{
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    "## Linear Regression: Model Estimation\n",
    "\n",
    "**Functions**\n",
    "\n",
    "`sm.OLS`\n",
    "\n",
    "### Exercise 32\n",
    "Use the OLS function to estimate the coefficients of the Fama-French portfolios (monthly data) on the\n",
    "market, size and value factors. Include a constant in the regressions. Use only the four\n",
    "extremum portfolios – that is the 1-1, 1-5, 5-1 and 5-5 portfolios. Estimate the model with\n",
    "homoskedastic errors and with White's covariance estimator."
   ]
  },
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    "execution": {
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   "source": [
    "import pandas as pd\n",
    "\n",
    "ff = pd.read_hdf(\"data/ff.h5\", \"ff\")\n",
    "ff.head()\n",
    "\n",
    "factors = ff.iloc[:, :3]\n",
    "portfolios = ff.iloc[:, 4:]\n",
    "portfolios = portfolios[[\"SMALL LoBM\", \"SMALL HiBM\", \"BIG LoBM\", \"BIG HiBM\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:07:16.760021Z",
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    },
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     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "factors = sm.add_constant(factors)\n",
    "all_results = {}\n",
    "homosk_results = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>SMALL LoBM</td>    <th>  R-squared:         </th> <td>   0.655</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.654</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   180.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 22 Sep 2021</td> <th>  Prob (F-statistic):</th> <td>1.77e-95</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:07:17</td>     <th>  Log-Likelihood:    </th> <td> -3776.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1117</td>      <th>  AIC:               </th> <td>   7562.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1113</td>      <th>  BIC:               </th> <td>   7582.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>         <td>HC0</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>   -0.4355</td> <td>    0.172</td> <td>   -2.526</td> <td> 0.012</td> <td>   -0.773</td> <td>   -0.098</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mkt-RF</th> <td>    1.2832</td> <td>    0.119</td> <td>   10.766</td> <td> 0.000</td> <td>    1.050</td> <td>    1.517</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SMB</th>    <td>    1.4336</td> <td>    0.177</td> <td>    8.120</td> <td> 0.000</td> <td>    1.088</td> <td>    1.780</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HML</th>    <td>    0.4214</td> <td>    0.274</td> <td>    1.536</td> <td> 0.125</td> <td>   -0.116</td> <td>    0.959</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>896.514</td> <th>  Durbin-Watson:     </th>  <td>   2.065</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>102194.780</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 2.973</td>  <th>  Prob(JB):          </th>  <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>49.480</td>  <th>  Cond. No.          </th>  <td>    5.68</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors are heteroscedasticity robust (HC0)"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             SMALL LoBM   R-squared:                       0.655\n",
       "Model:                            OLS   Adj. R-squared:                  0.654\n",
       "Method:                 Least Squares   F-statistic:                     180.8\n",
       "Date:                Wed, 22 Sep 2021   Prob (F-statistic):           1.77e-95\n",
       "Time:                        11:07:17   Log-Likelihood:                -3776.8\n",
       "No. Observations:                1117   AIC:                             7562.\n",
       "Df Residuals:                    1113   BIC:                             7582.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:                  HC0                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.4355      0.172     -2.526      0.012      -0.773      -0.098\n",
       "Mkt-RF         1.2832      0.119     10.766      0.000       1.050       1.517\n",
       "SMB            1.4336      0.177      8.120      0.000       1.088       1.780\n",
       "HML            0.4214      0.274      1.536      0.125      -0.116       0.959\n",
       "==============================================================================\n",
       "Omnibus:                      896.514   Durbin-Watson:                   2.065\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           102194.780\n",
       "Skew:                           2.973   Prob(JB):                         0.00\n",
       "Kurtosis:                      49.480   Cond. No.                         5.68\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors are heteroscedasticity robust (HC0)\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod = sm.OLS(portfolios[\"SMALL LoBM\"], factors)\n",
    "res = mod.fit(cov_type=\"HC0\")\n",
    "all_results[\"SMALL LoBM\"] = res\n",
    "homosk_results[\"SMALL LoBM\"] = sm.OLS(portfolios[\"SMALL LoBM\"], factors).fit()\n",
    "res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:07:17.680021Z",
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>SMALL HiBM</td>    <th>  R-squared:         </th> <td>   0.939</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.938</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   941.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 22 Sep 2021</td> <th>  Prob (F-statistic):</th> <td>1.19e-304</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:07:17</td>     <th>  Log-Likelihood:    </th> <td> -2506.2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1117</td>      <th>  AIC:               </th> <td>   5020.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1113</td>      <th>  BIC:               </th> <td>   5041.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>         <td>HC0</td>       <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.3696</td> <td>    0.062</td> <td>    6.008</td> <td> 0.000</td> <td>    0.249</td> <td>    0.490</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mkt-RF</th> <td>    0.9830</td> <td>    0.024</td> <td>   40.929</td> <td> 0.000</td> <td>    0.936</td> <td>    1.030</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SMB</th>    <td>    1.3001</td> <td>    0.065</td> <td>   20.068</td> <td> 0.000</td> <td>    1.173</td> <td>    1.427</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HML</th>    <td>    0.9124</td> <td>    0.058</td> <td>   15.624</td> <td> 0.000</td> <td>    0.798</td> <td>    1.027</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>589.467</td> <th>  Durbin-Watson:     </th> <td>   2.272</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>15321.552</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.888</td>  <th>  Prob(JB):          </th> <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>20.747</td>  <th>  Cond. No.          </th> <td>    5.68</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors are heteroscedasticity robust (HC0)"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             SMALL HiBM   R-squared:                       0.939\n",
       "Model:                            OLS   Adj. R-squared:                  0.938\n",
       "Method:                 Least Squares   F-statistic:                     941.0\n",
       "Date:                Wed, 22 Sep 2021   Prob (F-statistic):          1.19e-304\n",
       "Time:                        11:07:17   Log-Likelihood:                -2506.2\n",
       "No. Observations:                1117   AIC:                             5020.\n",
       "Df Residuals:                    1113   BIC:                             5041.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:                  HC0                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.3696      0.062      6.008      0.000       0.249       0.490\n",
       "Mkt-RF         0.9830      0.024     40.929      0.000       0.936       1.030\n",
       "SMB            1.3001      0.065     20.068      0.000       1.173       1.427\n",
       "HML            0.9124      0.058     15.624      0.000       0.798       1.027\n",
       "==============================================================================\n",
       "Omnibus:                      589.467   Durbin-Watson:                   2.272\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            15321.552\n",
       "Skew:                           1.888   Prob(JB):                         0.00\n",
       "Kurtosis:                      20.747   Cond. No.                         5.68\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors are heteroscedasticity robust (HC0)\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod = sm.OLS(portfolios[\"SMALL HiBM\"], factors)\n",
    "res = mod.fit(cov_type=\"HC0\")\n",
    "all_results[\"SMALL HiBM\"] = res\n",
    "homosk_results[\"SMALL HiBM\"] = sm.OLS(portfolios[\"SMALL HiBM\"], factors).fit()\n",
    "res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>BIG LoBM</td>     <th>  R-squared:         </th> <td>   0.952</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.952</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   4050.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 22 Sep 2021</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:07:17</td>     <th>  Log-Likelihood:    </th> <td> -1758.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1117</td>      <th>  AIC:               </th> <td>   3525.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1113</td>      <th>  BIC:               </th> <td>   3545.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>         <td>HC0</td>       <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.3594</td> <td>    0.035</td> <td>   10.270</td> <td> 0.000</td> <td>    0.291</td> <td>    0.428</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mkt-RF</th> <td>    1.0229</td> <td>    0.009</td> <td>  109.366</td> <td> 0.000</td> <td>    1.005</td> <td>    1.041</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SMB</th>    <td>   -0.1485</td> <td>    0.023</td> <td>   -6.524</td> <td> 0.000</td> <td>   -0.193</td> <td>   -0.104</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HML</th>    <td>   -0.2629</td> <td>    0.016</td> <td>  -16.645</td> <td> 0.000</td> <td>   -0.294</td> <td>   -0.232</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>109.852</td> <th>  Durbin-Watson:     </th> <td>   1.791</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 248.017</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.578</td>  <th>  Prob(JB):          </th> <td>1.39e-54</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.998</td>  <th>  Cond. No.          </th> <td>    5.68</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors are heteroscedasticity robust (HC0)"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               BIG LoBM   R-squared:                       0.952\n",
       "Model:                            OLS   Adj. R-squared:                  0.952\n",
       "Method:                 Least Squares   F-statistic:                     4050.\n",
       "Date:                Wed, 22 Sep 2021   Prob (F-statistic):               0.00\n",
       "Time:                        11:07:17   Log-Likelihood:                -1758.6\n",
       "No. Observations:                1117   AIC:                             3525.\n",
       "Df Residuals:                    1113   BIC:                             3545.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:                  HC0                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.3594      0.035     10.270      0.000       0.291       0.428\n",
       "Mkt-RF         1.0229      0.009    109.366      0.000       1.005       1.041\n",
       "SMB           -0.1485      0.023     -6.524      0.000      -0.193      -0.104\n",
       "HML           -0.2629      0.016    -16.645      0.000      -0.294      -0.232\n",
       "==============================================================================\n",
       "Omnibus:                      109.852   Durbin-Watson:                   1.791\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              248.017\n",
       "Skew:                           0.578   Prob(JB):                     1.39e-54\n",
       "Kurtosis:                       4.998   Cond. No.                         5.68\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors are heteroscedasticity robust (HC0)\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod = sm.OLS(portfolios[\"BIG LoBM\"], factors)\n",
    "res = mod.fit(cov_type=\"HC0\")\n",
    "all_results[\"BIG LoBM\"] = res\n",
    "homosk_results[\"BIG LoBM\"] = sm.OLS(portfolios[\"BIG LoBM\"], factors).fit()\n",
    "res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:07:17.712021Z",
     "iopub.status.busy": "2021-09-22T10:07:17.712021Z",
     "iopub.status.idle": "2021-09-22T10:07:17.725021Z",
     "shell.execute_reply": "2021-09-22T10:07:17.725021Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>BIG HiBM</td>     <th>  R-squared:         </th> <td>   0.838</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.838</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   376.3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 22 Sep 2021</td> <th>  Prob (F-statistic):</th> <td>1.04e-168</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:07:17</td>     <th>  Log-Likelihood:    </th> <td> -2956.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1117</td>      <th>  AIC:               </th> <td>   5920.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1113</td>      <th>  BIC:               </th> <td>   5940.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>         <td>HC0</td>       <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.1042</td> <td>    0.103</td> <td>    1.016</td> <td> 0.309</td> <td>   -0.097</td> <td>    0.305</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mkt-RF</th> <td>    1.1823</td> <td>    0.038</td> <td>   31.058</td> <td> 0.000</td> <td>    1.108</td> <td>    1.257</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SMB</th>    <td>   -0.1573</td> <td>    0.069</td> <td>   -2.268</td> <td> 0.023</td> <td>   -0.293</td> <td>   -0.021</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HML</th>    <td>    1.0162</td> <td>    0.073</td> <td>   13.961</td> <td> 0.000</td> <td>    0.874</td> <td>    1.159</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>436.752</td> <th>  Durbin-Watson:     </th> <td>   1.808</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>9887.813</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.257</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>17.357</td>  <th>  Cond. No.          </th> <td>    5.68</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors are heteroscedasticity robust (HC0)"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               BIG HiBM   R-squared:                       0.838\n",
       "Model:                            OLS   Adj. R-squared:                  0.838\n",
       "Method:                 Least Squares   F-statistic:                     376.3\n",
       "Date:                Wed, 22 Sep 2021   Prob (F-statistic):          1.04e-168\n",
       "Time:                        11:07:17   Log-Likelihood:                -2956.0\n",
       "No. Observations:                1117   AIC:                             5920.\n",
       "Df Residuals:                    1113   BIC:                             5940.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:                  HC0                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.1042      0.103      1.016      0.309      -0.097       0.305\n",
       "Mkt-RF         1.1823      0.038     31.058      0.000       1.108       1.257\n",
       "SMB           -0.1573      0.069     -2.268      0.023      -0.293      -0.021\n",
       "HML            1.0162      0.073     13.961      0.000       0.874       1.159\n",
       "==============================================================================\n",
       "Omnibus:                      436.752   Durbin-Watson:                   1.808\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             9887.813\n",
       "Skew:                           1.257   Prob(JB):                         0.00\n",
       "Kurtosis:                      17.357   Cond. No.                         5.68\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors are heteroscedasticity robust (HC0)\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod = sm.OLS(portfolios[\"BIG HiBM\"], factors)\n",
    "res = mod.fit(cov_type=\"HC0\")\n",
    "all_results[\"BIG HiBM\"] = res\n",
    "homosk_results[\"BIG HiBM\"] = sm.OLS(portfolios[\"BIG HiBM\"], factors).fit()\n",
    "res.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Exercise 33\n",
    "Are the parameter standard errors similar using the two covariance estimators?\n",
    "If not, what does this mean? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:07:17.729020Z",
     "iopub.status.busy": "2021-09-22T10:07:17.728021Z",
     "iopub.status.idle": "2021-09-22T10:07:17.757021Z",
     "shell.execute_reply": "2021-09-22T10:07:17.757021Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "SMALL LoBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>0.215569</td>\n",
       "      <td>0.172414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>0.043167</td>\n",
       "      <td>0.119187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>0.070797</td>\n",
       "      <td>0.176554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>0.063235</td>\n",
       "      <td>0.274367</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Homosk     White\n",
       "const   0.215569  0.172414\n",
       "Mkt-RF  0.043167  0.119187\n",
       "SMB     0.070797  0.176554\n",
       "HML     0.063235  0.274367"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "SMALL HiBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>0.069118</td>\n",
       "      <td>0.061514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>0.013841</td>\n",
       "      <td>0.024017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>0.022699</td>\n",
       "      <td>0.064785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>0.020275</td>\n",
       "      <td>0.058401</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Homosk     White\n",
       "const   0.069118  0.061514\n",
       "Mkt-RF  0.013841  0.024017\n",
       "SMB     0.022699  0.064785\n",
       "HML     0.020275  0.058401"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "BIG LoBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>0.035391</td>\n",
       "      <td>0.034997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>0.007087</td>\n",
       "      <td>0.009353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>0.011623</td>\n",
       "      <td>0.022765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>0.010382</td>\n",
       "      <td>0.015797</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Homosk     White\n",
       "const   0.035391  0.034997\n",
       "Mkt-RF  0.007087  0.009353\n",
       "SMB     0.011623  0.022765\n",
       "HML     0.010382  0.015797"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "BIG HiBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>0.103384</td>\n",
       "      <td>0.102525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>0.020702</td>\n",
       "      <td>0.038067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>0.033953</td>\n",
       "      <td>0.069341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>0.030327</td>\n",
       "      <td>0.072789</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Homosk     White\n",
       "const   0.103384  0.102525\n",
       "Mkt-RF  0.020702  0.038067\n",
       "SMB     0.033953  0.069341\n",
       "HML     0.030327  0.072789"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import HTML, display\n",
    "\n",
    "for key in all_results:\n",
    "    white_res = all_results[key]\n",
    "    homosk_res = homosk_results[key]\n",
    "    std_err = pd.DataFrame({\"Homosk\": homosk_res.bse, \"White\": white_res.bse})\n",
    "    display(HTML(key))\n",
    "    display(std_err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:07:17.761021Z",
     "iopub.status.busy": "2021-09-22T10:07:17.760021Z",
     "iopub.status.idle": "2021-09-22T10:07:17.788021Z",
     "shell.execute_reply": "2021-09-22T10:07:17.788021Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "SMALL LoBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>-2.020037</td>\n",
       "      <td>-2.525647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>29.725191</td>\n",
       "      <td>10.765843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>20.248866</td>\n",
       "      <td>8.119638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>6.664080</td>\n",
       "      <td>1.535905</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Homosk      White\n",
       "const   -2.020037  -2.525647\n",
       "Mkt-RF  29.725191  10.765843\n",
       "SMB     20.248866   8.119638\n",
       "HML      6.664080   1.535905"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "SMALL HiBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>5.346747</td>\n",
       "      <td>6.007648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>71.022641</td>\n",
       "      <td>40.929483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>57.274909</td>\n",
       "      <td>20.068010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>45.003201</td>\n",
       "      <td>15.623556</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Homosk      White\n",
       "const    5.346747   6.007648\n",
       "Mkt-RF  71.022641  40.929483\n",
       "SMB     57.274909  20.068010\n",
       "HML     45.003201  15.623556"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "BIG LoBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>10.155474</td>\n",
       "      <td>10.269912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>144.336719</td>\n",
       "      <td>109.365862</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>-12.777091</td>\n",
       "      <td>-6.523564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>-25.327247</td>\n",
       "      <td>-16.645120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Homosk       White\n",
       "const    10.155474   10.269912\n",
       "Mkt-RF  144.336719  109.365862\n",
       "SMB     -12.777091   -6.523564\n",
       "HML     -25.327247  -16.645120"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "BIG HiBM"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>Homosk</th>\n",
       "      <th>White</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>1.007916</td>\n",
       "      <td>1.016364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mkt-RF</th>\n",
       "      <td>57.107702</td>\n",
       "      <td>31.057592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMB</th>\n",
       "      <td>-4.632601</td>\n",
       "      <td>-2.268375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HML</th>\n",
       "      <td>33.508204</td>\n",
       "      <td>13.960789</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Homosk      White\n",
       "const    1.007916   1.016364\n",
       "Mkt-RF  57.107702  31.057592\n",
       "SMB     -4.632601  -2.268375\n",
       "HML     33.508204  13.960789"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for key in all_results:\n",
    "    white_res = all_results[key]\n",
    "    homosk_res = homosk_results[key]\n",
    "    t_stats = pd.DataFrame({\"Homosk\": homosk_res.tvalues, \"White\": white_res.tvalues})\n",
    "    display(HTML(key))\n",
    "    display(t_stats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 34\n",
    "How much of the variation is explained by these three regressors?"
   ]
  },
  {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SMALL LoBM</th>\n",
       "      <td>0.654851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMALL HiBM</th>\n",
       "      <td>0.938606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BIG LoBM</th>\n",
       "      <td>0.951723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BIG HiBM</th>\n",
       "      <td>0.838409</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  R2\n",
       "SMALL LoBM  0.654851\n",
       "SMALL HiBM  0.938606\n",
       "BIG LoBM    0.951723\n",
       "BIG HiBM    0.838409"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rsquare = {}\n",
    "for key in all_results:\n",
    "    rsquare[key] = all_results[key].rsquared\n",
    "pd.Series(rsquare, name=\"R2\").to_frame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-22T10:07:17.808021Z",
     "iopub.status.busy": "2021-09-22T10:07:17.807021Z",
     "iopub.status.idle": "2021-09-22T10:07:17.819021Z",
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    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>SMALL LoBM</th>\n",
       "      <td>0.508956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SMALL HiBM</th>\n",
       "      <td>0.629589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BIG LoBM</th>\n",
       "      <td>0.915187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BIG HiBM</th>\n",
       "      <td>0.674243</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  R2\n",
       "SMALL LoBM  0.508956\n",
       "SMALL HiBM  0.629589\n",
       "BIG LoBM    0.915187\n",
       "BIG HiBM    0.674243"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "capm_factor = factors.iloc[:, :2]\n",
    "for key in portfolios:\n",
    "    res = sm.OLS(portfolios[key], capm_factor).fit()\n",
    "    rsquare[key] = res.rsquared\n",
    "pd.Series(rsquare, name=\"R2\").to_frame()"
   ]
  }
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