fundamental_back_testing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import time\n",
    "from datetime import datetime as dt\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly\n",
    "import plotly.graph_objs as go\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Data Preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3 datasets:\n",
    "\n",
    "S&P 500 daily adjusted price\n",
    "\n",
    "Mean-variance weights table\n",
    "\n",
    "Min-variance weights table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_adj = pd.read_csv(\"1-sp500_adj_price.csv\")\n",
    "weight_meanv = pd.read_excel('mean_weighted_user8.xlsx')\n",
    "weight_minv = pd.read_excel('minimum_weighted_user8.xlsx')\n",
    "weight_equal=pd.read_excel('equally_weighted_user8.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>tic</th>\n",
       "      <th>predicted_return</th>\n",
       "      <th>weights</th>\n",
       "      <th>trade_date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>EOG</td>\n",
       "      <td>0.033723</td>\n",
       "      <td>0.000186</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>EQT</td>\n",
       "      <td>0.037745</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HES</td>\n",
       "      <td>0.051450</td>\n",
       "      <td>0.005125</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NFX</td>\n",
       "      <td>0.030283</td>\n",
       "      <td>0.050000</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OKE</td>\n",
       "      <td>0.041020</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   tic  predicted_return   weights  trade_date\n",
       "0  EOG          0.033723  0.000186    19950601\n",
       "1  EQT          0.037745  0.000000    19950601\n",
       "2  HES          0.051450  0.005125    19950601\n",
       "3  NFX          0.030283  0.050000    19950601\n",
       "4  OKE          0.041020  0.000000    19950601"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight_meanv.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>tic</th>\n",
       "      <th>predicted_return</th>\n",
       "      <th>weights</th>\n",
       "      <th>trade_date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>EOG</td>\n",
       "      <td>0.033723</td>\n",
       "      <td>0.009718</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>EQT</td>\n",
       "      <td>0.037745</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HES</td>\n",
       "      <td>0.051450</td>\n",
       "      <td>0.007371</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NFX</td>\n",
       "      <td>0.030283</td>\n",
       "      <td>0.050000</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OKE</td>\n",
       "      <td>0.041020</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   tic  predicted_return   weights  trade_date\n",
       "0  EOG          0.033723  0.009718    19950601\n",
       "1  EQT          0.037745  0.000000    19950601\n",
       "2  HES          0.051450  0.007371    19950601\n",
       "3  NFX          0.030283  0.050000    19950601\n",
       "4  OKE          0.041020  0.000000    19950601"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight_minv.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>tic</th>\n",
       "      <th>predicted_return</th>\n",
       "      <th>weights</th>\n",
       "      <th>trade_date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>EOG</td>\n",
       "      <td>0.033723</td>\n",
       "      <td>0.006993</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>EQT</td>\n",
       "      <td>0.037745</td>\n",
       "      <td>0.006993</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HES</td>\n",
       "      <td>0.051450</td>\n",
       "      <td>0.006993</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NFX</td>\n",
       "      <td>0.030283</td>\n",
       "      <td>0.006993</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>OKE</td>\n",
       "      <td>0.041020</td>\n",
       "      <td>0.006993</td>\n",
       "      <td>19950601</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   tic  predicted_return   weights  trade_date\n",
       "0  EOG          0.033723  0.006993    19950601\n",
       "1  EQT          0.037745  0.006993    19950601\n",
       "2  HES          0.051450  0.006993    19950601\n",
       "3  NFX          0.030283  0.006993    19950601\n",
       "4  OKE          0.041020  0.006993    19950601"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight_equal.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12932 12932 12932\n"
     ]
    }
   ],
   "source": [
    "#the length of the 3 tables should be the same\n",
    "print(len(weight_meanv),\n",
    "len(weight_minv),\n",
    "len(weight_equal))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Get stock name, trade date, daily date"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add 20170901 as tradedate_full\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#get unique stock name from table\n",
    "#stock names are the same between mean variance and minimum variance\n",
    "#only the weights are different\n",
    "stocks_name = list(set(weight_meanv['tic']))\n",
    "stocks_name.sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "982"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(stocks_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.series.Series'> <class 'list'>\n"
     ]
    }
   ],
   "source": [
    "#get all daily date\n",
    "#convert to list from pandas.core.series.Series\n",
    "#use set to get unique values\n",
    "daily = list(set(data_adj['datadate']))\n",
    "#sort it\n",
    "daily.sort()\n",
    "print(type(data_adj['datadate']),type(daily))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7155"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(daily)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "#get unique trade date from table\n",
    "tradedate = list(set(weight_meanv['trade_date']))\n",
    "tradedate.sort()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "89"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(tradedate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#add the last trade date 20170901\n",
    "tradedate_full = tradedate.copy()\n",
    "tradedate_full.append(20170901)\n",
    "len(tradedate_full)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Get the daily price matrix based on stock_name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#30mins running time\n",
    "##################match current all stocks to daily adjusted price table#######################\n",
    "# backtest daily price matrix:\n",
    "# covert original table to matrix\n",
    "# rows = all stocks: 971, columns = all dates:7155 days\n",
    "#\n",
    "start_time = time.time()\n",
    "\n",
    "balance_daily = pd.DataFrame(index = stocks_name, columns = daily)\n",
    "balance_daily = balance_daily.fillna(np.nan)\n",
    "\n",
    "for i in stocks_name:\n",
    "    ind = np.where(data_adj['tic'] == i)[0]\n",
    "    tmp = data_adj.loc[ind, :]\n",
    "    tmp.index = range(tmp.shape[0])\n",
    "    for j in daily:\n",
    "        ind2 = np.where(tmp['datadate'] == j)[0]\n",
    "        if(len(ind2) != 0):\n",
    "            balance_daily.loc[i,j] = tmp.loc[ind2[0], 'adj_price']\n",
    "\n",
    "elapsed_time = time.time() - start_time\n",
    "print(elapsed_time)\n",
    "#writer2 = pd.ExcelWriter('balance_daily.xlsx')\n",
    "#writer2 = pd.ExcelWriter('balance_daily_user8.xlsx')\n",
    "\n",
    "#balance_daily.to_excel(writer2,'Sheet1')\n",
    "#writer2.save()\n",
    "###############################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "balance_daily = pd.read_excel('balance_daily_user8.xlsx')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Function: calculate the rebalance matrix:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. shares table\n",
    "2. cost table\n",
    "3. cash table\n",
    "4. portfolio table\n",
    "5. portfolio_cost table\n",
    "6. portfolio_return table\n",
    "7. portfolio_cumsum table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set initial capital to 1 million and transaction percet to 0.1%\n",
    "\n",
    "capital = 1000000\n",
    "transaction_percent = 1/1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#construct an empty matrix\n",
    "#rows are stocks: 971 unique stocks\n",
    "#columns are trade dates\n",
    "#name the index as stock names\n",
    "\n",
    "def cal_portfolio(stocks_name,tradedate, weight_table, capital, transaction_percent):\n",
    "\n",
    "\n",
    "    balance_weight = pd.DataFrame(index = stocks_name, columns = tradedate)\n",
    "    balance_weight = balance_weight.fillna(0)\n",
    "    \n",
    "    #loop through the weights table to fill the matrix\n",
    "    #need weight tabele\n",
    "    #0. weights table\n",
    "    for i in range(weight_table.shape[0]):\n",
    "        tics = weight_table.loc[i, 'tic']\n",
    "        date = weight_table.loc[i, 'trade_date']\n",
    "        w = weight_table.loc[i, 'weights']\n",
    "        balance_weight.loc[tics, date] = w\n",
    "        \n",
    "    #1. shares table\n",
    "    balance_share = pd.DataFrame(index = stocks_name, columns = tradedate)\n",
    "    balance_share['initial'] = 0\n",
    "    balance_share = balance_share.fillna(0)\n",
    "    #2. costs table\n",
    "    balance_cost = pd.DataFrame(index = stocks_name, columns = tradedate)\n",
    "    balance_cost = balance_cost.fillna(0)\n",
    "    #3. cash table\n",
    "    balance_cash = pd.DataFrame(index = stocks_name, columns = tradedate)\n",
    "    balance_cash = balance_cash.fillna(0)\n",
    "\n",
    "    #4. portfolio without transaction costs table \n",
    "    portfolio = pd.DataFrame(index = range(1), columns = tradedate_full)\n",
    "    portfolio.loc[0,tradedate[0]] = capital\n",
    "    \n",
    "    \n",
    "    # calculate portfolio value without cost\n",
    "    balance_price_full = []\n",
    "    balance_price_full = balance_daily[tradedate_full]\n",
    "    balance_price = balance_daily[tradedate]\n",
    "    for j in range(len(tradedate)):\n",
    "        i = tradedate[j]\n",
    "        #current capital\n",
    "        cap = portfolio.loc[0, i]\n",
    "        #\n",
    "        balance_cash[i] = cap * balance_weight[i]\n",
    "        balance_share[i] = list(np.array(balance_cash[i])\n",
    "                                      / np.array(balance_price[i]))\n",
    "        balance_share[i] = balance_share[i].fillna(0)\n",
    "        balance_share[i] = balance_share[i].astype(int)\n",
    "        #next quarter price * current share to calculate next quarter total account value\n",
    "        a = balance_price_full[tradedate_full[j+1]].fillna(0)\n",
    "        portfolio.loc[0, tradedate_full[j+1]] = np.dot(balance_share[i], a)\n",
    "\n",
    "    balance_cost = abs(np.diff(balance_share, axis = 1))\n",
    "    balance_cost = balance_cost * balance_price\n",
    "    balance_cost = np.sum(balance_cost, axis = 0) * transaction_percent\n",
    "    balance_cost['20170901'] = 0\n",
    "    \n",
    "    #5. portfolio with transaction cost table\n",
    "    #calcualte portolio value with transaction cost\n",
    "    balance_cost.index = tradedate_full\n",
    "    portfolio_cost = []\n",
    "    portfolio_cost = portfolio.loc[0,] - balance_cost\n",
    "    portfolio_cost.index = tradedate_full\n",
    "    portfolio_cost_value = portfolio_cost.copy()\n",
    "    \n",
    "    #6. portfolio return P&L table\n",
    "    portfolio_cumsum = portfolio_cost_value.copy()\n",
    "    portfolio_cumsum.index = range(len(portfolio_cumsum))\n",
    "    tmp = portfolio_cumsum.shift(1)\n",
    "    tmp[0] = 0\n",
    "    tmp.index = tradedate_full\n",
    "\n",
    "    portfolio_cumsum = portfolio_cost_value- tmp\n",
    "    portfolio_cumsum.index = range(len(portfolio_cumsum))\n",
    "    tmp.index = range(len(tmp))\n",
    "    for i in range(len(portfolio_cumsum)):\n",
    "        if(tmp[i] != 0):\n",
    "            portfolio_cumsum[i] = portfolio_cumsum[i]/tmp[i]\n",
    "\n",
    "    portfolio_cumsum.index = range(len(portfolio_cumsum))\n",
    "    portfolio_cumsum[0] = 0\n",
    "    portfolio_return=portfolio_cumsum.copy()\n",
    "\n",
    "\n",
    "\n",
    "    # 7. portfolio accumulative return table\n",
    "    initial = 0\n",
    "    for i in range(portfolio_cumsum.shape[0]):\n",
    "        portfolio_cumsum[i] = initial + portfolio_cumsum[i]\n",
    "        initial = portfolio_cumsum[i]\n",
    "    \n",
    "    #1. shares table\n",
    "    #2. costs table\n",
    "    #3. cash table\n",
    "    #4. portfolio without transaction costs table \n",
    "    #5. portfolio with transaction cost table\n",
    "    #6. portfolio return P&L table\n",
    "    #7. portfolio accumulative return table\n",
    "\n",
    "    return(balance_share,\n",
    "           balance_cost,\n",
    "           balance_cash,\n",
    "           portfolio,\n",
    "           portfolio_cost,\n",
    "           portfolio_return,\n",
    "           portfolio_cumsum)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate mean variance allocation portolio\n",
    "(balance_share_meanv,\n",
    " balance_cost_meanv,\n",
    " balance_cash_meanv,\n",
    " portfolio_meanv,\n",
    " portfolio_cost_meanv,\n",
    " portfolio_return_meanv,\n",
    " portfolio_cumsum_meanv)=cal_portfolio(stocks_name,tradedate, weight_meanv, capital, transaction_percent)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.7725457672472325"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(portfolio_return_meanv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate minimum variance allocation portolio\n",
    "(balance_share_minv,\n",
    " balance_cost_minv,\n",
    " balance_cash_minv,\n",
    " portfolio_minv,\n",
    " portfolio_cost_minv,\n",
    " portfolio_return_minv,\n",
    " portfolio_cumsum_minv)=cal_portfolio(stocks_name,tradedate, weight_minv, capital, transaction_percent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate equally weighted allocation portolio\n",
    "(balance_share_equal,\n",
    " balance_cost_equal,\n",
    " balance_cash_equal,\n",
    " portfolio_equal,\n",
    " portfolio_cost_equal,\n",
    " portfolio_return_equal,\n",
    " portfolio_cumsum_equal)=cal_portfolio(stocks_name,tradedate, weight_equal, capital, transaction_percent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.9190887589936798"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(portfolio_return_equal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Calculate SPX Portfolio Value, Return and Cumulative Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# spx\n",
    "spx = pd.read_excel(\"1-spx_price.xlsx\")\n",
    "spx_daily = list(set(spx['datadate']))\n",
    "spx_daily.sort()\n",
    "spx = spx['AdjClose']\n",
    "spx.index = spx_daily\n",
    "\n",
    "spx = spx[tradedate_full]\n",
    "spx.index = range(len(spx))\n",
    "spx_return = (spx - spx.shift(1))/spx\n",
    "spx_return[0] = 0\n",
    "\n",
    "spx_return.index = tradedate_full\n",
    "spx_return.index = range(len(spx))\n",
    "spx_cumsum=spx_return.copy()\n",
    "\n",
    "spx_value = spx_return.copy()\n",
    "initial = 0\n",
    "for i in range(len(spx_cumsum)):\n",
    "    spx_cumsum[i] = initial + spx_cumsum[i]\n",
    "    initial = spx_cumsum[i]\n",
    "\n",
    "initial = capital\n",
    "for i in range(len(spx_value)):\n",
    "    spx_value[i] = initial * (1 + spx_value[i])\n",
    "    initial = spx_value[i]\n",
    "\n",
    "spx_cumsum.index = tradedate_full\n",
    "spx_value.index = tradedate_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.167518238034603"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(spx_return)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Plot the Portfolio Performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#convert tradedate_full to real date \n",
    "time_ind = pd.Series(tradedate_full)\n",
    "for i in range(len(time_ind)):\n",
    "    b = dt.strptime(str(time_ind[i]), '%Y%m%d')\n",
    "    time_ind[i] = b.strftime('%Y-%m-%d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1995-06-01\n",
       "1    1995-09-01\n",
       "2    1995-12-01\n",
       "3    1996-03-01\n",
       "4    1996-06-03\n",
       "dtype: object"
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time_ind.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Plot Portfolio Value with Transaction Cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "mode": "lines",
         "name": "Mean-Variance",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          998458.0630760784,
          1123260.5833325768,
          1178447.027953154,
          1281597.7306278015,
          1439651.3212386016,
          1407240.1609442772,
          1522977.9114179679,
          1632541.4833938628,
          1787791.7486830775,
          2078707.3315186682,
          2357477.9077981734,
          2611332.89101861,
          2806902.63148295,
          2366390.2467384133,
          2766567.1854805327,
          2611990.9474679576,
          2881841.138891825,
          2851221.5596200484,
          2617998.0212413752,
          2893875.4713748884,
          2917807.2271569637,
          3031924.036641939,
          2817091.5808808156,
          3154758.385911378,
          3365066.885125832,
          3471736.732395638,
          3741173.8796073054,
          3907594.602960381,
          4217630.294919859,
          3834067.9214990935,
          4260043.85824238,
          3993996.51440481,
          4701968.577813604,
          5308885.432475517,
          5853367.820215049,
          6618773.001116394,
          6539255.927722559,
          6468547.334574623,
          7436134.1190955015,
          7944078.807019354,
          7957335.581337408,
          8844770.634129183,
          8622682.881323332,
          9092850.931435268,
          9138967.413752554,
          8437678.854902243,
          9054360.48270095,
          9300605.191982558,
          10282141.758749923,
          9487186.517790463,
          9384022.650324833,
          8393009.009985894,
          8552184.401542058,
          8293192.756599575,
          5075783.972060018,
          4044780.186312367,
          6718298.065287237,
          7829872.683074835,
          8311003.439170952,
          8553868.35935759,
          8299430.41693535,
          8946225.511025935,
          9474641.375049528,
          10123084.22950246,
          11307464.823933912,
          9910426.346559089,
          9930291.745956,
          12681091.49574536,
          11728009.402130347,
          12981708.766953334,
          12705325.213600066,
          15097664.731719736,
          16825199.72007481,
          17119015.41862564,
          18936258.68357095,
          19772778.140000775,
          19678172.482051454,
          20655033.848588046,
          20151068.121828265,
          20300039.702423334,
          20965732.232030004,
          19049996.62788146,
          20313505.219360344,
          19445184.304117437,
          21645729.019172747,
          22770956.049426667,
          21317820.101990003,
          22455075.035350002,
          23165916.588,
          23495586.979999997
         ]
        },
        {
         "mode": "lines",
         "name": "Equally Weighted",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          998844.2963714534,
          1107344.9135422239,
          1158912.773857655,
          1220909.5625453917,
          1356890.941842029,
          1326003.1379586372,
          1512291.0613433875,
          1582973.7542575474,
          1750778.0958076618,
          1965553.0924391162,
          2074520.424219758,
          2245501.2071303097,
          2281219.1859449544,
          1931475.3738005555,
          2321450.8741147076,
          2364249.871267434,
          2693438.2648002906,
          2768052.231720082,
          2860993.5536182118,
          3162660.8443854596,
          3423287.9843922732,
          3838966.7777847038,
          3643423.2741229017,
          3732533.8746971576,
          3980803.6946178246,
          3714865.449827454,
          3753845.7489553825,
          4071322.356627598,
          4117068.567190412,
          3404556.1967559685,
          3913430.9643816655,
          3447636.9810599005,
          4396775.1012494,
          4958000.394492476,
          5366779.01783692,
          5831046.957691026,
          5790199.3136444995,
          5827610.523194131,
          6696203.7618838325,
          6915105.46430695,
          6945270.839356006,
          7531848.482949906,
          7960507.656158098,
          8384007.568282535,
          8424989.634917185,
          8206781.378723654,
          9069776.453184428,
          9460488.576536717,
          10492911.563779963,
          9922713.083179712,
          9767847.941226084,
          8809566.200748956,
          9472446.588164274,
          8763092.66339264,
          4699803.275151118,
          4035159.1867879936,
          7271536.11446665,
          8067270.093330809,
          9093620.683826402,
          9765393.692295585,
          9588534.73408103,
          9488790.63384071,
          10911377.99447061,
          12063609.880572775,
          12482344.526972676,
          10797743.79270264,
          11162427.595158875,
          12992089.958855718,
          11327256.443098137,
          12354305.99284345,
          12798281.092524074,
          14710398.01773131,
          16010046.45842947,
          16332137.683520209,
          18082031.55327043,
          19273209.392587975,
          19858999.266779292,
          20596553.115911547,
          20658576.652927022,
          21061735.513168395,
          21157556.809766382,
          18530992.405065876,
          19374628.72790116,
          17948235.218681417,
          20191514.455812532,
          21470876.869489755,
          22522422.216709904,
          24277940.320940778,
          23993084.06643459,
          24245301.54
         ]
        },
        {
         "mode": "lines",
         "name": "Min-Variance",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          998479.958225712,
          1102608.0965616514,
          1183454.376482888,
          1284604.2895499638,
          1413097.016081186,
          1381014.0801919147,
          1482399.9567024903,
          1596119.7020269996,
          1738390.6571687611,
          1947768.5734748628,
          2183604.233802087,
          2350561.659929291,
          2421948.1191230146,
          2048933.2045233422,
          2370014.0395823,
          2255129.421560097,
          2441315.796503577,
          2414511.8712351527,
          2203700.7429193407,
          2435685.4984426466,
          2631053.095119658,
          2921369.64599875,
          2827729.715354971,
          3170825.9006558335,
          3381797.4756947993,
          3535665.2350666667,
          3691848.6791572105,
          3893023.820417202,
          4106856.370110213,
          3719302.000181034,
          3733047.893048039,
          3613123.9857635996,
          4128253.987208261,
          4672672.843003778,
          5153722.947836058,
          5650738.698347072,
          5648898.964108766,
          5670705.756984031,
          6519444.534293969,
          6705707.054166436,
          6915843.566097567,
          7131463.446373296,
          7036814.553801632,
          7164036.7712609265,
          7198992.349405428,
          6900139.186151129,
          7286708.513759753,
          7394347.827045007,
          8181821.580076629,
          7477232.454576124,
          7505125.957472971,
          6723283.020676837,
          6886953.942791842,
          6603875.646600619,
          4650168.68363283,
          4066775.743775659,
          5188045.1741588,
          5706103.070676254,
          6092057.891372305,
          6308179.890054051,
          6365316.077767036,
          6746138.767968225,
          7244270.041761565,
          7893886.252425487,
          8582721.215359025,
          7921875.54377617,
          7851579.70769501,
          10088964.739385216,
          9747767.505601732,
          10299643.673649998,
          10331601.413466984,
          11586795.437344093,
          12461098.909675939,
          12482244.952336112,
          13863931.23268185,
          15048431.52041643,
          15510388.509925714,
          16253097.55276,
          16540914.00676279,
          16754204.92305132,
          16877477.587154016,
          15332073.965297999,
          15878745.02766017,
          16199001.517678333,
          16987180.593204,
          17479316.60787,
          16511320.91759,
          17565953.401690003,
          17994678.09118,
          18203679.26
         ]
        },
        {
         "mode": "lines",
         "name": "SPX",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          1000000,
          1053827.3899451268,
          1128726.176676685,
          1194221.2943952465,
          1235913.8660998933,
          1211449.2528236327,
          1374521.6131689236,
          1441492.621510624,
          1528439.2882870708,
          1662271.2872840187,
          1742744.2044073285,
          1864055.8590053502,
          1938004.4127041735,
          1749478.5474663517,
          2018938.2779885416,
          2118369.5563651035,
          2213464.2200594125,
          2274676.237146512,
          2383143.7637028177,
          2351125.167769826,
          2464104.5128510464,
          2580701.2778534796,
          2177397.3295371137,
          2047584.639719755,
          2079159.2588130033,
          1844750.340325074,
          1839787.1685389038,
          1842843.2474474926,
          1681522.7982603444,
          1370007.6285529356,
          1452850.4918287552,
          1279304.0603885213,
          1454186.3833475355,
          1532431.4693668392,
          1601354.519704557,
          1720281.698206608,
          1666933.2932241342,
          1643886.8690898418,
          1761807.0016350888,
          1789520.646663915,
          1777329.6273916373,
          1805511.6417779017,
          1867015.1009028493,
          1905432.8162743917,
          1897237.267471648,
          1933850.4096029266,
          2052508.463151598,
          2061958.048457997,
          2240688.536863728,
          2170102.0479820594,
          2145046.8777770447,
          1917739.5118458082,
          1992931.2486618091,
          1824318.6205173796,
          793106.3848716444,
          662521.4176434831,
          832601.3884143719,
          878626.202507137,
          966436.5331434475,
          972370.0349395794,
          931503.083882718,
          939763.7100837127,
          1037770.788734775,
          1117419.0500169776,
          1124406.4511570854,
          1021592.7453367246,
          1054557.340784991,
          1153950.9286358738,
          1067226.804919232,
          1163623.0799511934,
          1167354.7216716928,
          1250965.6720457997,
          1344169.3251811457,
          1343636.4807512716,
          1463854.2322270737,
          1499409.0108416323,
          1561131.093946486,
          1621407.9451713786,
          1661804.1048714146,
          1711994.3381823704,
          1707405.806929618,
          1530870.8265802197,
          1668316.6293852716,
          1563513.0111873583,
          1653615.07067482,
          1708101.8308206256,
          1723864.7277731486,
          1871273.3696047848,
          1897532.2289494267,
          1933152.8514295407
         ]
        }
       ],
       "layout": {
        "title": "Portfolio Value Performance Quarterly with Transaction cost",
        "xaxis": {
         "title": "Quarterly Trade Date"
        },
        "yaxis": {
         "title": "Portfolio Value"
        }
       }
      },
      "text/html": [
       "<div id=\"4226616d-f366-45f7-a54e-fba1925fe832\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"4226616d-f366-45f7-a54e-fba1925fe832\", [{\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [998458.0630760784, 1123260.5833325768, 1178447.027953154, 1281597.7306278015, 1439651.3212386016, 1407240.1609442772, 1522977.9114179679, 1632541.4833938628, 1787791.7486830775, 2078707.3315186682, 2357477.9077981734, 2611332.89101861, 2806902.63148295, 2366390.2467384133, 2766567.1854805327, 2611990.9474679576, 2881841.138891825, 2851221.5596200484, 2617998.0212413752, 2893875.4713748884, 2917807.2271569637, 3031924.036641939, 2817091.5808808156, 3154758.385911378, 3365066.885125832, 3471736.732395638, 3741173.8796073054, 3907594.602960381, 4217630.294919859, 3834067.9214990935, 4260043.85824238, 3993996.51440481, 4701968.577813604, 5308885.432475517, 5853367.820215049, 6618773.001116394, 6539255.927722559, 6468547.334574623, 7436134.1190955015, 7944078.807019354, 7957335.581337408, 8844770.634129183, 8622682.881323332, 9092850.931435268, 9138967.413752554, 8437678.854902243, 9054360.48270095, 9300605.191982558, 10282141.758749923, 9487186.517790463, 9384022.650324833, 8393009.009985894, 8552184.401542058, 8293192.756599575, 5075783.972060018, 4044780.186312367, 6718298.065287237, 7829872.683074835, 8311003.439170952, 8553868.35935759, 8299430.41693535, 8946225.511025935, 9474641.375049528, 10123084.22950246, 11307464.823933912, 9910426.346559089, 9930291.745956, 12681091.49574536, 11728009.402130347, 12981708.766953334, 12705325.213600066, 15097664.731719736, 16825199.72007481, 17119015.41862564, 18936258.68357095, 19772778.140000775, 19678172.482051454, 20655033.848588046, 20151068.121828265, 20300039.702423334, 20965732.232030004, 19049996.62788146, 20313505.219360344, 19445184.304117437, 21645729.019172747, 22770956.049426667, 21317820.101990003, 22455075.035350002, 23165916.588, 23495586.979999997], \"mode\": \"lines\", \"name\": \"Mean-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [998844.2963714534, 1107344.9135422239, 1158912.773857655, 1220909.5625453917, 1356890.941842029, 1326003.1379586372, 1512291.0613433875, 1582973.7542575474, 1750778.0958076618, 1965553.0924391162, 2074520.424219758, 2245501.2071303097, 2281219.1859449544, 1931475.3738005555, 2321450.8741147076, 2364249.871267434, 2693438.2648002906, 2768052.231720082, 2860993.5536182118, 3162660.8443854596, 3423287.9843922732, 3838966.7777847038, 3643423.2741229017, 3732533.8746971576, 3980803.6946178246, 3714865.449827454, 3753845.7489553825, 4071322.356627598, 4117068.567190412, 3404556.1967559685, 3913430.9643816655, 3447636.9810599005, 4396775.1012494, 4958000.394492476, 5366779.01783692, 5831046.957691026, 5790199.3136444995, 5827610.523194131, 6696203.7618838325, 6915105.46430695, 6945270.839356006, 7531848.482949906, 7960507.656158098, 8384007.568282535, 8424989.634917185, 8206781.378723654, 9069776.453184428, 9460488.576536717, 10492911.563779963, 9922713.083179712, 9767847.941226084, 8809566.200748956, 9472446.588164274, 8763092.66339264, 4699803.275151118, 4035159.1867879936, 7271536.11446665, 8067270.093330809, 9093620.683826402, 9765393.692295585, 9588534.73408103, 9488790.63384071, 10911377.99447061, 12063609.880572775, 12482344.526972676, 10797743.79270264, 11162427.595158875, 12992089.958855718, 11327256.443098137, 12354305.99284345, 12798281.092524074, 14710398.01773131, 16010046.45842947, 16332137.683520209, 18082031.55327043, 19273209.392587975, 19858999.266779292, 20596553.115911547, 20658576.652927022, 21061735.513168395, 21157556.809766382, 18530992.405065876, 19374628.72790116, 17948235.218681417, 20191514.455812532, 21470876.869489755, 22522422.216709904, 24277940.320940778, 23993084.06643459, 24245301.54], \"mode\": \"lines\", \"name\": \"Equally Weighted\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [998479.958225712, 1102608.0965616514, 1183454.376482888, 1284604.2895499638, 1413097.016081186, 1381014.0801919147, 1482399.9567024903, 1596119.7020269996, 1738390.6571687611, 1947768.5734748628, 2183604.233802087, 2350561.659929291, 2421948.1191230146, 2048933.2045233422, 2370014.0395823, 2255129.421560097, 2441315.796503577, 2414511.8712351527, 2203700.7429193407, 2435685.4984426466, 2631053.095119658, 2921369.64599875, 2827729.715354971, 3170825.9006558335, 3381797.4756947993, 3535665.2350666667, 3691848.6791572105, 3893023.820417202, 4106856.370110213, 3719302.000181034, 3733047.893048039, 3613123.9857635996, 4128253.987208261, 4672672.843003778, 5153722.947836058, 5650738.698347072, 5648898.964108766, 5670705.756984031, 6519444.534293969, 6705707.054166436, 6915843.566097567, 7131463.446373296, 7036814.553801632, 7164036.7712609265, 7198992.349405428, 6900139.186151129, 7286708.513759753, 7394347.827045007, 8181821.580076629, 7477232.454576124, 7505125.957472971, 6723283.020676837, 6886953.942791842, 6603875.646600619, 4650168.68363283, 4066775.743775659, 5188045.1741588, 5706103.070676254, 6092057.891372305, 6308179.890054051, 6365316.077767036, 6746138.767968225, 7244270.041761565, 7893886.252425487, 8582721.215359025, 7921875.54377617, 7851579.70769501, 10088964.739385216, 9747767.505601732, 10299643.673649998, 10331601.413466984, 11586795.437344093, 12461098.909675939, 12482244.952336112, 13863931.23268185, 15048431.52041643, 15510388.509925714, 16253097.55276, 16540914.00676279, 16754204.92305132, 16877477.587154016, 15332073.965297999, 15878745.02766017, 16199001.517678333, 16987180.593204, 17479316.60787, 16511320.91759, 17565953.401690003, 17994678.09118, 18203679.26], \"mode\": \"lines\", \"name\": \"Min-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [1000000.0, 1053827.3899451268, 1128726.176676685, 1194221.2943952465, 1235913.8660998933, 1211449.2528236327, 1374521.6131689236, 1441492.621510624, 1528439.2882870708, 1662271.2872840187, 1742744.2044073285, 1864055.8590053502, 1938004.4127041735, 1749478.5474663517, 2018938.2779885416, 2118369.5563651035, 2213464.2200594125, 2274676.237146512, 2383143.7637028177, 2351125.167769826, 2464104.5128510464, 2580701.2778534796, 2177397.3295371137, 2047584.639719755, 2079159.2588130033, 1844750.340325074, 1839787.1685389038, 1842843.2474474926, 1681522.7982603444, 1370007.6285529356, 1452850.4918287552, 1279304.0603885213, 1454186.3833475355, 1532431.4693668392, 1601354.519704557, 1720281.698206608, 1666933.2932241342, 1643886.8690898418, 1761807.0016350888, 1789520.646663915, 1777329.6273916373, 1805511.6417779017, 1867015.1009028493, 1905432.8162743917, 1897237.267471648, 1933850.4096029266, 2052508.463151598, 2061958.048457997, 2240688.536863728, 2170102.0479820594, 2145046.8777770447, 1917739.5118458082, 1992931.2486618091, 1824318.6205173796, 793106.3848716444, 662521.4176434831, 832601.3884143719, 878626.202507137, 966436.5331434475, 972370.0349395794, 931503.083882718, 939763.7100837127, 1037770.788734775, 1117419.0500169776, 1124406.4511570854, 1021592.7453367246, 1054557.340784991, 1153950.9286358738, 1067226.804919232, 1163623.0799511934, 1167354.7216716928, 1250965.6720457997, 1344169.3251811457, 1343636.4807512716, 1463854.2322270737, 1499409.0108416323, 1561131.093946486, 1621407.9451713786, 1661804.1048714146, 1711994.3381823704, 1707405.806929618, 1530870.8265802197, 1668316.6293852716, 1563513.0111873583, 1653615.07067482, 1708101.8308206256, 1723864.7277731486, 1871273.3696047848, 1897532.2289494267, 1933152.8514295407], \"mode\": \"lines\", \"name\": \"SPX\"}], {\"title\": \"Portfolio Value Performance Quarterly with Transaction cost\", \"xaxis\": {\"title\": \"Quarterly Trade Date\"}, \"yaxis\": {\"title\": \"Portfolio Value\"}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<div id=\"4226616d-f366-45f7-a54e-fba1925fe832\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"4226616d-f366-45f7-a54e-fba1925fe832\", [{\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [998458.0630760784, 1123260.5833325768, 1178447.027953154, 1281597.7306278015, 1439651.3212386016, 1407240.1609442772, 1522977.9114179679, 1632541.4833938628, 1787791.7486830775, 2078707.3315186682, 2357477.9077981734, 2611332.89101861, 2806902.63148295, 2366390.2467384133, 2766567.1854805327, 2611990.9474679576, 2881841.138891825, 2851221.5596200484, 2617998.0212413752, 2893875.4713748884, 2917807.2271569637, 3031924.036641939, 2817091.5808808156, 3154758.385911378, 3365066.885125832, 3471736.732395638, 3741173.8796073054, 3907594.602960381, 4217630.294919859, 3834067.9214990935, 4260043.85824238, 3993996.51440481, 4701968.577813604, 5308885.432475517, 5853367.820215049, 6618773.001116394, 6539255.927722559, 6468547.334574623, 7436134.1190955015, 7944078.807019354, 7957335.581337408, 8844770.634129183, 8622682.881323332, 9092850.931435268, 9138967.413752554, 8437678.854902243, 9054360.48270095, 9300605.191982558, 10282141.758749923, 9487186.517790463, 9384022.650324833, 8393009.009985894, 8552184.401542058, 8293192.756599575, 5075783.972060018, 4044780.186312367, 6718298.065287237, 7829872.683074835, 8311003.439170952, 8553868.35935759, 8299430.41693535, 8946225.511025935, 9474641.375049528, 10123084.22950246, 11307464.823933912, 9910426.346559089, 9930291.745956, 12681091.49574536, 11728009.402130347, 12981708.766953334, 12705325.213600066, 15097664.731719736, 16825199.72007481, 17119015.41862564, 18936258.68357095, 19772778.140000775, 19678172.482051454, 20655033.848588046, 20151068.121828265, 20300039.702423334, 20965732.232030004, 19049996.62788146, 20313505.219360344, 19445184.304117437, 21645729.019172747, 22770956.049426667, 21317820.101990003, 22455075.035350002, 23165916.588, 23495586.979999997], \"mode\": \"lines\", \"name\": \"Mean-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [998844.2963714534, 1107344.9135422239, 1158912.773857655, 1220909.5625453917, 1356890.941842029, 1326003.1379586372, 1512291.0613433875, 1582973.7542575474, 1750778.0958076618, 1965553.0924391162, 2074520.424219758, 2245501.2071303097, 2281219.1859449544, 1931475.3738005555, 2321450.8741147076, 2364249.871267434, 2693438.2648002906, 2768052.231720082, 2860993.5536182118, 3162660.8443854596, 3423287.9843922732, 3838966.7777847038, 3643423.2741229017, 3732533.8746971576, 3980803.6946178246, 3714865.449827454, 3753845.7489553825, 4071322.356627598, 4117068.567190412, 3404556.1967559685, 3913430.9643816655, 3447636.9810599005, 4396775.1012494, 4958000.394492476, 5366779.01783692, 5831046.957691026, 5790199.3136444995, 5827610.523194131, 6696203.7618838325, 6915105.46430695, 6945270.839356006, 7531848.482949906, 7960507.656158098, 8384007.568282535, 8424989.634917185, 8206781.378723654, 9069776.453184428, 9460488.576536717, 10492911.563779963, 9922713.083179712, 9767847.941226084, 8809566.200748956, 9472446.588164274, 8763092.66339264, 4699803.275151118, 4035159.1867879936, 7271536.11446665, 8067270.093330809, 9093620.683826402, 9765393.692295585, 9588534.73408103, 9488790.63384071, 10911377.99447061, 12063609.880572775, 12482344.526972676, 10797743.79270264, 11162427.595158875, 12992089.958855718, 11327256.443098137, 12354305.99284345, 12798281.092524074, 14710398.01773131, 16010046.45842947, 16332137.683520209, 18082031.55327043, 19273209.392587975, 19858999.266779292, 20596553.115911547, 20658576.652927022, 21061735.513168395, 21157556.809766382, 18530992.405065876, 19374628.72790116, 17948235.218681417, 20191514.455812532, 21470876.869489755, 22522422.216709904, 24277940.320940778, 23993084.06643459, 24245301.54], \"mode\": \"lines\", \"name\": \"Equally Weighted\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [998479.958225712, 1102608.0965616514, 1183454.376482888, 1284604.2895499638, 1413097.016081186, 1381014.0801919147, 1482399.9567024903, 1596119.7020269996, 1738390.6571687611, 1947768.5734748628, 2183604.233802087, 2350561.659929291, 2421948.1191230146, 2048933.2045233422, 2370014.0395823, 2255129.421560097, 2441315.796503577, 2414511.8712351527, 2203700.7429193407, 2435685.4984426466, 2631053.095119658, 2921369.64599875, 2827729.715354971, 3170825.9006558335, 3381797.4756947993, 3535665.2350666667, 3691848.6791572105, 3893023.820417202, 4106856.370110213, 3719302.000181034, 3733047.893048039, 3613123.9857635996, 4128253.987208261, 4672672.843003778, 5153722.947836058, 5650738.698347072, 5648898.964108766, 5670705.756984031, 6519444.534293969, 6705707.054166436, 6915843.566097567, 7131463.446373296, 7036814.553801632, 7164036.7712609265, 7198992.349405428, 6900139.186151129, 7286708.513759753, 7394347.827045007, 8181821.580076629, 7477232.454576124, 7505125.957472971, 6723283.020676837, 6886953.942791842, 6603875.646600619, 4650168.68363283, 4066775.743775659, 5188045.1741588, 5706103.070676254, 6092057.891372305, 6308179.890054051, 6365316.077767036, 6746138.767968225, 7244270.041761565, 7893886.252425487, 8582721.215359025, 7921875.54377617, 7851579.70769501, 10088964.739385216, 9747767.505601732, 10299643.673649998, 10331601.413466984, 11586795.437344093, 12461098.909675939, 12482244.952336112, 13863931.23268185, 15048431.52041643, 15510388.509925714, 16253097.55276, 16540914.00676279, 16754204.92305132, 16877477.587154016, 15332073.965297999, 15878745.02766017, 16199001.517678333, 16987180.593204, 17479316.60787, 16511320.91759, 17565953.401690003, 17994678.09118, 18203679.26], \"mode\": \"lines\", \"name\": \"Min-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [1000000.0, 1053827.3899451268, 1128726.176676685, 1194221.2943952465, 1235913.8660998933, 1211449.2528236327, 1374521.6131689236, 1441492.621510624, 1528439.2882870708, 1662271.2872840187, 1742744.2044073285, 1864055.8590053502, 1938004.4127041735, 1749478.5474663517, 2018938.2779885416, 2118369.5563651035, 2213464.2200594125, 2274676.237146512, 2383143.7637028177, 2351125.167769826, 2464104.5128510464, 2580701.2778534796, 2177397.3295371137, 2047584.639719755, 2079159.2588130033, 1844750.340325074, 1839787.1685389038, 1842843.2474474926, 1681522.7982603444, 1370007.6285529356, 1452850.4918287552, 1279304.0603885213, 1454186.3833475355, 1532431.4693668392, 1601354.519704557, 1720281.698206608, 1666933.2932241342, 1643886.8690898418, 1761807.0016350888, 1789520.646663915, 1777329.6273916373, 1805511.6417779017, 1867015.1009028493, 1905432.8162743917, 1897237.267471648, 1933850.4096029266, 2052508.463151598, 2061958.048457997, 2240688.536863728, 2170102.0479820594, 2145046.8777770447, 1917739.5118458082, 1992931.2486618091, 1824318.6205173796, 793106.3848716444, 662521.4176434831, 832601.3884143719, 878626.202507137, 966436.5331434475, 972370.0349395794, 931503.083882718, 939763.7100837127, 1037770.788734775, 1117419.0500169776, 1124406.4511570854, 1021592.7453367246, 1054557.340784991, 1153950.9286358738, 1067226.804919232, 1163623.0799511934, 1167354.7216716928, 1250965.6720457997, 1344169.3251811457, 1343636.4807512716, 1463854.2322270737, 1499409.0108416323, 1561131.093946486, 1621407.9451713786, 1661804.1048714146, 1711994.3381823704, 1707405.806929618, 1530870.8265802197, 1668316.6293852716, 1563513.0111873583, 1653615.07067482, 1708101.8308206256, 1723864.7277731486, 1871273.3696047848, 1897532.2289494267, 1933152.8514295407], \"mode\": \"lines\", \"name\": \"SPX\"}], {\"title\": \"Portfolio Value Performance Quarterly with Transaction cost\", \"xaxis\": {\"title\": \"Quarterly Trade Date\"}, \"yaxis\": {\"title\": \"Portfolio Value\"}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trace0 = go.Scatter(x = time_ind, y = portfolio_cost_meanv, mode = 'lines', name = 'Mean-Variance')\n",
    "trace1 = go.Scatter(x = time_ind, y = portfolio_cost_equal, mode = 'lines', name = 'Equally Weighted')\n",
    "trace2 = go.Scatter(x = time_ind, y = portfolio_cost_minv, mode = 'lines', name = 'Min-Variance')\n",
    "trace3 = go.Scatter(x = time_ind, y = spx_value, mode = 'lines', name = 'SPX')\n",
    "\n",
    "data = [trace0, trace1, trace2,trace3]\n",
    "layout = dict(title = \"Portfolio Value Performance Quarterly with Transaction cost\", \n",
    "              xaxis = dict(title = 'Quarterly Trade Date'), \n",
    "              yaxis = dict(title = 'Portfolio Value'))\n",
    "fig = dict(data = data, layout = layout)\n",
    "\n",
    "plotly.offline.iplot(fig)\n",
    "\n",
    "#portfolio_tmp = portfolio_cost_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 Plot Portfolio Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "mode": "lines",
         "name": "Mean-Variance",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.12499525505558357,
          0.049130580596753175,
          0.08753104741059947,
          0.12332542952723254,
          -0.022513201506625582,
          0.08224449080250033,
          0.07194035524381694,
          0.09509728657336629,
          0.16272341733867204,
          0.13410766010809233,
          0.10768074745503382,
          0.07489268838032118,
          -0.15693896175935534,
          0.16910859875867124,
          -0.05587293842846846,
          0.1033120699309689,
          -0.010625005958361385,
          -0.08179776053943431,
          0.10537725693264675,
          0.008269794612380187,
          0.03911046912998701,
          -0.07085680682127674,
          0.11986362364725987,
          0.06666390052362063,
          0.03169917594842007,
          0.07760874973539401,
          0.044483557489860444,
          0.07934182622849245,
          -0.0909426257400433,
          0.11110286658060385,
          -0.06245178516714541,
          0.17725905890388508,
          0.12907718216699068,
          0.10256058350945468,
          0.13076321263426502,
          -0.012013869244408676,
          -0.0108129417061311,
          0.14958331978945127,
          0.06830762863992514,
          0.0016687616827693967,
          0.11152414570438689,
          -0.025109498255261105,
          0.05452688642073535,
          0.0050717297209673185,
          -0.07673608265579256,
          0.07308664366153468,
          0.02719625640618991,
          0.10553469871116378,
          -0.077314168546934,
          -0.010874021215054253,
          -0.1056064842623365,
          0.018965235396123062,
          -0.030283683417278016,
          -0.38795779610683717,
          -0.20312207757912437,
          0.660979770426615,
          0.16545479331007815,
          0.061448094441706104,
          0.02922209357319968,
          -0.029745365691055452,
          0.07793246784391035,
          0.059065788512969716,
          0.06843983099566579,
          0.11699799859214088,
          -0.12355010598112022,
          0.0020044949331376196,
          0.27701097008651265,
          -0.07515773338082003,
          0.10689788197093855,
          -0.021290229068829502,
          0.18829423709350285,
          0.11442398669282776,
          0.017462835713044668,
          0.1061534919215116,
          0.04417554018500953,
          -0.004784641656294701,
          0.04964187438785744,
          -0.024399172156003547,
          0.007392738672432851,
          0.032792671313209426,
          -0.09137460990853519,
          0.06632592205447536,
          -0.04274599119482981,
          0.11316656508055585,
          0.051983789931826674,
          -0.06381532441073118,
          0.053347618467511,
          0.031656164654580383,
          0.014230837391979874
         ]
        },
        {
         "mode": "lines",
         "name": "Minimum-Variance",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.10428665841322851,
          0.07332277005161279,
          0.08547005704409465,
          0.10002514204295329,
          -0.022703986721480753,
          0.07341407880250317,
          0.07671326810982372,
          0.08913551719277941,
          0.12044353519887534,
          0.12107991859961484,
          0.07645956329572498,
          0.030369958129867213,
          -0.15401441164426793,
          0.1567063456974202,
          -0.048474235216957054,
          0.08256128147832699,
          -0.010979294570088994,
          -0.08731004010676939,
          0.10527053469881999,
          0.08021051847700676,
          0.11034233836542498,
          -0.03205343451556449,
          0.121332736802178,
          0.06653521248054955,
          0.045498809576186953,
          0.04417370811623201,
          0.054491708285811055,
          0.05492711053334758,
          -0.09436764644359308,
          0.003695825955067885,
          -0.03212493134839518,
          0.1425719137993527,
          0.13187629866826117,
          0.10294966521196518,
          0.09643819730738544,
          -0.00032557411278709647,
          0.0038603616410592427,
          0.14967074887718046,
          0.02857030516828203,
          0.03133696569708741,
          0.031177668814362423,
          -0.013272015384135227,
          0.01807951829433437,
          0.004879313054998381,
          -0.041513193617851496,
          0.05602341013417302,
          0.014772007564457226,
          0.1064967149843044,
          -0.08611641290446055,
          0.0037304581696902084,
          -0.10417452568103007,
          0.02434389889755493,
          -0.04110355587429242,
          -0.2958424821299399,
          -0.12545629622222865,
          0.2757145957947849,
          0.0998560882040609,
          0.0676389500707547,
          0.03547602510275252,
          0.009057475961183397,
          0.059827773758374406,
          0.07383946445906936,
          0.08967310811427967,
          0.0872618303464767,
          -0.07699721976291764,
          -0.008873635503701927,
          0.2849598571224382,
          -0.033818854817830875,
          0.056615647401430186,
          0.003102800526851703,
          0.12149075188295538,
          0.07545688340315194,
          0.0016969645144019605,
          0.11069212995112299,
          0.08543754782498648,
          0.03069801586182192,
          0.047884618902937,
          0.01770840623262702,
          0.012894747908206643,
          0.007357714953879479,
          -0.09156603016509249,
          0.03565538906213765,
          0.02016887918159075,
          0.04865602825368639,
          0.02897102388273245,
          -0.05537949291702657,
          0.06387329574440477,
          0.024406571034667025,
          0.011614610039756256
         ]
        },
        {
         "mode": "lines",
         "name": "Equally Weighted",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.10862615681435583,
          0.04656892327294265,
          0.05349564702904169,
          0.1113771105315442,
          -0.022763659871927935,
          0.1404882975401837,
          0.04673881551040289,
          0.10600576358185963,
          0.12267402542089455,
          0.055438508478761486,
          0.08241942615477442,
          0.01590646164037977,
          -0.1533144269078746,
          0.20190549960096,
          0.018436313957773568,
          0.13923587245724753,
          0.02770212627291229,
          0.03357643357776365,
          0.10544144372004555,
          0.08240755263704429,
          0.1214267672739268,
          -0.05093649280670292,
          0.024457932518342364,
          0.06651508820956396,
          -0.06680516428125499,
          0.010493058134780893,
          0.08457369559219705,
          0.01123620449467603,
          -0.17306303230229642,
          0.1494687525236265,
          -0.1190244538772289,
          0.2753010613947259,
          0.12764475787801777,
          0.08244828374732072,
          0.08650774297042495,
          -0.007005198953620025,
          0.0064611263832443705,
          0.14904792199695982,
          0.03269041836348389,
          0.004362243671446266,
          0.0844571302057804,
          0.05691287791815806,
          0.053200113663206615,
          0.004888123764306739,
          -0.025900121620229824,
          0.1051563377450405,
          0.043078473363597505,
          0.10912998614086317,
          -0.05434130242443812,
          -0.015607136944848788,
          -0.09810571850045018,
          0.07524551973500831,
          -0.07488603056975413,
          -0.4636821204933392,
          -0.14141955512845442,
          0.8020444244864671,
          0.10943134522581184,
          0.1272240272882489,
          0.07387299644727596,
          -0.018110786291605216,
          -0.010402434053431992,
          0.14992293702386064,
          0.10559911742458787,
          0.034710559322233235,
          -0.13495867948764267,
          0.03377407442309356,
          0.16391258515220872,
          -0.12814208653341344,
          0.0906706363455829,
          0.03593687091268493,
          0.14940419821878825,
          0.08834896507433836,
          0.020118069358952655,
          0.10714420265486338,
          0.06587632787877208,
          0.030393997297440186,
          0.0371395274869694,
          0.0030113551848420703,
          0.01951532610472708,
          0.004549544197726594,
          -0.12414308647811725,
          0.045525695785437685,
          -0.0736217209244176,
          0.12498606184947912,
          0.06336138958159886,
          0.04897542627680945,
          0.07794535096355729,
          -0.011733131012785648,
          0.010512090603569113
         ]
        },
        {
         "mode": "lines",
         "name": "SPX",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.053827389945126994,
          0.07107310689225696,
          0.058025692211196245,
          0.03491193123110393,
          -0.01979475588655899,
          0.13460932017185498,
          0.04872313952728657,
          0.060317108446472804,
          0.08756121360040031,
          0.0484114222142368,
          0.06960955847176517,
          0.03967078204313154,
          -0.09727834673748983,
          0.15402288351144955,
          0.0492492908082482,
          0.044890497698372035,
          0.027654396457990574,
          0.047684819837206086,
          -0.013435444567239557,
          0.04805330938139202,
          0.047318108624997766,
          -0.15627688170550968,
          -0.05961828282620115,
          0.01542042193555913,
          -0.11274216609157384,
          -0.0026904300694129903,
          0.0016611045890791052,
          -0.08753888829697902,
          -0.18525777350725997,
          0.060468906558806754,
          -0.1194523678907833,
          0.13670113960703212,
          0.053806779457791006,
          0.044976269226704786,
          0.07426661431847867,
          -0.031011435532964923,
          -0.013825642710463064,
          0.0717325107721888,
          0.015730238898531784,
          -0.006812449632813502,
          0.015856380241420564,
          0.03406428277825165,
          0.020577078007009426,
          -0.004301148134295284,
          0.01929813564123736,
          0.06135844476876331,
          0.004603920264420882,
          0.08667998291206339,
          -0.031502142185485485,
          -0.011545618432235904,
          -0.10596848408590474,
          0.03920852459447406,
          -0.08460534113138507,
          -0.5652588446163432,
          -0.16465000120922624,
          0.2567161849285489,
          0.0552783297424184,
          0.09994048707601261,
          0.006139566947901408,
          -0.04202818843486971,
          0.008868061033746103,
          0.10428906500585339,
          0.07674937678608969,
          0.0062531609247233055,
          -0.09143820343129393,
          0.03226784410787994,
          0.09425147785410723,
          -0.07515408286829113,
          0.090324075995502,
          0.0032069162126414823,
          0.07162428764957852,
          0.07450536431021561,
          -0.0003964116870486694,
          0.08947193173006482,
          0.024288469324207453,
          0.04116427382959935,
          0.03861101188658963,
          0.024914248027670987,
          0.030202256188818003,
          -0.0026802257171155757,
          -0.10339368627711083,
          0.08978275659749105,
          -0.06281998054322017,
          0.057627956302734394,
          0.03295008682012692,
          0.009228312193161198,
          0.0855105620857243,
          0.014032615314879298,
          0.018772077721091126
         ]
        }
       ],
       "layout": {
        "title": "Portfolio Return Quarterly",
        "xaxis": {
         "title": "Quarterly Trade Date"
        },
        "yaxis": {
         "title": "Portfolio Value"
        }
       }
      },
      "text/html": [
       "<div id=\"a316784e-af02-4b30-82da-1720a785ee67\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"a316784e-af02-4b30-82da-1720a785ee67\", [{\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.12499525505558357, 0.049130580596753175, 0.08753104741059947, 0.12332542952723254, -0.022513201506625582, 0.08224449080250033, 0.07194035524381694, 0.09509728657336629, 0.16272341733867204, 0.13410766010809233, 0.10768074745503382, 0.07489268838032118, -0.15693896175935534, 0.16910859875867124, -0.05587293842846846, 0.1033120699309689, -0.010625005958361385, -0.08179776053943431, 0.10537725693264675, 0.008269794612380187, 0.03911046912998701, -0.07085680682127674, 0.11986362364725987, 0.06666390052362063, 0.03169917594842007, 0.07760874973539401, 0.044483557489860444, 0.07934182622849245, -0.0909426257400433, 0.11110286658060385, -0.06245178516714541, 0.17725905890388508, 0.12907718216699068, 0.10256058350945468, 0.13076321263426502, -0.012013869244408676, -0.0108129417061311, 0.14958331978945127, 0.06830762863992514, 0.0016687616827693967, 0.11152414570438689, -0.025109498255261105, 0.05452688642073535, 0.0050717297209673185, -0.07673608265579256, 0.07308664366153468, 0.02719625640618991, 0.10553469871116378, -0.077314168546934, -0.010874021215054253, -0.1056064842623365, 0.018965235396123062, -0.030283683417278016, -0.38795779610683717, -0.20312207757912437, 0.660979770426615, 0.16545479331007815, 0.061448094441706104, 0.02922209357319968, -0.029745365691055452, 0.07793246784391035, 0.059065788512969716, 0.06843983099566579, 0.11699799859214088, -0.12355010598112022, 0.0020044949331376196, 0.27701097008651265, -0.07515773338082003, 0.10689788197093855, -0.021290229068829502, 0.18829423709350285, 0.11442398669282776, 0.017462835713044668, 0.1061534919215116, 0.04417554018500953, -0.004784641656294701, 0.04964187438785744, -0.024399172156003547, 0.007392738672432851, 0.032792671313209426, -0.09137460990853519, 0.06632592205447536, -0.04274599119482981, 0.11316656508055585, 0.051983789931826674, -0.06381532441073118, 0.053347618467511, 0.031656164654580383, 0.014230837391979874], \"mode\": \"lines\", \"name\": \"Mean-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10428665841322851, 0.07332277005161279, 0.08547005704409465, 0.10002514204295329, -0.022703986721480753, 0.07341407880250317, 0.07671326810982372, 0.08913551719277941, 0.12044353519887534, 0.12107991859961484, 0.07645956329572498, 0.030369958129867213, -0.15401441164426793, 0.1567063456974202, -0.048474235216957054, 0.08256128147832699, -0.010979294570088994, -0.08731004010676939, 0.10527053469881999, 0.08021051847700676, 0.11034233836542498, -0.03205343451556449, 0.121332736802178, 0.06653521248054955, 0.045498809576186953, 0.04417370811623201, 0.054491708285811055, 0.05492711053334758, -0.09436764644359308, 0.003695825955067885, -0.03212493134839518, 0.1425719137993527, 0.13187629866826117, 0.10294966521196518, 0.09643819730738544, -0.00032557411278709647, 0.0038603616410592427, 0.14967074887718046, 0.02857030516828203, 0.03133696569708741, 0.031177668814362423, -0.013272015384135227, 0.01807951829433437, 0.004879313054998381, -0.041513193617851496, 0.05602341013417302, 0.014772007564457226, 0.1064967149843044, -0.08611641290446055, 0.0037304581696902084, -0.10417452568103007, 0.02434389889755493, -0.04110355587429242, -0.2958424821299399, -0.12545629622222865, 0.2757145957947849, 0.0998560882040609, 0.0676389500707547, 0.03547602510275252, 0.009057475961183397, 0.059827773758374406, 0.07383946445906936, 0.08967310811427967, 0.0872618303464767, -0.07699721976291764, -0.008873635503701927, 0.2849598571224382, -0.033818854817830875, 0.056615647401430186, 0.003102800526851703, 0.12149075188295538, 0.07545688340315194, 0.0016969645144019605, 0.11069212995112299, 0.08543754782498648, 0.03069801586182192, 0.047884618902937, 0.01770840623262702, 0.012894747908206643, 0.007357714953879479, -0.09156603016509249, 0.03565538906213765, 0.02016887918159075, 0.04865602825368639, 0.02897102388273245, -0.05537949291702657, 0.06387329574440477, 0.024406571034667025, 0.011614610039756256], \"mode\": \"lines\", \"name\": \"Minimum-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10862615681435583, 0.04656892327294265, 0.05349564702904169, 0.1113771105315442, -0.022763659871927935, 0.1404882975401837, 0.04673881551040289, 0.10600576358185963, 0.12267402542089455, 0.055438508478761486, 0.08241942615477442, 0.01590646164037977, -0.1533144269078746, 0.20190549960096, 0.018436313957773568, 0.13923587245724753, 0.02770212627291229, 0.03357643357776365, 0.10544144372004555, 0.08240755263704429, 0.1214267672739268, -0.05093649280670292, 0.024457932518342364, 0.06651508820956396, -0.06680516428125499, 0.010493058134780893, 0.08457369559219705, 0.01123620449467603, -0.17306303230229642, 0.1494687525236265, -0.1190244538772289, 0.2753010613947259, 0.12764475787801777, 0.08244828374732072, 0.08650774297042495, -0.007005198953620025, 0.0064611263832443705, 0.14904792199695982, 0.03269041836348389, 0.004362243671446266, 0.0844571302057804, 0.05691287791815806, 0.053200113663206615, 0.004888123764306739, -0.025900121620229824, 0.1051563377450405, 0.043078473363597505, 0.10912998614086317, -0.05434130242443812, -0.015607136944848788, -0.09810571850045018, 0.07524551973500831, -0.07488603056975413, -0.4636821204933392, -0.14141955512845442, 0.8020444244864671, 0.10943134522581184, 0.1272240272882489, 0.07387299644727596, -0.018110786291605216, -0.010402434053431992, 0.14992293702386064, 0.10559911742458787, 0.034710559322233235, -0.13495867948764267, 0.03377407442309356, 0.16391258515220872, -0.12814208653341344, 0.0906706363455829, 0.03593687091268493, 0.14940419821878825, 0.08834896507433836, 0.020118069358952655, 0.10714420265486338, 0.06587632787877208, 0.030393997297440186, 0.0371395274869694, 0.0030113551848420703, 0.01951532610472708, 0.004549544197726594, -0.12414308647811725, 0.045525695785437685, -0.0736217209244176, 0.12498606184947912, 0.06336138958159886, 0.04897542627680945, 0.07794535096355729, -0.011733131012785648, 0.010512090603569113], \"mode\": \"lines\", \"name\": \"Equally Weighted\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0.0, 0.053827389945126994, 0.07107310689225696, 0.058025692211196245, 0.03491193123110393, -0.01979475588655899, 0.13460932017185498, 0.04872313952728657, 0.060317108446472804, 0.08756121360040031, 0.0484114222142368, 0.06960955847176517, 0.03967078204313154, -0.09727834673748983, 0.15402288351144955, 0.0492492908082482, 0.044890497698372035, 0.027654396457990574, 0.047684819837206086, -0.013435444567239557, 0.04805330938139202, 0.047318108624997766, -0.15627688170550968, -0.05961828282620115, 0.01542042193555913, -0.11274216609157384, -0.0026904300694129903, 0.0016611045890791052, -0.08753888829697902, -0.18525777350725997, 0.060468906558806754, -0.1194523678907833, 0.13670113960703212, 0.053806779457791006, 0.044976269226704786, 0.07426661431847867, -0.031011435532964923, -0.013825642710463064, 0.0717325107721888, 0.015730238898531784, -0.006812449632813502, 0.015856380241420564, 0.03406428277825165, 0.020577078007009426, -0.004301148134295284, 0.01929813564123736, 0.06135844476876331, 0.004603920264420882, 0.08667998291206339, -0.031502142185485485, -0.011545618432235904, -0.10596848408590474, 0.03920852459447406, -0.08460534113138507, -0.5652588446163432, -0.16465000120922624, 0.2567161849285489, 0.0552783297424184, 0.09994048707601261, 0.006139566947901408, -0.04202818843486971, 0.008868061033746103, 0.10428906500585339, 0.07674937678608969, 0.0062531609247233055, -0.09143820343129393, 0.03226784410787994, 0.09425147785410723, -0.07515408286829113, 0.090324075995502, 0.0032069162126414823, 0.07162428764957852, 0.07450536431021561, -0.0003964116870486694, 0.08947193173006482, 0.024288469324207453, 0.04116427382959935, 0.03861101188658963, 0.024914248027670987, 0.030202256188818003, -0.0026802257171155757, -0.10339368627711083, 0.08978275659749105, -0.06281998054322017, 0.057627956302734394, 0.03295008682012692, 0.009228312193161198, 0.0855105620857243, 0.014032615314879298, 0.018772077721091126], \"mode\": \"lines\", \"name\": \"SPX\"}], {\"title\": \"Portfolio Return Quarterly\", \"xaxis\": {\"title\": \"Quarterly Trade Date\"}, \"yaxis\": {\"title\": \"Portfolio Value\"}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<div id=\"a316784e-af02-4b30-82da-1720a785ee67\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"a316784e-af02-4b30-82da-1720a785ee67\", [{\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.12499525505558357, 0.049130580596753175, 0.08753104741059947, 0.12332542952723254, -0.022513201506625582, 0.08224449080250033, 0.07194035524381694, 0.09509728657336629, 0.16272341733867204, 0.13410766010809233, 0.10768074745503382, 0.07489268838032118, -0.15693896175935534, 0.16910859875867124, -0.05587293842846846, 0.1033120699309689, -0.010625005958361385, -0.08179776053943431, 0.10537725693264675, 0.008269794612380187, 0.03911046912998701, -0.07085680682127674, 0.11986362364725987, 0.06666390052362063, 0.03169917594842007, 0.07760874973539401, 0.044483557489860444, 0.07934182622849245, -0.0909426257400433, 0.11110286658060385, -0.06245178516714541, 0.17725905890388508, 0.12907718216699068, 0.10256058350945468, 0.13076321263426502, -0.012013869244408676, -0.0108129417061311, 0.14958331978945127, 0.06830762863992514, 0.0016687616827693967, 0.11152414570438689, -0.025109498255261105, 0.05452688642073535, 0.0050717297209673185, -0.07673608265579256, 0.07308664366153468, 0.02719625640618991, 0.10553469871116378, -0.077314168546934, -0.010874021215054253, -0.1056064842623365, 0.018965235396123062, -0.030283683417278016, -0.38795779610683717, -0.20312207757912437, 0.660979770426615, 0.16545479331007815, 0.061448094441706104, 0.02922209357319968, -0.029745365691055452, 0.07793246784391035, 0.059065788512969716, 0.06843983099566579, 0.11699799859214088, -0.12355010598112022, 0.0020044949331376196, 0.27701097008651265, -0.07515773338082003, 0.10689788197093855, -0.021290229068829502, 0.18829423709350285, 0.11442398669282776, 0.017462835713044668, 0.1061534919215116, 0.04417554018500953, -0.004784641656294701, 0.04964187438785744, -0.024399172156003547, 0.007392738672432851, 0.032792671313209426, -0.09137460990853519, 0.06632592205447536, -0.04274599119482981, 0.11316656508055585, 0.051983789931826674, -0.06381532441073118, 0.053347618467511, 0.031656164654580383, 0.014230837391979874], \"mode\": \"lines\", \"name\": \"Mean-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10428665841322851, 0.07332277005161279, 0.08547005704409465, 0.10002514204295329, -0.022703986721480753, 0.07341407880250317, 0.07671326810982372, 0.08913551719277941, 0.12044353519887534, 0.12107991859961484, 0.07645956329572498, 0.030369958129867213, -0.15401441164426793, 0.1567063456974202, -0.048474235216957054, 0.08256128147832699, -0.010979294570088994, -0.08731004010676939, 0.10527053469881999, 0.08021051847700676, 0.11034233836542498, -0.03205343451556449, 0.121332736802178, 0.06653521248054955, 0.045498809576186953, 0.04417370811623201, 0.054491708285811055, 0.05492711053334758, -0.09436764644359308, 0.003695825955067885, -0.03212493134839518, 0.1425719137993527, 0.13187629866826117, 0.10294966521196518, 0.09643819730738544, -0.00032557411278709647, 0.0038603616410592427, 0.14967074887718046, 0.02857030516828203, 0.03133696569708741, 0.031177668814362423, -0.013272015384135227, 0.01807951829433437, 0.004879313054998381, -0.041513193617851496, 0.05602341013417302, 0.014772007564457226, 0.1064967149843044, -0.08611641290446055, 0.0037304581696902084, -0.10417452568103007, 0.02434389889755493, -0.04110355587429242, -0.2958424821299399, -0.12545629622222865, 0.2757145957947849, 0.0998560882040609, 0.0676389500707547, 0.03547602510275252, 0.009057475961183397, 0.059827773758374406, 0.07383946445906936, 0.08967310811427967, 0.0872618303464767, -0.07699721976291764, -0.008873635503701927, 0.2849598571224382, -0.033818854817830875, 0.056615647401430186, 0.003102800526851703, 0.12149075188295538, 0.07545688340315194, 0.0016969645144019605, 0.11069212995112299, 0.08543754782498648, 0.03069801586182192, 0.047884618902937, 0.01770840623262702, 0.012894747908206643, 0.007357714953879479, -0.09156603016509249, 0.03565538906213765, 0.02016887918159075, 0.04865602825368639, 0.02897102388273245, -0.05537949291702657, 0.06387329574440477, 0.024406571034667025, 0.011614610039756256], \"mode\": \"lines\", \"name\": \"Minimum-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10862615681435583, 0.04656892327294265, 0.05349564702904169, 0.1113771105315442, -0.022763659871927935, 0.1404882975401837, 0.04673881551040289, 0.10600576358185963, 0.12267402542089455, 0.055438508478761486, 0.08241942615477442, 0.01590646164037977, -0.1533144269078746, 0.20190549960096, 0.018436313957773568, 0.13923587245724753, 0.02770212627291229, 0.03357643357776365, 0.10544144372004555, 0.08240755263704429, 0.1214267672739268, -0.05093649280670292, 0.024457932518342364, 0.06651508820956396, -0.06680516428125499, 0.010493058134780893, 0.08457369559219705, 0.01123620449467603, -0.17306303230229642, 0.1494687525236265, -0.1190244538772289, 0.2753010613947259, 0.12764475787801777, 0.08244828374732072, 0.08650774297042495, -0.007005198953620025, 0.0064611263832443705, 0.14904792199695982, 0.03269041836348389, 0.004362243671446266, 0.0844571302057804, 0.05691287791815806, 0.053200113663206615, 0.004888123764306739, -0.025900121620229824, 0.1051563377450405, 0.043078473363597505, 0.10912998614086317, -0.05434130242443812, -0.015607136944848788, -0.09810571850045018, 0.07524551973500831, -0.07488603056975413, -0.4636821204933392, -0.14141955512845442, 0.8020444244864671, 0.10943134522581184, 0.1272240272882489, 0.07387299644727596, -0.018110786291605216, -0.010402434053431992, 0.14992293702386064, 0.10559911742458787, 0.034710559322233235, -0.13495867948764267, 0.03377407442309356, 0.16391258515220872, -0.12814208653341344, 0.0906706363455829, 0.03593687091268493, 0.14940419821878825, 0.08834896507433836, 0.020118069358952655, 0.10714420265486338, 0.06587632787877208, 0.030393997297440186, 0.0371395274869694, 0.0030113551848420703, 0.01951532610472708, 0.004549544197726594, -0.12414308647811725, 0.045525695785437685, -0.0736217209244176, 0.12498606184947912, 0.06336138958159886, 0.04897542627680945, 0.07794535096355729, -0.011733131012785648, 0.010512090603569113], \"mode\": \"lines\", \"name\": \"Equally Weighted\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0.0, 0.053827389945126994, 0.07107310689225696, 0.058025692211196245, 0.03491193123110393, -0.01979475588655899, 0.13460932017185498, 0.04872313952728657, 0.060317108446472804, 0.08756121360040031, 0.0484114222142368, 0.06960955847176517, 0.03967078204313154, -0.09727834673748983, 0.15402288351144955, 0.0492492908082482, 0.044890497698372035, 0.027654396457990574, 0.047684819837206086, -0.013435444567239557, 0.04805330938139202, 0.047318108624997766, -0.15627688170550968, -0.05961828282620115, 0.01542042193555913, -0.11274216609157384, -0.0026904300694129903, 0.0016611045890791052, -0.08753888829697902, -0.18525777350725997, 0.060468906558806754, -0.1194523678907833, 0.13670113960703212, 0.053806779457791006, 0.044976269226704786, 0.07426661431847867, -0.031011435532964923, -0.013825642710463064, 0.0717325107721888, 0.015730238898531784, -0.006812449632813502, 0.015856380241420564, 0.03406428277825165, 0.020577078007009426, -0.004301148134295284, 0.01929813564123736, 0.06135844476876331, 0.004603920264420882, 0.08667998291206339, -0.031502142185485485, -0.011545618432235904, -0.10596848408590474, 0.03920852459447406, -0.08460534113138507, -0.5652588446163432, -0.16465000120922624, 0.2567161849285489, 0.0552783297424184, 0.09994048707601261, 0.006139566947901408, -0.04202818843486971, 0.008868061033746103, 0.10428906500585339, 0.07674937678608969, 0.0062531609247233055, -0.09143820343129393, 0.03226784410787994, 0.09425147785410723, -0.07515408286829113, 0.090324075995502, 0.0032069162126414823, 0.07162428764957852, 0.07450536431021561, -0.0003964116870486694, 0.08947193173006482, 0.024288469324207453, 0.04116427382959935, 0.03861101188658963, 0.024914248027670987, 0.030202256188818003, -0.0026802257171155757, -0.10339368627711083, 0.08978275659749105, -0.06281998054322017, 0.057627956302734394, 0.03295008682012692, 0.009228312193161198, 0.0855105620857243, 0.014032615314879298, 0.018772077721091126], \"mode\": \"lines\", \"name\": \"SPX\"}], {\"title\": \"Portfolio Return Quarterly\", \"xaxis\": {\"title\": \"Quarterly Trade Date\"}, \"yaxis\": {\"title\": \"Portfolio Value\"}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trace_return1 = go.Scatter(x = time_ind, y = portfolio_return_meanv, mode = 'lines', name = 'Mean-Variance')\n",
    "trace_return2 = go.Scatter(x = time_ind, y = portfolio_return_minv, mode = 'lines', name = 'Minimum-Variance')\n",
    "trace_return3 = go.Scatter(x = time_ind, y = portfolio_return_equal, mode = 'lines', name = 'Equally Weighted')\n",
    "trace_return4 = go.Scatter(x = time_ind, y = spx_return, mode = 'lines', name = 'SPX')\n",
    "\n",
    "data = [trace_return1,trace_return2,trace_return3,trace_return4]\n",
    "layout = dict(title = \"Portfolio Return Quarterly\", \n",
    "              xaxis = dict(title = 'Quarterly Trade Date'), \n",
    "              yaxis = dict(title = 'Portfolio Value'))\n",
    "fig = dict(data = data, layout = layout)\n",
    "plotly.offline.iplot(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3 Plot Portfolio Cumulative Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "mode": "lines",
         "name": "Mean-Variance",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.12499525505558357,
          0.17412583565233675,
          0.2616568830629362,
          0.38498231259016874,
          0.3624691110835432,
          0.44471360188604353,
          0.5166539571298605,
          0.6117512437032268,
          0.7744746610418988,
          0.908582321149991,
          1.016263068605025,
          1.091155756985346,
          0.9342167952259908,
          1.1033253939846621,
          1.0474524555561937,
          1.1507645254871626,
          1.140139519528801,
          1.0583417589893669,
          1.1637190159220137,
          1.1719888105343939,
          1.211099279664381,
          1.1402424728431042,
          1.260106096490364,
          1.3267699970139848,
          1.3584691729624048,
          1.4360779226977989,
          1.4805614801876594,
          1.5599033064161518,
          1.4689606806761084,
          1.5800635472567122,
          1.5176117620895668,
          1.694870820993452,
          1.8239480031604427,
          1.9265085866698974,
          2.0572717993041625,
          2.045257930059754,
          2.034444988353623,
          2.1840283081430742,
          2.2523359367829996,
          2.254004698465769,
          2.365528844170156,
          2.3404193459148948,
          2.3949462323356303,
          2.4000179620565976,
          2.323281879400805,
          2.39636852306234,
          2.42356477946853,
          2.5290994781796936,
          2.4517853096327595,
          2.440911288417705,
          2.335304804155369,
          2.354270039551492,
          2.323986356134214,
          1.9360285600273766,
          1.7329064824482523,
          2.3938862528748674,
          2.5593410461849455,
          2.6207891406266515,
          2.650011234199851,
          2.620265868508796,
          2.6981983363527062,
          2.7572641248656757,
          2.8257039558613415,
          2.9427019544534825,
          2.8191518484723623,
          2.8211563434055,
          3.0981673134920125,
          3.0230095801111925,
          3.129907462082131,
          3.1086172330133013,
          3.2969114701068043,
          3.411335456799632,
          3.4287982925126768,
          3.5349517844341882,
          3.579127324619198,
          3.5743426829629033,
          3.6239845573507607,
          3.5995853851947572,
          3.60697812386719,
          3.6397707951803997,
          3.5483961852718644,
          3.61472210732634,
          3.57197611613151,
          3.685142681212066,
          3.7371264711438923,
          3.673311146733161,
          3.726658765200672,
          3.7583149298552527,
          3.7725457672472325
         ]
        },
        {
         "mode": "lines",
         "name": "Minimum-Variance",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.10428665841322851,
          0.1776094284648413,
          0.26307948550893595,
          0.3631046275518892,
          0.34040064083040844,
          0.4138147196329116,
          0.4905279877427353,
          0.5796635049355148,
          0.7001070401343901,
          0.8211869587340049,
          0.8976465220297299,
          0.9280164801595971,
          0.7740020685153293,
          0.9307084142127495,
          0.8822341789957925,
          0.9647954604741195,
          0.9538161659040305,
          0.8665061257972612,
          0.9717766604960811,
          1.051987178973088,
          1.1623295173385129,
          1.1302760828229483,
          1.2516088196251263,
          1.3181440321056759,
          1.363642841681863,
          1.407816549798095,
          1.462308258083906,
          1.5172353686172535,
          1.4228677221736605,
          1.4265635481287284,
          1.3944386167803333,
          1.537010530579686,
          1.668886829247947,
          1.7718364944599123,
          1.8682746917672977,
          1.8679491176545107,
          1.87180947929557,
          2.0214802281727504,
          2.0500505333410324,
          2.0813874990381196,
          2.112565167852482,
          2.099293152468347,
          2.1173726707626814,
          2.1222519838176797,
          2.080738790199828,
          2.136762200334001,
          2.1515342078984583,
          2.258030922882763,
          2.1719145099783024,
          2.1756449681479926,
          2.0714704424669623,
          2.0958143413645174,
          2.054710785490225,
          1.758868303360285,
          1.6334120071380562,
          1.909126602932841,
          2.008982691136902,
          2.0766216412076566,
          2.112097666310409,
          2.121155142271592,
          2.1809829160299667,
          2.254822380489036,
          2.344495488603316,
          2.4317573189497925,
          2.354760099186875,
          2.345886463683173,
          2.630846320805611,
          2.59702746598778,
          2.65364311338921,
          2.656745913916062,
          2.7782366657990174,
          2.8536935492021693,
          2.8553905137165714,
          2.9660826436676944,
          3.051520191492681,
          3.0822182073545026,
          3.1301028262574397,
          3.1478112324900667,
          3.1607059803982733,
          3.168063695352153,
          3.0764976651870604,
          3.112153054249198,
          3.132321933430789,
          3.180977961684475,
          3.2099489855672076,
          3.154569492650181,
          3.2184427883945856,
          3.2428493594292527,
          3.254463969469009
         ]
        },
        {
         "mode": "lines",
         "name": "Equally Weighted",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.10862615681435583,
          0.1551950800872985,
          0.20869072711634018,
          0.3200678376478844,
          0.29730417777595647,
          0.4377924753161402,
          0.48453129082654306,
          0.5905370544084027,
          0.7132110798292972,
          0.7686495883080587,
          0.8510690144628331,
          0.8669754761032129,
          0.7136610491953383,
          0.9155665487962983,
          0.9340028627540718,
          1.0732387352113193,
          1.1009408614842315,
          1.1345172950619953,
          1.2399587387820408,
          1.322366291419085,
          1.4437930586930119,
          1.392856565886309,
          1.4173144984046513,
          1.4838295866142153,
          1.4170244223329602,
          1.427517480467741,
          1.512091176059938,
          1.5233273805546141,
          1.3502643482523178,
          1.4997331007759442,
          1.3807086468987153,
          1.6560097082934413,
          1.783654466171459,
          1.8661027499187797,
          1.9526104928892045,
          1.9456052939355846,
          1.952066420318829,
          2.101114342315789,
          2.133804760679273,
          2.138167004350719,
          2.2226241345564994,
          2.2795370124746577,
          2.3327371261378644,
          2.337625249902171,
          2.311725128281941,
          2.4168814660269815,
          2.459959939390579,
          2.569089925531442,
          2.514748623107004,
          2.4991414861621553,
          2.401035767661705,
          2.4762812873967133,
          2.401395256826959,
          1.93771313633362,
          1.7962935812051655,
          2.5983380056916325,
          2.7077693509174443,
          2.8349933782056933,
          2.9088663746529693,
          2.890755588361364,
          2.880353154307932,
          3.030276091331793,
          3.135875208756381,
          3.1705857680786145,
          3.0356270885909717,
          3.0694011630140654,
          3.233313748166274,
          3.105171661632861,
          3.1958422979784435,
          3.2317791688911286,
          3.3811833671099167,
          3.4695323321842553,
          3.4896504015432077,
          3.596794604198071,
          3.662670932076843,
          3.6930649293742834,
          3.730204456861253,
          3.7332158120460948,
          3.7527311381508217,
          3.7572806823485485,
          3.6331375958704313,
          3.678663291655869,
          3.6050415707314514,
          3.7300276325809305,
          3.7933890221625295,
          3.842364448439339,
          3.9203097994028964,
          3.908576668390111,
          3.91908875899368
         ]
        },
        {
         "mode": "lines",
         "name": "SPX",
         "type": "scatter",
         "x": [
          "1995-06-01",
          "1995-09-01",
          "1995-12-01",
          "1996-03-01",
          "1996-06-03",
          "1996-09-03",
          "1996-12-02",
          "1997-03-03",
          "1997-06-02",
          "1997-09-02",
          "1997-12-01",
          "1998-03-02",
          "1998-06-01",
          "1998-09-01",
          "1998-12-01",
          "1999-03-01",
          "1999-06-01",
          "1999-09-01",
          "1999-12-01",
          "2000-03-01",
          "2000-06-01",
          "2000-09-01",
          "2000-12-01",
          "2001-03-01",
          "2001-06-01",
          "2001-09-04",
          "2001-12-03",
          "2002-03-01",
          "2002-06-03",
          "2002-09-03",
          "2002-12-02",
          "2003-03-03",
          "2003-06-02",
          "2003-09-02",
          "2003-12-01",
          "2004-03-01",
          "2004-06-01",
          "2004-09-01",
          "2004-12-01",
          "2005-03-01",
          "2005-06-01",
          "2005-09-01",
          "2005-12-01",
          "2006-03-01",
          "2006-06-01",
          "2006-09-01",
          "2006-12-01",
          "2007-03-01",
          "2007-06-01",
          "2007-09-04",
          "2007-12-03",
          "2008-03-03",
          "2008-06-02",
          "2008-09-02",
          "2008-12-01",
          "2009-03-02",
          "2009-06-01",
          "2009-09-01",
          "2009-12-01",
          "2010-03-01",
          "2010-06-01",
          "2010-09-01",
          "2010-12-01",
          "2011-03-01",
          "2011-06-01",
          "2011-09-01",
          "2011-12-01",
          "2012-03-01",
          "2012-06-01",
          "2012-09-04",
          "2012-12-03",
          "2013-03-01",
          "2013-06-03",
          "2013-09-03",
          "2013-12-02",
          "2014-03-03",
          "2014-06-02",
          "2014-09-02",
          "2014-12-01",
          "2015-03-02",
          "2015-06-01",
          "2015-09-01",
          "2015-12-01",
          "2016-03-01",
          "2016-06-01",
          "2016-09-01",
          "2016-12-01",
          "2017-03-01",
          "2017-06-01",
          "2017-09-01"
         ],
         "y": [
          0,
          0.053827389945126994,
          0.12490049683738395,
          0.1829261890485802,
          0.21783812027968413,
          0.19804336439312514,
          0.3326526845649801,
          0.38137582409226667,
          0.4416929325387395,
          0.5292541461391398,
          0.5776655683533766,
          0.6472751268251418,
          0.6869459088682733,
          0.5896675621307835,
          0.7436904456422331,
          0.7929397364504813,
          0.8378302341488534,
          0.865484630606844,
          0.9131694504440501,
          0.8997340058768105,
          0.9477873152582026,
          0.9951054238832003,
          0.8388285421776907,
          0.7792102593514895,
          0.7946306812870486,
          0.6818885151954748,
          0.6791980851260618,
          0.6808591897151409,
          0.5933203014181619,
          0.408062527910902,
          0.46853143446970874,
          0.34907906657892546,
          0.4857802061859576,
          0.5395869856437486,
          0.5845632548704535,
          0.6588298691889322,
          0.6278184336559672,
          0.6139927909455042,
          0.685725301717693,
          0.7014555406162247,
          0.6946430909834113,
          0.7104994712248318,
          0.7445637540030835,
          0.765140832010093,
          0.7608396838757977,
          0.7801378195170351,
          0.8414962642857984,
          0.8461001845502193,
          0.9327801674622826,
          0.9012780252767971,
          0.8897324068445612,
          0.7837639227586565,
          0.8229724473531306,
          0.7383671062217455,
          0.17310826160540227,
          0.008458260396176032,
          0.26517444532472495,
          0.32045277506714337,
          0.420393262143156,
          0.4265328290910574,
          0.38450464065618767,
          0.39337270168993377,
          0.49766176669578716,
          0.5744111434818768,
          0.5806643044066001,
          0.48922610097530617,
          0.5214939450831861,
          0.6157454229372934,
          0.5405913400690022,
          0.6309154160645042,
          0.6341223322771457,
          0.7057466199267242,
          0.7802519842369398,
          0.7798555725498911,
          0.869327504279956,
          0.8936159736041634,
          0.9347802474337628,
          0.9733912593203524,
          0.9983055073480234,
          1.0285077635368414,
          1.0258275378197257,
          0.9224338515426148,
          1.0122166081401058,
          0.9493966275968857,
          1.0070245838996201,
          1.039974670719747,
          1.0492029829129081,
          1.1347135449986325,
          1.1487461603135118,
          1.167518238034603
         ]
        }
       ],
       "layout": {
        "title": "Portfolio Cumulative Return Quarterly",
        "xaxis": {
         "title": "Quarterly Trade Date"
        },
        "yaxis": {
         "title": "Portfolio Value"
        }
       }
      },
      "text/html": [
       "<div id=\"99adeb78-e40e-4013-ada8-46bc81431832\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"99adeb78-e40e-4013-ada8-46bc81431832\", [{\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.12499525505558357, 0.17412583565233675, 0.2616568830629362, 0.38498231259016874, 0.3624691110835432, 0.44471360188604353, 0.5166539571298605, 0.6117512437032268, 0.7744746610418988, 0.908582321149991, 1.016263068605025, 1.091155756985346, 0.9342167952259908, 1.1033253939846621, 1.0474524555561937, 1.1507645254871626, 1.140139519528801, 1.0583417589893669, 1.1637190159220137, 1.1719888105343939, 1.211099279664381, 1.1402424728431042, 1.260106096490364, 1.3267699970139848, 1.3584691729624048, 1.4360779226977989, 1.4805614801876594, 1.5599033064161518, 1.4689606806761084, 1.5800635472567122, 1.5176117620895668, 1.694870820993452, 1.8239480031604427, 1.9265085866698974, 2.0572717993041625, 2.045257930059754, 2.034444988353623, 2.1840283081430742, 2.2523359367829996, 2.254004698465769, 2.365528844170156, 2.3404193459148948, 2.3949462323356303, 2.4000179620565976, 2.323281879400805, 2.39636852306234, 2.42356477946853, 2.5290994781796936, 2.4517853096327595, 2.440911288417705, 2.335304804155369, 2.354270039551492, 2.323986356134214, 1.9360285600273766, 1.7329064824482523, 2.3938862528748674, 2.5593410461849455, 2.6207891406266515, 2.650011234199851, 2.620265868508796, 2.6981983363527062, 2.7572641248656757, 2.8257039558613415, 2.9427019544534825, 2.8191518484723623, 2.8211563434055, 3.0981673134920125, 3.0230095801111925, 3.129907462082131, 3.1086172330133013, 3.2969114701068043, 3.411335456799632, 3.4287982925126768, 3.5349517844341882, 3.579127324619198, 3.5743426829629033, 3.6239845573507607, 3.5995853851947572, 3.60697812386719, 3.6397707951803997, 3.5483961852718644, 3.61472210732634, 3.57197611613151, 3.685142681212066, 3.7371264711438923, 3.673311146733161, 3.726658765200672, 3.7583149298552527, 3.7725457672472325], \"mode\": \"lines\", \"name\": \"Mean-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10428665841322851, 0.1776094284648413, 0.26307948550893595, 0.3631046275518892, 0.34040064083040844, 0.4138147196329116, 0.4905279877427353, 0.5796635049355148, 0.7001070401343901, 0.8211869587340049, 0.8976465220297299, 0.9280164801595971, 0.7740020685153293, 0.9307084142127495, 0.8822341789957925, 0.9647954604741195, 0.9538161659040305, 0.8665061257972612, 0.9717766604960811, 1.051987178973088, 1.1623295173385129, 1.1302760828229483, 1.2516088196251263, 1.3181440321056759, 1.363642841681863, 1.407816549798095, 1.462308258083906, 1.5172353686172535, 1.4228677221736605, 1.4265635481287284, 1.3944386167803333, 1.537010530579686, 1.668886829247947, 1.7718364944599123, 1.8682746917672977, 1.8679491176545107, 1.87180947929557, 2.0214802281727504, 2.0500505333410324, 2.0813874990381196, 2.112565167852482, 2.099293152468347, 2.1173726707626814, 2.1222519838176797, 2.080738790199828, 2.136762200334001, 2.1515342078984583, 2.258030922882763, 2.1719145099783024, 2.1756449681479926, 2.0714704424669623, 2.0958143413645174, 2.054710785490225, 1.758868303360285, 1.6334120071380562, 1.909126602932841, 2.008982691136902, 2.0766216412076566, 2.112097666310409, 2.121155142271592, 2.1809829160299667, 2.254822380489036, 2.344495488603316, 2.4317573189497925, 2.354760099186875, 2.345886463683173, 2.630846320805611, 2.59702746598778, 2.65364311338921, 2.656745913916062, 2.7782366657990174, 2.8536935492021693, 2.8553905137165714, 2.9660826436676944, 3.051520191492681, 3.0822182073545026, 3.1301028262574397, 3.1478112324900667, 3.1607059803982733, 3.168063695352153, 3.0764976651870604, 3.112153054249198, 3.132321933430789, 3.180977961684475, 3.2099489855672076, 3.154569492650181, 3.2184427883945856, 3.2428493594292527, 3.254463969469009], \"mode\": \"lines\", \"name\": \"Minimum-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10862615681435583, 0.1551950800872985, 0.20869072711634018, 0.3200678376478844, 0.29730417777595647, 0.4377924753161402, 0.48453129082654306, 0.5905370544084027, 0.7132110798292972, 0.7686495883080587, 0.8510690144628331, 0.8669754761032129, 0.7136610491953383, 0.9155665487962983, 0.9340028627540718, 1.0732387352113193, 1.1009408614842315, 1.1345172950619953, 1.2399587387820408, 1.322366291419085, 1.4437930586930119, 1.392856565886309, 1.4173144984046513, 1.4838295866142153, 1.4170244223329602, 1.427517480467741, 1.512091176059938, 1.5233273805546141, 1.3502643482523178, 1.4997331007759442, 1.3807086468987153, 1.6560097082934413, 1.783654466171459, 1.8661027499187797, 1.9526104928892045, 1.9456052939355846, 1.952066420318829, 2.101114342315789, 2.133804760679273, 2.138167004350719, 2.2226241345564994, 2.2795370124746577, 2.3327371261378644, 2.337625249902171, 2.311725128281941, 2.4168814660269815, 2.459959939390579, 2.569089925531442, 2.514748623107004, 2.4991414861621553, 2.401035767661705, 2.4762812873967133, 2.401395256826959, 1.93771313633362, 1.7962935812051655, 2.5983380056916325, 2.7077693509174443, 2.8349933782056933, 2.9088663746529693, 2.890755588361364, 2.880353154307932, 3.030276091331793, 3.135875208756381, 3.1705857680786145, 3.0356270885909717, 3.0694011630140654, 3.233313748166274, 3.105171661632861, 3.1958422979784435, 3.2317791688911286, 3.3811833671099167, 3.4695323321842553, 3.4896504015432077, 3.596794604198071, 3.662670932076843, 3.6930649293742834, 3.730204456861253, 3.7332158120460948, 3.7527311381508217, 3.7572806823485485, 3.6331375958704313, 3.678663291655869, 3.6050415707314514, 3.7300276325809305, 3.7933890221625295, 3.842364448439339, 3.9203097994028964, 3.908576668390111, 3.91908875899368], \"mode\": \"lines\", \"name\": \"Equally Weighted\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0.0, 0.053827389945126994, 0.12490049683738395, 0.1829261890485802, 0.21783812027968413, 0.19804336439312514, 0.3326526845649801, 0.38137582409226667, 0.4416929325387395, 0.5292541461391398, 0.5776655683533766, 0.6472751268251418, 0.6869459088682733, 0.5896675621307835, 0.7436904456422331, 0.7929397364504813, 0.8378302341488534, 0.865484630606844, 0.9131694504440501, 0.8997340058768105, 0.9477873152582026, 0.9951054238832003, 0.8388285421776907, 0.7792102593514895, 0.7946306812870486, 0.6818885151954748, 0.6791980851260618, 0.6808591897151409, 0.5933203014181619, 0.408062527910902, 0.46853143446970874, 0.34907906657892546, 0.4857802061859576, 0.5395869856437486, 0.5845632548704535, 0.6588298691889322, 0.6278184336559672, 0.6139927909455042, 0.685725301717693, 0.7014555406162247, 0.6946430909834113, 0.7104994712248318, 0.7445637540030835, 0.765140832010093, 0.7608396838757977, 0.7801378195170351, 0.8414962642857984, 0.8461001845502193, 0.9327801674622826, 0.9012780252767971, 0.8897324068445612, 0.7837639227586565, 0.8229724473531306, 0.7383671062217455, 0.17310826160540227, 0.008458260396176032, 0.26517444532472495, 0.32045277506714337, 0.420393262143156, 0.4265328290910574, 0.38450464065618767, 0.39337270168993377, 0.49766176669578716, 0.5744111434818768, 0.5806643044066001, 0.48922610097530617, 0.5214939450831861, 0.6157454229372934, 0.5405913400690022, 0.6309154160645042, 0.6341223322771457, 0.7057466199267242, 0.7802519842369398, 0.7798555725498911, 0.869327504279956, 0.8936159736041634, 0.9347802474337628, 0.9733912593203524, 0.9983055073480234, 1.0285077635368414, 1.0258275378197257, 0.9224338515426148, 1.0122166081401058, 0.9493966275968857, 1.0070245838996201, 1.039974670719747, 1.0492029829129081, 1.1347135449986325, 1.1487461603135118, 1.167518238034603], \"mode\": \"lines\", \"name\": \"SPX\"}], {\"title\": \"Portfolio Cumulative Return Quarterly\", \"xaxis\": {\"title\": \"Quarterly Trade Date\"}, \"yaxis\": {\"title\": \"Portfolio Value\"}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<div id=\"99adeb78-e40e-4013-ada8-46bc81431832\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"99adeb78-e40e-4013-ada8-46bc81431832\", [{\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.12499525505558357, 0.17412583565233675, 0.2616568830629362, 0.38498231259016874, 0.3624691110835432, 0.44471360188604353, 0.5166539571298605, 0.6117512437032268, 0.7744746610418988, 0.908582321149991, 1.016263068605025, 1.091155756985346, 0.9342167952259908, 1.1033253939846621, 1.0474524555561937, 1.1507645254871626, 1.140139519528801, 1.0583417589893669, 1.1637190159220137, 1.1719888105343939, 1.211099279664381, 1.1402424728431042, 1.260106096490364, 1.3267699970139848, 1.3584691729624048, 1.4360779226977989, 1.4805614801876594, 1.5599033064161518, 1.4689606806761084, 1.5800635472567122, 1.5176117620895668, 1.694870820993452, 1.8239480031604427, 1.9265085866698974, 2.0572717993041625, 2.045257930059754, 2.034444988353623, 2.1840283081430742, 2.2523359367829996, 2.254004698465769, 2.365528844170156, 2.3404193459148948, 2.3949462323356303, 2.4000179620565976, 2.323281879400805, 2.39636852306234, 2.42356477946853, 2.5290994781796936, 2.4517853096327595, 2.440911288417705, 2.335304804155369, 2.354270039551492, 2.323986356134214, 1.9360285600273766, 1.7329064824482523, 2.3938862528748674, 2.5593410461849455, 2.6207891406266515, 2.650011234199851, 2.620265868508796, 2.6981983363527062, 2.7572641248656757, 2.8257039558613415, 2.9427019544534825, 2.8191518484723623, 2.8211563434055, 3.0981673134920125, 3.0230095801111925, 3.129907462082131, 3.1086172330133013, 3.2969114701068043, 3.411335456799632, 3.4287982925126768, 3.5349517844341882, 3.579127324619198, 3.5743426829629033, 3.6239845573507607, 3.5995853851947572, 3.60697812386719, 3.6397707951803997, 3.5483961852718644, 3.61472210732634, 3.57197611613151, 3.685142681212066, 3.7371264711438923, 3.673311146733161, 3.726658765200672, 3.7583149298552527, 3.7725457672472325], \"mode\": \"lines\", \"name\": \"Mean-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10428665841322851, 0.1776094284648413, 0.26307948550893595, 0.3631046275518892, 0.34040064083040844, 0.4138147196329116, 0.4905279877427353, 0.5796635049355148, 0.7001070401343901, 0.8211869587340049, 0.8976465220297299, 0.9280164801595971, 0.7740020685153293, 0.9307084142127495, 0.8822341789957925, 0.9647954604741195, 0.9538161659040305, 0.8665061257972612, 0.9717766604960811, 1.051987178973088, 1.1623295173385129, 1.1302760828229483, 1.2516088196251263, 1.3181440321056759, 1.363642841681863, 1.407816549798095, 1.462308258083906, 1.5172353686172535, 1.4228677221736605, 1.4265635481287284, 1.3944386167803333, 1.537010530579686, 1.668886829247947, 1.7718364944599123, 1.8682746917672977, 1.8679491176545107, 1.87180947929557, 2.0214802281727504, 2.0500505333410324, 2.0813874990381196, 2.112565167852482, 2.099293152468347, 2.1173726707626814, 2.1222519838176797, 2.080738790199828, 2.136762200334001, 2.1515342078984583, 2.258030922882763, 2.1719145099783024, 2.1756449681479926, 2.0714704424669623, 2.0958143413645174, 2.054710785490225, 1.758868303360285, 1.6334120071380562, 1.909126602932841, 2.008982691136902, 2.0766216412076566, 2.112097666310409, 2.121155142271592, 2.1809829160299667, 2.254822380489036, 2.344495488603316, 2.4317573189497925, 2.354760099186875, 2.345886463683173, 2.630846320805611, 2.59702746598778, 2.65364311338921, 2.656745913916062, 2.7782366657990174, 2.8536935492021693, 2.8553905137165714, 2.9660826436676944, 3.051520191492681, 3.0822182073545026, 3.1301028262574397, 3.1478112324900667, 3.1607059803982733, 3.168063695352153, 3.0764976651870604, 3.112153054249198, 3.132321933430789, 3.180977961684475, 3.2099489855672076, 3.154569492650181, 3.2184427883945856, 3.2428493594292527, 3.254463969469009], \"mode\": \"lines\", \"name\": \"Minimum-Variance\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0, 0.10862615681435583, 0.1551950800872985, 0.20869072711634018, 0.3200678376478844, 0.29730417777595647, 0.4377924753161402, 0.48453129082654306, 0.5905370544084027, 0.7132110798292972, 0.7686495883080587, 0.8510690144628331, 0.8669754761032129, 0.7136610491953383, 0.9155665487962983, 0.9340028627540718, 1.0732387352113193, 1.1009408614842315, 1.1345172950619953, 1.2399587387820408, 1.322366291419085, 1.4437930586930119, 1.392856565886309, 1.4173144984046513, 1.4838295866142153, 1.4170244223329602, 1.427517480467741, 1.512091176059938, 1.5233273805546141, 1.3502643482523178, 1.4997331007759442, 1.3807086468987153, 1.6560097082934413, 1.783654466171459, 1.8661027499187797, 1.9526104928892045, 1.9456052939355846, 1.952066420318829, 2.101114342315789, 2.133804760679273, 2.138167004350719, 2.2226241345564994, 2.2795370124746577, 2.3327371261378644, 2.337625249902171, 2.311725128281941, 2.4168814660269815, 2.459959939390579, 2.569089925531442, 2.514748623107004, 2.4991414861621553, 2.401035767661705, 2.4762812873967133, 2.401395256826959, 1.93771313633362, 1.7962935812051655, 2.5983380056916325, 2.7077693509174443, 2.8349933782056933, 2.9088663746529693, 2.890755588361364, 2.880353154307932, 3.030276091331793, 3.135875208756381, 3.1705857680786145, 3.0356270885909717, 3.0694011630140654, 3.233313748166274, 3.105171661632861, 3.1958422979784435, 3.2317791688911286, 3.3811833671099167, 3.4695323321842553, 3.4896504015432077, 3.596794604198071, 3.662670932076843, 3.6930649293742834, 3.730204456861253, 3.7332158120460948, 3.7527311381508217, 3.7572806823485485, 3.6331375958704313, 3.678663291655869, 3.6050415707314514, 3.7300276325809305, 3.7933890221625295, 3.842364448439339, 3.9203097994028964, 3.908576668390111, 3.91908875899368], \"mode\": \"lines\", \"name\": \"Equally Weighted\"}, {\"type\": \"scatter\", \"x\": [\"1995-06-01\", \"1995-09-01\", \"1995-12-01\", \"1996-03-01\", \"1996-06-03\", \"1996-09-03\", \"1996-12-02\", \"1997-03-03\", \"1997-06-02\", \"1997-09-02\", \"1997-12-01\", \"1998-03-02\", \"1998-06-01\", \"1998-09-01\", \"1998-12-01\", \"1999-03-01\", \"1999-06-01\", \"1999-09-01\", \"1999-12-01\", \"2000-03-01\", \"2000-06-01\", \"2000-09-01\", \"2000-12-01\", \"2001-03-01\", \"2001-06-01\", \"2001-09-04\", \"2001-12-03\", \"2002-03-01\", \"2002-06-03\", \"2002-09-03\", \"2002-12-02\", \"2003-03-03\", \"2003-06-02\", \"2003-09-02\", \"2003-12-01\", \"2004-03-01\", \"2004-06-01\", \"2004-09-01\", \"2004-12-01\", \"2005-03-01\", \"2005-06-01\", \"2005-09-01\", \"2005-12-01\", \"2006-03-01\", \"2006-06-01\", \"2006-09-01\", \"2006-12-01\", \"2007-03-01\", \"2007-06-01\", \"2007-09-04\", \"2007-12-03\", \"2008-03-03\", \"2008-06-02\", \"2008-09-02\", \"2008-12-01\", \"2009-03-02\", \"2009-06-01\", \"2009-09-01\", \"2009-12-01\", \"2010-03-01\", \"2010-06-01\", \"2010-09-01\", \"2010-12-01\", \"2011-03-01\", \"2011-06-01\", \"2011-09-01\", \"2011-12-01\", \"2012-03-01\", \"2012-06-01\", \"2012-09-04\", \"2012-12-03\", \"2013-03-01\", \"2013-06-03\", \"2013-09-03\", \"2013-12-02\", \"2014-03-03\", \"2014-06-02\", \"2014-09-02\", \"2014-12-01\", \"2015-03-02\", \"2015-06-01\", \"2015-09-01\", \"2015-12-01\", \"2016-03-01\", \"2016-06-01\", \"2016-09-01\", \"2016-12-01\", \"2017-03-01\", \"2017-06-01\", \"2017-09-01\"], \"y\": [0.0, 0.053827389945126994, 0.12490049683738395, 0.1829261890485802, 0.21783812027968413, 0.19804336439312514, 0.3326526845649801, 0.38137582409226667, 0.4416929325387395, 0.5292541461391398, 0.5776655683533766, 0.6472751268251418, 0.6869459088682733, 0.5896675621307835, 0.7436904456422331, 0.7929397364504813, 0.8378302341488534, 0.865484630606844, 0.9131694504440501, 0.8997340058768105, 0.9477873152582026, 0.9951054238832003, 0.8388285421776907, 0.7792102593514895, 0.7946306812870486, 0.6818885151954748, 0.6791980851260618, 0.6808591897151409, 0.5933203014181619, 0.408062527910902, 0.46853143446970874, 0.34907906657892546, 0.4857802061859576, 0.5395869856437486, 0.5845632548704535, 0.6588298691889322, 0.6278184336559672, 0.6139927909455042, 0.685725301717693, 0.7014555406162247, 0.6946430909834113, 0.7104994712248318, 0.7445637540030835, 0.765140832010093, 0.7608396838757977, 0.7801378195170351, 0.8414962642857984, 0.8461001845502193, 0.9327801674622826, 0.9012780252767971, 0.8897324068445612, 0.7837639227586565, 0.8229724473531306, 0.7383671062217455, 0.17310826160540227, 0.008458260396176032, 0.26517444532472495, 0.32045277506714337, 0.420393262143156, 0.4265328290910574, 0.38450464065618767, 0.39337270168993377, 0.49766176669578716, 0.5744111434818768, 0.5806643044066001, 0.48922610097530617, 0.5214939450831861, 0.6157454229372934, 0.5405913400690022, 0.6309154160645042, 0.6341223322771457, 0.7057466199267242, 0.7802519842369398, 0.7798555725498911, 0.869327504279956, 0.8936159736041634, 0.9347802474337628, 0.9733912593203524, 0.9983055073480234, 1.0285077635368414, 1.0258275378197257, 0.9224338515426148, 1.0122166081401058, 0.9493966275968857, 1.0070245838996201, 1.039974670719747, 1.0492029829129081, 1.1347135449986325, 1.1487461603135118, 1.167518238034603], \"mode\": \"lines\", \"name\": \"SPX\"}], {\"title\": \"Portfolio Cumulative Return Quarterly\", \"xaxis\": {\"title\": \"Quarterly Trade Date\"}, \"yaxis\": {\"title\": \"Portfolio Value\"}}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trace_return1 = go.Scatter(x = time_ind, y = portfolio_cumsum_meanv, mode = 'lines', name = 'Mean-Variance')\n",
    "trace_return2 = go.Scatter(x = time_ind, y = portfolio_cumsum_minv, mode = 'lines', name = 'Minimum-Variance')\n",
    "trace_return3 = go.Scatter(x = time_ind, y = portfolio_cumsum_equal, mode = 'lines', name = 'Equally Weighted')\n",
    "trace_return4 = go.Scatter(x = time_ind, y = spx_cumsum, mode = 'lines', name = 'SPX')\n",
    "\n",
    "data = [trace_return1,trace_return2,trace_return3,trace_return4]\n",
    "layout = dict(title = \"Portfolio Cumulative Return Quarterly\", \n",
    "              xaxis = dict(title = 'Quarterly Trade Date'), \n",
    "              yaxis = dict(title = 'Portfolio Value'))\n",
    "fig = dict(data = data, layout = layout)\n",
    "plotly.offline.iplot(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Get all Quarterly Return and Calcualte Annulized return, standard deviation and Sharpe ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [],
   "source": [
    "quarter_return = pd.DataFrame(index = range(len(spx_return)), columns = ['Mean-Var', 'Equally', 'Min-Var', 'SPX'])\n",
    "quarter_return['SPX'] = spx_return\n",
    "quarter_return['Mean-Var'] = portfolio_return_meanv\n",
    "quarter_return['Equally'] = portfolio_return_equal\n",
    "quarter_return['Min-Var'] = portfolio_return_minv\n",
    "\n",
    "#writer_return = pd.ExcelWriter('quarter_return_user8.xlsx')\n",
    "quarter_return.index=tradedate_full\n",
    "#quarter_return.to_excel(writer_return,'Sheet1')\n",
    "#writer_return.save()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mean-Var</th>\n",
       "      <th>Equally</th>\n",
       "      <th>Min-Var</th>\n",
       "      <th>SPX</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19950601</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19950901</th>\n",
       "      <td>0.124995</td>\n",
       "      <td>0.108626</td>\n",
       "      <td>0.104287</td>\n",
       "      <td>0.053827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19951201</th>\n",
       "      <td>0.0491306</td>\n",
       "      <td>0.0465689</td>\n",
       "      <td>0.0733228</td>\n",
       "      <td>0.071073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19960301</th>\n",
       "      <td>0.087531</td>\n",
       "      <td>0.0534956</td>\n",
       "      <td>0.0854701</td>\n",
       "      <td>0.058026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19960603</th>\n",
       "      <td>0.123325</td>\n",
       "      <td>0.111377</td>\n",
       "      <td>0.100025</td>\n",
       "      <td>0.034912</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Mean-Var    Equally    Min-Var       SPX\n",
       "19950601          0          0          0  0.000000\n",
       "19950901   0.124995   0.108626   0.104287  0.053827\n",
       "19951201  0.0491306  0.0465689  0.0733228  0.071073\n",
       "19960301   0.087531  0.0534956  0.0854701  0.058026\n",
       "19960603   0.123325   0.111377   0.100025  0.034912"
      ]
     },
     "execution_count": 348,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quarter_return.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [],
   "source": [
    "annulizedR_spx=quarter_return['SPX'].mean()*4\n",
    "annulizedR_meanv=quarter_return['Mean-Var'].mean()*4\n",
    "annulizedR_equal=quarter_return['Equally'].mean()*4\n",
    "annulizedR_minv=quarter_return['Min-Var'].mean()*4\n",
    "annulizedS_spx=quarter_return['SPX'].std()*2\n",
    "annulizedS_meanv=quarter_return['Mean-Var'].std()*2\n",
    "annulizedS_equal=quarter_return['Equally'].std()*2\n",
    "annulizedS_minv=quarter_return['Min-Var'].std()*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SPX 0.05188969946820458 0.18846361580122992\n",
      "Mean-Var 0.167668700767 0.230322449769\n",
      "Equally 0.174181722622 0.253878788234\n",
      "Min-Var 0.144642843088 0.164655054005\n"
     ]
    }
   ],
   "source": [
    "print(\"SPX\",annulizedR_spx,annulizedS_spx)\n",
    "print(\"Mean-Var\",annulizedR_meanv,annulizedS_meanv)\n",
    "print(\"Equally\",annulizedR_equal,annulizedS_equal)\n",
    "print(\"Min-Var\",annulizedR_minv,annulizedS_minv)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "risk_free=0.015"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {},
   "outputs": [],
   "source": [
    "sharpe_spx=(annulizedR_spx-risk_free)/annulizedS_spx\n",
    "sharpe_meanv=(annulizedR_meanv-risk_free)/annulizedS_meanv\n",
    "sharpe_equal=(annulizedR_equal-risk_free)/annulizedS_equal\n",
    "sharpe_minv=(annulizedR_minv-risk_free)/annulizedS_minv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SPX Sharpe 0.19573910492681865\n",
      "Mean-Var Sharpe 0.662847676898\n",
      "Equally Sharpe 0.626998906562\n",
      "Min-Var Sharpe 0.787360241511\n"
     ]
    }
   ],
   "source": [
    "print(\"SPX Sharpe\",sharpe_spx)\n",
    "print(\"Mean-Var Sharpe\",sharpe_meanv)\n",
    "print(\"Equally Sharpe\",sharpe_equal)\n",
    "print(\"Min-Var Sharpe\",sharpe_minv)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "insample_date=tradedate[1:51]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[19950901,\n",
       " 19951201,\n",
       " 19960301,\n",
       " 19960603,\n",
       " 19960903,\n",
       " 19961202,\n",
       " 19970303,\n",
       " 19970602,\n",
       " 19970902,\n",
       " 19971201,\n",
       " 19980302,\n",
       " 19980601,\n",
       " 19980901,\n",
       " 19981201,\n",
       " 19990301,\n",
       " 19990601,\n",
       " 19990901,\n",
       " 19991201,\n",
       " 20000301,\n",
       " 20000601,\n",
       " 20000901,\n",
       " 20001201,\n",
       " 20010301,\n",
       " 20010601,\n",
       " 20010904,\n",
       " 20011203,\n",
       " 20020301,\n",
       " 20020603,\n",
       " 20020903,\n",
       " 20021202,\n",
       " 20030303,\n",
       " 20030602,\n",
       " 20030902,\n",
       " 20031201,\n",
       " 20040301,\n",
       " 20040601,\n",
       " 20040901,\n",
       " 20041201,\n",
       " 20050301,\n",
       " 20050601,\n",
       " 20050901,\n",
       " 20051201,\n",
       " 20060301,\n",
       " 20060601,\n",
       " 20060901,\n",
       " 20061201,\n",
       " 20070301,\n",
       " 20070601,\n",
       " 20070904,\n",
       " 20071203]"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insample_date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19950901    0.053827\n",
       "19951201    0.071073\n",
       "19960301    0.058026\n",
       "19960603    0.034912\n",
       "19960903   -0.019795\n",
       "19961202    0.134609\n",
       "19970303    0.048723\n",
       "19970602    0.060317\n",
       "19970902    0.087561\n",
       "19971201    0.048411\n",
       "19980302    0.069610\n",
       "19980601    0.039671\n",
       "19980901   -0.097278\n",
       "19981201    0.154023\n",
       "19990301    0.049249\n",
       "19990601    0.044890\n",
       "19990901    0.027654\n",
       "19991201    0.047685\n",
       "20000301   -0.013435\n",
       "20000601    0.048053\n",
       "20000901    0.047318\n",
       "20001201   -0.156277\n",
       "20010301   -0.059618\n",
       "20010601    0.015420\n",
       "20010904   -0.112742\n",
       "20011203   -0.002690\n",
       "20020301    0.001661\n",
       "20020603   -0.087539\n",
       "20020903   -0.185258\n",
       "20021202    0.060469\n",
       "20030303   -0.119452\n",
       "20030602    0.136701\n",
       "20030902    0.053807\n",
       "20031201    0.044976\n",
       "20040301    0.074267\n",
       "20040601   -0.031011\n",
       "20040901   -0.013826\n",
       "20041201    0.071733\n",
       "20050301    0.015730\n",
       "20050601   -0.006812\n",
       "20050901    0.015856\n",
       "20051201    0.034064\n",
       "20060301    0.020577\n",
       "20060601   -0.004301\n",
       "20060901    0.019298\n",
       "20061201    0.061358\n",
       "20070301    0.004604\n",
       "20070601    0.086680\n",
       "20070904   -0.031502\n",
       "20071203   -0.011546\n",
       "Name: SPX, dtype: float64"
      ]
     },
     "execution_count": 356,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quarter_return['SPX'][insample_date]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SPX 0.0711785925475649 0.13828636298362326\n",
      "Mean-Var 0.195272903073 0.157365362189\n",
      "Equally 0.199931318893 0.166430681877\n",
      "Min-Var 0.174051597452 0.139022544778\n",
      "SPX Sharpe 0.4062482470105741\n",
      "Mean-Var Sharpe 1.14556914282\n",
      "Equally Sharpe 1.11116121624\n",
      "Min-Var Sharpe 1.14407053694\n"
     ]
    }
   ],
   "source": [
    "annulizedR_spx_insample=quarter_return['SPX'][insample_date].mean()*4\n",
    "annulizedR_meanv_insample=quarter_return['Mean-Var'][insample_date].mean()*4\n",
    "annulizedR_equal_insample=quarter_return['Equally'][insample_date].mean()*4\n",
    "annulizedR_minv_insample=quarter_return['Min-Var'][insample_date].mean()*4\n",
    "annulizedS_spx_insample=quarter_return['SPX'][insample_date].std()*2\n",
    "annulizedS_meanv_insample=quarter_return['Mean-Var'][insample_date].std()*2\n",
    "annulizedS_equal_insample=quarter_return['Equally'][insample_date].std()*2\n",
    "annulizedS_minv_insample=quarter_return['Min-Var'][insample_date].std()*2\n",
    "print(\"SPX\",annulizedR_spx_insample,annulizedS_spx_insample)\n",
    "print(\"Mean-Var\",annulizedR_meanv_insample,annulizedS_meanv_insample)\n",
    "print(\"Equally\",annulizedR_equal_insample,annulizedS_equal_insample)\n",
    "print(\"Min-Var\",annulizedR_minv_insample,annulizedS_minv_insample)\n",
    "sharpe_spx_insample=(annulizedR_spx_insample-risk_free)/annulizedS_spx_insample\n",
    "sharpe_meanv_insample=(annulizedR_meanv_insample-risk_free)/annulizedS_meanv_insample\n",
    "sharpe_equal_insample=(annulizedR_equal_insample-risk_free)/annulizedS_equal_insample\n",
    "sharpe_minv_insample=(annulizedR_minv_insample-risk_free)/annulizedS_minv_insample\n",
    "print(\"SPX Sharpe\",sharpe_spx_insample)\n",
    "print(\"Mean-Var Sharpe\",sharpe_meanv_insample)\n",
    "print(\"Equally Sharpe\",sharpe_equal_insample)\n",
    "print(\"Min-Var Sharpe\",sharpe_minv_insample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}