{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "id": "a6be4a95", "metadata": { "id": "a6be4a95" }, "source": [ "# Running the First Regression in Python" ] }, { "cell_type": "markdown", "id": "b7890b49", "metadata": { "id": "b7890b49" }, "source": [ "Suppose this is your first time to write the code. Perhaps, you want to run a simple regression using two series of asset prices to fin the equity beta. Let's use a step-by-step approach to complete the task.\n", "\n", " Step 1: Download two assets' prices from the web\n", " Step 2: Put them onto a matrix form\n", " Step 3: Run the OLS\n", " Step 4: Plot data" ] }, { "cell_type": "markdown", "id": "d844db66", "metadata": { "id": "d844db66" }, "source": [ "### Step 1: Download data\n", "We will use yahoo finance package (https://pypi.org/project/yfinance/) to download Yahoo Finance data from the web. We need to (1) install and (2) import this package." ] }, { "cell_type": "code", "execution_count": 1, "id": "47c20bb7", "metadata": { "id": "47c20bb7", "outputId": "6cce99f7-51f6-48f1-cca6-99832e742033", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", "Collecting yfinance\n", " Downloading yfinance-0.1.85-py2.py3-none-any.whl (29 kB)\n", "Collecting requests>=2.26\n", " Downloading requests-2.28.1-py3-none-any.whl (62 kB)\n", "\u001b[K |████████████████████████████████| 62 kB 1.7 MB/s \n", "\u001b[?25hRequirement already satisfied: appdirs>=1.4.4 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.4.4)\n", "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.21.6)\n", "Requirement already satisfied: multitasking>=0.0.7 in /usr/local/lib/python3.7/dist-packages (from yfinance) (0.0.11)\n", "Requirement already satisfied: pandas>=0.24.0 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.3.5)\n", "Requirement already satisfied: lxml>=4.5.1 in /usr/local/lib/python3.7/dist-packages (from yfinance) (4.9.1)\n", "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.24.0->yfinance) (2.8.2)\n", "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.24.0->yfinance) (2022.6)\n", "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7.3->pandas>=0.24.0->yfinance) (1.15.0)\n", "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests>=2.26->yfinance) (2.10)\n", "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests>=2.26->yfinance) (2022.9.24)\n", "Requirement already satisfied: charset-normalizer<3,>=2 in /usr/local/lib/python3.7/dist-packages (from requests>=2.26->yfinance) (2.1.1)\n", "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests>=2.26->yfinance) (1.24.3)\n", "Installing collected packages: requests, yfinance\n", " Attempting uninstall: requests\n", " Found existing installation: requests 2.23.0\n", " Uninstalling requests-2.23.0:\n", " Successfully uninstalled requests-2.23.0\n", "Successfully installed requests-2.28.1 yfinance-0.1.85\n" ] } ], "source": [ "!pip install yfinance # to install, remove # and run the cell\n", "import yfinance as yf # to import" ] }, { "cell_type": "code", "execution_count": 2, "id": "479eb94a", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "479eb94a", "outputId": "9d5e8c3c-b4f5-4e0d-b820-a4f4cde8a026" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[*********************100%***********************] 1 of 1 completed\n", "[*********************100%***********************] 1 of 1 completed\n" ] } ], "source": [ "# download\n", "mystock = yf.download(\"TSLA\", start=\"2011-01-01\", end=\"2022-05-31\", interval='1mo')['Adj Close'].rename('TSLA')\n", "index = yf.download(\"SPY\", start=\"2011-01-01\", end=\"2022-05-31\", interval='1mo')['Adj Close'].rename('SPY')" ] }, { "cell_type": "markdown", "id": "9621734b", "metadata": { "id": "9621734b" }, "source": [ "### Step 2: Put two time series onto a matrix\n", "We need pandas module, so let's install and import it. https://pandas.pydata.org/" ] }, { "cell_type": "code", "execution_count": 3, "id": "6b7ec623", "metadata": { "id": "6b7ec623" }, "outputs": [], "source": [ "#!pip install pandas # Actually, you have this alread when you isntalled Anaconda.\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 4, "id": "d16cf519", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 455 }, "id": "d16cf519", "outputId": "3a0a7543-42b2-4ea9-cbbb-3975cb1c1a61" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " TSLA SPY\n", "Date \n", "2011-02-01 -0.008714 0.034738\n", "2011-03-01 0.161574 -0.004206\n", "2011-04-01 -0.005405 0.033432\n", "2011-05-01 0.092029 -0.011215\n", "2011-06-01 -0.033510 -0.021720\n", "... ... ...\n", "2022-01-01 -0.113609 -0.049413\n", "2022-02-01 -0.070768 -0.029517\n", "2022-03-01 0.238009 0.034377\n", "2022-04-01 -0.191945 -0.084935\n", "2022-05-01 -0.129197 0.002257\n", "\n", "[136 rows x 2 columns]" ], "text/html": [ "\n", "
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TSLASPY
Date
2011-02-01-0.0087140.034738
2011-03-010.161574-0.004206
2011-04-01-0.0054050.033432
2011-05-010.092029-0.011215
2011-06-01-0.033510-0.021720
.........
2022-01-01-0.113609-0.049413
2022-02-01-0.070768-0.029517
2022-03-010.2380090.034377
2022-04-01-0.191945-0.084935
2022-05-01-0.1291970.002257
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136 rows × 2 columns

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\n", " \n", " \n", " \n", "\n", " \n", "
\n", "
\n", " " ] }, "metadata": {}, "execution_count": 4 } ], "source": [ "# combine two asset prices onto one matrix called pandas dataframe\n", "data = pd.concat([mystock, index], axis=1)\n", "\n", "# drop missing observations\n", "data2 = data.dropna()\n", "\n", "# compute monthly returns and drop the first observation\n", "data3 = data2.pct_change().dropna()\n", "data3" ] }, { "cell_type": "markdown", "source": [ "### Let's plot data." ], "metadata": { "id": "9VCMsnGjz0E4" }, "id": "9VCMsnGjz0E4" }, { "cell_type": "code", "source": [ "# need to import matplotlib. You already have this in your Jupyter environment, so no need to install.\n", "import matplotlib.pyplot as plt \n", "\n", "data3.plot(subplots=False, figsize=(10, 6)) # plot returns to see volatility levels\n", "\n", "(data2 / data2.iloc[0] * 100).plot(figsize = (10, 6), subplots=False) # plot the wealth change of $100 investment over time " ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 776 }, "id": "WWRly7sfzPiD", "outputId": "6e4cc804-8a6a-4960-89fa-41ce227750f4" }, "id": "WWRly7sfzPiD", "execution_count": 5, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 5 }, { "output_type": "display_data", "data": { "text/plain": [ "
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\n" 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\n" }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "code", "source": [ "data3.plot.hist(bins=50, alpha=0.7, edgecolor='black', subplots=False, figsize=(10,6))\n", "data3.plot.scatter(x='SPY', y='TSLA', c='blue',figsize=(10,6))" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 762 }, "id": "GPcFjGUw5gVF", "outputId": "46e8a392-22b1-4df2-a529-7a7afea5dc53" }, "id": "GPcFjGUw5gVF", "execution_count": 6, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 6 }, { "output_type": "display_data", "data": { "text/plain": [ "
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\n" 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\n" }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "id": "68175734", "metadata": { "id": "68175734" }, "source": [ "### Step 3: Run OLS\n", "We need to install and import statsmodels module. https://www.statsmodels.org/stable/index.html" ] }, { "cell_type": "code", "execution_count": 7, "id": "5dcb73ad", "metadata": { "id": "5dcb73ad" }, "outputs": [], "source": [ "#!pip install statsmodels\n", "import statsmodels.formula.api as smf\n", "import statsmodels.api as sm" ] }, { "cell_type": "code", "execution_count": 8, "id": "ddfd0025", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "ddfd0025", "outputId": "1d8ae556-ebf3-4412-9d2a-88a56aaf9ff3" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: TSLA R-squared: 0.159\n", "Model: OLS Adj. R-squared: 0.153\n", "Method: Least Squares F-statistic: 25.35\n", "Date: Sun, 13 Nov 2022 Prob (F-statistic): 1.51e-06\n", "Time: 19:48:56 Log-Likelihood: 54.624\n", "No. Observations: 136 AIC: -105.2\n", "Df Residuals: 134 BIC: -99.42\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 0.0319 0.015 2.198 0.030 0.003 0.061\n", "SPY 1.7553 0.349 5.035 0.000 1.066 2.445\n", "==============================================================================\n", "Omnibus: 43.834 Durbin-Watson: 1.592\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 109.883\n", "Skew: 1.285 Prob(JB): 1.38e-24\n", "Kurtosis: 6.576 Cond. No. 24.9\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "# run OLS\n", "formula = 'TSLA ~ SPY' # set dep var and indep var\n", "results = smf.ols(formula, data3).fit() # run OLS\n", "print(results.summary()) # print " ] }, { "cell_type": "markdown", "id": "6839b273", "metadata": { "id": "6839b273" }, "source": [ "### beta of TSLA = 1.7553" ] }, { "cell_type": "markdown", "id": "a3f1572a", "metadata": { "id": "a3f1572a" }, "source": [ "### Step 4: Plot the result\n", "We need to install and import matplotlib module. https://matplotlib.org/" ] }, { "cell_type": "code", "execution_count": 9, "id": "0b0e60bb", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 426 }, "id": "0b0e60bb", "outputId": "fabc6d2c-e524-4309-ca64-c4e482465531" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ], "source": [ "#!pip install matplotlib #again, if you installed Anaconda, you have this already.\n", "import matplotlib.pyplot as plt\n", "\n", "fig, ax=plt.subplots(figsize=(10,6))\n", "fig = sm.graphics.plot_partregress_grid(results, fig=fig)" ] }, { "cell_type": "markdown", "id": "f58ce303", "metadata": { "id": "f58ce303" }, "source": [ "### Extra 1: using scipy module, we can get the same beta!" ] }, { "cell_type": "code", "execution_count": 10, "id": "69ce9117", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "69ce9117", "outputId": "7161be2b-c242-4233-aff5-275c41cf4e19" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "1.7553\n", "0.0319\n", "0.4\n", "0.0\n" ] } ], "source": [ "#!pip install scipy # Again, you probabaly have this installed in your Jupyter environment already\n", "from scipy import stats\n", "\n", "beta,alpha,r_value,p_value,std_err = stats.linregress(data3['SPY'],data3[\"TSLA\"])\n", "\n", "print(beta.round(4))\n", "print(alpha.round(4))\n", "print(r_value.round(2))\n", "print(p_value.round(4))" ] }, { "cell_type": "markdown", "id": "b192016a", "metadata": { "id": "b192016a" }, "source": [ "### Extra 2: using a beta formula, we can get the same beta.\n", "\n", "$$ \n", "\\beta_{tsla} = \\frac{\\sigma_{tsla,spy}}{\\sigma_{spy}^2}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "642827eb", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "642827eb", "outputId": "f95ef2ab-dfa4-481d-b648-9c24ee33ae50" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ " TSLA SPY\n", "TSLA 0.376964 0.034167\n", "SPY 0.034167 0.019465\n", "\n", "\n", "1.7553\n" ] } ], "source": [ "# find covariance matrix\n", "cov = data3.cov() * 12\n", "print(cov)\n", "print('\\n') # to give a space \n", "print(round(cov.iloc[0,1]/cov.iloc[1,1], 4))" ] }, { "cell_type": "markdown", "id": "e3ff4c65", "metadata": { "id": "e3ff4c65" }, "source": [ "### Extra3: using linear algebra, we can get the same beta.\n", "Need to install numpy and import it. You probably have this alreay. So skip installation. Just import it. https://numpy.org/\n", "\n", "$$\n", "b=\\begin{bmatrix} b_0 \\\\ b_1 \\\\ \\vdots \\\\ b_{k} \\end{bmatrix}= (X^{'}X)^{-1}X^{'}Y\n", "$$\n", "\n", "\n", "So, a beta estimate form OLS is equal to X matrix transpose times X matrix and take an inverse times X transpose times times Y vector.\n" ] }, { "cell_type": "code", "source": [ "# warnings are annoying, so I include below to supress them. You do not need to do this.\n", "import warnings\n", "warnings.simplefilter(action='ignore', category=FutureWarning)" ], "metadata": { "id": "ApyNN1N27OM9" }, "id": "ApyNN1N27OM9", "execution_count": 12, "outputs": [] }, { "cell_type": "code", "execution_count": 56, "id": "c7903709", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "c7903709", "outputId": "5f12729b-42d6-4f17-b509-fd69323677de" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "1.7553\n" ] } ], "source": [ "import numpy as np\n", "\n", "X = data3['SPY']\n", "y = data3['TSLA']\n", "X_ols = sm.add_constant(X) # add a constant vector \n", "#print(X_ols)\n", "\n", "# compute beta using matrix operation\n", "beta = np.linalg.inv(X_ols.T.dot(X_ols)).dot(X_ols.T.dot(y))\n", "print(round(beta[1], 4))" ] }, { "cell_type": "code", "source": [], "metadata": { "id": "66huY1CAla_1" }, "id": "66huY1CAla_1", "execution_count": 39, "outputs": [] }, { "cell_type": "code", "source": [], "metadata": { "id": "4jWegIranW6y" }, "id": "4jWegIranW6y", "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "source": [ "#sklearn" ], "metadata": { "id": "n_9I-25MnqNA" }, "id": "n_9I-25MnqNA" }, { "cell_type": "code", "source": [ "type(y)" ], "metadata": { "id": "gik_dhRSla89", "outputId": "4eeeba71-177b-4428-b958-e4e788c1ea76", "colab": { "base_uri": "https://localhost:8080/" } }, "id": "gik_dhRSla89", "execution_count": 57, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "pandas.core.series.Series" ] }, "metadata": {}, "execution_count": 57 } ] }, { "cell_type": "code", "source": [ "x = np.array(X).reshape((-1, 1))\n", "x.shape" ], "metadata": { "id": "16P2lHyPltcl", "outputId": "a073c056-9d66-44a1-9e6c-73493b154a37", "colab": { "base_uri": "https://localhost:8080/" } }, "id": "16P2lHyPltcl", "execution_count": 52, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "(136, 1)" ] }, "metadata": {}, "execution_count": 52 } ] }, { "cell_type": "code", "source": [ "y=np.array(y).reshape((-1,1))\n", "y.shape" ], "metadata": { "id": "FHorwTR9ltWi", "outputId": "76082e4d-615c-427f-90c8-6ad28b601c22", "colab": { "base_uri": "https://localhost:8080/" } }, "id": "FHorwTR9ltWi", "execution_count": 53, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "(136, 1)" ] }, "metadata": {}, "execution_count": 53 } ] }, { "cell_type": "code", "source": [ "from sklearn.linear_model import LinearRegression\n", "model = LinearRegression().fit(x,y)" ], "metadata": { "id": "NYe0IYAfj-Wa" }, "id": "NYe0IYAfj-Wa", "execution_count": 54, "outputs": [] }, { "cell_type": "code", "source": [ "r_sq = model.score(x, y)\n", "print(f\"coefficient of determination: {r_sq}\")\n", "print(f\"intercept: {model.intercept_}\")\n", "print(f\"slope: {model.coef_}\")" ], "metadata": { "id": "e6v-eWcPnaev", "outputId": "491779c1-bcf9-4905-df6f-8c574c268a19", "colab": { "base_uri": "https://localhost:8080/" } }, "id": "e6v-eWcPnaev", "execution_count": 55, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "coefficient of determination: 0.1590925668519182\n", "intercept: [0.03187907]\n", "slope: [[1.75529024]]\n" ] } ] }, { "cell_type": "code", "source": [], "metadata": { "id": "epZdGEUQj-SJ" }, "id": "epZdGEUQj-SJ", "execution_count": null, "outputs": [] }, { "cell_type": "code", "source": [], "metadata": { "id": "90WYkmAaj-OP" }, "id": "90WYkmAaj-OP", "execution_count": null, "outputs": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "colab": { "name": "OLS_beta.ipynb", "provenance": [], "collapsed_sections": [], "include_colab_link": true } }, "nbformat": 4, "nbformat_minor": 5 }