoR4Ip89xD5HTdCssYFyfTAux0UvXPs+AtmTe9bFa07dd8DvzfQOA364fH\nh7uDn7grz73QJQcLAKov7spzj+tNpLUMgTjifuOB7vz9pwEfPuW/LXvuLnoacNdq4IPHgKUfNM4e\nG0HirqcSNtv3akYewn5L65bnbumNpSrDVRMVw//o6WjbP/Zjd76WsU6/Dlqq7SHf6aaBVl3cnYdW\n3B9caTCBCDH3XIeblaMPOAwAC97w36/ZRKA7vPE3d94vjNdIigWZANHLJyzzlcvceXW/mPfNuuK5\n15lkxdwBe7nPfhsAK8wS8jFQYhH14uveUi3TtOb7CFyLFpZRot61uro/AnXcICG15R+nYnjuV44H\nLnYG7TKHTQsq7awf95MXgs/R7Ogd+kQCxV05CX6eu57urL5Xc3jGnvowjxpz39x5a830sq+vEQkU\nd4vnvmoh8KetKz+P+lFU0pOsluUP7jzWvnyY0+4w7V7XdlH0PnRWzAdWLfLu996jwNV7RPPw1A8s\n6IFha8S/mXYIAAAgAElEQVRV1zBKJ6YVWh2O/ht61wW1Z+g2PfXL4HM0O7p3WEygCIaJu466L5ul\nOKCpJ37O457nAJNXVLWcbxQiiTsRTSCiD4hoJhH5dDMDiGgXIsoT0TGRzm67GLUo1K9uqsgNGtoT\n2M9zFwKY/qAsHxCGEMBbd0Yvo7Cx02lr/lRg+Vx3uR6auWpX4DJjJMMHJwGLZ0QbZFzZEiTQi6aX\nL6s05t5vuPdzPuBa6Mc1u3+va4wY784ncXAUdR9l2sK3Vd9rzgwx9tCwjBlD94upV3EAjjiEijsR\npQFcBeBQAFsDOIGIytxoZ7tLAAS0lJk7WcTWN6WqG6ibys9zn/sKMPdVzS7tS/LrGj37P8C9pwD/\n+r/w8896DnjoO8BT50exFhixs/ezuk76j8Im4KXX9ggNNyXP3UegF02X2Rkm6kbNd0qBtr0lTL0Z\nmP28sZ/htUT13Aes4+KuP9z+fmLj7PCj9FYcwStV95rZftRTwzImfp57JR0Fq0CUs+4KYKYQYhYA\nENHdACYCmGFsdw6A+wHsEvnsthKYtWhRDvPcbzpETic7r5j6l+TXe0559Dbv1kQJ8arPgrf78k+B\n6Q+VN0619JGNVuotwa8+i/o/o8RmcwHivvxT4Jo97ftlHQ/tv9fJ6bT7gHHHebd59AcW24zrGDXm\nnrQh1+pN0quiFmOEPEvibnz3PbVBtQw/z70x4h4lLDMCgBY8xTxnWQkiGgHgKADXxDp7vfI+4zRE\nFYuG5+7zKqzeMGx12MtQo7sHeCinPSOrY54ztXydyjRRtqxc4F2f75LxdyWgUWKzKizy3iPl3ndQ\ncS+zUSjfAaxZCjz/x+ACUGXnCOpDoP/YEzZYcr1JuriLCCHP774KjD3U3bZZwjImfp57nWPtimo1\nqP4ZwLlCBL9fEdGZRDSViKSC1St1SAlLWA2LJR8AFwwCPnzSXeYn7rqnYjZsmqiHRZCHEnTpSuLu\niK4p7v/8kYy/iwo8d6C86mPQjy1rxFZTaeDlq2R46u07/fcr5r2xx8CwjH4tmuSHXylJL6pVDAl5\nAsCwLYENxsn5j59tXs/dN+aeXHGfD0APfI50lumMB3A3EX0C4BgAVxPRkeaBhBDXCyHGCyFkK5Hf\nDXH+YncsxZZ+4RauXABcMETGzm0osQhrkFrwlpzqXmW+U96Qi41a1LoA+f0fxQIw5VL3Zg4S8CBB\nLuW9O/avNh4mM5/xfo7S8KY3aJqdu4IegqbnTik3zVF/KJqIonegg6gNqmr+/jNkCGhdo8d47iFS\non4jtx1pedtlca8FUcT9NQBjiGgTImoBcDyAR/QNhBCbCCFGCyFGA7gPwHeFEA+FHtnvVS7T6j7N\new1yl9tqj3e1Azd/RXo4L/3FfjxzIF4/bJ2qCl3yhrzaGLg2irfx4RPAsxcBT/7C2SdI3APWqUwE\nJdrm/9F7Pe/nKA23nrTKed51QYJivmJSyl2mZ/aYFPNerz+oU5ZH3J3rPO0e2bN1XSOJGTI6UWPu\nuvCtWuhd1zSee7IaVEPFXQiRB3A2gCcBvAfgHiHEdCKaRESTunf2gBtC3dRt/d1lNvF44Y/AF7Pl\nvG/jZ0TP3Vay0y82bPMu/Y6n8sVnBvSQHTTaf11WK0cAAA+c4V1vivt7j/ofC3Dq5mji/snzwN8O\ndwfwsIUCeg0GfvS+5WDkxtqDHgrFvLcPQ9D4sJ4fe5P88Csl6eVwlX1hAqYLn/l7aZZsmR7YoAoh\nxGNCiLFCiM2EEL9xll0rhCirTi+EOEUIEe39OehVTgmFXtjKjDUD3lGb/DwA5bmHveLaRj7ya1zU\nb0jf6o4Ri3Kd8SwwYKT/+t7O28say4hNKxcCs6d4l4XFaQtd8Ijm0g9laqcqz2D7f1r7Av21XqY7\nnSyn6az7Aw96eBYL8g3kOKcURNcq/231a7t6CdC+zP3c1R6eddRMJN1zj9KgChji3qQPbP1/POYm\ndz7J4l4zgsRdCVSrFnNfaSlB4BHZPDDnpfKsjWKAuOs3mq2Rz+/Hpe8Xt1v4zGdkdT9Fa3//bQFg\nyFj5oJj/evm6Z34d79yAf2eqUtuE5TqZbzV7nO3uo76rQs4/U6eYl29qWx0O7P1j2bPRb3Bu/Tt9\n9Rrg95u4n289ArhsC/t+zYhtlCNVNTQJRGlQBULEv0nEXg89rbe5O28L99aBBpcfCPjCVenfQRu7\ny8LEff5U4OZDZYchHSU+No9Wf+215V77vg1ECMvYXqkLOeD2Y2R1P0VoqhQBG+5oF3e/RsaFb/sf\nzjfU5Pyvtutk9rJTglPMuw+DQldAj96iu496o7lyvP+2fsx7zX9dM1LMlzdiJ6nGTCWeu/k23Cye\nvP4/6vPrpucecEMcOBn41pPe3pq2rv76jaE8wWn3AKu1uijqZrJ5pLrQ2Txavx9SlLCMTdw7V6HM\nUwkbnquYAwZvWt7wKQ2x7/NKwHiOYZ67zW7zAaRsLnRpnaeKAe0eefeGV29jZtYPU06hq7xui37v\nfTYNeOLn9RPIR74ny2crSg2qYbXMtfVm21OziLsn5q4Px9eYQYiS67lnWoBRu3tHFLd5hX5enh6f\nV2JmFXfNi3jaUqQqSszd13O3iH6nJdZsqz2hwh7qOL3XA9o/B965x36usmMGXNsrfEZpL1XtszxE\nTRuVQHeuct8SdC/epFhwPRg9JTLIjmbkwUnA85eFb6co5GR7h45+X91yGPDK1cagGDVEL0EMRPfc\nM0EOTJOIu6/nvi6GZaJ0YlpfK2NjjZn7dHjRa6+UPHeLaAX2lIQ7qEXQeeOEZea8WL7MJsQHXwQc\ndKFzfCG9N1Eoz5TxO3dQ934/1LFsDyDz7aK1PwCSIzp98E+5bO0yb+hsm/9ByYNRMXc1H8Qr8To6\n9yjevgv41wXRtl00XTZymzFb23de54EgSkRNhQyqGdXTPPftvgbs9M3y5fp34DeQdh1JvrjrWMMf\nPjeG3gtOCbhNVIK62gPAstk+K/QG1RjibrYHAPYfBpHWs7UYv1Fm/W3lj+ZfFwBLZ0bbZ8l7zgAb\nloZO8/yplBR4c9s373Dn19scgJB26J57i9YguOZz4B8/cBuzl38KTP1rNHubGSFkfZ/8WovnJxov\niGYdozDP3W8wD3mQqphUN46+ATjiivLlpue+1RFynsU9AtawjM+N4ellGiDuQR1vAP+h+SqNuZv0\nGRqQLaOe/iL+DVLIydDU85cBdxwdbZ+X/gI8fJZd3G3nT2fl29DgzTSTLR6LKEoRUA+xbf4HGDhK\n/t/P/Bp4/Wbg3fv8z7MuorcZpVuAbxp9Fxo9KpN6C1ZpqmH13NsG+a9r9IOqahgx96NvBH44I7w9\nokb0LHH/yFJNOJa4W34Qt5VVSfCixN20VVTouZt85VL/V2qyNMoMGBV8vK/dKj29/FrX5qh15AE5\n8pEt5m57c0hlvOEWAHjVacgdO8G9qYsFp0HV2S6VkgKf73CvY+kaRvyhN40g+LDsY3c+nQWGb+td\nX9YRqM7XQ73xrloov9ew4TEDxb9JvktPWCYle9oPGOG/fY1psLhHjBN+/52AlVHE3bkRK+ntVzqO\nYasn5u7nuUfwrtKt/uuUOAvNcw8Lz2zyZVloLLfW/X9XL4reiEcp+3UavXf5snRW9inQr7Xad9uj\nXTEXBW9YBpA3vq0NJKpINb24a2+M6Wx5aCYoHbJYBBYavxkhqtvoqr67Qpd8swjzToPCMs3yXfrF\n3BtEz/Dc9Vx3UzD9BLRUr1zrat+d/GBR8PfWr/uyvTKkrRem2TDZEpA5osQwlXHnwxpK062uuOsZ\nQ1Eb8ShlD39tfYTdvmJOXuuBo8rXlRpQC+Uevh6yASwefAgXDApvL+nJ6OKeypbfN+Z9r1+3l/8C\nXLc38Ol/3WWvXgtcMjqgDQnygWDrH7F6CfDPH3uvd8lhKkZL9Qvy3DfcMXz/nsY6L+6V1Oo2vT2/\nTjN5Pf1Rdc7pZp2Oa/cGZjws500R+tRSkdIm+Bsbg2C0BlS93PEkYNdvA/v8zCvuwwLGk820ym7+\n+Q77yD1KRPc5DzjkYmDc173r137hMzC2JRaeysiHSL4DGLpl+bqS5170dmLSj6ePEStn5GTwpr7/\nYglbVk8lLP0oed6jGpsUkJ57WMaM/lmNoKXGsF31GfCi0wC4fI7/Oa/bWzoqJk/+HHjtRuAifeAU\n9TAuRBuXwe+N86ALZGZYs1GvcuYB9IywDOB2uTbF3c97U8s9IQNHSD55QXbEmPmvco9zrx/527Bo\nGnCPU1MlihjYxMdM5wwqaZxtA77ye/lKq8Swqz1Y+FJpmUeeawfWLClfr6eu7fFdOUCITm6NPT3U\nJu6rFwPvPyobYM2HlN5pSRS8n/XjmQ9cdV33/on9/9NZPrf7ojznZdlT9rUbu3ecaqN/B+ls+W/F\nfAu1peaq633ZFsAqS12mqNhqGpXeuIrd81I33DEkB76nsq577nGebgdOllPTq/QTdxWKscWDbzlM\nTqfeVB6y32jXcFu++CRag5YtpmzmuQd57jrq/ynmwnu0Ztv8B8Mw62/bPKp2y4/Z1hGjU/MuzSJp\na7/QwjLF8pi7Om8pvGCEZaIIxg37dT9tUjVc2saLbST6fa2u/Ql/B/b8npw377cgcY9CUKO7zUkp\nlaooRAvLAMA5b5Qvq9dobPVmnffc4zzdlBiUee4WEWvp6+O5Gw+GbK9ykY6SivfJi+X73Wvp1BCl\nop/Z+9AP/XU649MIe6TT+Sfb215eWIks4P4gbQ8KWzgp7AdsPqTWflHuuVtj7j5hmaj3xuz/RNuu\np6GLu/qOtpjgvmnaYu5ffCLfSNXIWjaB8XvT0UtbLHgL+FSr4WNLjS157hHDMgDQZ0j5sgZ1za85\nPSXmTkQTiOgDIppJROdZ1p9IRO8Q0TQieomIxkU6e5ynmxJ3s8dooUt22Bn/LXdZps2Nues/ElPc\nU5ny19soN1tL72gNf1HEvZIKf+kW4Gu3lS/fwYmfL7HVXYds4DU7nfQaCHzjAe92tpovtoee/v2Z\nufrjv+Vey8/ekb1X9cwgvbFVR4lP1HtDf5Nb+wXw9t+j7ReVV68DPniiuseMgkfctWuvrsuUS+S1\nUlotipa3jxgCo+LzAHD9PsBfD3Q/r/XppQ3E89yt91CzinsP8NyJKA3gKgCHAtgawAlEZLbozQaw\njxBiOwAXArg+0tnjPN3UEG5Tfu9dnu8A+o9wez3u/RMp7iosob9umkLSZ0j5siieezaGuK83Bpi8\nAjh3jutZe84X8SbQz5dpDW5Ubf/cvrxjpb27+OYHeLdbvbj85gz7YertANsfD/Qe7K6/3elEpYeA\nVKhBPXBL2TJK3CPeG3qD+n2nAQ+e6d/xrBIe/xlw13HVO15U9DdOPSSmvrfXbvCKuRDl92Sc31dQ\n5pHtfvLE3Lsh7g3q4FN7eobnviuAmUKIWUKILgB3A5iobyCEeEkIoZJoX4EcZzUCMS7AuOPldP1t\nvMvznVLs1Mg+fYbKBprSkHTaj7+Qk97d+k6HkFTGHpbprV4ffeyLmq5X0OLjvQbKh1Cl7HmOO59u\nqey1r2OFFo8N+EHm1pSXmQ3z3Lc6XNs2Xb4e8IaASg2qKixTckHVwf3t09HfjtQ4t9XyBm2dueqF\nLSwDeK+pZ6CaYnnIJY73aLunhZYR47euWIgu0Po9pDo9sedeM6JYMAKA9s6Gec4yP04D8Hiks8cR\nqA13ktPeg73LlbircE2fIfL1v6Dl4QLS+/n0FZnru+hduayQK79xKQ38aAbwv4v8v6BF7wb/GBSF\nLm8mQFgX7SB6DQLGHCLnbdkTOpNesC/v9PHcbbQY4SLb9mrZ8XfKRlx1vZRt5j76uKlpw3NXxPXc\n9bCMig1Xq6rk6iqM+NS1xn9QkiA82TJ6WEa7pvr19BP3t+8OPk8hBzz6I3sZjq6goRB1zz2ikNmG\n2uOYe82o6uOFiPaDFPdzfdafSURTiWiqsyD6wVUjokolnDVFeuFK3FVcsG2g03PS2U6Jd5ulfksx\nXz5yUK+B8njZNn/7/n2RvfOULU0zXSVxB4AtDpXTlQuDf1DDt7Mv71xdni3jhynutmuhhEbF21VM\nXS03vbK12nB56kdtNqTGyZYBvG9mSoye/lW0fcOwDesIyE49KywDx9i4fBzwu43in1u/lzxvPGn7\nNkJYhokk4MFvB59n9hSZcfREWVOaPQXSPaEzidGgqn+npYd4s4p7z/Dc5wPQ786RzjIPRLQ9gBsB\nTBRCWIO+QojrhRDjhRDOEDwVZst0rpLDrd39DenhZNpcz12Jc6kHnRJ3i7CWPHfHjtOeBobqQ7gF\n2GfrPGXGLQu56oq7qoOu2xyHfEflnruNkqeu0ipbvJ/NkbP0sVBTRipkNcIyivceibZvGErc+2id\nd3JrgT9sbu/sY8PW1yAKfjF3XTT0hm9R9FZCVcuCePMOtz3Ehl/bjX7sOA2q3gPISbN67j0k5v4a\ngDFEtAkRtQA4HoDn10NEowA8AOAkIcSHkc8eK1vGEY58p9tIOucF6Q2msm58tNcguW2Z524R1mJO\n3qR7nAX872flOe5+3uO4E+y15U2hKXR5GxHNjBKzV2cczGt3ymP27XTyHeXZMn7o4t5vA/s2KUPc\nVQhK/WD1yoaAN+2zrBNThQ2qtYyLf/GJnPYb7i779FU5tfUFMAnrYNW+TKYd2gjLlgFkY2/pXEU3\n3FhaFlJuQ6VM+hHkuYsKPHcd9cBqWs+9B4i7ECIP4GwATwJ4D8A9QojpRDSJiCY5m/0KwHoAriai\nt0phlzDiXIDSsG658voqi94Fjr1ZNjoO2sQRd8Nzt5XVLeRczyPby7LeRzgybdFqw6uiSqX/wWiU\n9MtX96NU312Ui/voL3k/H2AJTeTWxvfcUxngxz6plWQ0nJaFZQwbD9OKl6lrsXiGnJqee9QHv0p5\njVP5UidIgNWbR6bNXdYZEIc20WPWtvP89WCZdmjD47n7iDvgdiSb+XT5KEm20KHuzeuhSlsBu67V\nst6+jZLnHrG2jOKo62Qar3IEEiCCNSEBYZlIxbOFEI8BeMxYdq02fzqA0+OfPsYXSySf9oWu8tfP\nTJsMp6gaFWktWyYo5p5rr8DzIHlj24TfjHmaYRkTXTSinhsAIMJ/FP0tCUv5TvcHH/Y/hw2FB1jC\nMlnv57whuL20mt6lcgpKAM3CYRHvDSXqSy0vjEJI77Pv0GjHMlEPcD0EF2eEq4LRHmB29Pr8o/Bz\nA97vyi9V96nzy5dZs1w0cdfvzUyr5f7tAu471cdA7fuKI2Qq600VsutuvaekkoBwU88pPwC4om3+\nwMxenpkW93VdeUytlrBMbm38m1PluFvHYzXDMp3B4r7vz6Of1yTM5v6WUEp+rfuDN2++c+cA530K\nDBkrP5vlBGyYKY/qTUQt3/mUgH2NcgZP/kL2kgwKy9hCa+pesIneC3+S8XHrwOLwP49CCaGekaPf\ne2FhF1249EJgQHlDftm+2nqzVHJUbJ57sSAbnK/dy3irtNynha7ydhOFp4dqBTKi/o9mreyZAM+9\n5xQOA9yRf/QUMADYaHdjOz3PPSDm3tUub9I4T9lsm/xR2zyOsph7gOd++OXAZvtFPy8ADHNi9Jvu\nC49nO/Hq8m1t8fxcQINqr4Hy7UZ5wEGliBWl8ItjS9p41d5gnDcUo2MT42cvRmBYpu/w8mWlwc8t\nb1KqGFicUIpOKfSgPcgXzShf74curmY6pF81U0D+T3q5aP27CqsrpGNN1y0AL14OfDbNP39eke/y\n/x8rqS2j86UfyOnACjKJegIJaEvoWZ67GuDB9Nx3M9K90s52Mx6WI8MDPuLu/IDifBGZXgBEZQ2q\nALDTydHPZTJ8O+AnM2UpYP3a9bOMgtPHEoqY8yLwwh/lfNj/rDyqfhv6b2OGZTJGzD0Is/0BkPHj\noLCMrSxCadAIy/dR8jojVI7MrS0P9xW1jBAAmPsq8N/r3PVh4q6HRco8d805mDxACq7iiYA3ujih\nPFs7hN5I+qrWY7osjRLB5TO626C6/bGy53avgOH3ejLrfFgmbrqQyoLRPfe+w8vfAJSHf8/JMo8X\nsMfclUcXpwt0KiV/1GGpkPkumQ1h3rxKCCsdA7PvUHgGz9aP6TkPARsbjayzpwDT7pXzYTefEMD/\n3AicGpCFkzI8d4UnlusjRjbPvWOlNyyz+1nekshmXSGdICEq5KSoLbXEuNX5pj8A/NYIZemhBwCY\n/qB3fdh3uFzr+2eKu/kw0ksOf/K8/zHjhGVs1Rz/8T37trYa/h89GVDKoZuee7PDYZkKwzK65267\nsTKt5V6e6blnermNebG+CPKPuevez9IP5QPA7FCkD2DRHcyR1m2c+hiwzVE++/v8ILc92j3m9scG\nvzabMfeVC+V0vc3dbbY/3mdfWwnhlfCEZSb8Fvjqn/zPr2OKu+6FF3OyZvuV46MdS6FEfdks+RAw\n3xj9vsOPnwX+ewNw8wR3mSm0fj1zAeDzmf7r4oi7+UAJwuasBFXcrKS2zLoEi3vcBlWnc5L+w7Xd\nWJ9/XL7MHJSjpY/ruYfdnKqRceAoabNfzF1vUFU5x+sbAxuXyuBWqYs8EGz/8O3ty/28rU2czjlR\nHrxmWEZdEz0rxBZ+Aeye+6IZwGM/VQePZseg0XJqPmz17JliwR0/dPqDXm80SoMqIHPCVXqiqhHk\n9x3ediTwmDHYiHm/mJ+DUjn189hSdv2wler1I2rWinob1IdFbNriX90gASmePSws45QVyGlhGZtI\n2TqY9F0f2OdcYIDjibb0cY8Tlvb3PzdIkTzxfkfcI3juqoTq4E282/iVuo1LFM8dkA1XZ/w7eH+d\nOAM9mA8V5elGESCb6Bc6gfmvO8e23Bvfego47nb387ivu3Fx3XPfdF+3AxLg/a7uPQW4YkcpTkEl\nBO46AXj3fvfz8jnScx+6FbD7d+WyOGPymuJp3j+BnaI0z33wpsBxd0Q756vXhm9TOkVEZ8MsG1Gs\nMFuGqTk9LCzTYslztzSW2eK8lAL2+4XrSXvKAlji8TobjAMmPQ8MHauJuyXGq3vu+U65rZndUArL\n1EncUylgxM6W5T6eexxxNx9Uat8o4h5WWpksnvuo3bzVJzOtbi69CkH0HiKP/dJf3O1sIYenzgf+\ntHV5L8zZTrz7A6OtIbdW/mV7WeriRMD8vv08ZVvs2zyPPg7vLmdEt6EalKqFdrNBlak5PUvcbdky\ner0ShS1dTP0gVQxcH9nI1nvVz05yYu76j1O9Deieu6p5Y/6PqSqFZfS3jUo8J78fZJzBMko9Zove\naZSMDlvM3XtwY2oh0+Y2Yqv7oM/Q8iH9bIL58pXOfoa4/+2r9nOtXiydimwvLbRmOBYdK4D7fcTW\nfFPzE3dbnDzoXrFlucRlwKjwbRQqM+ude4A3b+cG1QTTQHGvICZFKZlJMP0hd5ktrmgTdyVm+5wL\nnP5vYJSWGx/muZs2qFTIwZvKHPMTnLKqnmyZTnvjV3ezZRR+9UbCUCM/+f0g2wbKaV9LeqWJ+Rai\n/qcovVsje+4B/1u2TX7/T/zCuQ9INpyLgrcBPSiebMsoMWviAHJwjLkvecXd/A7fuguYdo/9PFHE\nferNwPtavZf+I4Fh2wDbfc3f/nwXcMaz7ufQh6aFOI6GqjP0+s3Aw2ex555gIpUfSAwqRSxsJHeb\nqCrBT2eAkTt7vcswz11HhWWKOflD2vFE12vUQzXKcy/bv0rZMqZNYfxgmkwh/dsRsq0hKFsm3wFs\nH2H0IX0AbMDNPoqSuxzm7Zm14XVOfkT2OlXtGq9cBexxtvzeU2m5LpWRvWy7Vgd3GLJ1cHorIKbt\n8dyN73BlQE9YMyxja7N59AfezwM3Ar5lGeJPv68KncCQMdo+o9xBv6MSp+G1n9GRLG5tGaZuNM5z\nr2Vjss1zNzsT9V7PnY/ruQshX/XVMdXDZOHbbi51riPYc6+quEe4mANHAcO2cj1mP885lQJ2Osk7\nyIjvec3/xbEjirib30f5wY2pxqb7yIeqfn1XL5YPW0rJbJilH7olFGxCqogjbICMOav/+7Kxsmyu\nIqiB9onzZGclRZBNCr/yBi29gUMvlfP5LiMEZcv3D7k/Yom70Rdg8XRuUE0ozfmt2G42U8wO+a07\nH8dzV3nuxZx7TFVR7+273FzqfEf5UHVAZY1xoSbF+BpL6YoRaseEMXgzOVWlCk5/Btj/l/7pjzqV\nNKia6Nd39SL5wNC9SPU/fuIzMhVgD8sEhXF0zx0AnpnszvvVYbERVDQsCqUU0E7vtbTVatnnZ8A5\nb7ift9VquMctO63Cdjos7omkZ8XcIx/acuwyz10bri9WWIZkRsVHT7k3dTpTfoPXOuYOuJ5pReLe\nL3i7KHz1jzI1UTVSj9gJ+PJPgvdRmLFhfYxYQPufgsRdu76zpzjDD2rirq7P1L/6H8MWlgkqNJbt\n7X2A6CGfwJGLDGylFMoIKJug3qzynd7/WYn7MTcDO5zo2LXEW45C9WUAgKNipEsCPo4Th2WSSCRV\nIKIJRPQBEc0korLxuEhyhbP+HSLaqfqmxkBPl1MEFVwK8jTNhkVKuTVp9FF2dO+pfVmEmHsVxN0M\nC0VBpSnG6QzjR0sf+7WOgikII42BUqJ0YjKv7+pF3uMO2jjcjthhmVavwOkP6Tg15bs7FOAGO8g3\nl71/LENp+/4cOHOKmz0zeBNgrNNDdtVnxvB8OeDUx4HvvQlsuGO88wYNt8gkitD3ZyJKA7gKwEGQ\ng2O/RkSPCCG08ng4FMAY5283ANc409rybZ/u0dscBTzyPe2HS5V5Fz+cXl761jPMmZZVocc6v/jE\n33NPVdFzP+gCmSmiwiNROOlBmW1ke72uJ6ZImO0eFCEVMhvw8ATcnsVB2MIy8wLGminmvfeAip1/\n9q69oX+rw8NHPPIjqKRwr4HA+doA3vs6Ppfy3LO9gdF7yft39+96r0ux4M2VjwN77j2GKNkyuwKY\nKbmpFf0AABLbSURBVISYBQBEdDeAiQB0cZ8I4FYhhADwChENJKINhBALgw48a8lqEBEIQIrIE2Yl\nIqQIIMjlBGBopg2kjVDzRf+t5Lq1udI2peN9+xW0PPZDpGc+CZHOIpcvyuM569X2gQywDHihi5Jf\njnH7MtndXcVFPftX0XPf6eT4VSaHbgHsax2/vHZsfpBszA3CHAmoNKhIDM8dgCeUMWQLy3oDm+du\nDlenk1trhEHWygfEtV+ybx/WthBIhGqWfvtke8nQ4y+cdgC9Abdb957l+wira880hCh33ggAWnk7\nzEO5V27bZgQAX3EvCmD/y6ZENFNyU3ZL7J+WY07OE0Ow14VPB24/KT0I52UBKnRh7PmPl63/xNGG\nTX/+T6/oex4A8uGScpbdQSugqrXMwzAcceHTIAAvI4MWOPHsO2SD1TPL1sOvLv6XPJ5TyPGA/EpM\nBnDF1A489M5zgPZQ0h9m0JcZD7nS8QDPw9E9ltw+lfI5HhDp/0XZOdx5qHOY9tmO128yUh0EPDK9\ndOx0itBv58cx8aPzMWrl67j97ZX4hvbdPDp9KZZ99gk2WrIU+znLHnhjHtIpuW+aCEOWdmIX4zv9\nor0LKlfno+JwjEEIcUcC6j24/I3sYosToBi+fXk1yahEeTj5UfbGqT2QzHLQrf29D7n1xngbfPf6\noRz4BLBnUXXrAcbUirp+K0R0JoAzAWDjEcPw5+N2gICAEE4tLiGk3yFQWl7U5j8rXIfpH12Nz/tt\nhQWDd8WvWwbLfQEI4RxHHQ9Atmt9tP/3aRRSWfzky2PLjndL+99RRBrfbRvl2U/aI4zjSvuGzSBg\nLbCkdRTuHHMlvpKRNtzQfg0mzvsDRq79oPT/vr/xidiz9xDP8ZYXv4rr1gzFx713xdYgy//rtQMQ\n0uaSPT7/r3b9RBEQKEIUtGXOfhDCcw2Crl/RmSmth2ZfaTxr43i26wfXPjjTghAoFoFrimdjfSzD\n7JfyeDJ1Hj4sjsT41Id4/IUMipiOfVNzsJ+jJz+6523P/ZQB4Zj06fhdVpbLPajz9+j6OIMprbKW\nzsS7F2OG5twf0Hkpvpd5EBPTLwEAPiiOxO2FA7EVzcG7YlMMxkrskJqJJ4u7YBuag0fFl5Am4O8Z\nGR9/CnvgNy9uiyKl8Qj6YxBWYikNwn0tE5FFETlqwcctYzGm8DEyJJBFHo/N2A13Oef/pGUMRnd9\nhC/S62FQwWdsUgDvDDoY7ww9DAsy4yCeeB9p52Go/2WMz2qbXUYdjdFz78ejH61FJr0QKSJk0oRM\nKoXBB92BPmvmYvmAA5Gdv8JZTuh11APovfgNUL/1Qa39QMO3Q8vyj5FZMQcpAlLjjpN1fFJpp+Pe\nVbK3bjoDtH8ObHdswK9+HeMbD3gHl28gJEJeqYhoDwCThRCHOJ9/DgBCiIu1ba4D8JwQ4i7n8wcA\n9g0Ky4wfP15MnRptHO1uUSzKV+dqXfC/jJdezaGXArudWb6+aw3wW2eAi8kxSq6uwwghUChKwS8U\nvX/pj5/BwAe/DgCYc84C5IsCxaJAXttm3F9lw+krJ89CoShA7Z8j074Iq/puigPu26Z0nocmzkC6\nfTEOf3pfAMBL20zGhxseKY8phOfYpXMIgVPfOQnD136Ev465CrN6j0OhKHDIgqux3+d34ZGhZ+LJ\nQSeU7VcUAvmC3P+ehbJh85o+38F31lyDj1KbYYhYikFC3h9foD/OyF6M+3JnAQAuwum4WxyMfLFY\n+h+LkSMfAmkUUUD14uApAjLpFLIpklPnYZFJE7LO52w6hUw6hRaf+Wya0JJ299Hnzc8t6RSyGWff\nVAotGXe7bFqf93727kegBFRmrAVE9LoQIrR+dRTP/TUAY4hoEwDzARwP4OvGNo8AONuJx+8GYEVY\nvL1upFLVfZKWGqx8sk1sue1MIKS8S9vK3m4IZOP1gr/H3TdVHdOGANhCvi7c564/cscRQHsvwInm\n7bnDtthzzCbmYcqZ2wdYC5y2z1bASCft85nhwAvAEdsPxxF7hySHTZaT7xy8I/AgMGZIG7CmBXCK\nkg4aNhL3ffcbwCP/Bd74G87/6jY4f/whnkOoB2Dgg6hof0jmiwL5QhG5gkC+WES+IJArFOVyZ12+\nIJAz1zn7FIruunyhiJxnH7VdEV0Fd35NV6E0n3OOqc935Yslm2tFixL/jBT+lozzlzamlmWlh0eG\n0Fqal+tbs2qaRmsm5fyl0eLMt2Xdz+p4rRn5kKsnoeIuhMgT0dkAngSQBnCTEGI6EU1y1l8L4DEA\nXwEwE0A7gFNrZ3KDKYSIO9e2ri7dcb6I5NuT3jNUT4ntOyzacVRM2dMQaRRNi4LqD2DG+ZVNARU5\nSw/AJktMKToPjlxBIJd3HgBFOd/lPBDUA6dLPaC0h4m5T05f5zxE1LTLOaY+zRWKWNOZR6d2vlxe\nyPl8EZ3OdtUgRXCE3nkoOA8B9TDQHxRyXQpt2TTanIeImkYlUsxdCPEYpIDry67V5gWAsyKftSez\nwTjZgalXQCrh4ZfLPGSmClT51VrvmWsbcNvGkDHA/KneB3qp9EKE/c+cIgVcibje8WmLw4AvOUPf\nxanI2SSkUoTWVBqtGQAxumvUE/XW1KU9JDrzRXTmC860iM6cfDh05txlcttCaV49QPRtOvMFdObc\n+dWdeXTkCujIyX06nPUd+ULspCRu5o7L124D5r4MbLKP/zY7n1I3c5qeasRNT/h7+aApANBnSLT9\nD7sM2OJQ75CJZrnjIDZ0HvTLZsup7rkfeok7lKHqNZyQBjlG4r41pdA7QsmlWiCEQK4g0JEvYMAl\n0fZhcY9Ltg3YbL/w7ZjqEMWLPfTS4Fo5W0ywL4/a+aalD7D1RNMwZxrDnVI9ivUObHpZjP3Pl1UX\ntz4y+jGZdQIiQkuG0FLtsAzDNI4InrstaymIHU4M7qgUBb8BO4JQsfti3h6Cae0L7PWD8v0YpgJY\n3JlkU4t0tiOv7v4xKindrMS9oFUU5d6dTI1gcWcSTkJzlePE3BX6mLOnPCqHqYuascMwMWFxZ5KN\nEtGk9R/Y0MltHxGjAKoqCbDn2cD62wATLg7enmG6AYs7k2zWfiGno2pfZDQWYw4EfjgDGDAi+j7p\nLPdaZurGupNQy/RMVPGsvSMOAlJP4gg7w9QZ9tyZZDN0LHu7DFMB7LkzDMM0ISzuDMMwTQiLO8Mw\nTBPC4s4wDNOEsLgzDMM0ISzuDMMwTQiLO8MwTBMSOoZqzU5MtATAnIac3GUIgKUNtgFIhh1JsAFI\nhh1JsAFIhh1JsAFIhh1JsAEANhZCDA3bqGHingSIaGqUgWbXBTuSYENS7EiCDUmxIwk2JMWOJNgQ\nBw7LMAzDNCEs7gzDME3Iui7u1zfaAIck2JEEG4Bk2JEEG4Bk2JEEG4Bk2JEEGyKzTsfcGYZhmpV1\n3XNnGIZpSljcGYZhmhAWd4ZhmCak6cWdiH5MRAc78w0ZbblR5zXha+HC18KFr4VLEq5FtWhacSei\ng4noSQDnAjgZAESdW4+JaCIR/Q3AuHqe12IHXwvXDr4Wrh18LVw7Gn4tqk1TDbPnPGmzAH4FYB8A\nFwNoAbALEWUB5Gv9hRERCSEEEe0H4EIAOQB7ENEcIcQXtTy3aQf4WpTsAF+Lkh3ga1GyAw2+FjVF\nCNEUf3DSOp35XbT5fQB83AAbRgPYAMD+AG4BsA9fC74WfC34WtTrrynCMkR0NoAHiOiHRLSBEOI1\nZ3lWCDEFwCwiOrSONgwXQnwihFgohPg3gEUA9iGiEbW0wWIHXwu+FjY7+Fo0+FrUgx4v7kR0FIBv\nArgCwPYA/peIVPwuT0SDIatPFupow/lEtIO2yR0AxgLYzdivqg02fC0C7eBrwdciEdeiXvR4cYe8\nGa4WQjwLYDKA2QC+D8gGESHEMgC9AOwHAERUi//ZZsP31EohxDsAXgOwLRHtT0TnKvvqYAdfC74W\nfC2C7aj3tagLPcZw8wmufZ4F4EQAEELMAfAogD5ENFHb/A4AuxJRmxCi2CAb7gJwOoC/Q9aFrtgr\nScK1CLCprteim3bwtXDha+FSk2tRb3qMuMOwVXui3wegXftyPgPwHICttC+0DcDd6P6rVrYSG4io\nL4DLAUwDsL0Q4qfG/nWxw1lWlWtBROrHl45jQ7WvRaV2OMuqdS1G658beC0qssNZVq1rMZ6IhsW1\noQbXoiI7nGXV0ouGknhxJ6Jdieh2ABcT0XbqNUn7MS8D8ACA7xIRCSFWAOgLoFX7Qh8WQtwghMhV\naMN4IroXwKVEtJc6t7IlwIY2x4YOAN8XQhwmhFhY4aXojh1VuRbOj7A3Ed0F4CHnnAW1rl7Xopt2\nVPO+2ImIngFwgfouItpQ7fuiUjuqeS22IaKXAPwawMAYNlT7WlRqR9WuRVJIrLgTUYqIfg3gRgCP\nQ+bknwWns4P2Y+4N4CkACwBcT0QbAtgRQF4dS21bgQ1ERL8DcC3k69siAGcDGOUctxhiQ87ZLi+E\nWFyJDVWyo9vXwtlXCCHanY9Dieg7znnT6odR62tRBTuqdV/8L2QY4W4hxMna/Ziq17Wogh1VuS8c\nvg/gQSHE4UKID2PYULX7opt2VPNaJILEirsjWHMBnCKEuAPAbwBsDED3TCYDeBDA+gB+DCl6dwJY\nDuB3VbBBAJgC4CAhxN8A3AxAAFii2XBBLW1Ikh2OmGzgHPs0AN8hooGaoNTchiTY4XwfLQBeEELc\n6JxzRyLKQH4vIKILa2lDUuwgojTJDBMB4Epn2VFENBJAb+fzRbW0IUl2JAqRgGR79QfZgWA37XMb\n5AOo1fl8D4DDnflhkF/MZsYxelfTBm353pApUi8D+DNka3pfx4bNq2lDUuzQbQCQ0pY/BGAkgL9A\n/ig2BtCnFt9HUuyw3Jt9ADwB4I+QWR6PQjbEHVnP+6IRdvj8Tt8DcBiA2x17bgFwDWT7UL2uRUPs\nSOpfww1wLnA/yDjYMgA3ARjsLNd7kWUBvARgrGX/VA1sGKQfG8A2APZz5k8BcCuATappQ1Ls8LPB\nWTcWwB+d+cMBrATwdrW/j6TYEWLD1wH8C07PSgDfhnyr2rjO16IudoTY8DMAnwA42fk8AsCrAA6o\n87Womx1J/0tKWKYLwL8BfAMyFnYMUNZSviWARUKID4moHxHtCpTqVFQjXcm04VjHhqIznS5kbiwA\n/AfyBss5NqSqZENS7LDa4LAAwBgiegTAHyDDRbPVynpcizrb4WuDEOJOAMcK2asRAJ4BMBh1vC/q\nbEfQ93E1pOc81LFpPuR3kq2yDUmyI9E0TNyJ6GQi2seJlXZCNpw+A+BDAOOJaKyznSputh5kCtMp\nkB78do6wV5QqFdMGM9f2IMhrtwpwhbcn2xHVBsiHyULIfOGdhRCHAxhJRDt314ak2BHn+xAy+0Jx\nEGTMd3V3bUiKHVFtEEKshuyUdDIR7eA0ch8I54Fbr2tRazt6EnUdQ9URp+GQsa8igI8hY4bfF0Is\ndbYZA9k9uEMIcZG278WQ5ThvAfBnIXu01c0GImqFjHdfAmAegHOFEO9XYkNS7IhpQ6cQ4kJn2QAh\nU8hg+9wT7ejG95ECsBdkjvZcNO6+qJod3fydHgeZ0bYNgF8IIaZXYkOS7Oix1Cv+AyDtTMcCuF0t\ng2wMe8DY9ijI16vN4TR4ANgTwHENsqEV8rVuOwBfbeC1qJod3bChF9wG7mrEcRtuRzdsaANAADYD\ncEQDr0XV7OiGDX0AZJ3l1B0bkmRHT/6reT13kp0qLgSQJqLHAPSH0/NLCFEgou8DWEBE+wgnZiiE\neJCItoJs7e5LRPsJIV5qpA2QjZjTIHvQ9Vg7qmUDgPdE9173G25HlWzYXwgxA9KrrIgk2FHl76M7\nodJE2NEU1PLJAZmq9BZkKtIZkA2AEyBfG3fVtpsE4Fnt87EA1gC4AcCwnm5DUuxIgg1JsSMJNiTF\njiTYkCQ7muWvtgeXseGTtM9XA/gOZArf686yFGRc7R44KX3Ofns3iw1JsSMJNiTFjiTYkBQ7kmBD\nkuxolr/aHlz2DGuFGz87EcDFzvxbAM5x5scDuLNZbUiKHUmwISl2JMGGpNiRBBuSZEez/NU0FVII\n0S6E6BRurYaD4HaZPxWyEtujkLUx3mxWG5JiRxJsSIodSbAhKXYkwYYk2dEs1GWAbKeRREDWdHjE\nWbwKwC8AbAtgtpCdDZrahqTYkQQbkmJHEmxIih1JsCFJdvR06tWJqQiZwrcUwPbO0/eXAIpCiBfq\n9EUlwYak2JEEG5JiRxJsSIodSbAhSXb0bOoV/wGwO+SX9gKA0xoRg0qCDUmxIwk2JMWOJNiQFDuS\nYEOS7OjJf3XroUqy9OZJkMWeOuty0gTakBQ7kmBDUuxIgg1JsSMJNiTJjp5MXcsPMAzDMPUhKVUh\nGYZhmCrC4s4wDNOEsLgzDMM0ISzuDMMwTQiLO8MwTBPC4s4wDNOEsLgzDMM0If8PVrexHo2g5gcA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d8b6978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_rank.h.USDOLLAR.plot()\n",
    "result_spo.h.USDOLLAR.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11ad757f0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aVc2Z2mGUdKmZ017hjnpCV0u/wuOLYf7GHY8Ld24AomOx60FHv0GW+f91NrT1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\n+dC1AXY9zbFWHMWe8ZhEtc9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7buIHfxnG7Z8rT6fCrTbrF6oxCu3+1NfQ4xfmTO5DvgJz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\nYrFYmgyr2C0Wi6XJsIrdYrFYmoz/D7ltvIDzGXTgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c9efba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_rank.h.AAPL.plot()\n",
    "result_spo.h.AAPL.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11fe9d7b8>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZC/r2hZHX87pf2EBfL2Hu1dNvhZSSAvnDX6etvucXoej5Od1a9Cbbi64bs23+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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fbc8668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_rank.simulator_TcostModel.sum(1).plot(logy=True)\n",
    "result_spo.simulator_TcostModel.sum(1).plot(logy=True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x115b40438>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fX9aHrMw0Zq/dzcEj5ewpKuOGYZ3o0y6bvNyWdG/dNI7pRUS8V2NxN7OpwJXA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\nCam4i4gkof8Pu7G5hJatvQ0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115b68828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_rank.leverage.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# plt.figure(figsize=(8,5))\n",
    "# for gamma_tcost in result_df_fine.columns[:]:\n",
    "#     x=[el.excess_returns.std()*100*np.sqrt(250) for el in result_df_fine[gamma_tcost]]\n",
    "#     y=[el.excess_returns.mean()*100*250 for el in result_df_fine[gamma_tcost]]\n",
    "#     plt.plot(np.array(x),np.array(y), '.-', label='$\\gamma^\\mathrm{trade} = %g$'%gamma_tcost)\n",
    "# plt.legend(loc='lower right')\n",
    "# plt.xlabel('Risk')\n",
    "# plt.ylabel('Return')\n",
    "# plt.xlim([0,20])\n",
    "# plt.ylim([0,30])\n",
    "\n",
    "\n",
    "# import matplotlib.ticker as mtick\n",
    "# ax = plt.gca()\n",
    "# ax.xaxis.set_major_formatter(mtick.FormatStrFormatter('%.0f%%'))\n",
    "# ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.0f%%'))\n",
    "\n",
    "# plt.savefig(plotdir+'spo_riskrewardfrontier_fine.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4ngr8IKXMN8b/AEwTQiwAzgKuNfq9BzwKvGKcrwQmCCH8gAAgCWi+Ch4ajaZD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\nNDlQSimllJf/BzBEZAkGCQrCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120836550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "(result_rank.v/1E6).plot(label='Rank')\n",
    "(result_spo.v/1E6).plot(label='SPO')\n",
    "plt.legend()\n",
    "\n",
    "import matplotlib.ticker as mtick\n",
    "ax = plt.gca()\n",
    "ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('$%dM'))\n",
    "\n",
    "\n",
    "plt.ylabel('Portfolio total value')\n",
    "plt.savefig(plotdir+'rank_vs_spo.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1159fd5f8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k1G6JrPchagE1gB4AnvKNo3YAeEFr/ZZS6iIA0Fo/DOAdAEcAWAGgDkCYFE8r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\nIiOgglpEREREZAT+P5L0zyeRYHNqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1198c9d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_rank.leverage.plot(figsize=(12,6), label='Rank')\n",
    "result_spo.leverage.plot(label='SPO')\n",
    "plt.legend()\n",
    "plt.ylabel('Leverage')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11fb7c128>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WuufqdYWz/w7NL4K4Mt7mizK+LPyx0bCAT3ElVYQzH3Uj/gd3gPqnQGJFaN3X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\nzNrI/wOxXqnaVNlM9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1207b2240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.abs(result_rank.u.iloc[10].sort_values()).plot(logy=True,  figsize=(8,8), label='rank, sample day')\n",
    "np.abs(result_spo.u.iloc[10].sort_values()).plot(logy=True, label='spo, sample day')\n",
    "plt.legend()\n",
    "plt.ylabel('abs. val. trades vector')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}