20_predictability.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross-sectional Predictability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from scipy import stats\n",
    "import plotly.graph_objects as go\n",
    "pd.options.display.float_format = '{:,.4f}'.format"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pull data from dropbox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>ticker</th>\n",
       "      <th>date</th>\n",
       "      <th>ret</th>\n",
       "      <th>beta</th>\n",
       "      <th>mve</th>\n",
       "      <th>bm</th>\n",
       "      <th>mom12m</th>\n",
       "      <th>illiq</th>\n",
       "      <th>idiovol</th>\n",
       "      <th>mdate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>GFGC</td>\n",
       "      <td>19880229</td>\n",
       "      <td>0.0800</td>\n",
       "      <td>0.0519</td>\n",
       "      <td>8.7323</td>\n",
       "      <td>0.9222</td>\n",
       "      <td>-0.0680</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0337</td>\n",
       "      <td>1988-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>GFGC</td>\n",
       "      <td>19880331</td>\n",
       "      <td>-0.0763</td>\n",
       "      <td>0.0508</td>\n",
       "      <td>8.8093</td>\n",
       "      <td>0.9222</td>\n",
       "      <td>0.0708</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0339</td>\n",
       "      <td>1988-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>GFGC</td>\n",
       "      <td>19880429</td>\n",
       "      <td>0.0306</td>\n",
       "      <td>0.0470</td>\n",
       "      <td>8.7121</td>\n",
       "      <td>0.9222</td>\n",
       "      <td>0.1154</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0336</td>\n",
       "      <td>1988-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>GFGC</td>\n",
       "      <td>19880531</td>\n",
       "      <td>0.0198</td>\n",
       "      <td>0.0363</td>\n",
       "      <td>8.7423</td>\n",
       "      <td>0.9222</td>\n",
       "      <td>0.0724</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0332</td>\n",
       "      <td>1988-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>GFGC</td>\n",
       "      <td>19880630</td>\n",
       "      <td>-0.0120</td>\n",
       "      <td>0.0243</td>\n",
       "      <td>8.7619</td>\n",
       "      <td>0.9222</td>\n",
       "      <td>0.1902</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0334</td>\n",
       "      <td>1988-06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  ticker      date     ret   beta    mve     bm  mom12m  illiq  idiovol  \\\n",
       "0   GFGC  19880229  0.0800 0.0519 8.7323 0.9222 -0.0680 0.0000   0.0337   \n",
       "1   GFGC  19880331 -0.0763 0.0508 8.8093 0.9222  0.0708 0.0000   0.0339   \n",
       "2   GFGC  19880429  0.0306 0.0470 8.7121 0.9222  0.1154 0.0000   0.0336   \n",
       "3   GFGC  19880531  0.0198 0.0363 8.7423 0.9222  0.0724 0.0000   0.0332   \n",
       "4   GFGC  19880630 -0.0120 0.0243 8.7619 0.9222  0.1902 0.0000   0.0334   \n",
       "\n",
       "     mdate  \n",
       "0  1988-02  \n",
       "1  1988-03  \n",
       "2  1988-04  \n",
       "3  1988-05  \n",
       "4  1988-06  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('https://www.dropbox.com/s/w2vb22u6kh7ysvn/stocks.csv?dl=1')\n",
    "df['mdate']=pd.to_datetime(df.date,format='%Y%m%d').dt.to_period('M')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of obs:\t  2,045,339\n",
      "First month:\t\t 1980-01\n",
      "Last month:\t\t 2022-12\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "count   2,045,339.0000\n",
       "mean            0.0116\n",
       "std             0.1894\n",
       "min            -1.8708\n",
       "25%            -0.0665\n",
       "50%             0.0000\n",
       "75%             0.0722\n",
       "max            24.0000\n",
       "Name: ret, dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(f'Total number of obs:\\t {len(df): ,.0f}')\n",
    "print(f'First month:\\t\\t {df.mdate.min()}')\n",
    "print(f'Last month:\\t\\t {df.mdate.max()}')\n",
    "df.ret.describe().round(4)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remove outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count   2,007,750.0000\n",
       "mean            0.0069\n",
       "std             0.1533\n",
       "min            -0.9354\n",
       "25%            -0.0657\n",
       "50%             0.0000\n",
       "75%             0.0712\n",
       "max             0.9584\n",
       "Name: ret, dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols_to_trim_on = ['ret', 'beta', 'mve', 'bm', 'mom12m', 'illiq','idiovol']\n",
    "df = df[(np.abs(stats.zscore(df[cols_to_trim_on])) < 5).all(axis=1)]\n",
    "df.ret.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-sectional Method #1: Sorting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sorting function\n",
    "def cut_quintiles(x):\n",
    "    try:\n",
    "        out = pd.qcut(x, 5, labels=[\"Lo 20\", \"Qnt 2\", \"Qnt 3\", \"Qnt 4\", \"Hi 20\"])\n",
    "    except:\n",
    "        out = pd.Series(np.nan, index=x.index)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Characteristic to sort on\n",
    "# CHAR = 'beta'\n",
    "# CHAR = 'mve'\n",
    "CHAR = 'bm'\n",
    "\n",
    "df[\"quintile\"] = df.groupby(\"mdate\")[CHAR].apply(cut_quintiles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lo 20    401756\n",
       "Hi 20    401654\n",
       "Qnt 2    401448\n",
       "Qnt 4    401448\n",
       "Qnt 3    401444\n",
       "Name: quintile, dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check to see we have about the same number of observations in each bin\n",
    "df.quintile.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mdate    quintile\n",
       "1980-01  Lo 20       0.0789\n",
       "         Qnt 2       0.0751\n",
       "         Qnt 3       0.0791\n",
       "         Qnt 4       0.0785\n",
       "         Hi 20       0.1267\n",
       "1980-02  Lo 20      -0.0157\n",
       "         Qnt 2      -0.0254\n",
       "         Qnt 3      -0.0363\n",
       "         Qnt 4      -0.0332\n",
       "         Hi 20      -0.0254\n",
       "Name: ret, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Time-series of EW average portfolio across stocks\n",
    "df = df.dropna(subset=[\"quintile\"])\n",
    "rets = df.groupby([\"mdate\", \"quintile\"]).ret.mean()\n",
    "rets.head(10).round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>quintile</th>\n",
       "      <th>Lo 20</th>\n",
       "      <th>Qnt 2</th>\n",
       "      <th>Qnt 3</th>\n",
       "      <th>Qnt 4</th>\n",
       "      <th>Hi 20</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mdate</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1980-01</th>\n",
       "      <td>0.0789</td>\n",
       "      <td>0.0751</td>\n",
       "      <td>0.0791</td>\n",
       "      <td>0.0785</td>\n",
       "      <td>0.1267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-02</th>\n",
       "      <td>-0.0157</td>\n",
       "      <td>-0.0254</td>\n",
       "      <td>-0.0363</td>\n",
       "      <td>-0.0332</td>\n",
       "      <td>-0.0254</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "quintile   Lo 20   Qnt 2   Qnt 3   Qnt 4   Hi 20\n",
       "mdate                                           \n",
       "1980-01   0.0789  0.0751  0.0791  0.0785  0.1267\n",
       "1980-02  -0.0157 -0.0254 -0.0363 -0.0332 -0.0254"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rets = rets.unstack()\n",
    "rets.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sorting on bm:\n",
      "Average monthly returns:\n",
      "quintile\n",
      "Lo 20   0.0012\n",
      "Qnt 2   0.0070\n",
      "Qnt 3   0.0094\n",
      "Qnt 4   0.0099\n",
      "Hi 20   0.0101\n",
      "dtype: float64\n",
      "\n",
      "Hi-Lo  average return is:  0.89% per month\n"
     ]
    }
   ],
   "source": [
    "# Time-series average of each portfolio\n",
    "mns = rets.mean()\n",
    "print(f'Sorting on {CHAR}:\\nAverage monthly returns:\\n{mns.round(4)}')\n",
    "\n",
    "hilo = mns['Hi 20']-mns['Lo 20']\n",
    "print(f'\\nHi-Lo  average return is: {hilo: .2%} per month')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-sectional Method #2: Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example #1: Single characteristic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>bm</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mdate</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1980-01</th>\n",
       "      <td>0.0571</td>\n",
       "      <td>0.0248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-02</th>\n",
       "      <td>-0.0227</td>\n",
       "      <td>-0.0036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-03</th>\n",
       "      <td>-0.1464</td>\n",
       "      <td>-0.0054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-04</th>\n",
       "      <td>0.0714</td>\n",
       "      <td>-0.0120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1980-05</th>\n",
       "      <td>0.0779</td>\n",
       "      <td>-0.0030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-08</th>\n",
       "      <td>-0.0130</td>\n",
       "      <td>0.0045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-09</th>\n",
       "      <td>-0.1143</td>\n",
       "      <td>-0.0040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-10</th>\n",
       "      <td>0.0681</td>\n",
       "      <td>0.0115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-11</th>\n",
       "      <td>0.0237</td>\n",
       "      <td>-0.0144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12</th>\n",
       "      <td>-0.0653</td>\n",
       "      <td>0.0033</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>516 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          const      bm\n",
       "mdate                  \n",
       "1980-01  0.0571  0.0248\n",
       "1980-02 -0.0227 -0.0036\n",
       "1980-03 -0.1464 -0.0054\n",
       "1980-04  0.0714 -0.0120\n",
       "1980-05  0.0779 -0.0030\n",
       "...         ...     ...\n",
       "2022-08 -0.0130  0.0045\n",
       "2022-09 -0.1143 -0.0040\n",
       "2022-10  0.0681  0.0115\n",
       "2022-11  0.0237 -0.0144\n",
       "2022-12 -0.0653  0.0033\n",
       "\n",
       "[516 rows x 2 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Run a cross-sectional regression for each date\n",
    "coefs = df.groupby('mdate').apply(lambda d: sm.OLS(d.ret,sm.add_constant(d[CHAR])).fit().params) \n",
    "coefs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "coefs.mean()\n",
    "T = len(coefs[CHAR])\n",
    "tsreg = sm.OLS(coefs[CHAR],np.ones(T)).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     bm   R-squared:                       0.000\n",
      "Model:                            OLS   Adj. R-squared:                  0.000\n",
      "Method:                 Least Squares   F-statistic:                       nan\n",
      "Date:                Thu, 23 Mar 2023   Prob (F-statistic):                nan\n",
      "Time:                        17:05:08   Log-Likelihood:                 1321.0\n",
      "No. Observations:                 516   AIC:                            -2640.\n",
      "Df Residuals:                     515   BIC:                            -2636.\n",
      "Df Model:                           0                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0040      0.001      4.798      0.000       0.002       0.006\n",
      "==============================================================================\n",
      "Omnibus:                        8.398   Durbin-Watson:                   1.627\n",
      "Prob(Omnibus):                  0.015   Jarque-Bera (JB):               13.305\n",
      "Skew:                          -0.018   Prob(JB):                      0.00129\n",
      "Kurtosis:                       3.786   Cond. No.                         1.00\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(tsreg.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
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       },
       "data": [
        {
         "mode": "lines",
         "name": "Monthly Coefficient",
         "type": "scatter",
         "x": [
          "1980-01-01T00:00:00",
          "1980-02-01T00:00:00",
          "1980-03-01T00:00:00",
          "1980-04-01T00:00:00",
          "1980-05-01T00:00:00",
          "1980-06-01T00:00:00",
          "1980-07-01T00:00:00",
          "1980-08-01T00:00:00",
          "1980-09-01T00:00:00",
          "1980-10-01T00:00:00",
          "1980-11-01T00:00:00",
          "1980-12-01T00:00:00",
          "1981-01-01T00:00:00",
          "1981-02-01T00:00:00",
          "1981-03-01T00:00:00",
          "1981-04-01T00:00:00",
          "1981-05-01T00:00:00",
          "1981-06-01T00:00:00",
          "1981-07-01T00:00:00",
          "1981-08-01T00:00:00",
          "1981-09-01T00:00:00",
          "1981-10-01T00:00:00",
          "1981-11-01T00:00:00",
          "1981-12-01T00:00:00",
          "1982-01-01T00:00:00",
          "1982-02-01T00:00:00",
          "1982-03-01T00:00:00",
          "1982-04-01T00:00:00",
          "1982-05-01T00:00:00",
          "1982-06-01T00:00:00",
          "1982-07-01T00:00:00",
          "1982-08-01T00:00:00",
          "1982-09-01T00:00:00",
          "1982-10-01T00:00:00",
          "1982-11-01T00:00:00",
          "1982-12-01T00:00:00",
          "1983-01-01T00:00:00",
          "1983-02-01T00:00:00",
          "1983-03-01T00:00:00",
          "1983-04-01T00:00:00",
          "1983-05-01T00:00:00",
          "1983-06-01T00:00:00",
          "1983-07-01T00:00:00",
          "1983-08-01T00:00:00",
          "1983-09-01T00:00:00",
          "1983-10-01T00:00:00",
          "1983-11-01T00:00:00",
          "1983-12-01T00:00:00",
          "1984-01-01T00:00:00",
          "1984-02-01T00:00:00",
          "1984-03-01T00:00:00",
          "1984-04-01T00:00:00",
          "1984-05-01T00:00:00",
          "1984-06-01T00:00:00",
          "1984-07-01T00:00:00",
          "1984-08-01T00:00:00",
          "1984-09-01T00:00:00",
          "1984-10-01T00:00:00",
          "1984-11-01T00:00:00",
          "1984-12-01T00:00:00",
          "1985-01-01T00:00:00",
          "1985-02-01T00:00:00",
          "1985-03-01T00:00:00",
          "1985-04-01T00:00:00",
          "1985-05-01T00:00:00",
          "1985-06-01T00:00:00",
          "1985-07-01T00:00:00",
          "1985-08-01T00:00:00",
          "1985-09-01T00:00:00",
          "1985-10-01T00:00:00",
          "1985-11-01T00:00:00",
          "1985-12-01T00:00:00",
          "1986-01-01T00:00:00",
          "1986-02-01T00:00:00",
          "1986-03-01T00:00:00",
          "1986-04-01T00:00:00",
          "1986-05-01T00:00:00",
          "1986-06-01T00:00:00",
          "1986-07-01T00:00:00",
          "1986-08-01T00:00:00",
          "1986-09-01T00:00:00",
          "1986-10-01T00:00:00",
          "1986-11-01T00:00:00",
          "1986-12-01T00:00:00",
          "1987-01-01T00:00:00",
          "1987-02-01T00:00:00",
          "1987-03-01T00:00:00",
          "1987-04-01T00:00:00",
          "1987-05-01T00:00:00",
          "1987-06-01T00:00:00",
          "1987-07-01T00:00:00",
          "1987-08-01T00:00:00",
          "1987-09-01T00:00:00",
          "1987-10-01T00:00:00",
          "1987-11-01T00:00:00",
          "1987-12-01T00:00:00",
          "1988-01-01T00:00:00",
          "1988-02-01T00:00:00",
          "1988-03-01T00:00:00",
          "1988-04-01T00:00:00",
          "1988-05-01T00:00:00",
          "1988-06-01T00:00:00",
          "1988-07-01T00:00:00",
          "1988-08-01T00:00:00",
          "1988-09-01T00:00:00",
          "1988-10-01T00:00:00",
          "1988-11-01T00:00:00",
          "1988-12-01T00:00:00",
          "1989-01-01T00:00:00",
          "1989-02-01T00:00:00",
          "1989-03-01T00:00:00",
          "1989-04-01T00:00:00",
          "1989-05-01T00:00:00",
          "1989-06-01T00:00:00",
          "1989-07-01T00:00:00",
          "1989-08-01T00:00:00",
          "1989-09-01T00:00:00",
          "1989-10-01T00:00:00",
          "1989-11-01T00:00:00",
          "1989-12-01T00:00:00",
          "1990-01-01T00:00:00",
          "1990-02-01T00:00:00",
          "1990-03-01T00:00:00",
          "1990-04-01T00:00:00",
          "1990-05-01T00:00:00",
          "1990-06-01T00:00:00",
          "1990-07-01T00:00:00",
          "1990-08-01T00:00:00",
          "1990-09-01T00:00:00",
          "1990-10-01T00:00:00",
          "1990-11-01T00:00:00",
          "1990-12-01T00:00:00",
          "1991-01-01T00:00:00",
          "1991-02-01T00:00:00",
          "1991-03-01T00:00:00",
          "1991-04-01T00:00:00",
          "1991-05-01T00:00:00",
          "1991-06-01T00:00:00",
          "1991-07-01T00:00:00",
          "1991-08-01T00:00:00",
          "1991-09-01T00:00:00",
          "1991-10-01T00:00:00",
          "1991-11-01T00:00:00",
          "1991-12-01T00:00:00",
          "1992-01-01T00:00:00",
          "1992-02-01T00:00:00",
          "1992-03-01T00:00:00",
          "1992-04-01T00:00:00",
          "1992-05-01T00:00:00",
          "1992-06-01T00:00:00",
          "1992-07-01T00:00:00",
          "1992-08-01T00:00:00",
          "1992-09-01T00:00:00",
          "1992-10-01T00:00:00",
          "1992-11-01T00:00:00",
          "1992-12-01T00:00:00",
          "1993-01-01T00:00:00",
          "1993-02-01T00:00:00",
          "1993-03-01T00:00:00",
          "1993-04-01T00:00:00",
          "1993-05-01T00:00:00",
          "1993-06-01T00:00:00",
          "1993-07-01T00:00:00",
          "1993-08-01T00:00:00",
          "1993-09-01T00:00:00",
          "1993-10-01T00:00:00",
          "1993-11-01T00:00:00",
          "1993-12-01T00:00:00",
          "1994-01-01T00:00:00",
          "1994-02-01T00:00:00",
          "1994-03-01T00:00:00",
          "1994-04-01T00:00:00",
          "1994-05-01T00:00:00",
          "1994-06-01T00:00:00",
          "1994-07-01T00:00:00",
          "1994-08-01T00:00:00",
          "1994-09-01T00:00:00",
          "1994-10-01T00:00:00",
          "1994-11-01T00:00:00",
          "1994-12-01T00:00:00",
          "1995-01-01T00:00:00",
          "1995-02-01T00:00:00",
          "1995-03-01T00:00:00",
          "1995-04-01T00:00:00",
          "1995-05-01T00:00:00",
          "1995-06-01T00:00:00",
          "1995-07-01T00:00:00",
          "1995-08-01T00:00:00",
          "1995-09-01T00:00:00",
          "1995-10-01T00:00:00",
          "1995-11-01T00:00:00",
          "1995-12-01T00:00:00",
          "1996-01-01T00:00:00",
          "1996-02-01T00:00:00",
          "1996-03-01T00:00:00",
          "1996-04-01T00:00:00",
          "1996-05-01T00:00:00",
          "1996-06-01T00:00:00",
          "1996-07-01T00:00:00",
          "1996-08-01T00:00:00",
          "1996-09-01T00:00:00",
          "1996-10-01T00:00:00",
          "1996-11-01T00:00:00",
          "1996-12-01T00:00:00",
          "1997-01-01T00:00:00",
          "1997-02-01T00:00:00",
          "1997-03-01T00:00:00",
          "1997-04-01T00:00:00",
          "1997-05-01T00:00:00",
          "1997-06-01T00:00:00",
          "1997-07-01T00:00:00",
          "1997-08-01T00:00:00",
          "1997-09-01T00:00:00",
          "1997-10-01T00:00:00",
          "1997-11-01T00:00:00",
          "1997-12-01T00:00:00",
          "1998-01-01T00:00:00",
          "1998-02-01T00:00:00",
          "1998-03-01T00:00:00",
          "1998-04-01T00:00:00",
          "1998-05-01T00:00:00",
          "1998-06-01T00:00:00",
          "1998-07-01T00:00:00",
          "1998-08-01T00:00:00",
          "1998-09-01T00:00:00",
          "1998-10-01T00:00:00",
          "1998-11-01T00:00:00",
          "1998-12-01T00:00:00",
          "1999-01-01T00:00:00",
          "1999-02-01T00:00:00",
          "1999-03-01T00:00:00",
          "1999-04-01T00:00:00",
          "1999-05-01T00:00:00",
          "1999-06-01T00:00:00",
          "1999-07-01T00:00:00",
          "1999-08-01T00:00:00",
          "1999-09-01T00:00:00",
          "1999-10-01T00:00:00",
          "1999-11-01T00:00:00",
          "1999-12-01T00:00:00",
          "2000-01-01T00:00:00",
          "2000-02-01T00:00:00",
          "2000-03-01T00:00:00",
          "2000-04-01T00:00:00",
          "2000-05-01T00:00:00",
          "2000-06-01T00:00:00",
          "2000-07-01T00:00:00",
          "2000-08-01T00:00:00",
          "2000-09-01T00:00:00",
          "2000-10-01T00:00:00",
          "2000-11-01T00:00:00",
          "2000-12-01T00:00:00",
          "2001-01-01T00:00:00",
          "2001-02-01T00:00:00",
          "2001-03-01T00:00:00",
          "2001-04-01T00:00:00",
          "2001-05-01T00:00:00",
          "2001-06-01T00:00:00",
          "2001-07-01T00:00:00",
          "2001-08-01T00:00:00",
          "2001-09-01T00:00:00",
          "2001-10-01T00:00:00",
          "2001-11-01T00:00:00",
          "2001-12-01T00:00:00",
          "2002-01-01T00:00:00",
          "2002-02-01T00:00:00",
          "2002-03-01T00:00:00",
          "2002-04-01T00:00:00",
          "2002-05-01T00:00:00",
          "2002-06-01T00:00:00",
          "2002-07-01T00:00:00",
          "2002-08-01T00:00:00",
          "2002-09-01T00:00:00",
          "2002-10-01T00:00:00",
          "2002-11-01T00:00:00",
          "2002-12-01T00:00:00",
          "2003-01-01T00:00:00",
          "2003-02-01T00:00:00",
          "2003-03-01T00:00:00",
          "2003-04-01T00:00:00",
          "2003-05-01T00:00:00",
          "2003-06-01T00:00:00",
          "2003-07-01T00:00:00",
          "2003-08-01T00:00:00",
          "2003-09-01T00:00:00",
          "2003-10-01T00:00:00",
          "2003-11-01T00:00:00",
          "2003-12-01T00:00:00",
          "2004-01-01T00:00:00",
          "2004-02-01T00:00:00",
          "2004-03-01T00:00:00",
          "2004-04-01T00:00:00",
          "2004-05-01T00:00:00",
          "2004-06-01T00:00:00",
          "2004-07-01T00:00:00",
          "2004-08-01T00:00:00",
          "2004-09-01T00:00:00",
          "2004-10-01T00:00:00",
          "2004-11-01T00:00:00",
          "2004-12-01T00:00:00",
          "2005-01-01T00:00:00",
          "2005-02-01T00:00:00",
          "2005-03-01T00:00:00",
          "2005-04-01T00:00:00",
          "2005-05-01T00:00:00",
          "2005-06-01T00:00:00",
          "2005-07-01T00:00:00",
          "2005-08-01T00:00:00",
          "2005-09-01T00:00:00",
          "2005-10-01T00:00:00",
          "2005-11-01T00:00:00",
          "2005-12-01T00:00:00",
          "2006-01-01T00:00:00",
          "2006-02-01T00:00:00",
          "2006-03-01T00:00:00",
          "2006-04-01T00:00:00",
          "2006-05-01T00:00:00",
          "2006-06-01T00:00:00",
          "2006-07-01T00:00:00",
          "2006-08-01T00:00:00",
          "2006-09-01T00:00:00",
          "2006-10-01T00:00:00",
          "2006-11-01T00:00:00",
          "2006-12-01T00:00:00",
          "2007-01-01T00:00:00",
          "2007-02-01T00:00:00",
          "2007-03-01T00:00:00",
          "2007-04-01T00:00:00",
          "2007-05-01T00:00:00",
          "2007-06-01T00:00:00",
          "2007-07-01T00:00:00",
          "2007-08-01T00:00:00",
          "2007-09-01T00:00:00",
          "2007-10-01T00:00:00",
          "2007-11-01T00:00:00",
          "2007-12-01T00:00:00",
          "2008-01-01T00:00:00",
          "2008-02-01T00:00:00",
          "2008-03-01T00:00:00",
          "2008-04-01T00:00:00",
          "2008-05-01T00:00:00",
          "2008-06-01T00:00:00",
          "2008-07-01T00:00:00",
          "2008-08-01T00:00:00",
          "2008-09-01T00:00:00",
          "2008-10-01T00:00:00",
          "2008-11-01T00:00:00",
          "2008-12-01T00:00:00",
          "2009-01-01T00:00:00",
          "2009-02-01T00:00:00",
          "2009-03-01T00:00:00",
          "2009-04-01T00:00:00",
          "2009-05-01T00:00:00",
          "2009-06-01T00:00:00",
          "2009-07-01T00:00:00",
          "2009-08-01T00:00:00",
          "2009-09-01T00:00:00",
          "2009-10-01T00:00:00",
          "2009-11-01T00:00:00",
          "2009-12-01T00:00:00",
          "2010-01-01T00:00:00",
          "2010-02-01T00:00:00",
          "2010-03-01T00:00:00",
          "2010-04-01T00:00:00",
          "2010-05-01T00:00:00",
          "2010-06-01T00:00:00",
          "2010-07-01T00:00:00",
          "2010-08-01T00:00:00",
          "2010-09-01T00:00:00",
          "2010-10-01T00:00:00",
          "2010-11-01T00:00:00",
          "2010-12-01T00:00:00",
          "2011-01-01T00:00:00",
          "2011-02-01T00:00:00",
          "2011-03-01T00:00:00",
          "2011-04-01T00:00:00",
          "2011-05-01T00:00:00",
          "2011-06-01T00:00:00",
          "2011-07-01T00:00:00",
          "2011-08-01T00:00:00",
          "2011-09-01T00:00:00",
          "2011-10-01T00:00:00",
          "2011-11-01T00:00:00",
          "2011-12-01T00:00:00",
          "2012-01-01T00:00:00",
          "2012-02-01T00:00:00",
          "2012-03-01T00:00:00",
          "2012-04-01T00:00:00",
          "2012-05-01T00:00:00",
          "2012-06-01T00:00:00",
          "2012-07-01T00:00:00",
          "2012-08-01T00:00:00",
          "2012-09-01T00:00:00",
          "2012-10-01T00:00:00",
          "2012-11-01T00:00:00",
          "2012-12-01T00:00:00",
          "2013-01-01T00:00:00",
          "2013-02-01T00:00:00",
          "2013-03-01T00:00:00",
          "2013-04-01T00:00:00",
          "2013-05-01T00:00:00",
          "2013-06-01T00:00:00",
          "2013-07-01T00:00:00",
          "2013-08-01T00:00:00",
          "2013-09-01T00:00:00",
          "2013-10-01T00:00:00",
          "2013-11-01T00:00:00",
          "2013-12-01T00:00:00",
          "2014-01-01T00:00:00",
          "2014-02-01T00:00:00",
          "2014-03-01T00:00:00",
          "2014-04-01T00:00:00",
          "2014-05-01T00:00:00",
          "2014-06-01T00:00:00",
          "2014-07-01T00:00:00",
          "2014-08-01T00:00:00",
          "2014-09-01T00:00:00",
          "2014-10-01T00:00:00",
          "2014-11-01T00:00:00",
          "2014-12-01T00:00:00",
          "2015-01-01T00:00:00",
          "2015-02-01T00:00:00",
          "2015-03-01T00:00:00",
          "2015-04-01T00:00:00",
          "2015-05-01T00:00:00",
          "2015-06-01T00:00:00",
          "2015-07-01T00:00:00",
          "2015-08-01T00:00:00",
          "2015-09-01T00:00:00",
          "2015-10-01T00:00:00",
          "2015-11-01T00:00:00",
          "2015-12-01T00:00:00",
          "2016-01-01T00:00:00",
          "2016-02-01T00:00:00",
          "2016-03-01T00:00:00",
          "2016-04-01T00:00:00",
          "2016-05-01T00:00:00",
          "2016-06-01T00:00:00",
          "2016-07-01T00:00:00",
          "2016-08-01T00:00:00",
          "2016-09-01T00:00:00",
          "2016-10-01T00:00:00",
          "2016-11-01T00:00:00",
          "2016-12-01T00:00:00",
          "2017-01-01T00:00:00",
          "2017-02-01T00:00:00",
          "2017-03-01T00:00:00",
          "2017-04-01T00:00:00",
          "2017-05-01T00:00:00",
          "2017-06-01T00:00:00",
          "2017-07-01T00:00:00",
          "2017-08-01T00:00:00",
          "2017-09-01T00:00:00",
          "2017-10-01T00:00:00",
          "2017-11-01T00:00:00",
          "2017-12-01T00:00:00",
          "2018-01-01T00:00:00",
          "2018-02-01T00:00:00",
          "2018-03-01T00:00:00",
          "2018-04-01T00:00:00",
          "2018-05-01T00:00:00",
          "2018-06-01T00:00:00",
          "2018-07-01T00:00:00",
          "2018-08-01T00:00:00",
          "2018-09-01T00:00:00",
          "2018-10-01T00:00:00",
          "2018-11-01T00:00:00",
          "2018-12-01T00:00:00",
          "2019-01-01T00:00:00",
          "2019-02-01T00:00:00",
          "2019-03-01T00:00:00",
          "2019-04-01T00:00:00",
          "2019-05-01T00:00:00",
          "2019-06-01T00:00:00",
          "2019-07-01T00:00:00",
          "2019-08-01T00:00:00",
          "2019-09-01T00:00:00",
          "2019-10-01T00:00:00",
          "2019-11-01T00:00:00",
          "2019-12-01T00:00:00",
          "2020-01-01T00:00:00",
          "2020-02-01T00:00:00",
          "2020-03-01T00:00:00",
          "2020-04-01T00:00:00",
          "2020-05-01T00:00:00",
          "2020-06-01T00:00:00",
          "2020-07-01T00:00:00",
          "2020-08-01T00:00:00",
          "2020-09-01T00:00:00",
          "2020-10-01T00:00:00",
          "2020-11-01T00:00:00",
          "2020-12-01T00:00:00",
          "2021-01-01T00:00:00",
          "2021-02-01T00:00:00",
          "2021-03-01T00:00:00",
          "2021-04-01T00:00:00",
          "2021-05-01T00:00:00",
          "2021-06-01T00:00:00",
          "2021-07-01T00:00:00",
          "2021-08-01T00:00:00",
          "2021-09-01T00:00:00",
          "2021-10-01T00:00:00",
          "2021-11-01T00:00:00",
          "2021-12-01T00:00:00",
          "2022-01-01T00:00:00",
          "2022-02-01T00:00:00",
          "2022-03-01T00:00:00",
          "2022-04-01T00:00:00",
          "2022-05-01T00:00:00",
          "2022-06-01T00:00:00",
          "2022-07-01T00:00:00",
          "2022-08-01T00:00:00",
          "2022-09-01T00:00:00",
          "2022-10-01T00:00:00",
          "2022-11-01T00:00:00",
          "2022-12-01T00:00:00"
         ],
         "y": [
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   ],
   "source": [
    "# Plot coefficient on CHAR\n",
    "fig = go.Figure()\n",
    "trace  = go.Scatter(x=coefs.index.to_timestamp(), y=coefs[CHAR], mode=\"lines\", name ='Monthly Coefficient')\n",
    "fig.add_trace(trace)\n",
    "trace_ma  = go.Scatter(x=coefs.index.to_timestamp(), y=coefs[CHAR].rolling(120).mean(), mode=\"lines\", name ='Rolling 10-yr Avg')\n",
    "fig.add_trace(trace_ma)\n",
    "fig.update_yaxes(title=f'Coefficient on {CHAR}',tickformat=\".4f\")\n",
    "fig.update_xaxes(title='Date')\n",
    "fig.update_layout(legend=dict(yanchor=\"top\", y=0.99, xanchor=\"left\", x=0.01))\n",
    "fig.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example #2: Multiple characteristics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "CHARS = ['beta','mve', 'bm','mom12m']\n",
    "coefs = df.groupby('mdate').apply(lambda d: sm.OLS(d.ret,sm.add_constant(d[CHARS])).fit().params) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>tstat</th>\n",
       "      <th>pval</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>-0.0118</td>\n",
       "      <td>-2.5700</td>\n",
       "      <td>0.0105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>-0.0028</td>\n",
       "      <td>-1.9697</td>\n",
       "      <td>0.0494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mve</th>\n",
       "      <td>0.0014</td>\n",
       "      <td>4.2606</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bm</th>\n",
       "      <td>0.0046</td>\n",
       "      <td>6.7982</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mom12m</th>\n",
       "      <td>0.0108</td>\n",
       "      <td>8.8704</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "          mean   tstat   pval\n",
       "const  -0.0118 -2.5700 0.0105\n",
       "beta   -0.0028 -1.9697 0.0494\n",
       "mve     0.0014  4.2606 0.0000\n",
       "bm      0.0046  6.7982 0.0000\n",
       "mom12m  0.0108  8.8704 0.0000"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats = pd.DataFrame(dtype=float,index=coefs.columns,columns=['mean','tstat','pval'])\n",
    "for coef in coefs.columns :\n",
    "    tsreg = sm.OLS(coefs[coef],np.ones(T)).fit()\n",
    "\n",
    "    stats.loc[coef,'mean'] = coefs[coef].mean()\n",
    "    stats.loc[coef,'tstat']= tsreg.tvalues['const']\n",
    "    stats.loc[coef,'pval'] = tsreg.pvalues['const']\n",
    "stats.round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "# Plot a chosen characteristic's coefficients over time\n",
    "CHAR = 'mom12m'\n",
    "fig = go.Figure()\n",
    "trace  = go.Scatter(x=coefs.index.to_timestamp(), y=coefs[CHAR], mode=\"lines\", name ='Monthly Coefficient')\n",
    "fig.add_trace(trace)\n",
    "trace_ma  = go.Scatter(x=coefs.index.to_timestamp(), y=coefs[CHAR].rolling(120).mean(), mode=\"lines\", name ='Rolling 10-yr Avg')\n",
    "fig.add_trace(trace_ma)\n",
    "fig.update_yaxes(title='Coefficient on '+CHAR,tickformat=\".4f\")\n",
    "fig.update_xaxes(title='Date')\n",
    "fig.update_layout(legend=dict(yanchor=\"top\", y=0.99, xanchor=\"left\", x=0.01))\n",
    "fig.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interpreting the economic magnitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A one-standard deviation change in mom12m results in:  0.51% per month\n"
     ]
    }
   ],
   "source": [
    "ts_avg_sd = df.groupby('mdate')[CHAR].std().mean()\n",
    "ts_avg_coef = stats.loc[CHAR,'mean']\n",
    "effect = ts_avg_sd * ts_avg_coef\n",
    "print(f'A one-standard deviation change in {CHAR} results in: {effect: .2%} per month')"
   ]
  }
 ],
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