Projects/8-Backtesting/project_8_starter.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project 8: Backtesting\n",
    "\n",
    "In this project, you will build a fairly realistic backtester that uses the Barra data. The backtester will perform portfolio optimization that includes transaction costs, and you'll implement it with computational efficiency in mind, to allow for a reasonably fast backtest. You'll also use performance attribution to identify the major drivers of your portfolio's profit-and-loss (PnL). You will have the option to modify and customize the backtest as well.\n",
    "\n",
    "\n",
    "## Instructions\n",
    "\n",
    "Each problem consists of a function to implement and instructions on how to implement the function.  The parts of the function that need to be implemented are marked with a `# TODO` comment. Your code will be checked for the correct solution when you submit it to Udacity.\n",
    "\n",
    "\n",
    "## Packages\n",
    "\n",
    "When you implement the functions, you'll only need to you use the packages you've used in the classroom, like [Pandas](https://pandas.pydata.org/) and [Numpy](http://www.numpy.org/). These packages will be imported for you. We recommend you don't add any import statements, otherwise the grader might not be able to run your code.\n",
    "\n",
    "### Install Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: matplotlib==2.1.0 in /opt/conda/lib/python3.6/site-packages (from -r requirements.txt (line 1)) (2.1.0)\n",
      "Requirement already satisfied: numpy==1.16.1 in /opt/conda/lib/python3.6/site-packages (from -r requirements.txt (line 2)) (1.16.1)\n",
      "Requirement already satisfied: pandas==0.24.1 in /opt/conda/lib/python3.6/site-packages (from -r requirements.txt (line 3)) (0.24.1)\n",
      "Requirement already satisfied: patsy==0.5.1 in /opt/conda/lib/python3.6/site-packages (from -r requirements.txt (line 4)) (0.5.1)\n",
      "Requirement already satisfied: scipy==0.19.1 in /opt/conda/lib/python3.6/site-packages (from -r requirements.txt (line 5)) (0.19.1)\n",
      "Requirement already satisfied: statsmodels==0.9.0 in /opt/conda/lib/python3.6/site-packages (from -r requirements.txt (line 6)) (0.9.0)\n",
      "Requirement already satisfied: tqdm==4.19.5 in /opt/conda/lib/python3.6/site-packages (from -r requirements.txt (line 7)) (4.19.5)\n",
      "Requirement already satisfied: six>=1.10 in /opt/conda/lib/python3.6/site-packages (from matplotlib==2.1.0->-r requirements.txt (line 1)) (1.11.0)\n",
      "Requirement already satisfied: python-dateutil>=2.0 in /opt/conda/lib/python3.6/site-packages (from matplotlib==2.1.0->-r requirements.txt (line 1)) (2.6.1)\n",
      "Requirement already satisfied: pytz in /opt/conda/lib/python3.6/site-packages (from matplotlib==2.1.0->-r requirements.txt (line 1)) (2017.3)\n",
      "Requirement already satisfied: cycler>=0.10 in /opt/conda/lib/python3.6/site-packages/cycler-0.10.0-py3.6.egg (from matplotlib==2.1.0->-r requirements.txt (line 1)) (0.10.0)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /opt/conda/lib/python3.6/site-packages (from matplotlib==2.1.0->-r requirements.txt (line 1)) (2.2.0)\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install -r requirements.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "import patsy\n",
    "import pickle\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import scipy.sparse\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from statistics import median\n",
    "from scipy.stats import gaussian_kde\n",
    "from statsmodels.formula.api import ols\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data\n",
    "\n",
    "We’ll be using the Barra dataset to get factors that can be used to predict risk. Loading and parsing the raw Barra data can be a very slow process that can significantly slow down your backtesting. For this reason, it's important to pre-process the data beforehand. For your convenience, the Barra data has already been pre-processed for you and saved into pickle files. You will load the Barra data from these pickle files.\n",
    "\n",
    "In the code below, we start by loading `2004` factor data from the `pandas-frames.2004.pickle` file. We also load the `2003` and `2004` covariance data from the `covaraince.2003.pickle`  and `covaraince.2004.pickle` files. You are encouraged  to customize the data range for your backtest. For example, we recommend starting with two or three years of factor data. Remember that the covariance data should include all the years that you choose for the factor data,   and also one year earlier. For example, in the code below we are using  `2004` factor data, therefore, we must include `2004` in our covariance data, but also the previous year, `2003`. If you don't remember why must include this previous year, feel free to review the lessons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "barra_dir = '../../data/project_8_barra/'\n",
    "\n",
    "data = {}\n",
    "for year in [2004]:\n",
    "    fil = barra_dir + \"pandas-frames.\" + str(year) + \".pickle\"\n",
    "    data.update(pickle.load( open( fil, \"rb\" ) ))\n",
    "    \n",
    "covariance = {}\n",
    "for year in [2004]:\n",
    "    fil = barra_dir + \"covariance.\" + str(year) + \".pickle\"\n",
    "    covariance.update(pickle.load( open(fil, \"rb\" ) ))\n",
    "    \n",
    "daily_return = {}\n",
    "for year in [2004, 2005]:\n",
    "    fil = barra_dir + \"price.\" + str(year) + \".pickle\"\n",
    "    daily_return.update(pickle.load( open(fil, \"rb\" ) ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shift Daily Returns Data (TODO)\n",
    "\n",
    "In the cell below, we want to incorporate a realistic time delay that exists in live trading, we’ll use a two day delay for the `daily_return` data. That means the `daily_return` should be two days after the data in `data` and `cov_data`. Combine `daily_return` and `data` together in a dict called `frames`.\n",
    "\n",
    "Since reporting of PnL is usually for the date of the returns, make sure to use the two day delay dates (dates that match the `daily_return`) when building `frames`. This means calling `frames['20040108']` will get you the prices from \"20040108\" and the data from `data` at \"20040106\".\n",
    "\n",
    "Note: We're not shifting `covariance`, since we'll use the \"DataDate\" field in `frames` to lookup the covariance data. The \"DataDate\" field contains the date when the `data` in `frames` was recorded. For example, `frames['20040108']` will give you a value of \"20040106\" for the field \"DataDate\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "frames ={}\n",
    "dlyreturn_n_days_delay = 2\n",
    "\n",
    "# TODO: Implement\n",
    "date_shifts = zip(\n",
    "        sorted(data.keys()),\n",
    "        sorted(daily_return.keys())[dlyreturn_n_days_delay : len(data) + dlyreturn_n_days_delay])\n",
    "\n",
    "# TODO\n",
    "for data_date, price_date in date_shifts:\n",
    "    frames[price_date] = data[data_date].merge(daily_return[price_date], on='Barrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>Barrid</th>\n",
       "      <th>USFASTD_1DREVRSL</th>\n",
       "      <th>USFASTD_AERODEF</th>\n",
       "      <th>USFASTD_AIRLINES</th>\n",
       "      <th>USFASTD_ALUMSTEL</th>\n",
       "      <th>USFASTD_APPAREL</th>\n",
       "      <th>USFASTD_AUTO</th>\n",
       "      <th>USFASTD_BANKS</th>\n",
       "      <th>USFASTD_BETA</th>\n",
       "      <th>USFASTD_BEVTOB</th>\n",
       "      <th>...</th>\n",
       "      <th>DailyVolume</th>\n",
       "      <th>ADTCA_30</th>\n",
       "      <th>IssuerMarketCap</th>\n",
       "      <th>Yield</th>\n",
       "      <th>TotalRisk</th>\n",
       "      <th>SpecRisk</th>\n",
       "      <th>HistBeta</th>\n",
       "      <th>PredBeta</th>\n",
       "      <th>DataDate</th>\n",
       "      <th>DlyReturn</th>\n",
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       "  </thead>\n",
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       "      <td>USA0001</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>5.592728e+10</td>\n",
       "      <td>0.188679</td>\n",
       "      <td>15.692850</td>\n",
       "      <td>10.050981</td>\n",
       "      <td>-0.000188</td>\n",
       "      <td>0.159701</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>USA0011</td>\n",
       "      <td>-0.595</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.158</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.029930e+09</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>19.050196</td>\n",
       "      <td>12.874902</td>\n",
       "      <td>0.000017</td>\n",
       "      <td>0.133397</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>USA0031</td>\n",
       "      <td>-0.109</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.049</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.251836e+10</td>\n",
       "      <td>2.103004</td>\n",
       "      <td>24.037181</td>\n",
       "      <td>19.772275</td>\n",
       "      <td>0.050603</td>\n",
       "      <td>0.210419</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>USA0062</td>\n",
       "      <td>0.163</td>\n",
       "      <td>0.431</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.997</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.918165e+10</td>\n",
       "      <td>2.243494</td>\n",
       "      <td>25.280406</td>\n",
       "      <td>22.709825</td>\n",
       "      <td>0.074781</td>\n",
       "      <td>0.372498</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>USA00E2</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.955</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.784320e+10</td>\n",
       "      <td>2.167256</td>\n",
       "      <td>27.885397</td>\n",
       "      <td>23.513232</td>\n",
       "      <td>0.094615</td>\n",
       "      <td>0.410219</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
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       "  </tbody>\n",
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       "<p>5 rows × 93 columns</p>\n",
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       "    Barrid  USFASTD_1DREVRSL  USFASTD_AERODEF  USFASTD_AIRLINES  \\\n",
       "0  USA0001            -0.481            0.000               0.0   \n",
       "1  USA0011            -0.595            0.000               0.0   \n",
       "2  USA0031            -0.109            0.000               0.0   \n",
       "3  USA0062             0.163            0.431               0.0   \n",
       "4  USA00E2             0.064            0.000               0.0   \n",
       "\n",
       "   USFASTD_ALUMSTEL  USFASTD_APPAREL  USFASTD_AUTO  USFASTD_BANKS  \\\n",
       "0               0.0              0.0           0.0            0.0   \n",
       "1               0.0              0.0           0.0            0.0   \n",
       "2               0.0              0.0           0.0            0.0   \n",
       "3               0.0              0.0           0.0            0.0   \n",
       "4               0.0              0.0           0.0            0.0   \n",
       "\n",
       "   USFASTD_BETA  USFASTD_BEVTOB  ...  DailyVolume  ADTCA_30  IssuerMarketCap  \\\n",
       "0        -2.158             0.0  ...          NaN       NaN     5.592728e+10   \n",
       "1        -2.158             0.0  ...          NaN       NaN     6.029930e+09   \n",
       "2        -2.049             0.0  ...          NaN       NaN     7.251836e+10   \n",
       "3        -1.997             0.0  ...          NaN       NaN     2.918165e+10   \n",
       "4        -1.955             0.0  ...          NaN       NaN     5.784320e+10   \n",
       "\n",
       "      Yield  TotalRisk   SpecRisk  HistBeta  PredBeta  DataDate  DlyReturn  \n",
       "0  0.188679  15.692850  10.050981 -0.000188  0.159701  20040106        0.0  \n",
       "1  0.000000  19.050196  12.874902  0.000017  0.133397  20040106        0.0  \n",
       "2  2.103004  24.037181  19.772275  0.050603  0.210419  20040106        0.0  \n",
       "3  2.243494  25.280406  22.709825  0.074781  0.372498  20040106        0.0  \n",
       "4  2.167256  27.885397  23.513232  0.094615  0.410219  20040106        0.0  \n",
       "\n",
       "[5 rows x 93 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = frames['20040108']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add Daily Returns date column (Optional)\n",
    "Name the column `DlyReturnDate`.\n",
    "**Hint**: create a list containing copies of the date, then create a pandas series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "for DlyReturnDate, df in frames.items():\n",
    "    n_rows = df.shape[0]\n",
    "    df['DlyReturnDate'] = pd.Series([DlyReturnDate] * n_rows)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "      <th>...</th>\n",
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       "      <th>SpecRisk</th>\n",
       "      <th>HistBeta</th>\n",
       "      <th>PredBeta</th>\n",
       "      <th>DataDate</th>\n",
       "      <th>DlyReturn</th>\n",
       "      <th>DlyReturnDate</th>\n",
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       "      <td>10.050981</td>\n",
       "      <td>-0.000188</td>\n",
       "      <td>0.159701</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
       "      <td>20040108</td>\n",
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       "      <th>1</th>\n",
       "      <td>USA0011</td>\n",
       "      <td>-0.595</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.158</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
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       "      <td>6.029930e+09</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>19.050196</td>\n",
       "      <td>12.874902</td>\n",
       "      <td>0.000017</td>\n",
       "      <td>0.133397</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
       "      <td>20040108</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>USA0031</td>\n",
       "      <td>-0.109</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-2.049</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7.251836e+10</td>\n",
       "      <td>2.103004</td>\n",
       "      <td>24.037181</td>\n",
       "      <td>19.772275</td>\n",
       "      <td>0.050603</td>\n",
       "      <td>0.210419</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
       "      <td>20040108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>USA0062</td>\n",
       "      <td>0.163</td>\n",
       "      <td>0.431</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.997</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.918165e+10</td>\n",
       "      <td>2.243494</td>\n",
       "      <td>25.280406</td>\n",
       "      <td>22.709825</td>\n",
       "      <td>0.074781</td>\n",
       "      <td>0.372498</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
       "      <td>20040108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>USA00E2</td>\n",
       "      <td>0.064</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-1.955</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.784320e+10</td>\n",
       "      <td>2.167256</td>\n",
       "      <td>27.885397</td>\n",
       "      <td>23.513232</td>\n",
       "      <td>0.094615</td>\n",
       "      <td>0.410219</td>\n",
       "      <td>20040106</td>\n",
       "      <td>0.0</td>\n",
       "      <td>20040108</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 94 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Barrid  USFASTD_1DREVRSL  USFASTD_AERODEF  USFASTD_AIRLINES  \\\n",
       "0  USA0001            -0.481            0.000               0.0   \n",
       "1  USA0011            -0.595            0.000               0.0   \n",
       "2  USA0031            -0.109            0.000               0.0   \n",
       "3  USA0062             0.163            0.431               0.0   \n",
       "4  USA00E2             0.064            0.000               0.0   \n",
       "\n",
       "   USFASTD_ALUMSTEL  USFASTD_APPAREL  USFASTD_AUTO  USFASTD_BANKS  \\\n",
       "0               0.0              0.0           0.0            0.0   \n",
       "1               0.0              0.0           0.0            0.0   \n",
       "2               0.0              0.0           0.0            0.0   \n",
       "3               0.0              0.0           0.0            0.0   \n",
       "4               0.0              0.0           0.0            0.0   \n",
       "\n",
       "   USFASTD_BETA  USFASTD_BEVTOB  ...  ADTCA_30  IssuerMarketCap     Yield  \\\n",
       "0        -2.158             0.0  ...       NaN     5.592728e+10  0.188679   \n",
       "1        -2.158             0.0  ...       NaN     6.029930e+09  0.000000   \n",
       "2        -2.049             0.0  ...       NaN     7.251836e+10  2.103004   \n",
       "3        -1.997             0.0  ...       NaN     2.918165e+10  2.243494   \n",
       "4        -1.955             0.0  ...       NaN     5.784320e+10  2.167256   \n",
       "\n",
       "   TotalRisk   SpecRisk  HistBeta  PredBeta  DataDate  DlyReturn  \\\n",
       "0  15.692850  10.050981 -0.000188  0.159701  20040106        0.0   \n",
       "1  19.050196  12.874902  0.000017  0.133397  20040106        0.0   \n",
       "2  24.037181  19.772275  0.050603  0.210419  20040106        0.0   \n",
       "3  25.280406  22.709825  0.074781  0.372498  20040106        0.0   \n",
       "4  27.885397  23.513232  0.094615  0.410219  20040106        0.0   \n",
       "\n",
       "   DlyReturnDate  \n",
       "0       20040108  \n",
       "1       20040108  \n",
       "2       20040108  \n",
       "3       20040108  \n",
       "4       20040108  \n",
       "\n",
       "[5 rows x 94 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = frames['20040108']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Winsorize\n",
    "\n",
    "As we have done in other projects, we'll want to avoid extremely positive or negative values in our data. Will therefore create a function, `wins`, that will clip our values to a minimum and maximum range. This process is called **Winsorizing**. Remember that this helps us handle noise, which may otherwise cause unusually large positions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def wins(x,a,b):\n",
    "    return np.where(x <= a,a, np.where(x >= b, b, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Density Plot\n",
    "\n",
    "Let's check our `wins` function by taking a look at the distribution of returns for a single day `20040102`. We will clip our data from `-0.1` to `0.1` and plot it using our `density_plot` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9112446438>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def density_plot(data): \n",
    "    density = gaussian_kde(data)\n",
    "    xs = np.linspace(np.min(data),np.max(data),200)\n",
    "    density.covariance_factor = lambda : .25\n",
    "    density._compute_covariance()\n",
    "    plt.plot(xs,density(xs))\n",
    "    plt.xlabel('Daily Returns')\n",
    "    plt.ylabel('Density')\n",
    "    plt.show()\n",
    "    \n",
    "test = frames['20040108']\n",
    "test['DlyReturn'] = wins(test['DlyReturn'],-0.1,0.1)\n",
    "density_plot(test['DlyReturn'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Factor Exposures and Factor Returns\n",
    "\n",
    "Recall that:\n",
    "\n",
    "$r_{i,t} = \\sum_{j=1}^{k} (\\beta_{i,j,t-2} \\times f_{j,t})$  \n",
    "where $i=1...N$ (N assets),   \n",
    "and $j=1...k$ (k factors).\n",
    "\n",
    "where $r_{i,t}$ is the return, $\\beta_{i,j,t-2}$ is the factor exposure, and $f_{j,t}$ is the factor return. Since we get the factor exposures from the Barra data, and we know the returns, it is possible to estimate the factor returns. In this notebook, we will use the Ordinary Least Squares (OLS) method to estimate the factor exposures, $f_{j,t}$, by using $\\beta_{i,j,t-2}$ as the independent variable, and $r_{i,t}$ as the dependent variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_formula(factors, Y):\n",
    "    L = [\"0\"]\n",
    "    L.extend(factors)\n",
    "    return Y + \" ~ \" + \" + \".join(L)\n",
    "\n",
    "def factors_from_names(n):\n",
    "    return list(filter(lambda x: \"USFASTD_\" in x, n))\n",
    "\n",
    "def estimate_factor_returns(df): \n",
    "    ## build universe based on filters \n",
    "    estu = df.loc[df.IssuerMarketCap > 1e9].copy(deep=True)\n",
    "  \n",
    "    ## winsorize returns for fitting \n",
    "    estu['DlyReturn'] = wins(estu['DlyReturn'], -0.25, 0.25)\n",
    "  \n",
    "    all_factors = factors_from_names(list(df))\n",
    "    form = get_formula(all_factors, \"DlyReturn\")\n",
    "    model = ols(form, data=estu)\n",
    "    results = model.fit()\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "facret = {}\n",
    "\n",
    "for date in frames:\n",
    "    facret[date] = estimate_factor_returns(frames[date]).params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_dates = sorted(list(map(lambda date: pd.to_datetime(date, format='%Y%m%d'), frames.keys())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choose Alpha Factors\n",
    "\n",
    "We will now choose our alpha factors. Barra's factors include some alpha factors that we have seen before, such as:\n",
    "\n",
    "* **USFASTD_1DREVRSL** : Reversal\n",
    "\n",
    "* **USFASTD_EARNYILD** : Earnings Yield\n",
    "\n",
    "* **USFASTD_VALUE** : Value\n",
    "\n",
    "* **USFASTD_SENTMT** : Sentiment\n",
    "\n",
    "We will choose these alpha factors for now, but you are encouraged to come back to this later and try other factors as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.6/site-packages/pandas/plotting/_converter.py:129: FutureWarning: Using an implicitly registered datetime converter for a matplotlib plotting method. The converter was registered by pandas on import. Future versions of pandas will require you to explicitly register matplotlib converters.\n",
      "\n",
      "To register the converters:\n",
      "\t>>> from pandas.plotting import register_matplotlib_converters\n",
      "\t>>> register_matplotlib_converters()\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f91125294e0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha_factors = [\"USFASTD_1DREVRSL\", \"USFASTD_EARNYILD\", \"USFASTD_VALUE\", \"USFASTD_SENTMT\"]\n",
    "\n",
    "facret_df = pd.DataFrame(index = my_dates)\n",
    "\n",
    "for dt in my_dates: \n",
    "    for alp in alpha_factors: \n",
    "        facret_df.at[dt, alp] = facret[dt.strftime('%Y%m%d')][alp]\n",
    "\n",
    "for column in facret_df.columns:\n",
    "        plt.plot(facret_df[column].cumsum(), label=column)\n",
    "plt.legend(loc='upper left')\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Cumulative Factor Returns')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Merge Previous Portfolio Holdings \n",
    "\n",
    "In order to optimize our portfolio we will use the previous day's holdings to estimate the trade size and transaction costs. In order to keep track of the holdings from the previous day we will include a column to hold the portfolio holdings of the previous day. These holdings of all our assets will be initialized to zero when the backtest first starts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def clean_nas(df): \n",
    "    numeric_columns = df.select_dtypes(include=[np.number]).columns.tolist()\n",
    "    \n",
    "    for numeric_column in numeric_columns: \n",
    "        df[numeric_column] = np.nan_to_num(df[numeric_column])\n",
    "    \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "previous_holdings = pd.DataFrame(data = {\"Barrid\" : [\"USA02P1\"], \"h.opt.previous\" : np.array(0)})\n",
    "df = frames[my_dates[0].strftime('%Y%m%d')]\n",
    "\n",
    "df = df.merge(previous_holdings, how = 'left', on = 'Barrid')\n",
    "df = clean_nas(df)\n",
    "df.loc[df['SpecRisk'] == 0]['SpecRisk'] = median(df['SpecRisk'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build Universe Based on Filters (TODO)\n",
    "\n",
    "In the cell below, implement the function `get_universe` that creates a stock universe by selecting only those companies that have a market capitalization of at least 1 billion dollars **OR** that are in the previous day's holdings, even if on the current day, the company no longer meets the 1 billion dollar criteria.\n",
    "\n",
    "When creating the universe, make sure you use the `.copy()` attribute to create a copy of the data. Also, it is very important to make sure that we are not looking at returns when forming the portfolio! to make this impossible, make sure to drop the column containing the daily return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_universe(df):\n",
    "    \"\"\"\n",
    "    Create a stock universe based on filters\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    df : DataFrame\n",
    "        All stocks\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    universe : DataFrame\n",
    "        Selected stocks based on filters\n",
    "    \"\"\"\n",
    "    \n",
    "    # TODO: Implement\n",
    "    universe = df.loc[(df['IssuerMarketCap'] >= 1e9) | (abs(df['h.opt.previous']) > 0)].copy()\n",
    "    universe = universe.drop(columns = 'DlyReturn')\n",
    "    \n",
    "    return universe\n",
    "\n",
    "universe = get_universe(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "date = str(int(universe['DataDate'][1])) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Factors\n",
    "\n",
    "We will now extract both the risk factors and alpha factors. We begin by first getting all the factors using the `factors_from_names` function defined previously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of factors: 81\n"
     ]
    }
   ],
   "source": [
    "all_factors = factors_from_names(list(universe))\n",
    "print('Number of factors:', len(all_factors))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now create the function `setdiff` to just select the factors that we have not defined as alpha factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def setdiff(temp1, temp2): \n",
    "    s = set(temp2)\n",
    "    temp3 = [x for x in temp1 if x not in s]\n",
    "    return temp3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of risk factors:  77\n"
     ]
    }
   ],
   "source": [
    "risk_factors = setdiff(all_factors, alpha_factors)\n",
    "print('Number of risk factors: ', len(risk_factors))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will also save the column that contains the previous holdings in a separate variable because we are going to use it later when we perform our portfolio optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of stocks in the portfolio:  2265\n"
     ]
    }
   ],
   "source": [
    "h0 = universe['h.opt.previous']\n",
    "print('Number of stocks in the portfolio: ', h0.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix of Risk Factor Exposures\n",
    "\n",
    "Our dataframe contains several columns that we'll use as risk factors exposures.  Extract these and put them into a matrix.\n",
    "\n",
    "The data, such as industry category, are already one-hot encoded, but if this were not the case, then using `patsy.dmatrices` would help, as this function extracts categories and performs the one-hot encoding.  We'll practice using this package, as you may find it useful with future data sets.  You could also store the factors in a dataframe if you prefer.\n",
    "\n",
    "#### How to use patsy.dmatrices\n",
    "\n",
    "`patsy.dmatrices` takes in a formula and the dataframe.  The formula tells the function which columns to take.  The formula will look something like this:  \n",
    "`SpecRisk ~ 0 + USFASTD_AERODEF + USFASTD_AIRLINES + ...`  \n",
    "where the variable to the left of the ~ is the \"dependent variable\" and the others to the right are the independent variables (as if we were preparing data to be fit to a model).\n",
    "\n",
    "This just means that the `pasty.dmatrices` function will return two matrix variables, one that contains the single column for the dependent variable `outcome`, and the independent variable columns are stored in a matrix `predictors`.\n",
    "\n",
    "The `predictors` matrix will contain the matrix of risk factors, which is what we want.  We don't actually need the `outcome` matrix; it's just created because that's the way patsy.dmatrices works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula = get_formula(risk_factors, \"SpecRisk\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_matrix(formula, data): \n",
    "    outcome, predictors = patsy.dmatrices(formula, data)\n",
    "\n",
    "    return predictors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2265, 77)\n"
     ]
    }
   ],
   "source": [
    "B = model_matrix(formula, universe)\n",
    "BT = B.transpose()\n",
    "print(B.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate Specific Variance\n",
    "\n",
    "Notice that the specific risk data is in percent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     9.014505\n",
       "1    11.726327\n",
       "Name: SpecRisk, dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "universe['SpecRisk'][0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, in order to get the specific variance for each stock in the universe we first need to multiply these values by `0.01`  and then square them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "specVar = (0.01 * universe['SpecRisk']) ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Factor covariance matrix (TODO)\n",
    "\n",
    "Note that we already have factor covariances from Barra data, which is stored in the variable `covariance`.  `covariance` is a dictionary, where the key is each day's date, and the value is a dataframe containing the factor covariances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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>Factor1</th>\n",
       "      <th>Factor2</th>\n",
       "      <th>VarCovar</th>\n",
       "      <th>DataDate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>USFASTD_1DREVRSL</td>\n",
       "      <td>USFASTD_1DREVRSL</td>\n",
       "      <td>1.958869</td>\n",
       "      <td>20040102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>USFASTD_1DREVRSL</td>\n",
       "      <td>USFASTD_BETA</td>\n",
       "      <td>1.602458</td>\n",
       "      <td>20040102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>USFASTD_1DREVRSL</td>\n",
       "      <td>USFASTD_DIVYILD</td>\n",
       "      <td>-0.012642</td>\n",
       "      <td>20040102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>USFASTD_1DREVRSL</td>\n",
       "      <td>USFASTD_DWNRISK</td>\n",
       "      <td>-0.064387</td>\n",
       "      <td>20040102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>USFASTD_1DREVRSL</td>\n",
       "      <td>USFASTD_EARNQLTY</td>\n",
       "      <td>0.046573</td>\n",
       "      <td>20040102</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Factor1           Factor2  VarCovar  DataDate\n",
       "0  USFASTD_1DREVRSL  USFASTD_1DREVRSL  1.958869  20040102\n",
       "1  USFASTD_1DREVRSL      USFASTD_BETA  1.602458  20040102\n",
       "2  USFASTD_1DREVRSL   USFASTD_DIVYILD -0.012642  20040102\n",
       "3  USFASTD_1DREVRSL   USFASTD_DWNRISK -0.064387  20040102\n",
       "4  USFASTD_1DREVRSL  USFASTD_EARNQLTY  0.046573  20040102"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covariance['20040102'].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the code below, implement the function `diagonal_factor_cov` to create the factor covariance matrix. Note that the covariances are given in percentage units squared.  Therefore you must re-scale them appropriately so that they're in decimals squared. Use the given `colnames` function to get the column names from `B`. \n",
    "\n",
    "When creating factor covariance matrix, you can store the factor variances and covariances, or just store the factor variances.  Try both, and see if you notice any differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def colnames(B):\n",
    "    if type(B) == patsy.design_info.DesignMatrix: \n",
    "        return B.design_info.column_names\n",
    "    if type(B) == pd.core.frame.DataFrame: \n",
    "        return B.columns.tolist()\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "## extract a diagonal element from the factor covariance matrix \n",
    "def get_cov(cv, factor1, factor2): \n",
    "    try:\n",
    "        return(cv.loc[(cv.Factor1==factor1) & (cv.Factor2==factor2),\"VarCovar\"].iloc[0])\n",
    "    except:\n",
    "        print(f\"didn't find covariance for: factor 1: {factor1} factor2: {factor2}\")\n",
    "        return 0\n",
    "\n",
    "def diagonal_factor_cov(date, B):\n",
    "    \"\"\"\n",
    "    Create the factor covariance matrix\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    date : string\n",
    "           date. For example 20040102\n",
    "        \n",
    "    B : patsy.design_info.DesignMatrix OR pandas.core.frame.DataFrame\n",
    "        Matrix of Risk Factors\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    Fm : Numpy ndarray\n",
    "        factor covariance matrix\n",
    "    \"\"\"\n",
    "    cv = covariance[date]\n",
    "    k = np.shape(B)[1]\n",
    "    Fm = np.zeros([k,k])\n",
    "    # Zero out covariance\n",
    "    for i in range(0, k):\n",
    "        fac = colnames(B)[i]\n",
    "        # Convert from percentage units squared to decimal\n",
    "        Fm[i,i] = (0.01 ** 2) * get_cov(cv, fac, fac)\n",
    "    return Fm\n",
    "\n",
    "Fvar = diagonal_factor_cov(date, B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transaction Costs\n",
    "\n",
    "To get the transaction cost, or slippage, we have to multiply the price change due to market impact by the amount of dollars traded:\n",
    "\n",
    "$$\n",
    "\\mbox{tcost_{i,t}} = \\% \\Delta \\mbox{price}_{i,t} \\times \\mbox{trade}_{i,t}\n",
    "$$\n",
    "\n",
    "In summation notation it looks like this:  \n",
    "$$\n",
    "\\mbox{tcost}_{i,t} = \\sum_i^{N} \\lambda_{i,t} (h_{i,t} - h_{i,t-1})^2\n",
    "$$  \n",
    "where\n",
    "$$\n",
    "\\lambda_{i,t} = \\frac{1}{10\\times \\mbox{ADV}_{i,t}}\n",
    "$$\n",
    "\n",
    "Note that since we're dividing by ADV, we'll want to handle cases when ADV is missing or zero.  In those instances, we can set ADV to a small positive number, such as 10,000, which, in practice assumes that the stock is illiquid. In the code below if there is no volume information we assume the asset is illiquid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_lambda(universe, composite_volume_column = 'ADTCA_30'):\n",
    "    universe.loc[np.isnan(universe[composite_volume_column]), composite_volume_column] = 1.0e4\n",
    "    universe.loc[universe[composite_volume_column] == 0, composite_volume_column] = 1.0e4 \n",
    "\n",
    "    adv = universe[composite_volume_column]\n",
    "    \n",
    "    return 0.1 / adv\n",
    "\n",
    "Lambda = get_lambda(universe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Alpha Combination (TODO)\n",
    "\n",
    "In the code below create a matrix of alpha factors and return it from the function `get_B_alpha`. Create this matrix in the same way you created the matrix of risk factors, i.e. using the `get_formula` and `model_matrix` functions we have defined above. Feel free to go back and look at the previous code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_B_alpha(alpha_factors, universe):\n",
    "    formula = get_formula(alpha_factors, \"SpecRisk\")\n",
    "    B_alpha = model_matrix(formula, universe)\n",
    "    return B_alpha\n",
    "\n",
    "B_alpha = get_B_alpha(alpha_factors, universe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have the matrix containing the alpha factors we will combine them by adding its rows. By doing this we will collapse the `B_alpha` matrix into a single alpha vector. We'll multiply by `1e-4` so that the expression of expected portfolio return, $\\alpha^T \\mathbf{h}$, is in dollar units. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_alpha_vec(B_alpha):\n",
    "    \"\"\"\n",
    "    Create an alpha vecrtor\n",
    "\n",
    "    Parameters\n",
    "    ----------        \n",
    "    B_alpha : patsy.design_info.DesignMatrix \n",
    "        Matrix of Alpha Factors\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    alpha_vec : patsy.design_info.DesignMatrix \n",
    "        alpha vecrtor\n",
    "    \"\"\"\n",
    "    \n",
    "    # TODO: Implement\n",
    "    alpha_vec = 1e-4 * np.sum(B_alpha, axis=1)\n",
    "    \n",
    "    return alpha_vec\n",
    "\n",
    "alpha_vec = get_alpha_vec(B_alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Optional Challenge\n",
    "\n",
    "You can also try to a more sophisticated method of alpha combination, by choosing the holding for each alpha based on the same metric of its performance, such as the factor returns, or sharpe ratio.  To make this more realistic, you can calculate a rolling average of the sharpe ratio, which is updated for each day.  Remember to only use data that occurs prior to the date of each optimization, and not data that occurs in the future.  Also, since factor returns and sharpe ratios may be negative, consider using a `max` function to give the holdings a lower bound of zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objective function (TODO)\n",
    "\n",
    "The objective function is given by:\n",
    "\n",
    "$$\n",
    "f(\\mathbf{h}) = \\frac{1}{2}\\kappa \\mathbf{h}_t^T\\mathbf{Q}^T\\mathbf{Q}\\mathbf{h}_t + \\frac{1}{2} \\kappa \\mathbf{h}_t^T \\mathbf{S} \\mathbf{h}_t - \\mathbf{\\alpha}^T \\mathbf{h}_t + (\\mathbf{h}_{t} - \\mathbf{h}_{t-1})^T \\mathbf{\\Lambda} (\\mathbf{h}_{t} - \\mathbf{h}_{t-1})\n",
    "$$\n",
    "\n",
    "Where the terms correspond to: factor risk + idiosyncratic risk - expected portfolio return + transaction costs, respectively. We should also note that $\\textbf{Q}^T\\textbf{Q}$ is defined to be the same as $\\textbf{BFB}^T$.  Review the lessons if you need a refresher of how we get $\\textbf{Q}$.\n",
    "\n",
    "Our objective is to minimize this objective function. To do this, we will use Scipy's optimization function:\n",
    "\n",
    "`scipy.optimize.fmin_l_bfgs_b(func, initial_guess, func_gradient)`\n",
    "\n",
    "where:\n",
    "\n",
    "* **func** : is the function we want to minimize\n",
    "\n",
    "* **initial_guess** : is out initial guess\n",
    "\n",
    "* **func_gradient** : is the gradient of the function we want to minimize\n",
    "\n",
    "So, in order to use the `scipy.optimize.fmin_l_bfgs_b` function we first need to define its parameters.\n",
    "\n",
    "In the code below implement the function `obj_func(h)` that corresponds to the objective function above that we want to minimize. We will set the risk aversion to be `1.0e-6`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "risk_aversion = 1.0e-6\n",
    "\n",
    "def get_obj_func(h0, risk_aversion, Q, specVar, alpha_vec, Lambda): \n",
    "    def obj_func(h):\n",
    "#         print(f'h: {h.shape}'\n",
    "#               f'h0: {h0.shape}'\n",
    "#               f'Q: {Q.shape}'\n",
    "#               f'risk_aversion: {risk_aversion}'\n",
    "#               f'specVar: {np.diag(specVar).shape}'\n",
    "#               f'alpha_vec: {alpha_vec.shape}'\n",
    "#               f'Lambda: {np.diag(Lambda).shape}')\n",
    "\n",
    "# h: (2265,)h0: (2265,)Q: (77, 2265)risk_aversion: 1e-06specVar: (2265, 2265)alpha_vec: (2265,)Lambda: (2265, 2265)\n",
    "        # TODO: Implement\n",
    "        factor_risk = 0.5 * risk_aversion * scipy.linalg.norm(Q @ h) ** 2\n",
    "        idiosyncratic_risk = 0.5 * risk_aversion * np.dot(h ** 2, specVar)\n",
    "        portfolio_return = np.dot(h, alpha_vec)\n",
    "        trans_cost = np.dot((h - h0) ** 2, Lambda)\n",
    "        \n",
    "        f = factor_risk + idiosyncratic_risk - portfolio_return + trans_cost\n",
    "        \n",
    "        return f\n",
    "    \n",
    "    return obj_func"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient (TODO)\n",
    "\n",
    "Now that we can generate the objective function using `get_obj_func`, we can now create a similar function with its gradient. The reason we're interested in calculating the gradient is so that we can tell the optimizer in which direction, and how much, it should shift the portfolio holdings in order to improve the objective function (minimize variance, minimize transaction cost, and maximize expected portfolio return).\n",
    "\n",
    "Before we implement the function we first need to know what the gradient looks like. The gradient, or derivative of the objective function, with respect to the portfolio holdings h, is given by:  \n",
    "\n",
    "$$\n",
    "f'(\\mathbf{h}) = \\frac{1}{2}\\kappa (2\\mathbf{Q}^T\\mathbf{Qh}) + \\frac{1}{2}\\kappa (2\\mathbf{Sh}) - \\mathbf{\\alpha} + 2(\\mathbf{h}_{t} - \\mathbf{h}_{t-1}) \\mathbf{\\Lambda}\n",
    "$$\n",
    "\n",
    "In the code below, implement the function `grad(h)` that corresponds to the function of the gradient given above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_grad_func(h0, risk_aversion, Q, QT, specVar, alpha_vec, Lambda):\n",
    "    def grad_func(h):\n",
    "        \n",
    "        # TODO: Implement\n",
    "        g = risk_aversion * (QT @ (Q @ h)) + risk_aversion * specVar * h - alpha_vec + 2 * (h - h0) * Lambda\n",
    "        \n",
    "        return np.asarray(g)\n",
    "    \n",
    "    return grad_func"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize (TODO)\n",
    "\n",
    "Now that we can generate the objective function using `get_obj_func`, and its corresponding gradient using `get_grad_func` we are ready to minimize the objective function using Scipy's optimization function. For this, we will use out initial holdings as our `initial_guess` parameter.\n",
    "\n",
    "In the cell below, implement the function `get_h_star` that optimizes the objective function. Use the objective function (`obj_func`) and gradient function (`grad_func`) provided within `get_h_star` to optimize the objective function using the `scipy.optimize.fmin_l_bfgs_b` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "risk_aversion = 1.0e-6\n",
    "\n",
    "Q = np.matmul(scipy.linalg.sqrtm(Fvar), BT)\n",
    "QT = Q.transpose()\n",
    "\n",
    "def get_h_star(risk_aversion, Q, QT, specVar, alpha_vec, h0, Lambda):\n",
    "    \"\"\"\n",
    "    Optimize the objective function\n",
    "\n",
    "    Parameters\n",
    "    ----------        \n",
    "    risk_aversion : int or float \n",
    "        Trader's risk aversion\n",
    "        \n",
    "    Q : patsy.design_info.DesignMatrix \n",
    "        Q Matrix\n",
    "        \n",
    "    QT : patsy.design_info.DesignMatrix \n",
    "        Transpose of the Q Matrix\n",
    "        \n",
    "    specVar: Pandas Series \n",
    "        Specific Variance\n",
    "        \n",
    "    alpha_vec: patsy.design_info.DesignMatrix \n",
    "        alpha vector\n",
    "        \n",
    "    h0 : Pandas Series  \n",
    "        initial holdings\n",
    "        \n",
    "    Lambda : Pandas Series  \n",
    "        Lambda\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    optimizer_result[0]: Numpy ndarray \n",
    "        optimized holdings\n",
    "    \"\"\"\n",
    "    obj_func = get_obj_func(h0, risk_aversion, Q, specVar, alpha_vec, Lambda)\n",
    "    grad_func = get_grad_func(h0, risk_aversion, Q, QT, specVar, alpha_vec, Lambda)\n",
    "    \n",
    "    # TODO: Implement \n",
    "    optimizer_result = scipy.optimize.fmin_l_bfgs_b(obj_func, h0, fprime=grad_func)\n",
    "    \n",
    "    return optimizer_result[0]\n",
    "\n",
    "h_star = get_h_star(risk_aversion, Q, QT, specVar, alpha_vec, h0, Lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we have optimized our objective function we can now use, `h_star` to create our optimal portfolio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt_portfolio = pd.DataFrame(data = {\"Barrid\" : universe['Barrid'], \"h.opt\" : h_star})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk Exposures (TODO)\n",
    "\n",
    "We can also use `h_star` to calculate our portfolio's risk and alpha exposures.\n",
    "\n",
    "In the cells below implement the functions `get_risk_exposures` and `get_portfolio_alpha_exposure` that calculate the portfolio's risk and alpha exposures, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_risk_exposures(B, BT, h_star):\n",
    "    \"\"\"\n",
    "    Calculate portfolio's Risk Exposure\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    B : patsy.design_info.DesignMatrix \n",
    "        Matrix of Risk Factors\n",
    "        \n",
    "    BT : patsy.design_info.DesignMatrix \n",
    "        Transpose of Matrix of Risk Factors\n",
    "        \n",
    "    h_star: Numpy ndarray \n",
    "        optimized holdings\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    risk_exposures : Pandas Series\n",
    "        Risk Exposures\n",
    "    \"\"\"\n",
    "    \n",
    "    # TODO: Implement\n",
    "    risk_exposures = pd.Series(BT @ h_star, index=colnames(B))\n",
    "    \n",
    "    return risk_exposures\n",
    "\n",
    "risk_exposures = get_risk_exposures(B, BT, h_star)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_portfolio_alpha_exposure(B_alpha, h_star):\n",
    "    \"\"\"\n",
    "    Calculate portfolio's Alpha Exposure\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    B_alpha : patsy.design_info.DesignMatrix \n",
    "        Matrix of Alpha Factors\n",
    "        \n",
    "    h_star: Numpy ndarray \n",
    "        optimized holdings\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    alpha_exposures : Pandas Series\n",
    "        Alpha Exposures\n",
    "    \"\"\"\n",
    "    \n",
    "    # TODO: Implement\n",
    "    \n",
    "    return pd.Series(B_alpha.T @ h_star, index = colnames(B_alpha))\n",
    "\n",
    "portfolio_alpha_exposure = get_portfolio_alpha_exposure(B_alpha, h_star)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transaction Costs (TODO)\n",
    "\n",
    "We can also use `h_star` to calculate our total transaction costs:\n",
    "$$\n",
    "\\mbox{tcost} = \\sum_i^{N} \\lambda_{i} (h_{i,t} - h_{i,t-1})^2\n",
    "$$\n",
    "\n",
    "In the cell below, implement the function `get_total_transaction_costs` that calculates the total transaction costs according to the equation above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_total_transaction_costs(h0, h_star, Lambda):\n",
    "    \"\"\"\n",
    "    Calculate Total Transaction Costs\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    h0 : Pandas Series\n",
    "        initial holdings (before optimization)\n",
    "        \n",
    "    h_star: Numpy ndarray \n",
    "        optimized holdings\n",
    "        \n",
    "    Lambda : Pandas Series  \n",
    "        Lambda\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    total_transaction_costs : float\n",
    "        Total Transaction Costs\n",
    "    \"\"\"\n",
    "    \n",
    "    # TODO: Implement\n",
    "    \n",
    "    return np.dot((h_star - h0) ** 2, Lambda)\n",
    "\n",
    "total_transaction_costs = get_total_transaction_costs(h0, h_star, Lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Putting It All Together\n",
    "\n",
    "We can now take all the above functions we created above and use them to create a single function, `form_optimal_portfolio` that returns the optimal portfolio, the risk and alpha exposures, and the total transactions costs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def form_optimal_portfolio(df, previous, risk_aversion):\n",
    "    df = df.merge(previous, how = 'left', on = 'Barrid')\n",
    "    df = clean_nas(df)\n",
    "    df.loc[df['SpecRisk'] == 0]['SpecRisk'] = median(df['SpecRisk'])\n",
    "  \n",
    "    universe = get_universe(df)\n",
    "    date = str(int(universe['DataDate'][1]))\n",
    "  \n",
    "    all_factors = factors_from_names(list(universe))\n",
    "    risk_factors = setdiff(all_factors, alpha_factors)\n",
    "  \n",
    "    h0 = universe['h.opt.previous']\n",
    "  \n",
    "    B = model_matrix(get_formula(risk_factors, \"SpecRisk\"), universe)\n",
    "    BT = B.transpose()\n",
    "  \n",
    "    specVar = (0.01 * universe['SpecRisk']) ** 2\n",
    "    Fvar = diagonal_factor_cov(date, B)\n",
    "    \n",
    "    Lambda = get_lambda(universe)\n",
    "    B_alpha = get_B_alpha(alpha_factors, universe)\n",
    "    alpha_vec = get_alpha_vec(B_alpha)\n",
    "  \n",
    "    Q = np.matmul(scipy.linalg.sqrtm(Fvar), BT)\n",
    "    QT = Q.transpose()\n",
    "    \n",
    "    h_star = get_h_star(risk_aversion, Q, QT, specVar, alpha_vec, h0, Lambda)\n",
    "    opt_portfolio = pd.DataFrame(data = {\"Barrid\" : universe['Barrid'], \"h.opt\" : h_star})\n",
    "    \n",
    "    risk_exposures = get_risk_exposures(B, BT, h_star)\n",
    "    portfolio_alpha_exposure = get_portfolio_alpha_exposure(B_alpha, h_star)\n",
    "    total_transaction_costs = get_total_transaction_costs(h0, h_star, Lambda)\n",
    "  \n",
    "    return {\n",
    "        \"opt.portfolio\" : opt_portfolio, \n",
    "        \"risk.exposures\" : risk_exposures, \n",
    "        \"alpha.exposures\" : portfolio_alpha_exposure,\n",
    "        \"total.cost\" : total_transaction_costs}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build tradelist\n",
    "\n",
    "The trade list is the most recent optimal asset holdings minus the previous day's optimal holdings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_tradelist(prev_holdings, opt_result):\n",
    "    tmp = prev_holdings.merge(opt_result['opt.portfolio'], how='outer', on = 'Barrid')\n",
    "    tmp['h.opt.previous'] = np.nan_to_num(tmp['h.opt.previous'])\n",
    "    tmp['h.opt'] = np.nan_to_num(tmp['h.opt'])\n",
    "    return tmp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save optimal holdings as previous optimal holdings.\n",
    "\n",
    "As we walk through each day, we'll re-use the column for previous holdings by storing the \"current\" optimal holdings as the \"previous\" optimal holdings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_to_previous(result): \n",
    "    prev = result['opt.portfolio']\n",
    "    prev = prev.rename(index=str, columns={\"h.opt\": \"h.opt.previous\"}, copy=True, inplace=False)\n",
    "    return prev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the backtest\n",
    "\n",
    "Walk through each day, calculating the optimal portfolio holdings and trade list.  This may take some time, but should finish sooner if you've chosen all the optimizations you learned in the lessons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Optimizing Portfolio: 100%|██████████| 252/252 [21:29<00:00,  5.12s/day]\n"
     ]
    }
   ],
   "source": [
    "trades = {}\n",
    "port = {}\n",
    "\n",
    "for dt in tqdm(my_dates, desc='Optimizing Portfolio', unit='day'):\n",
    "    date = dt.strftime('%Y%m%d')\n",
    "\n",
    "    result = form_optimal_portfolio(frames[date], previous_holdings, risk_aversion)\n",
    "    trades[date] = build_tradelist(previous_holdings, result)\n",
    "    port[date] = result\n",
    "    previous_holdings = convert_to_previous(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Profit-and-Loss (PnL) attribution (TODO)\n",
    "\n",
    "Profit and Loss is the aggregate realized daily returns of the assets, weighted by the optimal portfolio holdings chosen, and summed up to get the portfolio's profit and loss.\n",
    "\n",
    "The PnL attributed to the alpha factors equals the factor returns times factor exposures for the alpha factors.  \n",
    "\n",
    "$$\n",
    "\\mbox{PnL}_{alpha}= f \\times b_{alpha}\n",
    "$$\n",
    "\n",
    "Similarly, the PnL attributed to the risk factors equals the factor returns times factor exposures of the risk factors.\n",
    "\n",
    "$$\n",
    "\\mbox{PnL}_{risk} = f \\times b_{risk}\n",
    "$$\n",
    "\n",
    "In the code below, in the function `build_pnl_attribution` calculate the PnL attributed to the alpha factors, the PnL attributed to the risk factors, and attribution to cost. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "## assumes v, w are pandas Series \n",
    "def partial_dot_product(v, w):\n",
    "    common = v.index.intersection(w.index)\n",
    "    return np.sum(v[common] * w[common])\n",
    "\n",
    "def build_pnl_attribution(): \n",
    "\n",
    "    df = pd.DataFrame(index = my_dates)\n",
    "    \n",
    "    for dt in my_dates:\n",
    "        date = dt.strftime('%Y%m%d')\n",
    "\n",
    "        p = port[date]\n",
    "        fr = facret[date]\n",
    "\n",
    "        mf = p['opt.portfolio'].merge(frames[date], how = 'left', on = \"Barrid\")\n",
    "        \n",
    "        mf['DlyReturn'] = wins(mf['DlyReturn'], -0.5, 0.5)\n",
    "        df.at[dt,\"daily.pnl\"] = np.sum(mf['h.opt'] * mf['DlyReturn'])\n",
    "        \n",
    "        # TODO: Implement\n",
    "    \n",
    "        df.at[dt,\"attribution.alpha.pnl\"] = partial_dot_product(fr,p['alpha.exposures'])\n",
    "        df.at[dt,\"attribution.risk.pnl\"] = partial_dot_product(fr,p['risk.exposures'])\n",
    "        df.at[dt,\"attribution.cost\"] = p['total.cost']\n",
    "        \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f913e9d4438>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "attr = build_pnl_attribution()\n",
    "\n",
    "for column in attr.columns:\n",
    "        plt.plot(attr[column].cumsum(), label=column)\n",
    "plt.legend(loc='upper left')\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('PnL Attribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build portfolio characteristics (TODO)\n",
    "Calculate the sum of long positions, short positions, net positions, gross market value, and amount of dollars traded.\n",
    "\n",
    "In the code below, in the function `build_portfolio_characteristics` calculate the sum of long positions, short positions, net positions, gross market value, and amount of dollars traded.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_portfolio_characteristics(): \n",
    "    df = pd.DataFrame(index = my_dates)\n",
    "    \n",
    "    for dt in my_dates:\n",
    "        date = dt.strftime('%Y%m%d')\n",
    "  \n",
    "        p = port[date]\n",
    "        tradelist = trades[date]\n",
    "        h = p['opt.portfolio']['h.opt']\n",
    "        \n",
    "        # TODO: Implement\n",
    "        \n",
    "        long = np.sum(h[h>0])\n",
    "        short = np.sum(h[h<0])\n",
    "        df.at[dt,\"long\"] = long\n",
    "        df.at[dt,\"short\"] = short\n",
    "        df.at[dt,\"net\"] = long + short\n",
    "        df.at[dt,\"gmv\"] = np.abs(long) + np.abs(short)\n",
    "        df.at[dt,\"traded\"] = np.sum(np.abs(tradelist['h.opt'] - tradelist['h.opt.previous']))\n",
    "        \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f90fd278b38>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pchar = build_portfolio_characteristics()\n",
    "\n",
    "for column in pchar.columns:\n",
    "        plt.plot(pchar[column], label=column)\n",
    "plt.legend(loc='upper left')\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Portfolio')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Optional\n",
    "Choose additional metrics to evaluate your portfolio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Submission\n",
    "Now that you're done with the project, it's time to submit it. Click the submit button in the bottom right. One of our reviewers will give you feedback on your project with a pass or not passed grade."
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}