AFML 13.1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Synthetic Data Backtest\n",
    "\n",
    "Most of the functions below can be found under:\n",
    "\n",
    "* Tool/backtest \n",
    "* Sample_data/make_data\n",
    "\n",
    "A quick slideshow: [Seven Sins of Backtesting](https://newyork.qwafafew.org/wp-content/uploads/sites/4/2015/10/Luo_20150128.pdf)\n",
    "\n",
    "The below is a code snippet for trading rules optimization.\n",
    "\n",
    "The origin exercise required to use real-HFT data to deduce a certain outcome.. which I don't have.\n",
    "\n",
    "Hence, I will just replace this exercise with multiprocessing methods (Parallelization!).\n",
    "\n",
    "If you are keen on generating synthetic data for your research, copy the code snippets [Generate synthetic raw data](https://gist.github.com/boyboi86/5e00faf48f60abfdbe838fbdee269471) in my gist.\n",
    "\n",
    "Contact: boyboi86@gmail.com"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Num of CPU core:  4\n",
      "Machine info:  Windows-10-10.0.18362-SP0\n",
      "Python 3.7.4 (default, Aug  9 2019, 18:34:13) [MSC v.1915 64 bit (AMD64)]\n",
      "Numpy 1.18.5\n",
      "Pandas 1.0.4\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import research as rs\n",
    "from random import gauss\n",
    "from itertools import product\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': '1', 'b': '+', 'c': '!'}\n",
      "{'a': '1', 'b': '+', 'c': 'A'}\n",
      "{'a': '1', 'b': '*', 'c': '!'}\n",
      "{'a': '1', 'b': '*', 'c': 'A'}\n",
      "{'a': '2', 'b': '+', 'c': '!'}\n",
      "{'a': '2', 'b': '+', 'c': 'A'}\n",
      "{'a': '2', 'b': '*', 'c': '!'}\n",
      "{'a': '2', 'b': '*', 'c': 'A'}\n"
     ]
    }
   ],
   "source": [
    "dict0 = {'a':['1', '2'], 'b':['+', '*'], 'c':['!','A']}\n",
    "for a in dict0['a']:\n",
    "    for b in dict0['b']:\n",
    "        for c in dict0['c']:\n",
    "            print({'a':a, 'b':b, 'c':c})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "The above is scalar operation. Notice loop after loop after loop.\n",
    "\n",
    "The below is vectorization operation, which is what we will do for Monte-Carlos.\n",
    "\n",
    "The result is actually the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': '1', 'b': '+', 'c': '!'}\n",
      "{'a': '1', 'b': '+', 'c': 'A'}\n",
      "{'a': '1', 'b': '*', 'c': '!'}\n",
      "{'a': '1', 'b': '*', 'c': 'A'}\n",
      "{'a': '2', 'b': '+', 'c': '!'}\n",
      "{'a': '2', 'b': '+', 'c': 'A'}\n",
      "{'a': '2', 'b': '*', 'c': '!'}\n",
      "{'a': '2', 'b': '*', 'c': 'A'}\n"
     ]
    }
   ],
   "source": [
    "jobs = (dict(zip(dict0, i )) for i in product(*dict0.values()))\n",
    "for i in jobs: print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "Given the parameters below. It should look like the below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000\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>forecast</th>\n",
       "      <th>half_life</th>\n",
       "      <th>sigma</th>\n",
       "      <th>profit_range</th>\n",
       "      <th>loss_range</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>-10</td>\n",
       "      <td>100</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>-10</td>\n",
       "      <td>100</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "      <td>8.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>-10</td>\n",
       "      <td>100</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>-10</td>\n",
       "      <td>100</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "      <td>9.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>-10</td>\n",
       "      <td>100</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      forecast  half_life  sigma  profit_range  loss_range\n",
       "0           10          5      1           0.5         0.5\n",
       "1           10          5      1           0.5         1.0\n",
       "2           10          5      1           0.5         1.5\n",
       "3           10          5      1           0.5         2.0\n",
       "4           10          5      1           0.5         2.5\n",
       "...        ...        ...    ...           ...         ...\n",
       "9995       -10        100      1          10.0         8.0\n",
       "9996       -10        100      1          10.0         8.5\n",
       "9997       -10        100      1          10.0         9.0\n",
       "9998       -10        100      1          10.0         9.5\n",
       "9999       -10        100      1          10.0        10.0\n",
       "\n",
       "[10000 rows x 5 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forecast = [10,5,0,-5,-10]\n",
    "half_life = [5,10,25,50,100]\n",
    "loss_range = profit_range = np.linspace(.5, 10, 20)\n",
    "sigma = [1]\n",
    "max_period = half_life[-1]\n",
    "n_run = 100\n",
    "\n",
    "coeff = dict({'forecast': forecast,\n",
    "              'half_life': half_life,\n",
    "              'sigma':sigma,\n",
    "              'profit_range': profit_range,\n",
    "              'loss_range':loss_range})\n",
    "jobs = list(dict(zip(coeff, idx)) for idx in product(*coeff.values()))\n",
    "\n",
    "print(len(jobs)) #forecast * half_life * loss * profit * sigma\n",
    "out = pd.DataFrame(jobs)\n",
    "out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "The below is the end product for a non-parallized Monte-Carlos Simulation, for optimizied Trading Rule Algorithm.\n",
    "\n",
    "Primarily we will use it to create scenarios for our models to be backtest with.\n",
    "\n",
    "There is another algorithm which MLfinlab has implemented, you may wish to read that as well.\n",
    "\n",
    "[Backtesting by Campbell and Yan [2015]](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2345489)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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     "name": "stderr",
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    }
   ],
   "source": [
    "def _opt_tr(coeff: dict = None,\n",
    "            n_run: float = 100,\n",
    "            max_period: int = 100,\n",
    "            seed: int = 0):\n",
    "    \n",
    "    phi, output1 = 2 ** (-1/ coeff['half_life']), []\n",
    "    for iter_ in range(int(n_run)):\n",
    "        p, hold_period, count = seed, 0, 0\n",
    "        while True:\n",
    "            p = (1 - phi) * coeff['forecast'] + phi * p + coeff['sigma'] * gauss(0,1)\n",
    "            cp = p - seed\n",
    "            hold_period += 1\n",
    "            if coeff['profit_range'] < cp or -coeff['loss_range'] > cp or hold_period > max_period:\n",
    "                output1.append(cp)\n",
    "                break\n",
    "    mean, std = np.mean(output1), np.std(output1)\n",
    "    return {'profit': coeff['profit_range'], 'loss': coeff['loss_range'], 'mean': mean, 'std': std, 'sharpe': mean/std}\n",
    "\n",
    "def opt_tr(profit_range: list = np.linspace(.5, 10, 20),\n",
    "          loss_range: list = np.linspace(.5, 10, 20),\n",
    "          sigma: list = [1],\n",
    "          n_run: float = 100,\n",
    "          max_period: int = 100,\n",
    "          forecast: list = [10,5,0,-5,-10], \n",
    "          half_life: list = [5,10,25,50,100],\n",
    "          num_threads: int = 1):\n",
    "    \n",
    "    if profit_range is None:\n",
    "        profit_range = np.linspace(0,10,21)\n",
    "        \n",
    "    if loss_range is None:\n",
    "        loss_range = np.linspace(0,10,21)\n",
    "        \n",
    "    _coeff_list = []\n",
    "    _coeff = dict({'forecast': forecast,\n",
    "                   'half_life': half_life,\n",
    "                   'sigma':sigma,\n",
    "                   'profit_range': profit_range,\n",
    "                   'loss_range':loss_range})\n",
    "    \n",
    "    _coeff = list(dict(zip(_coeff, idx )) for idx in product(*_coeff.values()))\n",
    "    out = []\n",
    "    for coeff in _coeff:\n",
    "        jobs = [{'func': _opt_tr,\n",
    "                   'coeff': coeff,\n",
    "                   'n_run': n_run, \n",
    "                   'max_period': max_period}]\n",
    "        \n",
    "        if num_threads == 1:\n",
    "            out_ = rs.process_jobs_(jobs)\n",
    "            out.append(out_)\n",
    "        else:\n",
    "            out_ = rs.process_jobs(jobs, num_threads = num_threads)\n",
    "            out.append(out_)\n",
    "\n",
    "    return out\n",
    "\n",
    "df = opt_tr(profit_range = profit_range,\n",
    "              loss_range = loss_range,\n",
    "              sigma = sigma,\n",
    "              n_run = n_run,\n",
    "              max_period = max_period,\n",
    "              forecast = forecast, \n",
    "              half_life = half_life,\n",
    "              num_threads = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "Before parallization. Total runs for estimated 1,000,000 loops took about 3 min\n",
    "\n",
    "* 2020-06-17 14:41:28.739905 (Beginning!)\n",
    "\n",
    "* 2020-06-17 14:46:51.676526 (End!)\n",
    "\n",
    "**Note**\n",
    "\n",
    "Try to change the above code snippet to run parallelization.\n",
    "\n",
    "Please do not use jupyter notbook, it won't reflect anything.\n",
    "\n",
    "If you are like me, curious about strategy's mean-reversion velocity, you might want to read this research report.\n",
    "\n",
    "[Critical-Line Algorithm for Portfolio Optimization by Bailey and Lopez [2013]](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2197616)\n",
    "\n",
    "**Hint**\n",
    "\n",
    "Vectorize iterable then try using \"iterrows()\" or \"itertuples()\" if you are using pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total count provided: 10000, total count retrieved: 10000\n"
     ]
    },
    {
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       " [{'profit': 4.0,\n",
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       "   'mean': 1.9462254612225092,\n",
       "   'std': 3.2291243254675455,\n",
       "   'sharpe': 0.6027099811156125}],\n",
       " [{'profit': 4.0,\n",
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       " [{'profit': 4.0,\n",
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       "   'mean': 3.435705863059732,\n",
       "   'std': 2.8976311158711927,\n",
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       " [{'profit': 4.0,\n",
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       "   'mean': 3.9691612127442353,\n",
       "   'std': 2.4304177195265027,\n",
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       " [{'profit': 4.0,\n",
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       " [{'profit': 4.0,\n",
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       "   'mean': 4.350069034546955,\n",
       "   'std': 1.7113370947599376,\n",
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       " [{'profit': 4.0,\n",
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       "   'mean': 4.34427279659109,\n",
       "   'std': 1.8149182402975919,\n",
       "   'sharpe': 2.3936465567059155}],\n",
       " [{'profit': 4.0,\n",
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       "   'std': 1.9315874122747367,\n",
       "   'sharpe': 2.2746428752156906}],\n",
       " [{'profit': 4.0,\n",
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       "   'mean': 4.527326023147945,\n",
       "   'std': 1.6203608571383092,\n",
       "   'sharpe': 2.794023320918512}],\n",
       " [{'profit': 4.0,\n",
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       "   'std': 1.3036350470319709,\n",
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       " [{'profit': 4.0,\n",
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       "   'mean': 4.636615520523242,\n",
       "   'std': 0.5404251367622487,\n",
       "   'sharpe': 8.579570425427947}],\n",
       " [{'profit': 4.0,\n",
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       "   'std': 1.8053768569353896,\n",
       "   'sharpe': 2.4094031725504896}],\n",
       " [{'profit': 4.0,\n",
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       "   'std': 0.6475124665332446,\n",
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       "   'std': 0.5730202779511543,\n",
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       "   'std': 0.5515670647048418,\n",
       "   'sharpe': 8.503485283928567}],\n",
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       " [{'profit': 4.0,\n",
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       "   'std': 3.128795168766133,\n",
       "   'sharpe': 0.5284758540259414}],\n",
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       "   'std': 3.281464963900905,\n",
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       " [{'profit': 4.5,\n",
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       " [{'profit': 4.5,\n",
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       "   'std': 3.002670322932144,\n",
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       "   'std': 1.7841013295015078,\n",
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       " [{'profit': 4.5,\n",
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       "   'mean': 4.706714429281004,\n",
       "   'std': 1.8362432753658118,\n",
       "   'sharpe': 2.5632303150808515}],\n",
       " [{'profit': 4.5,\n",
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       "   'mean': 4.88104423984073,\n",
       "   'std': 1.6471836608577022,\n",
       "   'sharpe': 2.96326654751974}],\n",
       " [{'profit': 4.5,\n",
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       "   'std': 1.197888219888352,\n",
       "   'sharpe': 4.146877257470165}],\n",
       " [{'profit': 4.5,\n",
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       "   'mean': 4.878440685970987,\n",
       "   'std': 1.7763659949026243,\n",
       "   'sharpe': 2.746303802240039}],\n",
       " [{'profit': 4.5,\n",
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       "   'mean': 4.932894996385949,\n",
       "   'std': 1.298247484359273,\n",
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       "   'std': 1.3690759692720498,\n",
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       " [{'profit': 4.5,\n",
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       "   'std': 0.6438817090690122,\n",
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       " [{'profit': 4.5,\n",
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       "   'mean': 5.122818911004167,\n",
       "   'std': 0.6014248835086193,\n",
       "   'sharpe': 8.517803389042431}],\n",
       " [{'profit': 4.5,\n",
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       "   'mean': 5.106221495821436,\n",
       "   'std': 0.5176112993964574,\n",
       "   'sharpe': 9.864973005371727}],\n",
       " [{'profit': 4.5,\n",
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       "   'mean': 5.125634277484336,\n",
       "   'std': 0.46407067234183014,\n",
       "   'sharpe': 11.044943330762434}],\n",
       " [{'profit': 4.5,\n",
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       "   'mean': 5.116858804669507,\n",
       "   'std': 0.5002514470853557,\n",
       "   'sharpe': 10.228573719240915}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 0.5,\n",
       "   'mean': 2.1862570491684754,\n",
       "   'std': 3.435230578328835,\n",
       "   'sharpe': 0.6364222136820994}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 1.0,\n",
       "   'mean': 2.62062760883363,\n",
       "   'std': 3.6122277430546994,\n",
       "   'sharpe': 0.7254879246947709}],\n",
       " [{'profit': 5.0,\n",
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       "   'mean': 3.0758130855753647,\n",
       "   'std': 3.6250197645964803,\n",
       "   'sharpe': 0.8484955352837226}],\n",
       " [{'profit': 5.0,\n",
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       "   'mean': 3.77739712096555,\n",
       "   'std': 3.3761507414339103,\n",
       "   'sharpe': 1.1188472939336895}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 2.5,\n",
       "   'mean': 4.329862797451003,\n",
       "   'std': 3.213395985915581,\n",
       "   'sharpe': 1.347441403558395}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 3.0,\n",
       "   'mean': 4.417173972944834,\n",
       "   'std': 3.0648565724611663,\n",
       "   'sharpe': 1.441233502616313}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 3.5,\n",
       "   'mean': 4.790618914758063,\n",
       "   'std': 2.8430972628575844,\n",
       "   'sharpe': 1.6850000094414757}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 4.0,\n",
       "   'mean': 4.900849447893354,\n",
       "   'std': 2.6196077918360543,\n",
       "   'sharpe': 1.8708332839621014}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 4.5,\n",
       "   'mean': 5.134238406303146,\n",
       "   'std': 2.4278849580615125,\n",
       "   'sharpe': 2.1146959164006094}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 5.0,\n",
       "   'mean': 5.448443396670658,\n",
       "   'std': 1.619953792726178,\n",
       "   'sharpe': 3.3633325969758774}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 5.5,\n",
       "   'mean': 5.258978826801629,\n",
       "   'std': 2.1867533721732357,\n",
       "   'sharpe': 2.404925445056092}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 6.0,\n",
       "   'mean': 5.602161009285485,\n",
       "   'std': 0.5522446150455322,\n",
       "   'sharpe': 10.144347009746017}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 6.5,\n",
       "   'mean': 5.450075064676119,\n",
       "   'std': 1.3457454694386823,\n",
       "   'sharpe': 4.049855777667506}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 7.0,\n",
       "   'mean': 5.600905081266943,\n",
       "   'std': 0.5241128820631081,\n",
       "   'sharpe': 10.686448040009331}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 7.5,\n",
       "   'mean': 5.6157882818862195,\n",
       "   'std': 0.43458422265097824,\n",
       "   'sharpe': 12.922209296116927}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 8.0,\n",
       "   'mean': 5.515803345226861,\n",
       "   'std': 0.4943625543537927,\n",
       "   'sharpe': 11.157405221430773}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 8.5,\n",
       "   'mean': 5.655786682053067,\n",
       "   'std': 0.5467299056030014,\n",
       "   'sharpe': 10.344754556301737}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 9.0,\n",
       "   'mean': 5.619273723250731,\n",
       "   'std': 0.5372985909460607,\n",
       "   'sharpe': 10.458381648380033}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 9.5,\n",
       "   'mean': 5.552859118346519,\n",
       "   'std': 0.46321060695605,\n",
       "   'sharpe': 11.987763308868661}],\n",
       " [{'profit': 5.0,\n",
       "   'loss': 10.0,\n",
       "   'mean': 5.584036350542907,\n",
       "   'std': 0.5035453463762886,\n",
       "   'sharpe': 11.089440882986688}],\n",
       " ...]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Total count provided: {0}, total count retrieved: {1}\".format(len(jobs), len(df)))\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[      profit  loss      mean       std    sharpe\n",
      "0        0.5   0.5  1.396264  0.984278  1.418566\n",
      "1        0.5   1.0  1.587675  0.774706  2.049392\n",
      "2        0.5   1.5  1.712608  0.826244  2.072764\n",
      "3        0.5   2.0  1.600266  0.662226  2.416496\n",
      "4        0.5   2.5  1.610815  0.680407  2.367427\n",
      "...      ...   ...       ...       ...       ...\n",
      "3329     3.5   5.0  1.380343  4.395407  0.314042\n",
      "3330     3.5   5.5  2.112414  3.886711  0.543497\n",
      "3331     3.5   6.0  2.024534  4.154450  0.487317\n",
      "3332     3.5   6.5  1.968073  4.356944  0.451709\n",
      "3333     3.5   7.0  3.004285  3.233671  0.929063\n",
      "\n",
      "[3334 rows x 5 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-17 14:49:16.186467 33.33% _opt_tr done after 2.37 mins. Remaining 4.75 mins.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[      profit  loss      mean       std    sharpe\n",
      "0        0.5   0.5  1.396264  0.984278  1.418566\n",
      "1        0.5   1.0  1.587675  0.774706  2.049392\n",
      "2        0.5   1.5  1.712608  0.826244  2.072764\n",
      "3        0.5   2.0  1.600266  0.662226  2.416496\n",
      "4        0.5   2.5  1.610815  0.680407  2.367427\n",
      "...      ...   ...       ...       ...       ...\n",
      "3329     3.5   5.0  1.380343  4.395407  0.314042\n",
      "3330     3.5   5.5  2.112414  3.886711  0.543497\n",
      "3331     3.5   6.0  2.024534  4.154450  0.487317\n",
      "3332     3.5   6.5  1.968073  4.356944  0.451709\n",
      "3333     3.5   7.0  3.004285  3.233671  0.929063\n",
      "\n",
      "[3334 rows x 5 columns],       profit  loss      mean       std     sharpe\n",
      "6667     7.0   4.0 -4.659314  0.477871  -9.750155\n",
      "6668     7.0   4.5 -5.038846  0.450071 -11.195665\n",
      "6669     7.0   5.0 -5.680721  0.604291  -9.400631\n",
      "6670     7.0   5.5 -6.030476  0.483595 -12.470101\n",
      "6671     7.0   6.0 -6.486064  0.876892  -7.396649\n",
      "...      ...   ...       ...       ...        ...\n",
      "9995    10.0   8.0 -3.843756  6.173427  -0.622629\n",
      "9996    10.0   8.5 -4.054103  7.336595  -0.552587\n",
      "9997    10.0   9.0 -4.632491  6.437791  -0.719578\n",
      "9998    10.0   9.5 -4.404237  7.476366  -0.589088\n",
      "9999    10.0  10.0 -4.952120  6.615454  -0.748568\n",
      "\n",
      "[3333 rows x 5 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-17 14:49:21.045204 66.67% _opt_tr done after 2.45 mins. Remaining 1.23 mins.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[      profit  loss      mean       std    sharpe\n",
      "0        0.5   0.5  1.396264  0.984278  1.418566\n",
      "1        0.5   1.0  1.587675  0.774706  2.049392\n",
      "2        0.5   1.5  1.712608  0.826244  2.072764\n",
      "3        0.5   2.0  1.600266  0.662226  2.416496\n",
      "4        0.5   2.5  1.610815  0.680407  2.367427\n",
      "...      ...   ...       ...       ...       ...\n",
      "3329     3.5   5.0  1.380343  4.395407  0.314042\n",
      "3330     3.5   5.5  2.112414  3.886711  0.543497\n",
      "3331     3.5   6.0  2.024534  4.154450  0.487317\n",
      "3332     3.5   6.5  1.968073  4.356944  0.451709\n",
      "3333     3.5   7.0  3.004285  3.233671  0.929063\n",
      "\n",
      "[3334 rows x 5 columns],       profit  loss      mean       std     sharpe\n",
      "6667     7.0   4.0 -4.659314  0.477871  -9.750155\n",
      "6668     7.0   4.5 -5.038846  0.450071 -11.195665\n",
      "6669     7.0   5.0 -5.680721  0.604291  -9.400631\n",
      "6670     7.0   5.5 -6.030476  0.483595 -12.470101\n",
      "6671     7.0   6.0 -6.486064  0.876892  -7.396649\n",
      "...      ...   ...       ...       ...        ...\n",
      "9995    10.0   8.0 -3.843756  6.173427  -0.622629\n",
      "9996    10.0   8.5 -4.054103  7.336595  -0.552587\n",
      "9997    10.0   9.0 -4.632491  6.437791  -0.719578\n",
      "9998    10.0   9.5 -4.404237  7.476366  -0.589088\n",
      "9999    10.0  10.0 -4.952120  6.615454  -0.748568\n",
      "\n",
      "[3333 rows x 5 columns],       profit  loss      mean       std    sharpe\n",
      "3334     3.5   7.5  2.794291  3.647403  0.766104\n",
      "3335     3.5   8.0  2.977291  3.519886  0.845849\n",
      "3336     3.5   8.5  2.380115  4.128464  0.576514\n",
      "3337     3.5   9.0  2.607929  4.075040  0.639976\n",
      "3338     3.5   9.5  3.013816  3.534308  0.852731\n",
      "...      ...   ...       ...       ...       ...\n",
      "6662     7.0   1.5 -2.133240  0.587431 -3.631475\n",
      "6663     7.0   2.0 -2.705199  0.612009 -4.420195\n",
      "6664     7.0   2.5 -3.194195  0.529410 -6.033496\n",
      "6665     7.0   3.0 -3.632257  0.548559 -6.621451\n",
      "6666     7.0   3.5 -4.133265  0.530504 -7.791211\n",
      "\n",
      "[3333 rows x 5 columns]] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-17 14:49:46.331662 100.0% _opt_tr done after 2.88 mins. Remaining 0.0 mins.\n"
     ]
    }
   ],
   "source": [
    "df1 = rs.opt_tr(profit_range = profit_range,\n",
    "                  loss_range = loss_range,\n",
    "                  sigma = sigma,\n",
    "                  n_run = n_run,\n",
    "                  max_period = max_period,\n",
    "                  forecast = forecast, \n",
    "                  half_life = half_life,\n",
    "                  num_threads = 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "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>profit</th>\n",
       "      <th>loss</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>sharpe</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>1.396264</td>\n",
       "      <td>0.984278</td>\n",
       "      <td>1.418566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.5</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.587675</td>\n",
       "      <td>0.774706</td>\n",
       "      <td>2.049392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1.712608</td>\n",
       "      <td>0.826244</td>\n",
       "      <td>2.072764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.5</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.600266</td>\n",
       "      <td>0.662226</td>\n",
       "      <td>2.416496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.5</td>\n",
       "      <td>2.5</td>\n",
       "      <td>1.610815</td>\n",
       "      <td>0.680407</td>\n",
       "      <td>2.367427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>10.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>-3.843756</td>\n",
       "      <td>6.173427</td>\n",
       "      <td>-0.622629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>10.0</td>\n",
       "      <td>8.5</td>\n",
       "      <td>-4.054103</td>\n",
       "      <td>7.336595</td>\n",
       "      <td>-0.552587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>10.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>-4.632491</td>\n",
       "      <td>6.437791</td>\n",
       "      <td>-0.719578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>10.0</td>\n",
       "      <td>9.5</td>\n",
       "      <td>-4.404237</td>\n",
       "      <td>7.476366</td>\n",
       "      <td>-0.589088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-4.952120</td>\n",
       "      <td>6.615454</td>\n",
       "      <td>-0.748568</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      profit  loss      mean       std    sharpe\n",
       "0        0.5   0.5  1.396264  0.984278  1.418566\n",
       "1        0.5   1.0  1.587675  0.774706  2.049392\n",
       "2        0.5   1.5  1.712608  0.826244  2.072764\n",
       "3        0.5   2.0  1.600266  0.662226  2.416496\n",
       "4        0.5   2.5  1.610815  0.680407  2.367427\n",
       "...      ...   ...       ...       ...       ...\n",
       "9995    10.0   8.0 -3.843756  6.173427 -0.622629\n",
       "9996    10.0   8.5 -4.054103  7.336595 -0.552587\n",
       "9997    10.0   9.0 -4.632491  6.437791 -0.719578\n",
       "9998    10.0   9.5 -4.404237  7.476366 -0.589088\n",
       "9999    10.0  10.0 -4.952120  6.615454 -0.748568\n",
       "\n",
       "[10000 rows x 5 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conclusion**\n",
    "\n",
    "The above was ran parallel with 3 threads:\n",
    "    \n",
    "1. 2020-06-17 14:49:16.186467\n",
    "2. 2020-06-17 14:49:21.045204\n",
    "3. 2020-06-17 14:49:46.331662\n",
    "\n",
    "Based on the time provided by python system, it seems that it took less than 40 seconds.\n",
    "\n",
    "When running large dataset, especially with Pandas parallelization can save time and always vectorize the datasets.\n",
    "\n",
    "**Note**\n",
    "\n",
    "If the answer to the above will not tally with the initial run (Scalar Operations), since we are running a Monte-Carlos."
   ]
  }
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