21a_equity_factors.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Equity factor models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "from pandas_datareader import DataReader as pdr\n",
    "import plotly.graph_objects as go\n",
    "import plotly.express as px\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pull data\n",
    "ff3 = pdr(\"F-F_Research_Data_Factors\", \"famafrench\", start=1926)[0]/100\n",
    "ff5 = pdr(\"F-F_Research_Data_5_Factors_2x3\", \"famafrench\", start=1964)[0]/100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cumulative returns\n",
    "cum_rets = ff3 +1 \n",
    "vars = ['Mkt-RF', 'SMB', 'HML']\n",
    "cum_rets[vars] = cum_rets[vars].cumprod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "# Plot cumulative returns\n",
    "fig = go.Figure()\n",
    "cum_rets.index = cum_rets.index.astype(str)\n",
    "for v in vars:\n",
    "    trace  = go.Scatter(x=cum_rets.index, y=cum_rets[v], mode=\"lines\", name=v,\n",
    "    hovertemplate= v + \"<br>Date: %{x}<br>Accumulation: $%{y:.2f}<extra></extra>\")\n",
    "    fig.add_trace(trace)\n",
    "fig.update_layout(\n",
    "    xaxis_title=\"Date\",\n",
    "    yaxis_title=\"Accumulation from $1\",\n",
    "    yaxis_tickformat=\",.0f\",\n",
    "    width=1000,\n",
    "    height=460,\n",
    "    legend=dict(\n",
    "        yanchor=\"top\", \n",
    "        y=0.99, \n",
    "        xanchor=\"left\", \n",
    "        x=0.01\n",
    "    ),\n",
    "    yaxis_type=\"log\",\n",
    "  )\n",
    "fig.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    HML   R-squared:                       0.053\n",
      "Model:                            OLS   Adj. R-squared:                  0.052\n",
      "Method:                 Least Squares   F-statistic:                     64.31\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):           2.59e-15\n",
      "Time:                        10:47:02   Log-Likelihood:                 2252.0\n",
      "No. Observations:                1159   AIC:                            -4500.\n",
      "Df Residuals:                    1157   BIC:                            -4490.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0025      0.001      2.474      0.014       0.001       0.005\n",
      "Mkt-RF         0.1527      0.019      8.019      0.000       0.115       0.190\n",
      "==============================================================================\n",
      "Omnibus:                      468.501   Durbin-Watson:                   1.618\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6040.796\n",
      "Skew:                           1.499   Prob(JB):                         0.00\n",
      "Kurtosis:                      13.775   Cond. No.                         18.7\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results = sm.OLS(ff3.HML, sm.add_constant(ff3['Mkt-RF'])).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    SMB   R-squared:                       0.100\n",
      "Model:                            OLS   Adj. R-squared:                  0.099\n",
      "Method:                 Least Squares   F-statistic:                     128.4\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):           2.69e-28\n",
      "Time:                        10:47:03   Log-Likelihood:                 2416.8\n",
      "No. Observations:                1159   AIC:                            -4830.\n",
      "Df Residuals:                    1157   BIC:                            -4819.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0007      0.001      0.757      0.449      -0.001       0.002\n",
      "Mkt-RF         0.1872      0.017     11.331      0.000       0.155       0.220\n",
      "==============================================================================\n",
      "Omnibus:                      497.972   Durbin-Watson:                   2.027\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            12053.125\n",
      "Skew:                           1.424   Prob(JB):                         0.00\n",
      "Kurtosis:                      18.539   Cond. No.                         18.7\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "results = sm.OLS(ff3.SMB, sm.add_constant(ff3['Mkt-RF'])).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Momentum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "wml = pdr('F-F_Momentum_Factor','famafrench', start=1900)[0]/100\n",
    "ffc = ff3.merge(wml,how='inner', left_index=True,right_index=True)\n",
    "ffc.columns = ['Mkt-RF', 'SMB', 'HML', 'RF', 'WML']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cumulative returns\n",
    "cum_rets = ffc +1 \n",
    "vars = ['Mkt-RF', 'SMB', 'HML','WML']\n",
    "cum_rets[vars] = cum_rets[vars].cumprod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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          "font": {
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          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
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           "showland": true,
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           "radialaxis": {
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          "title": {
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        "width": 1000,
        "xaxis": {
         "title": {
          "text": "Date"
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        },
        "yaxis": {
         "tickformat": ",.0f",
         "title": {
          "text": "Accumulation from $1"
         },
         "type": "log"
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       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot cumulative returns\n",
    "fig = go.Figure()\n",
    "cum_rets.index = cum_rets.index.astype(str)\n",
    "for v in vars:\n",
    "    trace  = go.Scatter(x=cum_rets.index, y=cum_rets[v], mode=\"lines\", name=v,\n",
    "    hovertemplate= v + \"<br>Date: %{x}<br>Accumulation: $%{y:.2f}<extra></extra>\")\n",
    "    fig.add_trace(trace)\n",
    "fig.update_layout(\n",
    "    xaxis_title=\"Date\",\n",
    "    yaxis_title=\"Accumulation from $1\",\n",
    "    yaxis_tickformat=\",.0f\",\n",
    "    width=1000,\n",
    "    height=460,\n",
    "    legend=dict(\n",
    "        yanchor=\"top\", \n",
    "        y=0.99, \n",
    "        xanchor=\"left\", \n",
    "        x=0.01\n",
    "    ),\n",
    "    yaxis_type=\"log\",\n",
    "  )\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    WML   R-squared:                       0.120\n",
      "Model:                            OLS   Adj. R-squared:                  0.119\n",
      "Method:                 Least Squares   F-statistic:                     156.3\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):           9.98e-34\n",
      "Time:                        10:47:11   Log-Likelihood:                 1959.5\n",
      "No. Observations:                1153   AIC:                            -3915.\n",
      "Df Residuals:                    1151   BIC:                            -3905.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0084      0.001      6.370      0.000       0.006       0.011\n",
      "Mkt-RF        -0.3039      0.024    -12.503      0.000      -0.352      -0.256\n",
      "==============================================================================\n",
      "Omnibus:                      607.873   Durbin-Watson:                   1.920\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            11714.962\n",
      "Skew:                          -1.988   Prob(JB):                         0.00\n",
      "Kurtosis:                      18.101   Cond. No.                         18.6\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Estimate CAPM alpha\n",
    "results = sm.OLS(ffc.WML, sm.add_constant(ffc['Mkt-RF'])).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    WML   R-squared:                       0.235\n",
      "Model:                            OLS   Adj. R-squared:                  0.233\n",
      "Method:                 Least Squares   F-statistic:                     117.8\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):           1.65e-66\n",
      "Time:                        10:47:12   Log-Likelihood:                 2040.7\n",
      "No. Observations:                1153   AIC:                            -4073.\n",
      "Df Residuals:                    1149   BIC:                            -4053.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0096      0.001      7.788      0.000       0.007       0.012\n",
      "Mkt-RF        -0.2240      0.024     -9.171      0.000      -0.272      -0.176\n",
      "SMB           -0.0529      0.040     -1.310      0.191      -0.132       0.026\n",
      "HML           -0.4573      0.035    -13.047      0.000      -0.526      -0.388\n",
      "==============================================================================\n",
      "Omnibus:                      397.745   Durbin-Watson:                   1.944\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3361.044\n",
      "Skew:                          -1.349   Prob(JB):                         0.00\n",
      "Kurtosis:                      10.917   Cond. No.                         34.0\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Estimate FF3 alpha\n",
    "results = sm.OLS(ffc.WML, sm.add_constant(ffc[['Mkt-RF','SMB','HML']])).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fama-French 5-factor model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cumulative returns\n",
    "cum_rets = ff5 +1 \n",
    "vars = ['Mkt-RF', 'SMB', 'HML','RMW','CMA']\n",
    "cum_rets[vars] = cum_rets[vars].cumprod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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          "font": {
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          "geo": {
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           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
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          "hoverlabel": {
           "align": "left"
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          "hovermode": "closest",
          "mapbox": {
           "style": "light"
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          "polar": {
           "angularaxis": {
            "gridcolor": "white",
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           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
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          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
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           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
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           "zaxis": {
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            "gridwidth": 2,
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            "gridcolor": "white",
            "linecolor": "white",
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           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
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           "zerolinewidth": 2
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          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
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            "standoff": 15
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           "zerolinewidth": 2
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        },
        "width": 1000,
        "xaxis": {
         "title": {
          "text": "Date"
         }
        },
        "yaxis": {
         "tickformat": ",.0f",
         "title": {
          "text": "Accumulation from $1"
         },
         "type": "log"
        }
       }
      }
     },
     "metadata": {},
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   ],
   "source": [
    "# Plot cumulative returns\n",
    "fig = go.Figure()\n",
    "cum_rets.index = cum_rets.index.astype(str)\n",
    "for v in vars:\n",
    "    trace  = go.Scatter(x=cum_rets.index, y=cum_rets[v], mode=\"lines\", name=v,\n",
    "    hovertemplate= v + \"<br>Date: %{x}<br>Accumulation: $%{y:.2f}<extra></extra>\")\n",
    "    fig.add_trace(trace)\n",
    "fig.update_layout(\n",
    "    xaxis_title=\"Date\",\n",
    "    yaxis_title=\"Accumulation from $1\",\n",
    "    yaxis_tickformat=\",.0f\",\n",
    "    width=1000,\n",
    "    height=460,\n",
    "    legend=dict(\n",
    "        yanchor=\"top\", \n",
    "        y=0.99, \n",
    "        xanchor=\"left\", \n",
    "        x=0.01\n",
    "    ),\n",
    "    yaxis_type=\"log\",\n",
    "  )\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    RMW   R-squared:                       0.034\n",
      "Model:                            OLS   Adj. R-squared:                  0.032\n",
      "Method:                 Least Squares   F-statistic:                     24.70\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):           8.42e-07\n",
      "Time:                        10:47:18   Log-Likelihood:                 1702.8\n",
      "No. Observations:                 709   AIC:                            -3402.\n",
      "Df Residuals:                     707   BIC:                            -3392.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0033      0.001      3.932      0.000       0.002       0.005\n",
      "Mkt-RF        -0.0908      0.018     -4.970      0.000      -0.127      -0.055\n",
      "==============================================================================\n",
      "Omnibus:                      158.719   Durbin-Watson:                   1.686\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3604.382\n",
      "Skew:                          -0.368   Prob(JB):                         0.00\n",
      "Kurtosis:                      14.021   Cond. No.                         22.2\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    RMW   R-squared:                       0.135\n",
      "Model:                            OLS   Adj. R-squared:                  0.131\n",
      "Method:                 Least Squares   F-statistic:                     36.62\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):           5.32e-22\n",
      "Time:                        10:47:18   Log-Likelihood:                 1741.9\n",
      "No. Observations:                 709   AIC:                            -3476.\n",
      "Df Residuals:                     705   BIC:                            -3458.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0034      0.001      4.275      0.000       0.002       0.005\n",
      "Mkt-RF        -0.0381      0.018     -2.062      0.040      -0.074      -0.002\n",
      "SMB           -0.2403      0.027     -8.934      0.000      -0.293      -0.187\n",
      "HML            0.0506      0.027      1.889      0.059      -0.002       0.103\n",
      "==============================================================================\n",
      "Omnibus:                       92.057   Durbin-Watson:                   1.590\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              893.729\n",
      "Skew:                           0.021   Prob(JB):                    8.49e-195\n",
      "Kurtosis:                       8.500   Cond. No.                         36.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Estimate RMW alphas\n",
    "results = sm.OLS(ff5.RMW, sm.add_constant(ff5['Mkt-RF'])).fit()\n",
    "print(results.summary())\n",
    "\n",
    "results = sm.OLS(ff5.RMW, sm.add_constant(ff5[['Mkt-RF','SMB','HML']])).fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    CMA   R-squared:                       0.136\n",
      "Model:                            OLS   Adj. R-squared:                  0.134\n",
      "Method:                 Least Squares   F-statistic:                     110.9\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):           3.49e-24\n",
      "Time:                        10:47:19   Log-Likelihood:                 1796.4\n",
      "No. Observations:                 709   AIC:                            -3589.\n",
      "Df Residuals:                     707   BIC:                            -3580.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0039      0.001      5.376      0.000       0.002       0.005\n",
      "Mkt-RF        -0.1686      0.016    -10.530      0.000      -0.200      -0.137\n",
      "==============================================================================\n",
      "Omnibus:                       18.649   Durbin-Watson:                   1.717\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               29.271\n",
      "Skew:                           0.212   Prob(JB):                     4.41e-07\n",
      "Kurtosis:                       3.900   Cond. No.                         22.2\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    CMA   R-squared:                       0.521\n",
      "Model:                            OLS   Adj. R-squared:                  0.519\n",
      "Method:                 Least Squares   F-statistic:                     255.5\n",
      "Date:                Mon, 27 Mar 2023   Prob (F-statistic):          3.44e-112\n",
      "Time:                        10:47:19   Log-Likelihood:                 2005.6\n",
      "No. Observations:                 709   AIC:                            -4003.\n",
      "Df Residuals:                     705   BIC:                            -3985.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0022      0.001      4.108      0.000       0.001       0.003\n",
      "Mkt-RF        -0.1042      0.013     -8.185      0.000      -0.129      -0.079\n",
      "SMB           -0.0134      0.019     -0.720      0.472      -0.050       0.023\n",
      "HML            0.4400      0.018     23.812      0.000       0.404       0.476\n",
      "==============================================================================\n",
      "Omnibus:                       27.630   Durbin-Watson:                   1.865\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               66.233\n",
      "Skew:                           0.137   Prob(JB):                     4.15e-15\n",
      "Kurtosis:                       4.472   Cond. No.                         36.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Estimate FF3 alpha\n",
    "results = sm.OLS(ff5.CMA, sm.add_constant(ff5['Mkt-RF'])).fit()\n",
    "print(results.summary())\n",
    "\n",
    "results = sm.OLS(ff5.CMA, sm.add_constant(ff5[['Mkt-RF','SMB','HML']])).fit()\n",
    "print(results.summary())"
   ]
  }
 ],
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