Capital Asset Pricing Model

capm.ipynb

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   "source": [
    "# Capital Asset Pricing Model"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Capital Asset Pricing Model was introduced by Jack Treynor, William F. Sharpe and John Lintner <br>\n",
    "\n",
    "The CAPM is a model for pricing an individual security or portfolio. For individual securities, we make use of the security market line (SML) and its relation to expected return and systematic risk (beta), to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. <br>"
   ]
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "returns = pd.read_excel(\"../sep500_returns.xlsx\")\n",
    "factors = pd.read_excel(\"../FF_factors_monthly.xlsx\")\n",
    "returns.set_index(\"Date\", inplace=True)\n",
    "factors.set_index(\"Date\", inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Massaging\n",
    "excess_returns = returns.sub(factors.RF, axis=0).reset_index(drop=True)\n",
    "factors[\"Mkt\"] = factors[\"Mkt-RF\"] + factors[\"RF\"]\n",
    "factors.reset_index(drop=True, inplace=True)\n",
    "factor_names = factors.columns.to_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((162, 87), (162, 5))"
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     "execution_count": 4,
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   ],
   "source": [
    "excess_returns.shape, factors.shape"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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     "data": {
      "text/plain": [
       "(          A       AAL      AAPL       ABT      ACGL       ACN      ADBE  \\\n",
       " 0  0.122369  0.380414  0.065396  0.025312  0.034107 -0.024884  0.072755   \n",
       " 1  0.093134  0.002728  0.148471 -0.029477  0.030684  0.049537  0.020779   \n",
       " \n",
       "         ADI       ADM       ADP  ...       CPT      GOOG     GOOGL       KMX  \\\n",
       " 0  0.084570 -0.015393  0.020103  ...  0.033015 -0.005925 -0.005925 -0.021328   \n",
       " 1 -0.007663 -0.015667  0.077120  ...  0.050538  0.076538  0.076538  0.244180   \n",
       " \n",
       "         LNT       MMM        MO         T      TECH       WRB  \n",
       " 0  0.013782  0.002315  0.013092 -0.021688 -0.021751  0.057953  \n",
       " 1  0.051533  0.042670  0.037319  0.041516 -0.005319  0.015962  \n",
       " \n",
       " [2 rows x 87 columns],\n",
       "      Mkt-RF       SMB       HML   RF       Mkt\n",
       " 0  0.034190  0.011231  0.032191  0.0  0.034190\n",
       " 1  0.062818  0.013868  0.021340  0.0  0.062818)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "excess_returns.head(2), factors.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. CAPM regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Capital Asset Pricing Model Formula\n",
    "\n",
    "The CAPM states that the expected return of stock $i$ is equal to the Risk free rate plus a component which is defined by the excess market return and the relationship between the stock and the market. \n",
    "\n",
    "$E[r_i] = R_f + \\beta_i(E[R_m] - Rf)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "stock_excess_ret = excess_returns[\"A\"].copy()\n",
    "mkt_excess_ret = factors[\"Mkt-RF\"].copy()\n",
    "mkt_excess_ret = sm.add_constant(mkt_excess_ret)"
   ]
  },
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   "execution_count": 7,
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     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>A</td>        <th>  R-squared:         </th> <td>   0.512</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.509</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   168.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 04 Oct 2023</td> <th>  Prob (F-statistic):</th> <td>9.55e-27</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:40:14</td>     <th>  Log-Likelihood:    </th> <td>  250.55</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   162</td>      <th>  AIC:               </th> <td>  -497.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   160</td>      <th>  BIC:               </th> <td>  -490.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</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>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>    0.0008</td> <td>    0.004</td> <td>    0.191</td> <td> 0.849</td> <td>   -0.007</td> <td>    0.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mkt-RF</th> <td>    1.2016</td> <td>    0.093</td> <td>   12.969</td> <td> 0.000</td> <td>    1.019</td> <td>    1.385</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.534</td> <th>  Durbin-Watson:     </th> <td>   1.989</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.766</td> <th>  Jarque-Bera (JB):  </th> <td>   0.236</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.033</td> <th>  Prob(JB):          </th> <td>   0.888</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.175</td> <th>  Cond. No.          </th> <td>    22.7</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      A   R-squared:                       0.512\n",
       "Model:                            OLS   Adj. R-squared:                  0.509\n",
       "Method:                 Least Squares   F-statistic:                     168.2\n",
       "Date:                Wed, 04 Oct 2023   Prob (F-statistic):           9.55e-27\n",
       "Time:                        11:40:14   Log-Likelihood:                 250.55\n",
       "No. Observations:                 162   AIC:                            -497.1\n",
       "Df Residuals:                     160   BIC:                            -490.9\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.0008      0.004      0.191      0.849      -0.007       0.009\n",
       "Mkt-RF         1.2016      0.093     12.969      0.000       1.019       1.385\n",
       "==============================================================================\n",
       "Omnibus:                        0.534   Durbin-Watson:                   1.989\n",
       "Prob(Omnibus):                  0.766   Jarque-Bera (JB):                0.236\n",
       "Skew:                           0.033   Prob(JB):                        0.888\n",
       "Kurtosis:                       3.175   Cond. No.                         22.7\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.OLS(stock_excess_ret, mkt_excess_ret)\n",
    "model_res = model.fit()\n",
    "model_res.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Fitted Line"
   ]
  },
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   "cell_type": "code",
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    {
     "data": {
      "text/plain": [
       "0    0.041883\n",
       "1    0.076282\n",
       "2    0.024920\n",
       "Name: Best Line, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = model_res.params.loc[\"const\"]\n",
    "beta = model_res.params.loc[\"Mkt-RF\"]\n",
    "line = beta * factors[\"Mkt-RF\"] + alpha\n",
    "line.name = \"Best Line\"\n",
    "line.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_capm(mkt_ret, stock_ret, line):\n",
    "    fig, axis = plt.subplots(1, figsize=(20, 10))\n",
    "    axis.scatter(mkt_ret, stock_ret, label=\"Datapoints\")\n",
    "    axis.plot(mkt_ret, line, color='red', label='CAPM Line')\n",
    "    plt.title('Capital Asset Pricing Model', fontsize=25)\n",
    "    plt.xlabel('Mkt Return $R_m$', fontsize=15)\n",
    "    plt.ylabel('Stock Return $R_s$', fontsize=15)\n",
    "    plt.text(0.08, 0.05, r'$R_a = \\beta * R_m + \\alpha$', fontsize=18)\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
  },
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   "cell_type": "code",
   "execution_count": 10,
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_capm(mkt_ret=factors[\"Mkt-RF\"], stock_ret=stock_excess_ret, line=line)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "source": [
    "### Chart Explanation\n",
    "Each point in the scatter plot represents a single observation in the data. <br>\n",
    "\n",
    "- The horizontal coordinate is the return $r_{mkt,t}$ on the market portfolio in the period t\n",
    "- The vertical coordinate is the return $r_{k,t}$ on the asset in the same period t\n",
    "- The slope of the \"best fit\" (regression) line is the asset's estimated beta $\\beta_k$\n",
    "- The vertical distance of a point from the regression line is the \"residual\" $\\epsilon_{k,t}$, which represents the idiosyncratic risk of the asset in the given period t\n",
    "- The intercept of the regression line is the asset's estimated alpha $\\alpha_{k}$, which should be =0 if the CAPM is true"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Beta Explanation\n",
    "- A high beta is usually associated to a strongly \"ciclical\" asset, sensitive to business cycle\n",
    "- A Low beta is usually associated to assets that are mostly insensitive to business cycle\n",
    "\n",
    "- If we have a \"good fit\", that is high $R^2$, then the asset shows low idiosyncratic risk\n",
    "- If we have a \"bad fit\" instead, that is low $R^2$, then the asset shows a high idiosyncratic risk\n",
    "\n",
    "Also:\n",
    "1) $\\beta_k = 1$\n",
    "    - it is not the market portfolio, but same level of systematic risk\n",
    "    - Should have same average return\n",
    "    - May have more idiosyncratic risk\n",
    "\n",
    "2) $\\beta_k = 0$\n",
    "    - NOT the risk-free asset, but no systematic risk\n",
    "    - Average return = risk-free rate (but not necessarily negative)\n",
    "    - May have idiosyncratic risk\n",
    "\n",
    "3) $\\beta_k < 0$\n",
    "    - Average return < risk-free rate (but not necessarily negative)\n",
    "    - Useful to reduce your portfolio's sensitivity to business cycle\n",
    "    - Lower average return -> cost of hedging!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Alpha Explanation\n",
    "The intercept alpha measures the difference between:\n",
    "\n",
    "- The \"realized\" risk premium $(\\mu - r_f)$ <br>\n",
    "and\n",
    "- The \"should be\" risk premium (as predicted by the model) $\\beta_k (\\mu_{m} - r_f)$\n",
    "\n",
    "If the CAPM was true, this diference should be zero!\n",
    "\n",
    "Alpha is therefore a measure of:\n",
    "- Over-performance: $\\alpha_{k} > 0$\n",
    "- Under-performance: $\\alpha_{k} < 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What if alpha is significantly difrent from 0 ?\n",
    "### Either the model is wrong, or the asset is incorrectly priced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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