0205_LinearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression\n",
    "\n",
    "Running a SLR in Python is fairly simple once you know how to use the relevant functions. What might be confusing is that there exist several packages which provide functions for linear regression. We will use functions from the `statsmodels` (sub-)package. Other packages such as e.g. `scikit-learn` have linear regression functions too, but what makes `statsmodels` stand out from other packages is its broad set of auxiliary functions for regression diagnostics. As usual we start by importing the packages needed for our task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Load relevant packages\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "plt.rcParams['font.size'] = 14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As toy data we will use the 'Advertising' data set introduced in the chapter 4 of the script. The data is taken from James et al. (2013). A copy is provided on the book's website where we will download it from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      TV  radio  newspaper  sales\n",
      "0  230.1   37.8       69.2   22.1\n",
      "1   44.5   39.3       45.1   10.4\n",
      "2   17.2   45.9       69.3    9.3\n",
      "3  151.5   41.3       58.5   18.5\n",
      "4  180.8   10.8       58.4   12.9\n"
     ]
    }
   ],
   "source": [
    "# From Advertising data set read cols 2:4\n",
    "url = 'https://www.statlearning.com/s/Advertising.csv'\n",
    "ad = pd.read_csv(url, sep=',', usecols=(np.arange(1, 5, 1)))\n",
    "print(ad.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we run a linear regression of `TV` on `sales` to calculate the coefficients and print a summary output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.612\n",
      "Model:                            OLS   Adj. R-squared:                  0.610\n",
      "Method:                 Least Squares   F-statistic:                     312.1\n",
      "Date:                Thu, 16 Feb 2023   Prob (F-statistic):           1.47e-42\n",
      "Time:                        19:40:26   Log-Likelihood:                -519.05\n",
      "No. Observations:                 200   AIC:                             1042.\n",
      "Df Residuals:                     198   BIC:                             1049.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          7.0326      0.458     15.360      0.000       6.130       7.935\n",
      "TV             0.0475      0.003     17.668      0.000       0.042       0.053\n",
      "==============================================================================\n",
      "Omnibus:                        0.531   Durbin-Watson:                   1.935\n",
      "Prob(Omnibus):                  0.767   Jarque-Bera (JB):                0.669\n",
      "Skew:                          -0.089   Prob(JB):                        0.716\n",
      "Kurtosis:                       2.779   Cond. No.                         338.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Ben Zimmermann\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "# Run regression and calculate fit\n",
    "reg = sm.OLS(ad.sales, exog=sm.add_constant(ad.TV)).fit()\n",
    "# Alternatively: reg = sm.OLS(ad.sales, sm.add_constant(ad.TV)).fit()\n",
    "print(reg.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Side note:** If you are an `R` guy and prefer their syntax, you could import the statsmodels.formula.api subpackage and run something like:\n",
    "\n",
    "> `from statsmodels.formula.api import ols\n",
    "reg = ols(\"Sales ~ TV\", data=ad).fit()\n",
    "reg.summary()`\n",
    "\n",
    "Intercept will automatically be calculated in the above setting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both p-values for intercept ($\\hat{\\beta}_0$) and slope ($\\hat{\\beta}_1$) are smaller than any reasonable significance level and thus we can reject the null hypothesis that either of the coefficients is zero (or irrelevant)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of printing the whole summary, we could also access each of the three summary as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<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>    7.0326</td> <td>    0.458</td> <td>   15.360</td> <td> 0.000</td> <td>    6.130</td> <td>    7.935</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TV</th>    <td>    0.0475</td> <td>    0.003</td> <td>   17.668</td> <td> 0.000</td> <td>    0.042</td> <td>    0.053</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the Fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `sm.OLS()` function calculates all kind of regression-related results. All this information is attached to the `reg` object. For example to plot the data we would need the model's fitted values. These can be accessed by combining the regression variable/object with the attribute `.fittedvalues` as in `reg.fittedvalues`. In below plot it is shown how this can be of use. We plot the data and fit using the standard plotting functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot scatter & lm\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.scatter(ad.TV, ad.sales, marker='.', label='Sample') # Training data\n",
    "plt.plot(ad.TV, reg.fittedvalues, c='k', label='Fit')  # Linear fit\n",
    "plt.ylabel('Sales')\n",
    "plt.xlabel('TV')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot residuals versus fitted values to do some visual regression diagnostics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "plt.scatter(ad.TV, reg.resid)\n",
    "plt.axhline(y=0, c='k')  #Black horizontal line at 0\n",
    "plt.xlabel('TV (fitted)')\n",
    "plt.ylabel('Residuals');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above two plots are just standard `matplotlib` plots serving the purpose of visual diagnostics. Beyond that, the `statsmodel` package has separate built-in plotting functions suited for visual regression diagnostics. We will not discuss them here but if interested you'll find plenty of sources on the web (e.g. [here](http://www.statsmodels.org/dev/examples/notebooks/generated/regression_plots.html), [here](http://www.statsmodels.org/stable/graphics.html) or [here](http://mpastell.com/2013/04/19/python_regression/))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accessing the Output\n",
    "\n",
    "The `reg` object contains a ton of information which you can all access. To see what there is, type `reg.` and press tab. Two examples are shown below. Notice that some are attributes (like `x.shape`, `x.size`) and do not need paranthesis to call them. Others are methods (similar to `.sum()`, `.min()`) and require parenthesis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "const    7.032594\n",
      "TV       0.047537\n",
      "dtype: float64 \n",
      "\n",
      "0    4.129225\n",
      "1    1.252026\n",
      "2    1.449776\n",
      "3    4.265605\n",
      "4   -2.727218\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Regression coefficients\n",
    "print(reg.params, '\\n')\n",
    "print(reg.resid.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confidence Intervals & Hypthesis Testing\n",
    "\n",
    "The 95%-confidence interval (CI) is printed in the summary above. If one wishes to calculate it for a different significance level (`alpha`), it is done as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>const</th>\n",
       "      <td>5.841796</td>\n",
       "      <td>8.223391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TV</th>\n",
       "      <td>0.040539</td>\n",
       "      <td>0.054535</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              0         1\n",
       "const  5.841796  8.223391\n",
       "TV     0.040539  0.054535"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 99% CI (alpha = 1%) based on t-distribution\n",
    "reg.conf_int(alpha=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regression summary provides $t$-statistic and p-value for the null hypothesis $H_0: \\hat{\\beta}_j = 0$, $H_a: \\hat{\\beta}_j \\neq 0$. You can call the resulting $t$-statistic and p-value with its attributes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "const    15.360275\n",
      "TV       17.667626\n",
      "dtype: float64 \n",
      "\n",
      "const    1.406300e-35\n",
      "TV       1.467390e-42\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(reg.tvalues, '\\n')\n",
    "print(reg.pvalues)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you wish to test a different null hypothesis, e.g. $H_0: \\hat{\\beta}_{TV} = 0.054$ vs. $H_1: \\hat{\\beta}_{TV} \\neq 0.054$ use the following code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.contrast.ContrastResults'>\n",
       "                             Test for Constraints                             \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "c0             0.0475      0.003     -2.402      0.017       0.042       0.053\n",
       "=============================================================================="
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.t_test('TV=0.054')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As far as I know, `Statsmodels` does not provide a function to calculate 'greater than' or 'smaller than' alternative hypothesis. Reason being: because with symmetric distributions, the one-sided test can be derived from the two-sided test. A one-sided p-value is just half of the two-sided p-value. This means that given p and $t$ values from a two-tailed test, you would reject the null hypothesis of a greater-than test when p/2 < alpha and $t$ > 0, and of a less-than test when p/2 < alpha and $t$ < 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coefficient of Determination\n",
    "\n",
    "The $R^2$ measure, or \"coefficient of determination\", displays the proportion of the variability in $y$ that is well explained by the regression fit. It is defined as \n",
    "\n",
    "$$\\begin{equation}\n",
    "R^2 = \\frac{TSS - SSR}{TSS} = 1 - \\frac{SSR}{TSS}\n",
    "\\end{equation}$$\n",
    "\n",
    "where TSS is the *total sum of squares*, defined as $TSS = \\sum (y_i - \\bar{y})^2$, and SSR is the *sum of squared residuals*, given by $SSR = \\sum (y_i - \\hat{y}_i)^2$.\n",
    "\n",
    "It is easy to call the $R^2$ value from the regression object `reg` as the following line shows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.611875050850071"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# R squared measure\n",
    "reg.rsquared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression Diagnostics\n",
    "### Test of Homoskedasticity\n",
    "\n",
    "In general we assume a constant variance of the error term (homoskedasticity; $Var(\\epsilon_i) = \\sigma^2$ for $i = 1, \\ldots, N$). From the residuals vs. fitted plot we have to question this assumption. To test it mathematically, you can run a heteroskedasticity test. The stats package offers several test options; the more common ones are White's or the one from Breusch-Pagan. See [here for more details](http://www.statsmodels.org/dev/diagnostic.html) on tests on heteroskedasticity.\n",
    "\n",
    "Below the White test is applied as an example. The parameter 'reg.model.exog' simply contains the matrix X (here it is a [200 x 2] matrix with constant 1 in first column and values for TV in second). The output should become more clear when you check the function's help page (use `?sm.stats.diagnostic.het_white`). \n",
    "\n",
    "The null hypothesis is that the error variance does **not** depend on X, thus is homoskedastic. Based on the large f-statistic value we can gently reject the null-hypothesis that the error variance is homoskedastic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f-statistic:             35.1683 \n",
      "p-value for f-statistic:  0.0000\n"
     ]
    }
   ],
   "source": [
    "# Test for heteroskedasticity with White test\n",
    "wht = sm.stats.diagnostic.het_white(resid=reg.resid, exog=reg.model.exog)\n",
    "print('f-statistic: {0:>19.4f} \\n'\n",
    "      'p-value for f-statistic: {1:>7.4f}'.format(wht[2], wht[3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you wish to run tests with heteroskedastistic robust standard errors you can either access the `reg` object's robust standard errors (`reg.HC0_se`, `reg.HC1_se`, `reg.HC2_se`, `reg.HC3_se`) or, more conveniently, directly define the covariance estimator (e.g. 'HC3' as below) when you generate the object in the first place. Below example shows how you can do this. See also [here](http://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.RegressionResults.html) or [here](https://stackoverflow.com/questions/30553838/getting-statsmodels-to-use-heteroskedasticity-corrected-standard-errors-in-coeff) for some further information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "const    0.336426\n",
      "TV       0.002890\n",
      "dtype: float64 \n",
      "\n",
      "const    0.336426\n",
      "TV       0.002890\n",
      "dtype: float64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Ben Zimmermann\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "regRobust = sm.OLS(ad.sales, exog=sm.add_constant(ad.TV)).fit(cov_type='HC3')\n",
    "print(regRobust.HC3_se, '\\n')\n",
    "print(reg.HC3_se)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other Relevant Checks\n",
    "\n",
    "The `statsmodels` package offers many more functions to run regression diagnostics, e.g. checks for autocorrelation, non-linearity, normality of residuals etc. These functions are applicable to both simple as well as multiple linear regression models. There's a short [Jupyther notebook](http://www.statsmodels.org/dev/examples/notebooks/generated/regression_diagnostics.html) detailing some of the options. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application: Stock Beta\n",
    "\n",
    "A stock beta measures the systematic risk of a security, the tendency of a security to respond to swings in the broad market. Typically, a large, well diversified index is taken as a proxy for the market portfolio (e.g. S&P500, Euro Stoxx 50, SPI, etc.). There are different ways to calculate a stock beta. We will show the regression approach, where a stock's beta is the slope of the following linear regression:\n",
    "\n",
    "$$\\begin{equation}\n",
    "r - r_f = \\alpha + \\beta(r_M - r_f) + e\n",
    "\\end{equation}$$\n",
    "\n",
    "Let us look into Geberit's stock beta. As a proxy for the market portfolio we use the Swiss market index (SMI). The risk free rate is set to $r_f=0$, which is a fairly reasonable approach in light of [the Swiss national bank's (SNB) interest rates](https://data.snb.ch/de/topics/ziredev#!/cube/zimoma) for the past eight years (at the time of this writing in 2021). We will work with monthly returns for the past five years (60 months) - though other approaches (e.g. last 24 monthly returns, weekly returns for last 2 years, etc.) are reasonable choices too. The stock and SMI data we will load from a csv that was sourced through a financial data provider."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ABBN</th>\n",
       "      <th>ADEN</th>\n",
       "      <th>BAER</th>\n",
       "      <th>CFR</th>\n",
       "      <th>CSGN</th>\n",
       "      <th>GEBN</th>\n",
       "      <th>GIVN</th>\n",
       "      <th>LHN</th>\n",
       "      <th>LONN</th>\n",
       "      <th>NESN</th>\n",
       "      <th>...</th>\n",
       "      <th>ROG</th>\n",
       "      <th>SCMN</th>\n",
       "      <th>SGSN</th>\n",
       "      <th>SLHN</th>\n",
       "      <th>SREN</th>\n",
       "      <th>UBSG</th>\n",
       "      <th>UHR</th>\n",
       "      <th>ZURN</th>\n",
       "      <th>SIK</th>\n",
       "      <th>SMI</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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>2018-01-31</th>\n",
       "      <td>25.95</td>\n",
       "      <td>76.60</td>\n",
       "      <td>63.9</td>\n",
       "      <td>89.32</td>\n",
       "      <td>17.96</td>\n",
       "      <td>441.0</td>\n",
       "      <td>2240.0</td>\n",
       "      <td>57.00</td>\n",
       "      <td>258.9</td>\n",
       "      <td>80.42</td>\n",
       "      <td>...</td>\n",
       "      <td>229.45</td>\n",
       "      <td>508.4</td>\n",
       "      <td>2503</td>\n",
       "      <td>349.5</td>\n",
       "      <td>91.80</td>\n",
       "      <td>18.90</td>\n",
       "      <td>426.5</td>\n",
       "      <td>305.9</td>\n",
       "      <td>8065</td>\n",
       "      <td>9335.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-29</th>\n",
       "      <td>26.12</td>\n",
       "      <td>74.55</td>\n",
       "      <td>59.6</td>\n",
       "      <td>88.30</td>\n",
       "      <td>17.40</td>\n",
       "      <td>429.1</td>\n",
       "      <td>2252.0</td>\n",
       "      <td>54.95</td>\n",
       "      <td>263.3</td>\n",
       "      <td>83.80</td>\n",
       "      <td>...</td>\n",
       "      <td>246.50</td>\n",
       "      <td>518.5</td>\n",
       "      <td>2541</td>\n",
       "      <td>345.0</td>\n",
       "      <td>91.25</td>\n",
       "      <td>17.94</td>\n",
       "      <td>397.4</td>\n",
       "      <td>296.6</td>\n",
       "      <td>7740</td>\n",
       "      <td>9381.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-30</th>\n",
       "      <td>25.19</td>\n",
       "      <td>74.40</td>\n",
       "      <td>57.8</td>\n",
       "      <td>84.70</td>\n",
       "      <td>16.66</td>\n",
       "      <td>427.8</td>\n",
       "      <td>2238.0</td>\n",
       "      <td>53.80</td>\n",
       "      <td>257.1</td>\n",
       "      <td>84.25</td>\n",
       "      <td>...</td>\n",
       "      <td>248.20</td>\n",
       "      <td>519.0</td>\n",
       "      <td>2432</td>\n",
       "      <td>330.2</td>\n",
       "      <td>92.20</td>\n",
       "      <td>16.99</td>\n",
       "      <td>358.7</td>\n",
       "      <td>297.2</td>\n",
       "      <td>7600</td>\n",
       "      <td>9318.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-31</th>\n",
       "      <td>26.08</td>\n",
       "      <td>79.15</td>\n",
       "      <td>59.0</td>\n",
       "      <td>92.00</td>\n",
       "      <td>15.73</td>\n",
       "      <td>451.6</td>\n",
       "      <td>2228.0</td>\n",
       "      <td>56.35</td>\n",
       "      <td>265.0</td>\n",
       "      <td>83.90</td>\n",
       "      <td>...</td>\n",
       "      <td>230.50</td>\n",
       "      <td>504.0</td>\n",
       "      <td>2464</td>\n",
       "      <td>346.8</td>\n",
       "      <td>93.85</td>\n",
       "      <td>16.98</td>\n",
       "      <td>391.0</td>\n",
       "      <td>304.5</td>\n",
       "      <td>7385</td>\n",
       "      <td>9242.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-29</th>\n",
       "      <td>23.94</td>\n",
       "      <td>75.40</td>\n",
       "      <td>57.3</td>\n",
       "      <td>88.50</td>\n",
       "      <td>15.33</td>\n",
       "      <td>458.1</td>\n",
       "      <td>2107.0</td>\n",
       "      <td>56.60</td>\n",
       "      <td>254.0</td>\n",
       "      <td>81.10</td>\n",
       "      <td>...</td>\n",
       "      <td>247.20</td>\n",
       "      <td>496.2</td>\n",
       "      <td>2323</td>\n",
       "      <td>341.1</td>\n",
       "      <td>87.70</td>\n",
       "      <td>16.55</td>\n",
       "      <td>402.8</td>\n",
       "      <td>295.4</td>\n",
       "      <td>7205</td>\n",
       "      <td>9157.46</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             ABBN   ADEN  BAER    CFR   CSGN   GEBN    GIVN    LHN   LONN  \\\n",
       "Date                                                                        \n",
       "2018-01-31  25.95  76.60  63.9  89.32  17.96  441.0  2240.0  57.00  258.9   \n",
       "2017-12-29  26.12  74.55  59.6  88.30  17.40  429.1  2252.0  54.95  263.3   \n",
       "2017-11-30  25.19  74.40  57.8  84.70  16.66  427.8  2238.0  53.80  257.1   \n",
       "2017-10-31  26.08  79.15  59.0  92.00  15.73  451.6  2228.0  56.35  265.0   \n",
       "2017-09-29  23.94  75.40  57.3  88.50  15.33  458.1  2107.0  56.60  254.0   \n",
       "\n",
       "             NESN  ...     ROG   SCMN  SGSN   SLHN   SREN   UBSG    UHR  \\\n",
       "Date               ...                                                    \n",
       "2018-01-31  80.42  ...  229.45  508.4  2503  349.5  91.80  18.90  426.5   \n",
       "2017-12-29  83.80  ...  246.50  518.5  2541  345.0  91.25  17.94  397.4   \n",
       "2017-11-30  84.25  ...  248.20  519.0  2432  330.2  92.20  16.99  358.7   \n",
       "2017-10-31  83.90  ...  230.50  504.0  2464  346.8  93.85  16.98  391.0   \n",
       "2017-09-29  81.10  ...  247.20  496.2  2323  341.1  87.70  16.55  402.8   \n",
       "\n",
       "             ZURN   SIK      SMI  \n",
       "Date                              \n",
       "2018-01-31  305.9  8065  9335.40  \n",
       "2017-12-29  296.6  7740  9381.87  \n",
       "2017-11-30  297.2  7600  9318.77  \n",
       "2017-10-31  304.5  7385  9242.18  \n",
       "2017-09-29  295.4  7205  9157.46  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('Data/SMIDataMonthly.csv', sep=',',\n",
    "                 parse_dates=['Date'], dayfirst=True,\n",
    "                 index_col=['Date'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataframe `df` contains monthly closing prices on all SMI-stocks (incl. SMI index) with a date index in descending order. Let us create a separate Pandas dataframe with the returns of the past 60 months (`dfRets`) for both GEBN as well as the index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            GEBNrets   SMIrets\n",
      "Date                          \n",
      "2018-01-31  0.027355 -0.004965\n",
      "2017-12-29  0.003034  0.006748\n",
      "2017-11-30 -0.054141  0.008253\n",
      "2017-10-31 -0.014291  0.009209\n",
      "2017-09-29  0.044640  0.025662\n"
     ]
    }
   ],
   "source": [
    "# Calculate returns and assign to variable dfRets\n",
    "dfRets = pd.DataFrame()\n",
    "dfRets['GEBNrets'] = np.log(df['GEBN'] / df['GEBN'].shift(-1))\n",
    "dfRets['SMIrets'] = np.log(df['SMI'] / df['SMI'].shift(-1))\n",
    "print(dfRets.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having done that, we are already set to run the regression and print the results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               GEBNrets   R-squared:                       0.311\n",
      "Model:                            OLS   Adj. R-squared:                  0.300\n",
      "Method:                 Least Squares   F-statistic:                     26.23\n",
      "Date:                Thu, 16 Feb 2023   Prob (F-statistic):           3.62e-06\n",
      "Time:                        19:40:27   Log-Likelihood:                 107.89\n",
      "No. Observations:                  60   AIC:                            -211.8\n",
      "Df Residuals:                      58   BIC:                            -207.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0086      0.005      1.617      0.111      -0.002       0.019\n",
      "SMIrets        0.9156      0.179      5.121      0.000       0.558       1.273\n",
      "==============================================================================\n",
      "Omnibus:                        4.808   Durbin-Watson:                   2.225\n",
      "Prob(Omnibus):                  0.090   Jarque-Bera (JB):                4.204\n",
      "Skew:                           0.405   Prob(JB):                        0.122\n",
      "Kurtosis:                       4.013   Cond. No.                         34.0\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Ben Zimmermann\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "# Set observation period (last 60 monthly returns)\n",
    "months = 60\n",
    "\n",
    "# Create OLS object, run regression and calculate fit\n",
    "regBeta = sm.OLS(endog=dfRets.iloc[:months, 0], \n",
    "                 exog=sm.add_constant(dfRets.iloc[:months, 1])).fit()\n",
    "\n",
    "# Show table on coefficients\n",
    "print(regBeta.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the regression output we have no reason to reject the null of Geberit's stock beta being equal to zero. The $R^2$ measure, though, shows that only a small portion of the variation in Geberits monthly returns is explained by SMI's monthly returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get relevant information\n",
    "beta = regBeta.params['SMIrets']\n",
    "alpha = regBeta.params[\"const\"]\n",
    "rsqr = regBeta.rsquared\n",
    "\n",
    "# Plot scatter & lm; add text with alpha, beta , R2\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.scatter(dfRets.iloc[:months, 1], \n",
    "            dfRets.iloc[:months, 0], \n",
    "            marker='.', label='Monthly Returns')\n",
    "plt.plot(dfRets.iloc[:months, 1], regBeta.fittedvalues, c='k', label='Fit')\n",
    "plt.gca().set_aspect('equal')\n",
    "plt.gca().set_xlim(-0.1, 0.15)\n",
    "plt.ylabel('Geberit Monthly Returns')\n",
    "plt.xlabel('SMI Monthly Returns')\n",
    "plt.legend(loc='lower right')\n",
    "plt.text(-0.08, 0.13, 'Beta: {0: .2f}'.format(beta))\n",
    "plt.text(-0.08, 0.12, 'Alpha: {0: .2f}'.format(alpha))\n",
    "plt.text(-0.08, 0.11, 'R^2: {0: .2f}'.format(rsqr));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we calculated above is often referred to as the raw beta. The beta value of a stock has been found to be on average closer to the mean value of 1.0, the beta of an average-systematic-risk portfolio, than to the value of the raw beta (Pinto et al. (2016)). This is why data providers such as Bloomberg publish the adjusted beta as first introduced by Blume (1971), which is calculated as \n",
    "\n",
    "$$ \\text{Adjusted beta} = 2/3 \\cdot \\text{raw beta} + 1/3 \\cdot 1$$\n",
    "\n",
    "Now, let us assume we are given the task to investigate whether a beta indeed regresses to 1 over time. For that we could, as a starting point, assess a stock's rolling beta over the past years. Note that this is just an example of use. Computationally it would be much faster to calculate the stock beta via the covariance/variance formula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rollingBeta(df, window=60):\n",
    "    \n",
    "    '''Calculates the running beta of a stock.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    df : [n x 2] pandas dataframe with log-returns for\n",
    "         stock and market portfolio. Index should be\n",
    "         datetime series.\n",
    "    window : rolling window with default value 60 [optional]\n",
    "        \n",
    "    Returns\n",
    "    =======\n",
    "    rb : Pandas dataframe with (backward-looking) rolling beta. \n",
    "    '''\n",
    "    \n",
    "    # Drop NA rows from df\n",
    "    df = df.dropna()\n",
    "    # Set up empty results array\n",
    "    res = np.empty(len(df) - window + 1)\n",
    "    \n",
    "    # Loop through df\n",
    "    for i in range(0, len(df)):\n",
    "        \n",
    "        # As long as remaining subset is >= window, we proceed\n",
    "        if (len(df) - i) >= window:\n",
    "            \n",
    "            # Subset df\n",
    "            sub = df.iloc[i:window+i, :]\n",
    "            # Run Regression\n",
    "            model = sm.OLS(endog=sub.iloc[:, 0],\n",
    "                           exog=sm.add_constant(sub.iloc[:, 1])).fit()\n",
    "            # Read out beta coefficient\n",
    "            res[i] = model.params[1]\n",
    "    \n",
    "    # Format output to dataframe\n",
    "    rb = pd.DataFrame(data=res, index=df.index[:(len(df)-window+1)])\n",
    "    rb.columns = ['RollingBeta']\n",
    "    \n",
    "    return rb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to call the function. This time we use the last two years of monthly returns. Thus we set `window=24` to overwrite the default value of 60."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Ben Zimmermann\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "# Call function and save output to 'rollBeta'\n",
    "rollBeta = rollingBeta(df=dfRets, window=24)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though this is far away from a thorough analysis, plotting the results shows that at least in Geberit's case, there is indeed some truth to the assessment, that the beta exhibits some reversion to the market beta value of 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import 'mdates' library to format dates in x-axis\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "# Plot rolling beta\n",
    "fig, ax = plt.subplots(1, figsize=(12, 8))\n",
    "ax.plot(rollBeta, label='Geberit Rolling Beta')\n",
    "ax.axhline(y=1, c='gray', linestyle=':')  # Horizontal line\n",
    "ax.legend(fontsize=12)\n",
    "ax.xaxis.set_major_locator(mdates.MonthLocator(interval=6))\n",
    "ax.xaxis.set_major_formatter(mdates.DateFormatter('%m-%Y'))\n",
    "fig.autofmt_xdate();  # Autorotate x-axis for readability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating the Regression Coefficients\n",
    "\n",
    "Simple linear regression serves well to introduce the concept and to build a good understanding. However, in reality we often have to work with more than one predictor. In the advertising data set for example we had not only data on TV advertising spendings but also on radio newspaper. It thus makes sense to extend the simple to a multiple linear regression model.\n",
    "\n",
    "We again use the Advertising data set to see how this is done in Python. The same functions from the `statsmodels` package apply to multiple linear regression. We run the following regression\n",
    "\n",
    "$$\\text{sales} = \\beta_0 + \\beta_1 \\text{TV} + \\beta_2 \\text{radio} + \\beta_3 \\text{newspaper} + \\epsilon$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assign features and response to X and y\n",
    "y = ad.sales\n",
    "X = ad[['TV', 'radio', 'newspaper']]\n",
    "X = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.897\n",
      "Model:                            OLS   Adj. R-squared:                  0.896\n",
      "Method:                 Least Squares   F-statistic:                     570.3\n",
      "Date:                Thu, 16 Feb 2023   Prob (F-statistic):           1.58e-96\n",
      "Time:                        19:40:29   Log-Likelihood:                -386.18\n",
      "No. Observations:                 200   AIC:                             780.4\n",
      "Df Residuals:                     196   BIC:                             793.6\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          2.9389      0.312      9.422      0.000       2.324       3.554\n",
      "TV             0.0458      0.001     32.809      0.000       0.043       0.049\n",
      "radio          0.1885      0.009     21.893      0.000       0.172       0.206\n",
      "newspaper     -0.0010      0.006     -0.177      0.860      -0.013       0.011\n",
      "==============================================================================\n",
      "Omnibus:                       60.414   Durbin-Watson:                   2.084\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.241\n",
      "Skew:                          -1.327   Prob(JB):                     1.44e-33\n",
      "Kurtosis:                       6.332   Cond. No.                         454.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Run regression and print summary\n",
    "mlReg = sm.OLS(endog=y, exog=X).fit()\n",
    "print(mlReg.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficient for radio (0.1885) tells us, that - holding all other factors fixed - an additional 1'000 dollars in radio advertising spendings will boost the product's sales by 188.5 units."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again: If you are an `R` guy and prefer their syntax, you could import the statsmodels.formula.api subpackage and run something like:\n",
    "\n",
    "> `from statsmodels.formula.api import ols\n",
    "mlReg = ols(\"Sales ~ TV + radio + newspaper\", data=ad).fit()\n",
    "mlReg.summary()`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis Tests\n",
    "\n",
    "Again the summary above provides $t$-statistic and p-value for each individual regression coefficient. As was the case for the simple linear regression, the underlying null hypothesis is that each parameter is zero ($H_0: \\beta_{j,\\, H_0} = 0$). For TV and Radio we reject the null even at the 1% significance level. However, given the large p-value for Newspaper we fail to reject the null for $\\beta_{\\text{Newspaper}} = 0$ at any reasonable level. Thus we can conclude that leaving Newspaper data out might be a reasonable option. If other null hypothesis' ought to be tested, we can use the same command as shown above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.contrast.ContrastResults'>\n",
       "                             Test for Constraints                             \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "c0             0.0458      0.001     -1.244      0.215       0.043       0.049\n",
       "=============================================================================="
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# t-test on H0: beta(TV) = 0.0475\n",
    "mlReg.t_test('TV=0.0475')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output shows that we fail to reject the null hypothesis that $\\beta_{TV} = 0.0475$.\n",
    "\n",
    "\n",
    "Beyond the element-wise hypothesis tests the regression summary also provides **F-statistic** (and the corresponding p-value) on the combined hypothesis that \n",
    "\n",
    "$$\\begin{align}\n",
    "H_0&: \\quad \\beta_j = \\beta_1, \\beta_2, \\ldots \\beta_p = 0 \\\\\n",
    "H_a&: \\quad \\beta_j \\neq 0 \\text{ for at least one $j$}\n",
    "\\end{align}$$\n",
    "\n",
    "On the basis of the corresponding p-value (i.e. 1.58e-96) we can reject the null at any reasonable significance level. Should we be interested in assessing a particular hypothesis, say \n",
    "\n",
    "$$\\begin{align}\n",
    "H_0&: \\quad \\beta_{TV} = \\beta_{\\text{Radio}} = 0.1 \\\\\n",
    "H_a&: \\quad \\beta_{TV} \\neq \\beta_{\\text{Radio}} \\neq 0.1\n",
    "\\end{align}$$\n",
    "we use the `.f_test()` method. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.contrast.ContrastResults'>\n",
       "<F test: F=array([[158.25546736]]), p=1.23080057155986e-41, df_denom=196, df_num=2>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test H0: beta(radio) = beta(newspaper) = 0.1\n",
    "mlReg.f_test('radio = newspaper = 0.1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See the [documentation page](http://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.RegressionResults.f_test.html) for further examples on how this function can be used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Coefficient of Determination\n",
    "\n",
    "The $R^2$ measure for the MLR is the same as for the SLR. However, in the case of MLR it has one drawback: the value will always increase when more explanatory variables are added to the model - even if those variables are only weakly associated with the response. To make good on this disadvantage a modificated measure is often used: **adjusted $R^2$**.\n",
    "\n",
    "$$\\begin{equation}\n",
    "R^2_{adj} = 1 - (1-R^2) \\frac{n-1}{n-p-1}\n",
    "\\end{equation}$$\n",
    "\n",
    "To get this measure in Python, simply use the OLS object and call the `.rsquareed_adj` attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8956373316204668"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlReg.rsquared_adj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Application: Factor Models\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fama-French Three Factor Model\n",
    "\n",
    "We will apply the concept of multiple linear regression in the context of Fama-French's three factor model (Fama and French (1993)). Their model follows Ross' arbitrage pricinge theory which postulates that excess returns are linearly related to a set of systematic risk factors (Ross et al. (1973)). The factors can be returns on other assets, such as the market portfolio, or any other variable (e.g. interest rates, inflation, consumption growth, market sentiment, hedging demands etc.. Fama-French empirically discovered three factors to capture the systematic risk: (A) firm size, (B) book-to-market ratio (B/M) and (C) market risk. To quantify their findings, Fama-French constructed zero-net-investment factor portfolios capturing the systematic risk on firm size (factor is labeled 'small minus big' (SMB) and is constructed by going long on small and short on big size stocks) and B/M (labeled 'high minus low' (HML), i.e. going long on high B/M, short on low B/M stocks). The sensitivity of individual stocks to the three factors is then given by the estimated coefficients of a multiple linear regression. As a group the three factors combine for the total risk premium. \n",
    "\n",
    "The expected excess return $R_{it}$ of asset $i$ at time $t$ in the Fama-French three-factor model is described by\n",
    "\n",
    "$$\\begin{equation}\n",
    "R_{it} = \\alpha_i + \\beta_i^{M} (r_{M,t} - r_{f,t}) + \\beta_i^{SMB} SMB_t + \\beta_i^{HML} HML_t + \\epsilon_{it}\n",
    "\\end{equation}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above Fama-French factors are calculated on a monthly basis and published on [Kenneth R. French's website](http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). There you will also find information on the methodology of the model and lots of other possible factors besides the three we look into here. To run this regression in Python we use a shortcut. The `pandas_datareader` package is capable of loading the data without having to download a txt or csv file in a separate step. \n",
    "\n",
    "We will calculate the factor beta for all 20 SMI stocks. For that we use Fama-French's 'European 3 Factors' data. Following our 'Stock Beta' example from above and for the sake of simplicity, the risk free rate for Switzerland is again assumed to be zero (wrt. $R_{it}$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare Data for Fama-French Model\n",
    "We start by importing the `pandas_datareader.data` package and defining some key parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas_datareader as web\n",
    "\n",
    "# Define obs. period, start & enddate\n",
    "months = 60\n",
    "startdate = '2012-06-01'\n",
    "enddate   = '2017-12-31'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Side Note:** If you want to know what data is available (and their labels), you can run the `get_available_datasets()` function.\n",
    "\n",
    "> `from pandas_datareader.famafrench import get_available_datasets\n",
    "get_available_datasets()`\n",
    "\n",
    "or simply check [Kenneth R. French's website](http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Load FF factors \n",
    "data = web.DataReader('Europe_3_Factors', data_source='famafrench',\n",
    "                      start=startdate, end=enddate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variable `data` is a dictionary with three entries: monhtly data, annual data and a description. We select the monthly rates in dictionary 0 and format the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Mkt-RF     SMB     HML      RF\n",
      "Date                                   \n",
      "2017-12  0.0147  0.0155  0.0050  0.0009\n",
      "2017-11 -0.0001 -0.0038  0.0129  0.0008\n",
      "2017-10  0.0059 -0.0096 -0.0013  0.0009\n"
     ]
    }
   ],
   "source": [
    "# Select monthly data\n",
    "ff = data[0]\n",
    "\n",
    "# Sort data in descending order\n",
    "ff = ff.sort_index(ascending=False)\n",
    "\n",
    "# Convert returns to decimal percentages\n",
    "ff = ff/100\n",
    "print(ff.head(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we calculate the log-returns of all SMI stocks. The share prices are taken from dataframe `df` which we loaded above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\BENZIM~1\\AppData\\Local\\Temp/ipykernel_8780/504962713.py:2: FutureWarning: Value based partial slicing on non-monotonic DatetimeIndexes with non-existing keys is deprecated and will raise a KeyError in a future Version.\n",
      "  shsRets = shsRets['2012-06-01':'2017-12-31']\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ABBN</th>\n",
       "      <th>ADEN</th>\n",
       "      <th>BAER</th>\n",
       "      <th>CFR</th>\n",
       "      <th>CSGN</th>\n",
       "      <th>GEBN</th>\n",
       "      <th>GIVN</th>\n",
       "      <th>LHN</th>\n",
       "      <th>LONN</th>\n",
       "      <th>NESN</th>\n",
       "      <th>NOVN</th>\n",
       "      <th>ROG</th>\n",
       "      <th>SCMN</th>\n",
       "      <th>SGSN</th>\n",
       "      <th>SLHN</th>\n",
       "      <th>SREN</th>\n",
       "      <th>UBSG</th>\n",
       "      <th>UHR</th>\n",
       "      <th>ZURN</th>\n",
       "      <th>SIK</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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>2017-12-29</th>\n",
       "      <td>0.036254</td>\n",
       "      <td>0.002014</td>\n",
       "      <td>0.030667</td>\n",
       "      <td>0.041625</td>\n",
       "      <td>0.043460</td>\n",
       "      <td>0.003034</td>\n",
       "      <td>0.006236</td>\n",
       "      <td>0.021150</td>\n",
       "      <td>0.023829</td>\n",
       "      <td>-0.005356</td>\n",
       "      <td>-0.021609</td>\n",
       "      <td>-0.006873</td>\n",
       "      <td>-0.000964</td>\n",
       "      <td>0.043844</td>\n",
       "      <td>0.043846</td>\n",
       "      <td>-0.010357</td>\n",
       "      <td>0.054408</td>\n",
       "      <td>0.102457</td>\n",
       "      <td>-0.002021</td>\n",
       "      <td>0.018253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-11-30</th>\n",
       "      <td>-0.034722</td>\n",
       "      <td>-0.061889</td>\n",
       "      <td>-0.020549</td>\n",
       "      <td>-0.082673</td>\n",
       "      <td>0.057441</td>\n",
       "      <td>-0.054141</td>\n",
       "      <td>0.004478</td>\n",
       "      <td>-0.046309</td>\n",
       "      <td>-0.030265</td>\n",
       "      <td>0.004163</td>\n",
       "      <td>0.024040</td>\n",
       "      <td>0.073984</td>\n",
       "      <td>0.029328</td>\n",
       "      <td>-0.013072</td>\n",
       "      <td>-0.049050</td>\n",
       "      <td>-0.017738</td>\n",
       "      <td>0.000589</td>\n",
       "      <td>-0.086221</td>\n",
       "      <td>-0.024266</td>\n",
       "      <td>0.028697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-10-31</th>\n",
       "      <td>0.085618</td>\n",
       "      <td>0.048538</td>\n",
       "      <td>0.029237</td>\n",
       "      <td>0.038786</td>\n",
       "      <td>0.025758</td>\n",
       "      <td>-0.014291</td>\n",
       "      <td>0.055839</td>\n",
       "      <td>-0.004427</td>\n",
       "      <td>0.042396</td>\n",
       "      <td>0.033943</td>\n",
       "      <td>-0.008480</td>\n",
       "      <td>-0.069947</td>\n",
       "      <td>0.015597</td>\n",
       "      <td>0.058927</td>\n",
       "      <td>0.016573</td>\n",
       "      <td>0.067776</td>\n",
       "      <td>0.025650</td>\n",
       "      <td>-0.029733</td>\n",
       "      <td>0.030341</td>\n",
       "      <td>0.024676</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                ABBN      ADEN      BAER       CFR      CSGN      GEBN  \\\n",
       "Date                                                                     \n",
       "2017-12-29  0.036254  0.002014  0.030667  0.041625  0.043460  0.003034   \n",
       "2017-11-30 -0.034722 -0.061889 -0.020549 -0.082673  0.057441 -0.054141   \n",
       "2017-10-31  0.085618  0.048538  0.029237  0.038786  0.025758 -0.014291   \n",
       "\n",
       "                GIVN       LHN      LONN      NESN      NOVN       ROG  \\\n",
       "Date                                                                     \n",
       "2017-12-29  0.006236  0.021150  0.023829 -0.005356 -0.021609 -0.006873   \n",
       "2017-11-30  0.004478 -0.046309 -0.030265  0.004163  0.024040  0.073984   \n",
       "2017-10-31  0.055839 -0.004427  0.042396  0.033943 -0.008480 -0.069947   \n",
       "\n",
       "                SCMN      SGSN      SLHN      SREN      UBSG       UHR  \\\n",
       "Date                                                                     \n",
       "2017-12-29 -0.000964  0.043844  0.043846 -0.010357  0.054408  0.102457   \n",
       "2017-11-30  0.029328 -0.013072 -0.049050 -0.017738  0.000589 -0.086221   \n",
       "2017-10-31  0.015597  0.058927  0.016573  0.067776  0.025650 -0.029733   \n",
       "\n",
       "                ZURN       SIK  \n",
       "Date                            \n",
       "2017-12-29 -0.002021  0.018253  \n",
       "2017-11-30 -0.024266  0.028697  \n",
       "2017-10-31  0.030341  0.024676  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shsRets = np.log(df / df.shift(-1))\n",
    "shsRets = shsRets['2012-06-01':'2017-12-31']\n",
    "shsRets = shsRets.iloc[:, :-1]  # We exclude the last column (with SMI data)\n",
    "shsRets.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate Fama-French Coefficients\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to run the regression we need to have matching indices. Fama-French's index is 'yyyy-mm' while our dataframe with returns has format 'yyyy-mm-dd'. Since we know that the length of both dataframes is equal, we can simply overwrite the index of one of the dataframes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create matching indices\n",
    "ff.index = shsRets.index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now in a position to run the multiple linear regression. We will again use the past 60 months. From the Fama French set we just need the first three columns. Column 4 is the risk free rate which we do not use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Ben Zimmermann\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    }
   ],
   "source": [
    "# Add constant to matrix for alphas (=intercept)\n",
    "X = sm.add_constant(ff.iloc[:months, :3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assign ticker to variable\n",
    "tickers = shsRets.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create results matrix to paste beta factors\n",
    "res = np.empty(shape=(5, len(tickers)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Run regression for each ticker\n",
    "for i in range(0, len(tickers)):\n",
    "    \n",
    "    # Select returns of share i\n",
    "    sub = shsRets.iloc[:months, i]\n",
    "    # Run regression\n",
    "    model = sm.OLS(endog=sub, exog=X).fit()\n",
    "    # Paste beta factors to 'res' matrix\n",
    "    res[0:4, i] = model.params\n",
    "    res[4, i] = model.rsquared_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Format output to dataframe\n",
    "ff3f = pd.DataFrame(data=res, index=['Alpha', 'BetaMkt', 'BetaSMB', 'BetaHML', 'R2_adj'])\n",
    "ff3f.columns = tickers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here are our factors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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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>ABBN</th>\n",
       "      <th>ADEN</th>\n",
       "      <th>BAER</th>\n",
       "      <th>CFR</th>\n",
       "      <th>CSGN</th>\n",
       "      <th>GEBN</th>\n",
       "      <th>GIVN</th>\n",
       "      <th>LHN</th>\n",
       "      <th>LONN</th>\n",
       "      <th>NESN</th>\n",
       "      <th>NOVN</th>\n",
       "      <th>ROG</th>\n",
       "      <th>SCMN</th>\n",
       "      <th>SGSN</th>\n",
       "      <th>SLHN</th>\n",
       "      <th>SREN</th>\n",
       "      <th>UBSG</th>\n",
       "      <th>UHR</th>\n",
       "      <th>ZURN</th>\n",
       "      <th>SIK</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alpha</th>\n",
       "      <td>-0.000906</td>\n",
       "      <td>-0.001914</td>\n",
       "      <td>0.005105</td>\n",
       "      <td>-0.002015</td>\n",
       "      <td>-0.011465</td>\n",
       "      <td>0.011036</td>\n",
       "      <td>0.013076</td>\n",
       "      <td>-0.011962</td>\n",
       "      <td>0.022730</td>\n",
       "      <td>0.003479</td>\n",
       "      <td>0.003800</td>\n",
       "      <td>0.002710</td>\n",
       "      <td>0.005065</td>\n",
       "      <td>0.000988</td>\n",
       "      <td>0.010169</td>\n",
       "      <td>0.005657</td>\n",
       "      <td>-0.002030</td>\n",
       "      <td>-0.009120</td>\n",
       "      <td>0.002555</td>\n",
       "      <td>0.018161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BetaMkt</th>\n",
       "      <td>0.693293</td>\n",
       "      <td>0.845470</td>\n",
       "      <td>0.625330</td>\n",
       "      <td>0.912283</td>\n",
       "      <td>0.937398</td>\n",
       "      <td>0.464959</td>\n",
       "      <td>0.501213</td>\n",
       "      <td>1.176732</td>\n",
       "      <td>0.803426</td>\n",
       "      <td>0.509535</td>\n",
       "      <td>0.503625</td>\n",
       "      <td>0.448914</td>\n",
       "      <td>0.345137</td>\n",
       "      <td>0.519122</td>\n",
       "      <td>0.481308</td>\n",
       "      <td>0.260073</td>\n",
       "      <td>0.731883</td>\n",
       "      <td>0.926187</td>\n",
       "      <td>0.416506</td>\n",
       "      <td>0.660433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BetaSMB</th>\n",
       "      <td>0.279470</td>\n",
       "      <td>0.693865</td>\n",
       "      <td>0.041670</td>\n",
       "      <td>-0.395494</td>\n",
       "      <td>0.345019</td>\n",
       "      <td>-0.517202</td>\n",
       "      <td>-0.700818</td>\n",
       "      <td>0.099676</td>\n",
       "      <td>0.078710</td>\n",
       "      <td>-0.423302</td>\n",
       "      <td>-0.418416</td>\n",
       "      <td>-0.324102</td>\n",
       "      <td>-0.809450</td>\n",
       "      <td>-0.296927</td>\n",
       "      <td>0.898115</td>\n",
       "      <td>-0.570457</td>\n",
       "      <td>0.007746</td>\n",
       "      <td>-0.141485</td>\n",
       "      <td>-0.645586</td>\n",
       "      <td>-0.413393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BetaHML</th>\n",
       "      <td>0.140517</td>\n",
       "      <td>0.423802</td>\n",
       "      <td>0.674928</td>\n",
       "      <td>0.284910</td>\n",
       "      <td>1.700849</td>\n",
       "      <td>-0.157164</td>\n",
       "      <td>-0.524454</td>\n",
       "      <td>0.331936</td>\n",
       "      <td>-0.206294</td>\n",
       "      <td>-0.576125</td>\n",
       "      <td>-0.359140</td>\n",
       "      <td>-0.289612</td>\n",
       "      <td>-0.207932</td>\n",
       "      <td>-0.411242</td>\n",
       "      <td>0.542230</td>\n",
       "      <td>-0.284763</td>\n",
       "      <td>1.046295</td>\n",
       "      <td>0.297058</td>\n",
       "      <td>0.039949</td>\n",
       "      <td>0.006759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R2_adj</th>\n",
       "      <td>0.187997</td>\n",
       "      <td>0.336439</td>\n",
       "      <td>0.178910</td>\n",
       "      <td>0.294399</td>\n",
       "      <td>0.356713</td>\n",
       "      <td>0.103455</td>\n",
       "      <td>0.223414</td>\n",
       "      <td>0.432733</td>\n",
       "      <td>0.213924</td>\n",
       "      <td>0.312858</td>\n",
       "      <td>0.164864</td>\n",
       "      <td>0.107853</td>\n",
       "      <td>0.165120</td>\n",
       "      <td>0.100622</td>\n",
       "      <td>0.155472</td>\n",
       "      <td>0.042623</td>\n",
       "      <td>0.295308</td>\n",
       "      <td>0.216747</td>\n",
       "      <td>0.099964</td>\n",
       "      <td>0.169966</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             ABBN      ADEN      BAER       CFR      CSGN      GEBN      GIVN  \\\n",
       "Alpha   -0.000906 -0.001914  0.005105 -0.002015 -0.011465  0.011036  0.013076   \n",
       "BetaMkt  0.693293  0.845470  0.625330  0.912283  0.937398  0.464959  0.501213   \n",
       "BetaSMB  0.279470  0.693865  0.041670 -0.395494  0.345019 -0.517202 -0.700818   \n",
       "BetaHML  0.140517  0.423802  0.674928  0.284910  1.700849 -0.157164 -0.524454   \n",
       "R2_adj   0.187997  0.336439  0.178910  0.294399  0.356713  0.103455  0.223414   \n",
       "\n",
       "              LHN      LONN      NESN      NOVN       ROG      SCMN      SGSN  \\\n",
       "Alpha   -0.011962  0.022730  0.003479  0.003800  0.002710  0.005065  0.000988   \n",
       "BetaMkt  1.176732  0.803426  0.509535  0.503625  0.448914  0.345137  0.519122   \n",
       "BetaSMB  0.099676  0.078710 -0.423302 -0.418416 -0.324102 -0.809450 -0.296927   \n",
       "BetaHML  0.331936 -0.206294 -0.576125 -0.359140 -0.289612 -0.207932 -0.411242   \n",
       "R2_adj   0.432733  0.213924  0.312858  0.164864  0.107853  0.165120  0.100622   \n",
       "\n",
       "             SLHN      SREN      UBSG       UHR      ZURN       SIK  \n",
       "Alpha    0.010169  0.005657 -0.002030 -0.009120  0.002555  0.018161  \n",
       "BetaMkt  0.481308  0.260073  0.731883  0.926187  0.416506  0.660433  \n",
       "BetaSMB  0.898115 -0.570457  0.007746 -0.141485 -0.645586 -0.413393  \n",
       "BetaHML  0.542230 -0.284763  1.046295  0.297058  0.039949  0.006759  \n",
       "R2_adj   0.155472  0.042623  0.295308  0.216747  0.099964  0.169966  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ff3f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Alpha    BetaMkt    BetaSMB    BetaHML     R2_adj\n",
      "count  20.000000  20.000000  20.000000  20.000000  20.000000\n",
      "mean    0.003256   0.638141  -0.160618   0.123625   0.207969\n",
      "std     0.008962   0.235797   0.461006   0.566272   0.101621\n",
      "min    -0.011962   0.260073  -0.809450  -0.576125   0.042623\n",
      "25%    -0.001940   0.477221  -0.446777  -0.285975   0.143567\n",
      "50%     0.003095   0.572226  -0.310515   0.023354   0.183454\n",
      "75%     0.006785   0.813937   0.083951   0.354903   0.294626\n",
      "max     0.022730   1.176732   0.898115   1.700849   0.432733\n"
     ]
    }
   ],
   "source": [
    "# Transpose matrix (.T) and display stats summary\n",
    "print(ff3f.T.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hedge a Portolio\n",
    "\n",
    "Now that we have all the factors, let's assume we want to build a portfolio with all 20 SMI stocks that maximizes the Sharpe ratio (SR). As a further condition we want to limit our exposure to the SMB factor to, let's say, $\\beta_p^{SMB} = 0$. How would we allocate our investment under these conditions? In mathematical terms we have the following optimization problem:\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\max_{w_i} SR = \\frac{\\mathbb{E}[r_p] - r_f}{\\sigma_p} \\qquad s.t. \\qquad \n",
    "\\begin{cases}\n",
    "\\sum w_i &= 1 \\\\\n",
    "\\beta_p^{SMB} &= 0\n",
    "\\end{cases}\n",
    "\\end{equation}$$\n",
    "\n",
    "Usually, to calculate the expected return $\\mathbb{E}[r_p]$, historical returns are taken. For our case here, we will take the expected returns given by our Fama-French 3 Factor model (denoted $\\mathbf{R_{ff}}$). The portfolio variance $\\sigma_p$ however, we estimate using historical data. Alternatively one could think of taking the SMI volatility index value as proxy. But this is only approximately true because we will not have the same weights per stock as the SMI and this thus might be questionable. With that we have\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\max_{w_i} SR = \\frac{\\mathbf{w}^T \\left(r_f + \\mathbf{\\alpha} + \\mathbf{\\beta}^{M} (r_{M} - r_{f}) + \\mathbf{\\beta}^{SMB} SMB + \\mathbf{\\beta}^{HML} HML \\right) - r_f}{\\mathbf{w}^T \\mathbf{\\Sigma}\\mathbf{w}} \\qquad s.t. \\qquad \n",
    "\\begin{cases}\n",
    "\\sum w_i &= 1 \\\\\n",
    "\\beta_p^{SMB} &= 0\n",
    "\\end{cases}\n",
    "\\end{equation}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python can solve this problem numerically. We first set the stage by defining a auxiliary function `pfStats` that returns the expected portfolio return, volatility and Sharpe ratio given a vector of weights. Note that the function also makes use of other data like monthly returns and the riskfree rate as previously defined (which is set to 0) but only weights are a function input value. This is necessary for the optimization function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define rf and (equally spread) start weights\n",
    "rf = 0\n",
    "wghts = np.repeat(1. / len(tickers), len(tickers))\n",
    "\n",
    "# Expected stock returns based on ff3f model\n",
    "expShsRets = rf + ff3f.T.Alpha + \\\n",
    "    ff3f.T.BetaMkt * ff['Mkt-RF'].mean() + \\\n",
    "    ff3f.T.BetaSMB * ff.SMB.mean() + \\\n",
    "    ff3f.T.BetaHML * ff.HML.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pfStats(weights):\n",
    "    '''Returns basic measures for a portfolio\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    weights : array-like\n",
    "        weights for different securities in portfolio\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    expPfRet : float\n",
    "        weighted, annualized expected portfolio return based on ff3f model\n",
    "    pfVol : float\n",
    "        historical annualized portfolio volatility\n",
    "    SR : float\n",
    "        portfolio Sharpe ratio for given riskfree rate\n",
    "    '''\n",
    "    \n",
    "    expPfRet = np.sum(weights * expShsRets) * 12\n",
    "    pfVol    = np.sqrt(np.dot(weights.T, np.dot(shsRets.cov() * 12, weights)))\n",
    "    SR       = (expPfRet - rf) / pfVol \n",
    "    \n",
    "    return np.array([expPfRet, pfVol, SR])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python's scipy package has a sublibrary for constrained optimization problems. We will use the minimize function and minimize the negative value of the Sharpe ratio (which is obviously equal to maximizing the SR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as sco\n",
    "\n",
    "def minSR(wghts):\n",
    "    return -pfStats(wghts)[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our constraints are as stated above: $\\sum w_i = 1$, $\\beta_P^{SMB} = 0$. Additionally we set bounds for the weights such that short/long position are allowed but only up to 100% per share ($w_i \\in [-1, 1]\\; \\forall i \\in [1, 2, \\ldots, n]$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constraints and bounds\n",
    "constr = [{'type': 'eq', 'fun': lambda x: np.sum(x) - 1},\n",
    "          {'type': 'eq', 'fun': lambda x: np.sum(x * ff3f.T.BetaSMB) - 0}]\n",
    "bnds   = tuple((-1,1) for x in range(len(tickers)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Minimization function\n",
    "optPf = sco.minimize(minSR, x0=wghts, method='SLSQP', bounds=bnds, constraints=constr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of weights:   1.0\n",
      "Beta SMB factor:  -2.963684853085624e-12\n"
     ]
    }
   ],
   "source": [
    "# Check if conditions are actually met\n",
    "print('Sum of weights:  ', np.sum(optPf['x']))\n",
    "print('Beta SMB factor: ', np.sum(optPf['x'] * ff3f.T.BetaSMB))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Portfolio return:      0.6625784189236861\n",
      "Portfolio volatility:  0.2005679622860137\n",
      "Portfolio SR:          3.303510747039633 \n",
      "\n",
      "      optimalWghts\n",
      "ABBN     -0.054099\n",
      "ADEN     -0.257005\n",
      "BAER      0.099358\n",
      "CFR       0.263547\n",
      "CSGN     -0.191775\n",
      "GEBN      0.078464\n",
      "GIVN      0.606703\n",
      "LHN      -0.465790\n",
      "LONN      0.525159\n",
      "NESN      0.233943\n",
      "NOVN      0.392504\n",
      "ROG      -0.679709\n",
      "SCMN     -0.118646\n",
      "SGSN     -0.266730\n",
      "SLHN      0.739888\n",
      "SREN     -0.049775\n",
      "UBSG      0.078083\n",
      "UHR      -0.280615\n",
      "ZURN     -0.466523\n",
      "SIK       0.813018\n"
     ]
    }
   ],
   "source": [
    "# Calculate portfolio stats given optimal weights\n",
    "rsltsOptPf = pfStats(optPf['x'])\n",
    "\n",
    "# Format weights into dataframe with Tickers as heading\n",
    "optWghts = pd.DataFrame(data=optPf['x'], index=tickers)\n",
    "optWghts.columns = ['optimalWghts']\n",
    "\n",
    "# Print results\n",
    "print('Portfolio return:     ', str(rsltsOptPf[0]))\n",
    "print('Portfolio volatility: ', str(rsltsOptPf[1]))\n",
    "print('Portfolio SR:         ', str(rsltsOptPf[2]), '\\n')\n",
    "print(str(optWghts))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Further Ressources\n",
    "\n",
    "\n",
    "In writing this notebook, many ressources were consulted. For internet ressources the links are provided within the textflow above and will therefore not be listed again. Beyond these links, the following ressources were consulted and are recommended as further reading on the discussed topics:\n",
    "\n",
    "* Blume, Marshall E., 1971, On the Assessment of Risk, *The Journal of Finance* 26, 1-10.\n",
    "* Fama, Eugene F, and Kenneth R French, 1993, Common risk factors in the returns on stocks and bonds, *Journal of Financial Economics* 33, 3–56.\n",
    "* Hilpisch, Yves, 2019, Python for Finance (O'Reilly Media, Sebastopol, CA).\n",
    "* James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani, 2013, *An Introduction to Statistical Learning: With Applications in R* (Springer Science & Business Media, New York, NY).\n",
    "* Müller, Andreas C., and Sarah Guido, 2017, *Introduction to Machine Learning with Python* (O’Reilly Media, Sebastopol, CA).\n",
    "* Pinto, Jerald E., Elaine Henry, Thomas R. Robinson, and John D. Stowe, 2016, *Equity Asset Valuation* (MIT Press, Cambridge, MA).\n",
    "* Ross, Stephen A., et al., 1973, Return, risk and arbitrage (Rodney L. White Center for Financial Research, The Wharton School, University of Pennyslvania).\n",
    "*   Sheppard, Kevin, 2017, Introduction to Python for Econometrics, Statistics and Data Analysis from Website https://www.kevinsheppard.com/images/b/b3/Python_introduction-2016.pdf, 07/07/2017.\n",
    "* Wooldridge, Jeffrey M, 2015, *Introductory Econometrics: A modern approach* (Cengage Learning, Boston, MA).\n",
    "\n"
   ]
  }
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