equity-options-backtesting-engine.ipynb

{
 "cells": [
  { 
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a backtesting engine for equity options. \n",
    "\n",
    "In order to run the code, we need to (1) have internet access to use YahooFinance and (2) download options data from OptionsDX and save locally. \n",
    "\n",
    "As of 6/23/2023, OptionsDX provides free end-of-day data for a limited number of tickers, such as SPY, SPX, VIX, and AAPL. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import datetime\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import polars as pl\n",
    "import yfinance as yf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getDatesList(start, end):\n",
    "    dates_list = [] \n",
    "    for i in range(1880,2150): # (including, not including)\n",
    "        for j in range(1, 13): # (including, not including)\n",
    "            if j <=9:\n",
    "                dates_list.append((str(i)+str(0)+str(j)))\n",
    "            else:\n",
    "                dates_list.append((str(i)+str(j)))\n",
    "    dates_list = dates_list[dates_list.index(str(start)):dates_list.index(str(end))+2]\n",
    "    return dates_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def addFrequencyBasedSignals(stock_data, condition, dates_list): # condition = 'monthly' , 'bimonthly' , 'weekly'\n",
    "    stock_data['signal'] = 0 \n",
    "\n",
    "    stock_data['Month'] = stock_data.index.month\n",
    "    stock_data['Year'] = stock_data.index.year\n",
    "    stock_data['Day'] = stock_data.index.day\n",
    "\n",
    "    def last(df):\n",
    "        return df.iloc[-1] # get the last element in a groupby\n",
    "    def q25(df):\n",
    "        return df.iloc[int(len(df)/4)] # get the last element in a groupby\n",
    "    def q75(df):\n",
    "        return df.iloc[int(len(df)/4*3)] # get the last element in a groupby\n",
    "    def q50(df):\n",
    "        return df.iloc[int(len(df)/4*2)] # get the last element in a groupby\n",
    "\n",
    "    d2=stock_data.groupby(['Year','Month']).apply(q50)['Day'] # mid-months\n",
    "    d4=stock_data.groupby(['Year','Month']).apply(last)['Day']\n",
    "    d1=stock_data.groupby(['Year','Month']).apply(q25)['Day']\n",
    "    d3=stock_data.groupby(['Year','Month']).apply(q75)['Day']\n",
    "\n",
    "    ind = stock_data.groupby(['Year','Month']).apply(q75)['Day'].index\n",
    "    \n",
    "    if condition == 'monthly':\n",
    "        for i in range(len(ind)):\n",
    "            stock_data.loc[stock_data[(stock_data['Year']==ind[i][0])&\n",
    "                                      (stock_data['Month']==ind[i][1])&\n",
    "                                      (stock_data['Day']==int(d4.values[i]))].index, 'signal']=1\n",
    "    \n",
    "    elif condition == 'bimonthly':\n",
    "        for i in range(len(ind)):\n",
    "            stock_data.loc[stock_data[(stock_data['Year']==ind[i][0])&\n",
    "                                      (stock_data['Month']==ind[i][1])&\n",
    "                                      (stock_data['Day']==int(d2.values[i]))].index, 'signal']=1\n",
    "            stock_data.loc[stock_data[(stock_data['Year']==ind[i][0])&\n",
    "                                      (stock_data['Month']==ind[i][1])&\n",
    "                                      (stock_data['Day']==int(d4.values[i]))].index, 'signal']=1\n",
    "            \n",
    "    elif condition == 'weekly':\n",
    "        for i in range(len(ind)):\n",
    "            stock_data.loc[stock_data[(stock_data['Year']==ind[i][0])&\n",
    "                                      (stock_data['Month']==ind[i][1])&\n",
    "                                      (stock_data['Day']==int(d1.values[i]))].index, 'signal']=1\n",
    "            stock_data.loc[stock_data[(stock_data['Year']==ind[i][0])&\n",
    "                                      (stock_data['Month']==ind[i][1])&\n",
    "                                      (stock_data['Day']==int(d2.values[i]))].index, 'signal']=1              \n",
    "            stock_data.loc[stock_data[(stock_data['Year']==ind[i][0])&\n",
    "                                      (stock_data['Month']==ind[i][1])&\n",
    "                                      (stock_data['Day']==int(d3.values[i]))].index, 'signal']=1\n",
    "            stock_data.loc[stock_data[(stock_data['Year']==ind[i][0])&\n",
    "                                      (stock_data['Month']==ind[i][1])&\n",
    "                                      (stock_data['Day']==int(d4.values[i]))].index, 'signal']=1    \n",
    "    \n",
    "    \n",
    "    # find all signals and calculate the holding period in between\n",
    "\n",
    "    stock_data['count_days'] = range(0,len(stock_data))\n",
    "\n",
    "    temp = pd.DataFrame(stock_data[stock_data['signal']==1].diff().shift(-1)['count_days'].values,\n",
    "                 index=stock_data[stock_data['signal']==1].diff().shift(-1)['count_days'].index,\n",
    "                 columns=['Holding Period'])\n",
    "\n",
    "    # merge the holding period with the original dataframe\n",
    "\n",
    "    frames = [stock_data, temp] \n",
    "    stock_data = pd.concat(frames, axis=1, join='outer') # outer for union and inner for intersection\n",
    "\n",
    "    # get a copy with rows that have a positive signal\n",
    "\n",
    "    signals = stock_data[stock_data['signal']==1].copy()\n",
    "    signals['next_signal_date'] = signals.index\n",
    "    signals['next_signal_date'] = signals['next_signal_date'].shift(-1)\n",
    "    signals\n",
    "\n",
    "    # limit the signals dataframe to the date range specified\n",
    "\n",
    "    signals = signals[(signals.index >= datetime.datetime(int(dates_list[0][:-2]),\n",
    "                                                               int(dates_list[0][-2:]),1))] \n",
    "    signals = signals[signals['next_signal_date'] < datetime.datetime(int(dates_list[-1][:-2]),\n",
    "                                                                      int(dates_list[-1][-2:]),1)]\n",
    "    signals = signals[signals['signal'] == 1]\n",
    "    stock_data = stock_data[(stock_data.index >= datetime.datetime(int(dates_list[0][:-2]),\n",
    "                                                                   int(dates_list[0][-2:]),1)) &\n",
    "                            (stock_data.index < datetime.datetime(int(dates_list[-1][:-2]),\n",
    "                                                                  int(dates_list[-1][-2:]),1))]\n",
    "\n",
    "    return stock_data, signals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def clean_one_file(ticker, yyyymm): # enter 'spy' and '202001'\n",
    "    df1 = (pl.scan_csv('optionsdx_data.nosync/'+ticker+\"_eod_\"+yyyymm+\".txt\")).collect()\n",
    "\n",
    "    # rename the columns\n",
    "    for i in range(1, len(df1.columns)):\n",
    "        df1 = df1.rename({df1.columns[i]: df1.columns[i][1:]})\n",
    "\n",
    "        \n",
    "    # drop some of the columns\n",
    "    df1 = df1.drop(['[QUOTE_UNIXTIME]', '[QUOTE_READTIME]', \n",
    "                    '[QUOTE_TIME_HOURS]', '[EXPIRE_UNIX]',\n",
    "                    '[STRIKE_DISTANCE]', '[STRIKE_DISTANCE_PCT]',\n",
    "                    '[C_SIZE]', '[P_SIZE]'])\n",
    "\n",
    "    # get rid of the space charater\n",
    "    df1 = pl.concat([df1.select([pl.col(pl.Utf8)]).select(pl.all().str.strip()), \n",
    "                     df1.select([pl.col(pl.Float64)])], how='horizontal')\n",
    "\n",
    "    # convert strings to datetimes\n",
    "    df1 = df1.with_columns(pl.col('[EXPIRE_DATE]').str.strptime(pl.Date, fmt='%Y-%m-%d').cast(pl.Datetime))\n",
    "    df1 = df1.with_columns(pl.col('[QUOTE_DATE]').str.strptime(pl.Date, fmt='%Y-%m-%d').cast(pl.Datetime))\n",
    "\n",
    "    # convert the rest of the strings to floats\n",
    "    df1 = pl.concat([df1.select([pl.col(pl.Utf8)]).select(pl.all().cast(pl.Float64, strict=False)), \n",
    "                     df1.select([pl.exclude(pl.Utf8)])], how='horizontal')\n",
    "    \n",
    "    # replace nulls with zeros for call and put volumes\n",
    "    df1 = df1.with_columns(pl.col(\"[C_VOLUME]\").fill_null(strategy=\"zero\"))\n",
    "    df1 = df1.with_columns(pl.col(\"[P_VOLUME]\").fill_null(strategy=\"zero\"))\n",
    "    \n",
    "    # sort the columns\n",
    "    df1 = df1.select(sorted(df1.columns))\n",
    "    \n",
    "    return df1\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_options_data(ticker, dates_list):\n",
    "    for i in range(len(dates_list[:-1])): \n",
    "        print(dates_list[i])\n",
    "        if i == 0:\n",
    "            df = clean_one_file(ticker, dates_list[i])\n",
    "        else:\n",
    "            df1 = clean_one_file(ticker, dates_list[i])\n",
    "            df = pl.concat([df, df1])\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def get_price_list(i, options, call_or_put, buy_or_sell, DTE_lower, DTE_upper, \n",
    "                   delta_lower, delta_upper, volume_threshold):\n",
    "\n",
    "    # find all options that satisfy the requirement on the singal day\n",
    "\n",
    "    selected_options = options.filter((pl.col(\"[QUOTE_DATE]\") == signals[i,'Date'])&\n",
    "                       (pl.col(\"[DTE]\") >= DTE_lower)&\n",
    "                       (pl.col(\"[DTE]\") <= DTE_upper)&\n",
    "                       (pl.col(\"[\"+call_or_put[0].upper()+\"_DELTA]\") >= delta_lower)&\n",
    "                       (pl.col(\"[\"+call_or_put[0].upper()+\"_DELTA]\") <= delta_upper)&\n",
    "                                      (pl.col(['['+call_or_put[0].upper()+'_VOLUME]'])>= volume_threshold))\n",
    "    \n",
    "    # exclude options with bid prices equal to zero\n",
    "    if (call_or_put == 'call'):\n",
    "        selected_options = selected_options.filter((pl.col(\"[C_BID]\") != 0))\n",
    "    elif (call_or_put == 'put'):\n",
    "        selected_options = selected_options.filter((pl.col(\"[P_BID]\") != 0))\n",
    "        \n",
    "    vmax = selected_options.select(pl.max('['+call_or_put[0].upper()+'_VOLUME]'))\n",
    "    vmax = vmax[0,0]\n",
    "\n",
    "    # added index zero in case we find more than one option, and if so we will just pick the first one\n",
    "\n",
    "        \n",
    "    selected_options = selected_options.filter((pl.col('['+call_or_put[0].upper()+'_VOLUME]') == vmax))[0]\n",
    "\n",
    "    if len(selected_options) == 0:\n",
    "        print('Cannot find enough options that satisfy the criteria.')\n",
    "        return None, None\n",
    "    else:\n",
    "        # find the price list that matches the option\n",
    "                \n",
    "        exp_date = selected_options['[EXPIRE_DATE]'][0]\n",
    "        strike = selected_options['[STRIKE]'][0]\n",
    "        next_signal_date = signals[i,'next_signal_date']\n",
    "        signal_date = signals[i,'Date']\n",
    "\n",
    "        sequetial_data = options.filter((pl.col(['[STRIKE]']) == strike))\n",
    "        sequetial_data = sequetial_data.filter((pl.col(['[EXPIRE_DATE]']) == exp_date))\n",
    "        sequetial_data = sequetial_data.filter((pl.col(['[QUOTE_DATE]']) <= next_signal_date))\n",
    "        sequetial_data = sequetial_data.filter((pl.col(['[QUOTE_DATE]']) >= signal_date))\n",
    "        price_list, price_diff_list, volume_list = [], [], []\n",
    "        if (call_or_put == 'call') and (buy_or_sell == 'buy'):\n",
    "            volume_list = sequetial_data[:, '[C_VOLUME]']\n",
    "            price_list = [sequetial_data[0, '[C_ASK]']]+sequetial_data['[C_BID]'].to_list()[1:]\n",
    "            price_diff_list = [0]+(np.array(price_list[1:]) - np.array(price_list[:-1])).tolist()\n",
    "        elif (call_or_put == 'call') and (buy_or_sell == 'sell'):\n",
    "            volume_list = sequetial_data[:, '[C_VOLUME]']\n",
    "            price_list = [sequetial_data[0, '[C_BID]']]+sequetial_data['[C_BID]'].to_list()[1:]\n",
    "            price_diff_list = [0]+(-np.array(price_list[1:]) + np.array(price_list[:-1])).tolist()\n",
    "        elif (call_or_put == 'put') and (buy_or_sell == 'buy'):\n",
    "            volume_list = sequetial_data[:, '[P_VOLUME]']\n",
    "            price_list = [sequetial_data[0, '[P_ASK]']]+sequetial_data['[P_BID]'].to_list()[1:]\n",
    "            price_diff_list = [0]+(np.array(price_list[1:]) - np.array(price_list[:-1])).tolist()\n",
    "        elif (call_or_put == 'put') and (buy_or_sell == 'sell'):   \n",
    "            volume_list = sequetial_data[:, '[P_VOLUME]']\n",
    "            price_list = [sequetial_data[0, '[P_BID]']]+sequetial_data['[P_ASK]'].to_list()[1:]\n",
    "            price_diff_list = [0]+(-np.array(price_list[1:]) + np.array(price_list[:-1])).tolist()\n",
    "        \n",
    "        return price_list, price_diff_list, volume_list, sequetial_data['[QUOTE_DATE]'].to_list()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Input parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose frequency to be monthly, bimonthly, or weekly\n",
    "\n",
    "frequency = 'weekly' \n",
    "\n",
    "# data available from 201501 to 202212\n",
    "\n",
    "start = 201501 # including\n",
    "end   = 202212 # including\n",
    "\n",
    "volume_threshold = 0 # minimum daily volume threshold for each option contract\n",
    "initial_equity = 100 # initial equity\n",
    "bet_size_largest_leg = 0.01 # the percentage of equity to bet each time on the leg with the largest price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4-legged strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ticker                = ['spy',  'spy' ,  'spy',  'spy' ] # ticker to read files\n",
    "buy_or_sell           = ['sell', 'sell' , 'buy',  'buy' ]\n",
    "call_or_put           = ['put',  'call',  'put',  'call'] \n",
    "DTE_lower             = [20,      5    ,  20,      5    ] # including\n",
    "DTE_upper             = [30,      10   ,  30,      10   ] # including\n",
    "delta_upper           = [-0.3,    0.4  ,  -0.1,    0.2  ] # including\n",
    "delta_lower           = [-0.4,    0.3  ,  -0.2,    0.1  ] # including\n",
    "num_shares_multiplier = [1,       2    ,  1,       2    ] # cannot be zero"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2-legged strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ticker                = ['spy',  'spy'  ] # ticker to read files\n",
    "buy_or_sell           = ['sell',  'sell']\n",
    "call_or_put           = ['call',  'put' ] \n",
    "DTE_lower             = [5,       5     ] # including\n",
    "DTE_upper             = [10,      10    ] # including\n",
    "delta_upper           = [0.2,     -0.0  ] # including\n",
    "delta_lower           = [0.0,     -0.2  ] # including\n",
    "num_shares_multiplier = [1,       1     ] # cannot be zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ticker                = ['spy',  'spy' ] # ticker to read files\n",
    "# buy_or_sell           = ['sell',  'buy']\n",
    "# call_or_put           = ['put',   'put'] \n",
    "# DTE_lower             = [5,       30   ] # including\n",
    "# DTE_upper             = [10,      60   ] # including\n",
    "# delta_upper           = [-0.8,    -0.0 ] # including\n",
    "# delta_lower           = [-1,      -0.2 ] # including\n",
    "# num_shares_multiplier = [1,       1    ] # cannot be zero"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1-legged strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ticker                = ['spy' ] # ticker to read files\n",
    "# buy_or_sell           = ['sell'] \n",
    "# call_or_put           = ['put' ] \n",
    "# DTE_lower             = [10    ] # including\n",
    "# DTE_upper             = [20    ] # including\n",
    "# delta_upper           = [-0.4  ] # including\n",
    "# delta_lower           = [-0.6  ] # including\n",
    "# num_shares_multiplier = [1     ] # cannot be zero"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data preperation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1993-01-29</th>\n",
       "      <td>25.047173</td>\n",
       "      <td>25.047173</td>\n",
       "      <td>24.922560</td>\n",
       "      <td>25.029371</td>\n",
       "      <td>1003200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1993-02-01</th>\n",
       "      <td>25.047168</td>\n",
       "      <td>25.207384</td>\n",
       "      <td>25.047168</td>\n",
       "      <td>25.207384</td>\n",
       "      <td>480500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1993-02-02</th>\n",
       "      <td>25.189596</td>\n",
       "      <td>25.278605</td>\n",
       "      <td>25.136190</td>\n",
       "      <td>25.260803</td>\n",
       "      <td>201300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1993-02-03</th>\n",
       "      <td>25.296391</td>\n",
       "      <td>25.545617</td>\n",
       "      <td>25.278589</td>\n",
       "      <td>25.527815</td>\n",
       "      <td>529400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1993-02-04</th>\n",
       "      <td>25.616828</td>\n",
       "      <td>25.688036</td>\n",
       "      <td>25.331999</td>\n",
       "      <td>25.634630</td>\n",
       "      <td>531500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Open       High        Low      Close   Volume\n",
       "Date                                                           \n",
       "1993-01-29  25.047173  25.047173  24.922560  25.029371  1003200\n",
       "1993-02-01  25.047168  25.207384  25.047168  25.207384   480500\n",
       "1993-02-02  25.189596  25.278605  25.136190  25.260803   201300\n",
       "1993-02-03  25.296391  25.545617  25.278589  25.527815   529400\n",
       "1993-02-04  25.616828  25.688036  25.331999  25.634630   531500"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get a list of relevant months to access the locally saved options data\n",
    "\n",
    "dates_list = getDatesList(start, end)\n",
    "dates_list[:5]\n",
    "\n",
    "# download data from yahoo finance\n",
    "\n",
    "tickers_list = [\"SPY\"] \n",
    "\n",
    "stock_data = yf.download(  # or \"pdr.get_data_yahoo(...\n",
    "        # tickers list or string as well\n",
    "        tickers = tickers_list,\n",
    "\n",
    "        # use \"period\" instead of start/end\n",
    "        # valid periods: 1d,5d,1mo,3mo,6mo,1y,2y,5y,10y,ytd,max\n",
    "        # (optional, default is '1mo')\n",
    "        \n",
    "        period = \"max\",\n",
    "\n",
    "        # fetch data by interval (including intraday if period < 60 days)\n",
    "        # valid intervals: 1m,2m,5m,15m,30m,60m,90m,1h,1d,5d,1wk,1mo,3mo\n",
    "        # (optional, default is '1d')\n",
    "        interval = \"1d\",\n",
    "\n",
    "        # group by ticker (to access via data['SPY'])\n",
    "        # (optional, default is 'column')\n",
    "        group_by = 'ticker',\n",
    "\n",
    "        # adjust all OHLC automatically\n",
    "        # (optional, default is False)\n",
    "        auto_adjust = True,\n",
    "\n",
    "        # download pre/post regular market hours data\n",
    "        # (optional, default is False)\n",
    "        prepost = True,\n",
    "\n",
    "        # use threads for mass downloading? (True/False/Integer)\n",
    "        # (optional, default is True)\"\"\n",
    "        threads = True,\n",
    "\n",
    "        # proxy URL scheme use use when downloading?\n",
    "        # (optional, default is None)\n",
    "        proxy = None\n",
    "    )\n",
    "\n",
    "index_list_nan =list(np.unique(np.where(stock_data.isnull())[0]))\n",
    "stock_data.index[index_list_nan]\n",
    "stock_data=stock_data.drop(stock_data.index[index_list_nan])\n",
    "stock_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add trading signals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "</style>\n",
       "<small>shape: (5, 13)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>Open</th><th>High</th><th>Low</th><th>Close</th><th>Volume</th><th>signal</th><th>Month</th><th>Year</th><th>Day</th><th>count_days</th><th>Holding Period</th><th>next_signal_date</th><th>Date</th></tr><tr><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>i64</td><td>i64</td><td>i64</td><td>i64</td><td>i64</td><td>i64</td><td>f64</td><td>datetime[ns]</td><td>datetime[ns]</td></tr></thead><tbody><tr><td>176.966303</td><td>176.983455</td><td>174.488433</td><td>175.12291</td><td>158567300</td><td>1</td><td>1</td><td>2015</td><td>9</td><td>5527</td><td>5.0</td><td>2015-01-16 00:00:00</td><td>2015-01-09 00:00:00</td></tr><tr><td>170.424361</td><td>173.039418</td><td>170.235733</td><td>172.876511</td><td>211879600</td><td>1</td><td>1</td><td>2015</td><td>16</td><td>5532</td><td>5.0</td><td>2015-01-26 00:00:00</td><td>2015-01-16 00:00:00</td></tr><tr><td>175.517315</td><td>176.246093</td><td>174.779955</td><td>176.151779</td><td>92009700</td><td>1</td><td>1</td><td>2015</td><td>26</td><td>5537</td><td>4.0</td><td>2015-01-30 00:00:00</td><td>2015-01-26 00:00:00</td></tr><tr><td>171.967692</td><td>173.339516</td><td>170.733041</td><td>171.007401</td><td>197729700</td><td>1</td><td>1</td><td>2015</td><td>30</td><td>5541</td><td>5.0</td><td>2015-02-06 00:00:00</td><td>2015-01-30 00:00:00</td></tr><tr><td>177.103498</td><td>177.686533</td><td>175.697371</td><td>176.237534</td><td>125672000</td><td>1</td><td>2</td><td>2015</td><td>6</td><td>5546</td><td>5.0</td><td>2015-02-13 00:00:00</td><td>2015-02-06 00:00:00</td></tr></tbody></table></div>"
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       "shape: (5, 13)\n",
       "┌───────┬───────┬───────┬───────┬───┬──────────┬────────────┬────────────┬─────┐\n",
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       "│ 176.9 ┆ 176.9 ┆ 174.4 ┆ 175.1 ┆ … ┆ 5527     ┆ 5.0        ┆ 2015-01-16 ┆ 201 │\n",
       "│ 66303 ┆ 83455 ┆ 88433 ┆ 2291  ┆   ┆          ┆            ┆ 00:00:00   ┆ 5-0 │\n",
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       "│       ┆       ┆       ┆       ┆   ┆          ┆            ┆            ┆ 00  │\n",
       "│ 170.4 ┆ 173.0 ┆ 170.2 ┆ 172.8 ┆ … ┆ 5532     ┆ 5.0        ┆ 2015-01-26 ┆ 201 │\n",
       "│ 24361 ┆ 39418 ┆ 35733 ┆ 76511 ┆   ┆          ┆            ┆ 00:00:00   ┆ 5-0 │\n",
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       "│       ┆       ┆       ┆       ┆   ┆          ┆            ┆            ┆ 00  │\n",
       "│ 175.5 ┆ 176.2 ┆ 174.7 ┆ 176.1 ┆ … ┆ 5537     ┆ 4.0        ┆ 2015-01-30 ┆ 201 │\n",
       "│ 17315 ┆ 46093 ┆ 79955 ┆ 51779 ┆   ┆          ┆            ┆ 00:00:00   ┆ 5-0 │\n",
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       "│       ┆       ┆       ┆       ┆   ┆          ┆            ┆            ┆ 00  │\n",
       "│ 171.9 ┆ 173.3 ┆ 170.7 ┆ 171.0 ┆ … ┆ 5541     ┆ 5.0        ┆ 2015-02-06 ┆ 201 │\n",
       "│ 67692 ┆ 39516 ┆ 33041 ┆ 07401 ┆   ┆          ┆            ┆ 00:00:00   ┆ 5-0 │\n",
       "│       ┆       ┆       ┆       ┆   ┆          ┆            ┆            ┆ 1-3 │\n",
       "│       ┆       ┆       ┆       ┆   ┆          ┆            ┆            ┆ 0   │\n",
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       "│       ┆       ┆       ┆       ┆   ┆          ┆            ┆            ┆ 00  │\n",
       "│ 177.1 ┆ 177.6 ┆ 175.6 ┆ 176.2 ┆ … ┆ 5546     ┆ 5.0        ┆ 2015-02-13 ┆ 201 │\n",
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       "└───────┴───────┴───────┴───────┴───┴──────────┴────────────┴────────────┴─────┘"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# enter 'weekly' 'monthly' or 'bimonthly' for frequency\n",
    "\n",
    "stock_data, signals = addFrequencyBasedSignals(stock_data, frequency, dates_list) \n",
    "stock_data\n",
    "\n",
    "# data cleaning\n",
    "\n",
    "signals['Date'] = signals.index\n",
    "signals.index = range(len(signals))\n",
    "\n",
    "signals = pl.from_pandas(signals)\n",
    "\n",
    "signals.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>signal</th>\n",
       "      <th>Month</th>\n",
       "      <th>Year</th>\n",
       "      <th>Day</th>\n",
       "      <th>count_days</th>\n",
       "      <th>Holding Period</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-01-02</th>\n",
       "      <td>176.949164</td>\n",
       "      <td>177.377861</td>\n",
       "      <td>175.062885</td>\n",
       "      <td>176.134628</td>\n",
       "      <td>121465900</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2015</td>\n",
       "      <td>2</td>\n",
       "      <td>5522</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-05</th>\n",
       "      <td>175.054304</td>\n",
       "      <td>175.225781</td>\n",
       "      <td>172.636458</td>\n",
       "      <td>172.953690</td>\n",
       "      <td>169632600</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2015</td>\n",
       "      <td>5</td>\n",
       "      <td>5523</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-06</th>\n",
       "      <td>173.270892</td>\n",
       "      <td>173.811055</td>\n",
       "      <td>170.501511</td>\n",
       "      <td>171.324615</td>\n",
       "      <td>209151400</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2015</td>\n",
       "      <td>6</td>\n",
       "      <td>5524</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-07</th>\n",
       "      <td>172.696468</td>\n",
       "      <td>173.811084</td>\n",
       "      <td>172.233481</td>\n",
       "      <td>173.459549</td>\n",
       "      <td>125346700</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2015</td>\n",
       "      <td>7</td>\n",
       "      <td>5525</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01-08</th>\n",
       "      <td>174.917107</td>\n",
       "      <td>176.760513</td>\n",
       "      <td>174.899968</td>\n",
       "      <td>176.537582</td>\n",
       "      <td>147217800</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2015</td>\n",
       "      <td>8</td>\n",
       "      <td>5526</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Open        High         Low       Close     Volume  signal  \\\n",
       "Date                                                                            \n",
       "2015-01-02  176.949164  177.377861  175.062885  176.134628  121465900       0   \n",
       "2015-01-05  175.054304  175.225781  172.636458  172.953690  169632600       0   \n",
       "2015-01-06  173.270892  173.811055  170.501511  171.324615  209151400       0   \n",
       "2015-01-07  172.696468  173.811084  172.233481  173.459549  125346700       0   \n",
       "2015-01-08  174.917107  176.760513  174.899968  176.537582  147217800       0   \n",
       "\n",
       "            Month  Year  Day  count_days  Holding Period  \n",
       "Date                                                      \n",
       "2015-01-02      1  2015    2        5522             NaN  \n",
       "2015-01-05      1  2015    5        5523             NaN  \n",
       "2015-01-06      1  2015    6        5524             NaN  \n",
       "2015-01-07      1  2015    7        5525             NaN  \n",
       "2015-01-08      1  2015    8        5526             NaN  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make a copy called reference\n",
    "\n",
    "reference = stock_data.copy()\n",
    "\n",
    "reference.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "201501\n",
      "201502\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/twang/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:20: DeprecationWarning: `fmt` is deprecated as an argument to `strptime`; use `format` instead.\n",
      "/Users/twang/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:21: DeprecationWarning: `fmt` is deprecated as an argument to `strptime`; use `format` instead.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "201503\n",
      "201504\n",
      "201505\n",
      "201506\n",
      "201507\n",
      "201508\n",
      "201509\n",
      "201510\n",
      "201511\n",
      "201512\n",
      "201601\n",
      "201602\n",
      "201603\n",
      "201604\n",
      "201605\n",
      "201606\n",
      "201607\n",
      "201608\n",
      "201609\n",
      "201610\n",
      "201611\n",
      "201612\n",
      "201701\n",
      "201702\n",
      "201703\n",
      "201704\n",
      "201705\n",
      "201706\n",
      "201707\n",
      "201708\n",
      "201709\n",
      "201710\n",
      "201711\n",
      "201712\n",
      "201801\n",
      "201802\n",
      "201803\n",
      "201804\n",
      "201805\n",
      "201806\n",
      "201807\n",
      "201808\n",
      "201809\n",
      "201810\n",
      "201811\n",
      "201812\n",
      "201901\n",
      "201902\n",
      "201903\n",
      "201904\n",
      "201905\n",
      "201906\n",
      "201907\n",
      "201908\n",
      "201909\n",
      "201910\n",
      "201911\n",
      "201912\n",
      "202001\n",
      "202002\n",
      "202003\n",
      "202004\n",
      "202005\n",
      "202006\n",
      "202007\n",
      "202008\n",
      "202009\n",
      "202010\n",
      "202011\n",
      "202012\n",
      "202101\n",
      "202102\n",
      "202103\n",
      "202104\n",
      "202105\n",
      "202106\n",
      "202107\n",
      "202108\n",
      "202109\n",
      "202110\n",
      "202111\n",
      "202112\n",
      "202201\n",
      "202202\n",
      "202203\n",
      "202204\n",
      "202205\n",
      "202206\n",
      "202207\n",
      "202208\n",
      "202209\n",
      "202210\n",
      "202211\n",
      "202212\n"
     ]
    }
   ],
   "source": [
    "# get the options data based on the tickers that are specified earlier\n",
    "\n",
    "for i in range(len(np.unique(ticker))):\n",
    "    globals()[ticker[i]+'_options'] = get_options_data(ticker[i], dates_list)\n",
    "#     print(globals()[ticker[i]+'_options'].head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run a backtest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "2015-01-09 00:00:00\n",
      "1\n",
      "2015-01-16 00:00:00\n",
      "2\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "3\n",
      "2015-01-30 00:00:00\n",
      "4\n",
      "2015-02-06 00:00:00\n",
      "5\n",
      "2015-02-13 00:00:00\n",
      "6\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "7\n",
      "2015-02-27 00:00:00\n",
      "8\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "9\n",
      "2015-03-17 00:00:00\n",
      "10\n",
      "2015-03-24 00:00:00\n",
      "11\n",
      "2015-03-31 00:00:00\n",
      "12\n",
      "2015-04-09 00:00:00\n",
      "13\n",
      "2015-04-16 00:00:00\n",
      "14\n",
      "2015-04-23 00:00:00\n",
      "15\n",
      "2015-04-30 00:00:00\n",
      "16\n",
      "2015-05-08 00:00:00\n",
      "17\n",
      "2015-05-15 00:00:00\n",
      "18\n",
      "2015-05-22 00:00:00\n",
      "19\n",
      "2015-05-29 00:00:00\n",
      "20\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "21\n",
      "2015-06-16 00:00:00\n",
      "22\n",
      "2015-06-23 00:00:00\n",
      "23\n",
      "2015-06-30 00:00:00\n",
      "24\n",
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      "26\n",
      "2015-07-24 00:00:00\n",
      "27\n",
      "2015-07-31 00:00:00\n",
      "28\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "29\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "30\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "31\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "32\n",
      "2015-09-09 00:00:00\n",
      "33\n",
      "2015-09-16 00:00:00\n",
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      "38\n",
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      "39\n",
      "2015-10-30 00:00:00\n",
      "40\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "41\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "42\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "43\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "44\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "45\n",
      "2015-12-16 00:00:00\n",
      "46\n",
      "2015-12-23 00:00:00\n",
      "47\n",
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      "48\n",
      "2016-01-08 00:00:00\n",
      "49\n",
      "2016-01-15 00:00:00\n",
      "50\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "51\n",
      "2016-01-29 00:00:00\n",
      "52\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "53\n",
      "2016-02-16 00:00:00\n",
      "54\n",
      "2016-02-23 00:00:00\n",
      "55\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "56\n",
      "2016-03-08 00:00:00\n",
      "57\n",
      "2016-03-16 00:00:00\n",
      "58\n",
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      "63\n",
      "2016-04-29 00:00:00\n",
      "64\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "65\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "66\n",
      "2016-05-23 00:00:00\n",
      "67\n",
      "2016-05-31 00:00:00\n",
      "68\n",
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      "70\n",
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      "71\n",
      "2016-06-30 00:00:00\n",
      "72\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "73\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "74\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "75\n",
      "2016-07-29 00:00:00\n",
      "76\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "77\n",
      "2016-08-16 00:00:00\n",
      "78\n",
      "2016-08-24 00:00:00\n",
      "79\n",
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      "225\n",
      "2019-09-17 00:00:00\n",
      "226\n",
      "2019-09-24 00:00:00\n",
      "227\n",
      "Cannot find enough options that satisfy the criteria.\n",
      "228\n",
      "2019-10-08 00:00:00\n",
      "229\n",
      "2019-10-16 00:00:00\n",
      "230\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "2022-03-31 00:00:00\n",
      "348\n",
      "2022-04-08 00:00:00\n",
      "349\n",
      "2022-04-18 00:00:00\n",
      "350\n",
      "2022-04-25 00:00:00\n",
      "351\n",
      "2022-04-29 00:00:00\n",
      "352\n",
      "2022-05-09 00:00:00\n",
      "353\n",
      "2022-05-16 00:00:00\n",
      "354\n",
      "2022-05-23 00:00:00\n",
      "355\n",
      "2022-05-31 00:00:00\n",
      "356\n",
      "2022-06-08 00:00:00\n",
      "357\n",
      "2022-06-15 00:00:00\n",
      "358\n",
      "2022-06-23 00:00:00\n",
      "359\n",
      "2022-06-30 00:00:00\n",
      "360\n",
      "2022-07-11 00:00:00\n",
      "361\n",
      "2022-07-18 00:00:00\n",
      "362\n",
      "2022-07-25 00:00:00\n",
      "363\n",
      "2022-07-29 00:00:00\n",
      "364\n",
      "2022-08-08 00:00:00\n",
      "365\n",
      "2022-08-16 00:00:00\n",
      "366\n",
      "2022-08-24 00:00:00\n",
      "367\n",
      "2022-08-31 00:00:00\n",
      "368\n",
      "2022-09-09 00:00:00\n",
      "369\n",
      "2022-09-16 00:00:00\n",
      "370\n",
      "2022-09-23 00:00:00\n",
      "371\n",
      "2022-09-30 00:00:00\n",
      "372\n",
      "2022-10-10 00:00:00\n",
      "373\n",
      "2022-10-17 00:00:00\n",
      "374\n",
      "2022-10-24 00:00:00\n",
      "375\n",
      "2022-10-31 00:00:00\n",
      "376\n",
      "2022-11-08 00:00:00\n",
      "377\n",
      "2022-11-15 00:00:00\n",
      "378\n",
      "2022-11-22 00:00:00\n",
      "379\n",
      "2022-11-30 00:00:00\n",
      "380\n",
      "2022-12-08 00:00:00\n",
      "381\n",
      "2022-12-15 00:00:00\n",
      "382\n",
      "2022-12-22 00:00:00\n"
     ]
    }
   ],
   "source": [
    "df = pd.DataFrame()\n",
    "\n",
    "beg_equity = initial_equity\n",
    "\n",
    "# if no signal\n",
    "if len(signals)==0:\n",
    "    print('There is no trading signal.')\n",
    "\n",
    "# if there is at least one signal\n",
    "else:\n",
    "    \n",
    "    # for every signal\n",
    "    for i in range(len(signals)):\n",
    "        print(i)\n",
    "        price_list, date_list, diff_list, price_lists, diff_lists, len_lists, equity = [], [], [], [], [], [], []\n",
    "        volume_list, volume_lists = [], []\n",
    "        for j in range(len(ticker)):\n",
    "            \n",
    "            # get a list of prices and a list of dates\n",
    "            try:\n",
    "                price_list, diff_list, volume_list, date_list = get_price_list(i, globals()[ticker[j]+'_options'], \n",
    "                                 call_or_put[j], buy_or_sell[j], DTE_lower[j], DTE_upper[j], \n",
    "                                 delta_lower[j], delta_upper[j], volume_threshold)\n",
    "            # error\n",
    "            except:\n",
    "                break\n",
    "            else:\n",
    "                diff_lists.append(diff_list)\n",
    "                price_lists.append(price_list)\n",
    "                volume_lists.append(volume_list)\n",
    "                len_lists.append(len(price_list))\n",
    "        \n",
    "        # after getting all legs, only do something if the length matches\n",
    "        if len(price_lists) == len(ticker):\n",
    "            \n",
    "            # once one leg expires, close out the position\n",
    "            price_lists = [price_lists[i][:min(len_lists)] for i in range(len(price_lists))]\n",
    "            price_lists = np.array(price_lists)\n",
    "#             print(price_lists)\n",
    "            diff_lists = [diff_lists[i][:min(len_lists)] for i in range(len(diff_lists))]\n",
    "            diff_lists = np.array(diff_lists)\n",
    "#             print(diff_lists)\n",
    "            date_list = date_list[:min(len_lists)]\n",
    "    \n",
    "            volume_lists = [volume_lists[i][:min(len_lists)] for i in range(len(volume_lists))]\n",
    "            volume_lists = np.array(volume_lists)\n",
    "            \n",
    "            # the date of opening the position\n",
    "            print(date_list[0])\n",
    "            # the list of prices of options traded\n",
    "#             print(price_lists) \n",
    "#             print(volume_lists.reshape(len(ticker),-1))\n",
    "            \n",
    "            num_shares = beg_equity*bet_size_largest_leg/max(price_lists[:,0])\n",
    "#             print(num_shares)\n",
    "            ind = list(price_lists.T[0]).index(max(price_lists[:,0]))\n",
    "            num_shares_list = (np.array(num_shares_multiplier)/num_shares_multiplier[ind]*num_shares).reshape(-1,1)\n",
    "#             print(num_shares_list)\n",
    "#             print(diff_lists*num_shares_list)\n",
    "            equity = np.cumsum([beg_equity]+sum(diff_lists*num_shares_list)[1:].tolist())\n",
    "#             print(equity)\n",
    "            beg_equity = equity[-1]  \n",
    "#             print(beg_equity)\n",
    "            df = pd.concat([df, pd.DataFrame(equity, index=date_list, columns=['Equity'])])\n",
    "#             print(df)\n",
    "\n",
    "# remove duplicate indices\n",
    "df = df[~df.index.duplicated(keep='first')]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sharpe Ratio (Rf = 0.02): 0.8284\n",
      "Annualized Return: 0.2165\n",
      "Max Drawdown: -0.4076\n"
     ]
    }
   ],
   "source": [
    "# define the risk free rate\n",
    "Rf = 0.02\n",
    "\n",
    "# combine the dataframes\n",
    "res = pd.concat([df, reference] , axis=1, join='outer') \n",
    "\n",
    "# fill the values that are nan\n",
    "res.iloc[0, res.columns.get_loc('Equity')] = initial_equity\n",
    "res['Equity'] = res['Equity'].fillna(method='ffill')\n",
    "\n",
    "# plot the equity curve\n",
    "plt.plot(res['Equity'])\n",
    "plt.xticks(rotation = 45) # Rotates X-Axis Ticks by 45-degrees\n",
    "plt.show()\n",
    "\n",
    "# print the summary\n",
    "mean_ret = np.mean(res['Equity']/res['Equity'].shift(1)-1)\n",
    "stdev = np.std(res['Equity']/res['Equity'].shift(1)-1)\n",
    "print('Sharpe Ratio (Rf = '+str(Rf)+'): ',\n",
    "      \"{:.4f}\".format((mean_ret-Rf/250)/stdev*np.sqrt(250)),sep='')\n",
    "print('Annualized Return: ',\"{:.4f}\".format(mean_ret*250),sep='')\n",
    "\n",
    "Roll_Max = pd.DataFrame(res['Equity']).cummax()\n",
    "Daily_Drawdown = pd.DataFrame(res['Equity'])/Roll_Max - 1.0\n",
    "Max_Daily_Drawdown = Daily_Drawdown.cummin()\n",
    "\n",
    "print('Max Drawdown: ',\"{:.4f}\".format(Max_Daily_Drawdown.values.min()),sep='')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}