From 635160106b99d961cbe981cfd2b644afa01d67ab Mon Sep 17 00:00:00 2001 From: carlobortolan Date: Sun, 11 Aug 2024 22:50:00 +0200 Subject: [PATCH] Update notebook --- case1.py | 13 +- case2.ipynb | 756 --- notebook.html | 8963 +++++++++++++++++++++++++++++++++ case1.ipynb => notebook.ipynb | 5375 ++++++++++++++++---- 4 files changed, 13302 insertions(+), 1805 deletions(-) delete mode 100644 case2.ipynb create mode 100644 notebook.html rename case1.ipynb => notebook.ipynb (79%) diff --git a/case1.py b/case1.py index f0fe71e..95d1759 100644 --- a/case1.py +++ b/case1.py @@ -75,13 +75,14 @@ correlation_matrix_avg = pd.DataFrame() -for year in range(1993, 2018, 5): - returns_sub = returns[returns['Year'].between(year, year+4)] +time_delta = 1 +for year in range(1993, 2018, time_delta): + returns_sub = returns[returns['Year'].between(year, year+time_delta)] correlation_matrix = returns_sub.drop(columns=['Date', 'Year']).corr() - correlation_matrix_avg[f'{year}-{year + 4}'] = correlation_matrix.mean() + correlation_matrix_avg[f'{year}-{year + time_delta}'] = correlation_matrix.mean() - fig = px.imshow(correlation_matrix, text_auto=True, title=f'Correlation Matrix ({year}-{year + 4})', color_continuous_scale='RdBu_r') - # fig.show() + fig = px.imshow(correlation_matrix, text_auto=True, title=f'Correlation Matrix ({year}-{year + time_delta})', color_continuous_scale='RdBu_r', zmin=0, zmax=1) + fig.show() -fig = px.imshow(correlation_matrix_avg, text_auto=True, title='Average correlation over sub-periods', color_continuous_scale='RdBu_r') +fig = px.imshow(correlation_matrix_avg, text_auto=True, title='Average correlation over sub-periods', color_continuous_scale='RdBu_r', zmin=0, zmax=1) # fig.show() diff --git a/case2.ipynb b/case2.ipynb deleted file mode 100644 index 58b6bfb..0000000 --- a/case2.ipynb +++ /dev/null @@ -1,756 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "import statsmodels.api as sm" - ] - }, - { - "cell_type": "markdown", - "id": "e6fb4fc0", - "metadata": {}, - "source": [ - "Prepare MSCI world return data (Switzerland, Germany, France, UK, Japan, USA)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "1c26349b", - "metadata": {}, - "outputs": [], - "source": [ - "dataMSCI = pd.read_csv('data/Case2MSCI.csv')\n", - "# print(dataMSCI.info())\n", - "# print(dataMSCI.describe())\n", - "dataMSCI['Date'] = pd.to_datetime(dataMSCI['Date'])\n", - "\n", - "returnsMSCI = dataMSCI.copy()\n", - "for index in dataMSCI.columns[1:]:\n", - " for i in range(1, len(dataMSCI[index])):\n", - " returnsMSCI.loc[i, index] = np.log(dataMSCI.loc[i, index] / dataMSCI.loc[i - 1, index])\n", - "\n", - "# First row needs to be removed as it is 100% return\n", - "returnsMSCI = returnsMSCI.drop(0)\n", - "\n", - "# print(returnsMSCI.info())\n", - "# print(returnsMSCI.head())" - ] - }, - { - "cell_type": "markdown", - "id": "eff06195", - "metadata": {}, - "source": [ - "Prepare global factors return data (MSCI World, CRB Index, EUR 10Y Rate, FX USD/EUR)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "922755b0", - "metadata": {}, - "outputs": [], - "source": [ - "dataFactors = pd.read_csv('data/Case2Factors.csv')\n", - "# print(dataFactors.info())\n", - "# print(dataFactors.describe())\n", - "dataFactors['Date'] = pd.to_datetime(dataFactors['Date'])\n", - "\n", - "returnsFactors = dataFactors.copy()\n", - "for index in dataFactors.columns[1:]:\n", - " for i in range(1, len(dataFactors[index])):\n", - " returnsFactors.loc[i, index] = np.log(dataFactors.loc[i, index] / dataFactors.loc[i - 1, index])\n", - "\n", - "# First row needs to be removed as it is 100% return\n", - "returnsFactors = returnsFactors.drop(0)\n", - "\n", - "# print(returnsFactors.info())\n", - "# print(returnsFactors.head())" - ] - }, - { - "cell_type": "markdown", - "id": "1ef9a264", - "metadata": {}, - "source": [ - "Market return on the MSCI World index return (single factor model)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "5b3cffde", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n", - "================================ Switzerland =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Switzerland R-squared: 0.631\n", - "Model: OLS Adj. R-squared: 0.628\n", - "Method: Least Squares F-statistic: 202.0\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 2.50e-27\n", - "Time: 23:18:02 Log-Likelihood: 273.35\n", - "No. Observations: 120 AIC: -542.7\n", - "Df Residuals: 118 BIC: -537.1\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0032 0.002 1.404 0.163 -0.001 0.008\n", - "MSCI World 0.6919 0.049 14.214 0.000 0.596 0.788\n", - "==============================================================================\n", - "Omnibus: 1.468 Durbin-Watson: 1.809\n", - "Prob(Omnibus): 0.480 Jarque-Bera (JB): 1.024\n", - "Skew: -0.018 Prob(JB): 0.599\n", - "Kurtosis: 3.451 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Germany =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Germany R-squared: 0.726\n", - "Model: OLS Adj. R-squared: 0.724\n", - "Method: Least Squares F-statistic: 312.7\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 5.74e-35\n", - "Time: 23:18:02 Log-Likelihood: 227.65\n", - "No. Observations: 120 AIC: -451.3\n", - "Df Residuals: 118 BIC: -445.7\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0021 0.003 0.632 0.529 -0.005 0.009\n", - "MSCI World 1.2598 0.071 17.683 0.000 1.119 1.401\n", - "==============================================================================\n", - "Omnibus: 14.964 Durbin-Watson: 2.272\n", - "Prob(Omnibus): 0.001 Jarque-Bera (JB): 30.839\n", - "Skew: -0.472 Prob(JB): 2.01e-07\n", - "Kurtosis: 5.297 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ UK =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: UK R-squared: 0.826\n", - "Model: OLS Adj. R-squared: 0.824\n", - "Method: Least Squares F-statistic: 559.2\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 1.37e-46\n", - "Time: 23:18:02 Log-Likelihood: 303.42\n", - "No. Observations: 120 AIC: -602.8\n", - "Df Residuals: 118 BIC: -597.3\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0007 0.002 0.369 0.712 -0.003 0.004\n", - "MSCI World 0.8960 0.038 23.647 0.000 0.821 0.971\n", - "==============================================================================\n", - "Omnibus: 5.877 Durbin-Watson: 2.333\n", - "Prob(Omnibus): 0.053 Jarque-Bera (JB): 5.334\n", - "Skew: -0.458 Prob(JB): 0.0695\n", - "Kurtosis: 3.477 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Sweden =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Sweden R-squared: 0.652\n", - "Model: OLS Adj. R-squared: 0.649\n", - "Method: Least Squares F-statistic: 220.9\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 8.32e-29\n", - "Time: 23:18:02 Log-Likelihood: 194.41\n", - "No. Observations: 120 AIC: -384.8\n", - "Df Residuals: 118 BIC: -379.3\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0029 0.004 0.659 0.511 -0.006 0.012\n", - "MSCI World 1.3969 0.094 14.864 0.000 1.211 1.583\n", - "==============================================================================\n", - "Omnibus: 12.053 Durbin-Watson: 2.158\n", - "Prob(Omnibus): 0.002 Jarque-Bera (JB): 34.968\n", - "Skew: 0.058 Prob(JB): 2.55e-08\n", - "Kurtosis: 5.642 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Norway =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Norway R-squared: 0.555\n", - "Model: OLS Adj. R-squared: 0.551\n", - "Method: Least Squares F-statistic: 146.9\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 1.85e-22\n", - "Time: 23:18:02 Log-Likelihood: 182.68\n", - "No. Observations: 120 AIC: -361.4\n", - "Df Residuals: 118 BIC: -355.8\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0101 0.005 2.069 0.041 0.000 0.020\n", - "MSCI World 1.2562 0.104 12.122 0.000 1.051 1.461\n", - "==============================================================================\n", - "Omnibus: 27.978 Durbin-Watson: 1.688\n", - "Prob(Omnibus): 0.000 Jarque-Bera (JB): 57.320\n", - "Skew: -0.955 Prob(JB): 3.57e-13\n", - "Kurtosis: 5.796 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ France =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: France R-squared: 0.786\n", - "Model: OLS Adj. R-squared: 0.784\n", - "Method: Least Squares F-statistic: 434.0\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 2.41e-41\n", - "Time: 23:18:02 Log-Likelihood: 269.52\n", - "No. Observations: 120 AIC: -535.0\n", - "Df Residuals: 118 BIC: -529.5\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0021 0.002 0.892 0.374 -0.003 0.007\n", - "MSCI World 1.0470 0.050 20.833 0.000 0.947 1.147\n", - "==============================================================================\n", - "Omnibus: 2.279 Durbin-Watson: 2.394\n", - "Prob(Omnibus): 0.320 Jarque-Bera (JB): 2.014\n", - "Skew: -0.045 Prob(JB): 0.365\n", - "Kurtosis: 3.628 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Italy =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Italy R-squared: 0.630\n", - "Model: OLS Adj. R-squared: 0.627\n", - "Method: Least Squares F-statistic: 201.2\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 2.89e-27\n", - "Time: 23:18:02 Log-Likelihood: 235.38\n", - "No. Observations: 120 AIC: -466.8\n", - "Df Residuals: 118 BIC: -461.2\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0014 0.003 0.446 0.657 -0.005 0.008\n", - "MSCI World 0.9476 0.067 14.186 0.000 0.815 1.080\n", - "==============================================================================\n", - "Omnibus: 8.166 Durbin-Watson: 2.093\n", - "Prob(Omnibus): 0.017 Jarque-Bera (JB): 15.022\n", - "Skew: -0.169 Prob(JB): 0.000547\n", - "Kurtosis: 4.700 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Spain =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Spain R-squared: 0.646\n", - "Model: OLS Adj. R-squared: 0.643\n", - "Method: Least Squares F-statistic: 215.0\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 2.38e-28\n", - "Time: 23:18:02 Log-Likelihood: 230.99\n", - "No. Observations: 120 AIC: -458.0\n", - "Df Residuals: 118 BIC: -452.4\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0066 0.003 2.034 0.044 0.000 0.013\n", - "MSCI World 1.0159 0.069 14.662 0.000 0.879 1.153\n", - "==============================================================================\n", - "Omnibus: 0.012 Durbin-Watson: 2.125\n", - "Prob(Omnibus): 0.994 Jarque-Bera (JB): 0.120\n", - "Skew: 0.012 Prob(JB): 0.942\n", - "Kurtosis: 2.847 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Netherlands =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Netherlands R-squared: 0.763\n", - "Model: OLS Adj. R-squared: 0.761\n", - "Method: Least Squares F-statistic: 380.5\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 1.01e-38\n", - "Time: 23:18:03 Log-Likelihood: 249.86\n", - "No. Observations: 120 AIC: -495.7\n", - "Df Residuals: 118 BIC: -490.2\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0018 0.003 0.665 0.508 -0.004 0.007\n", - "MSCI World 1.1548 0.059 19.506 0.000 1.038 1.272\n", - "==============================================================================\n", - "Omnibus: 3.142 Durbin-Watson: 2.120\n", - "Prob(Omnibus): 0.208 Jarque-Bera (JB): 2.607\n", - "Skew: -0.339 Prob(JB): 0.272\n", - "Kurtosis: 3.247 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Austria =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Austria R-squared: 0.372\n", - "Model: OLS Adj. R-squared: 0.367\n", - "Method: Least Squares F-statistic: 69.89\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 1.43e-13\n", - "Time: 23:18:03 Log-Likelihood: 172.24\n", - "No. Observations: 120 AIC: -340.5\n", - "Df Residuals: 118 BIC: -334.9\n", - "Df Model: 1 \n", - "Covariance Type: nonrobust \n", - "==============================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "------------------------------------------------------------------------------\n", - "const 0.0061 0.005 1.153 0.251 -0.004 0.017\n", - "MSCI World 0.9451 0.113 8.360 0.000 0.721 1.169\n", - "==============================================================================\n", - "Omnibus: 42.561 Durbin-Watson: 1.424\n", - "Prob(Omnibus): 0.000 Jarque-Bera (JB): 193.645\n", - "Skew: -1.099 Prob(JB): 8.92e-43\n", - "Kurtosis: 8.822 Cond. No. 21.3\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" - ] - } - ], - "source": [ - "for country in returnsMSCI.columns[1:]:\n", - " y = returnsMSCI[country]\n", - " X = returnsFactors['MSCI World']\n", - " # Add a constant to the independent variable\n", - " X = sm.add_constant(X)\n", - "\n", - " model = sm.OLS(y, X).fit()\n", - " print(f\"\\n\\n{\"=\"*32} {country} {\"=\"*33}\")\n", - " print(model.summary())" - ] - }, - { - "cell_type": "markdown", - "id": "390ea807", - "metadata": {}, - "source": [ - "Market return on the 4 global factors (4-factor model)" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "0c06cadb", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n", - "================================ Switzerland =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Switzerland R-squared: 0.674\n", - "Model: OLS Adj. R-squared: 0.662\n", - "Method: Least Squares F-statistic: 59.37\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 4.25e-27\n", - "Time: 23:18:03 Log-Likelihood: 280.69\n", - "No. Observations: 120 AIC: -551.4\n", - "Df Residuals: 115 BIC: -537.4\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0035 0.002 1.565 0.120 -0.001 0.008\n", - "FX USD/EUR 0.2081 0.075 2.759 0.007 0.059 0.358\n", - "EUR 10Y Rate 0.0626 0.052 1.206 0.230 -0.040 0.165\n", - "CRB Index -0.1146 0.048 -2.383 0.019 -0.210 -0.019\n", - "MSCI World 0.7431 0.053 14.017 0.000 0.638 0.848\n", - "==============================================================================\n", - "Omnibus: 4.731 Durbin-Watson: 1.689\n", - "Prob(Omnibus): 0.094 Jarque-Bera (JB): 4.503\n", - "Skew: 0.314 Prob(JB): 0.105\n", - "Kurtosis: 3.711 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Germany =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Germany R-squared: 0.807\n", - "Model: OLS Adj. R-squared: 0.800\n", - "Method: Least Squares F-statistic: 120.4\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 3.73e-40\n", - "Time: 23:18:03 Log-Likelihood: 248.73\n", - "No. Observations: 120 AIC: -487.5\n", - "Df Residuals: 115 BIC: -473.5\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0019 0.003 0.655 0.514 -0.004 0.008\n", - "FX USD/EUR 0.5952 0.098 6.046 0.000 0.400 0.790\n", - "EUR 10Y Rate 0.1419 0.068 2.094 0.038 0.008 0.276\n", - "CRB Index -0.1684 0.063 -2.684 0.008 -0.293 -0.044\n", - "MSCI World 1.3622 0.069 19.686 0.000 1.225 1.499\n", - "==============================================================================\n", - "Omnibus: 16.175 Durbin-Watson: 2.404\n", - "Prob(Omnibus): 0.000 Jarque-Bera (JB): 40.147\n", - "Skew: -0.438 Prob(JB): 1.92e-09\n", - "Kurtosis: 5.695 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ UK =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: UK R-squared: 0.839\n", - "Model: OLS Adj. R-squared: 0.834\n", - "Method: Least Squares F-statistic: 150.0\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 1.16e-44\n", - "Time: 23:18:03 Log-Likelihood: 308.22\n", - "No. Observations: 120 AIC: -606.4\n", - "Df Residuals: 115 BIC: -592.5\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0005 0.002 0.279 0.781 -0.003 0.004\n", - "FX USD/EUR 0.1063 0.060 1.772 0.079 -0.013 0.225\n", - "EUR 10Y Rate 0.0983 0.041 2.381 0.019 0.017 0.180\n", - "CRB Index 0.0334 0.038 0.875 0.384 -0.042 0.109\n", - "MSCI World 0.8620 0.042 20.452 0.000 0.779 0.946\n", - "==============================================================================\n", - "Omnibus: 7.626 Durbin-Watson: 2.411\n", - "Prob(Omnibus): 0.022 Jarque-Bera (JB): 7.234\n", - "Skew: -0.550 Prob(JB): 0.0269\n", - "Kurtosis: 3.489 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Sweden =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Sweden R-squared: 0.696\n", - "Model: OLS Adj. R-squared: 0.685\n", - "Method: Least Squares F-statistic: 65.68\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 8.24e-29\n", - "Time: 23:18:03 Log-Likelihood: 202.46\n", - "No. Observations: 120 AIC: -394.9\n", - "Df Residuals: 115 BIC: -381.0\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0018 0.004 0.424 0.673 -0.007 0.010\n", - "FX USD/EUR 0.5744 0.145 3.968 0.000 0.288 0.861\n", - "EUR 10Y Rate 0.0408 0.100 0.409 0.683 -0.157 0.238\n", - "CRB Index -0.0427 0.092 -0.463 0.644 -0.226 0.140\n", - "MSCI World 1.4895 0.102 14.639 0.000 1.288 1.691\n", - "==============================================================================\n", - "Omnibus: 22.814 Durbin-Watson: 2.313\n", - "Prob(Omnibus): 0.000 Jarque-Bera (JB): 94.146\n", - "Skew: 0.465 Prob(JB): 3.60e-21\n", - "Kurtosis: 7.238 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Norway =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Norway R-squared: 0.747\n", - "Model: OLS Adj. R-squared: 0.738\n", - "Method: Least Squares F-statistic: 84.70\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 2.31e-33\n", - "Time: 23:18:03 Log-Likelihood: 216.51\n", - "No. Observations: 120 AIC: -423.0\n", - "Df Residuals: 115 BIC: -409.1\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0065 0.004 1.735 0.085 -0.001 0.014\n", - "FX USD/EUR 0.9059 0.129 7.036 0.000 0.651 1.161\n", - "EUR 10Y Rate 0.3405 0.089 3.843 0.000 0.165 0.516\n", - "CRB Index 0.4185 0.082 5.098 0.000 0.256 0.581\n", - "MSCI World 1.1142 0.091 12.311 0.000 0.935 1.293\n", - "==============================================================================\n", - "Omnibus: 15.924 Durbin-Watson: 1.868\n", - "Prob(Omnibus): 0.000 Jarque-Bera (JB): 33.019\n", - "Skew: -0.509 Prob(JB): 6.76e-08\n", - "Kurtosis: 5.360 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ France =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: France R-squared: 0.852\n", - "Model: OLS Adj. R-squared: 0.847\n", - "Method: Least Squares F-statistic: 165.6\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 9.55e-47\n", - "Time: 23:18:03 Log-Likelihood: 291.60\n", - "No. Observations: 120 AIC: -573.2\n", - "Df Residuals: 115 BIC: -559.3\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0014 0.002 0.676 0.500 -0.003 0.005\n", - "FX USD/EUR 0.4732 0.069 6.872 0.000 0.337 0.610\n", - "EUR 10Y Rate 0.0582 0.047 1.228 0.222 -0.036 0.152\n", - "CRB Index -0.0556 0.044 -1.266 0.208 -0.143 0.031\n", - "MSCI World 1.1211 0.048 23.160 0.000 1.025 1.217\n", - "==============================================================================\n", - "Omnibus: 12.951 Durbin-Watson: 2.605\n", - "Prob(Omnibus): 0.002 Jarque-Bera (JB): 29.042\n", - "Skew: 0.342 Prob(JB): 4.94e-07\n", - "Kurtosis: 5.311 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Italy =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Italy R-squared: 0.706\n", - "Model: OLS Adj. R-squared: 0.696\n", - "Method: Least Squares F-statistic: 68.97\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 1.16e-29\n", - "Time: 23:18:03 Log-Likelihood: 249.08\n", - "No. Observations: 120 AIC: -488.2\n", - "Df Residuals: 115 BIC: -474.2\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const -0.0005 0.003 -0.161 0.873 -0.006 0.005\n", - "FX USD/EUR 0.5203 0.098 5.301 0.000 0.326 0.715\n", - "EUR 10Y Rate -0.0382 0.068 -0.566 0.573 -0.172 0.096\n", - "CRB Index 0.0835 0.063 1.335 0.185 -0.040 0.207\n", - "MSCI World 1.0161 0.069 14.727 0.000 0.879 1.153\n", - "==============================================================================\n", - "Omnibus: 17.824 Durbin-Watson: 2.452\n", - "Prob(Omnibus): 0.000 Jarque-Bera (JB): 76.127\n", - "Skew: -0.185 Prob(JB): 2.95e-17\n", - "Kurtosis: 6.884 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Spain =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Spain R-squared: 0.737\n", - "Model: OLS Adj. R-squared: 0.727\n", - "Method: Least Squares F-statistic: 80.38\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 2.13e-32\n", - "Time: 23:18:03 Log-Likelihood: 248.77\n", - "No. Observations: 120 AIC: -487.5\n", - "Df Residuals: 115 BIC: -473.6\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0057 0.003 1.964 0.052 -4.98e-05 0.011\n", - "FX USD/EUR 0.5245 0.098 5.330 0.000 0.330 0.719\n", - "EUR 10Y Rate -0.0898 0.068 -1.325 0.188 -0.224 0.044\n", - "CRB Index -0.1187 0.063 -1.893 0.061 -0.243 0.006\n", - "MSCI World 1.1800 0.069 17.060 0.000 1.043 1.317\n", - "==============================================================================\n", - "Omnibus: 2.041 Durbin-Watson: 2.419\n", - "Prob(Omnibus): 0.360 Jarque-Bera (JB): 1.545\n", - "Skew: 0.162 Prob(JB): 0.462\n", - "Kurtosis: 3.451 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Netherlands =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Netherlands R-squared: 0.806\n", - "Model: OLS Adj. R-squared: 0.799\n", - "Method: Least Squares F-statistic: 119.4\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 5.33e-40\n", - "Time: 23:18:03 Log-Likelihood: 261.80\n", - "No. Observations: 120 AIC: -513.6\n", - "Df Residuals: 115 BIC: -499.7\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0011 0.003 0.428 0.669 -0.004 0.006\n", - "FX USD/EUR 0.4316 0.088 4.889 0.000 0.257 0.606\n", - "EUR 10Y Rate 0.0570 0.061 0.939 0.350 -0.063 0.177\n", - "CRB Index -0.0364 0.056 -0.647 0.519 -0.148 0.075\n", - "MSCI World 1.2156 0.062 19.588 0.000 1.093 1.339\n", - "==============================================================================\n", - "Omnibus: 1.008 Durbin-Watson: 2.216\n", - "Prob(Omnibus): 0.604 Jarque-Bera (JB): 0.703\n", - "Skew: -0.179 Prob(JB): 0.704\n", - "Kurtosis: 3.110 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", - "\n", - "\n", - "================================ Austria =================================\n", - " OLS Regression Results \n", - "==============================================================================\n", - "Dep. Variable: Austria R-squared: 0.607\n", - "Model: OLS Adj. R-squared: 0.593\n", - "Method: Least Squares F-statistic: 44.37\n", - "Date: Sat, 10 Aug 2024 Prob (F-statistic): 1.75e-22\n", - "Time: 23:18:03 Log-Likelihood: 200.34\n", - "No. Observations: 120 AIC: -390.7\n", - "Df Residuals: 115 BIC: -376.7\n", - "Df Model: 4 \n", - "Covariance Type: nonrobust \n", - "================================================================================\n", - " coef std err t P>|t| [0.025 0.975]\n", - "--------------------------------------------------------------------------------\n", - "const 0.0020 0.004 0.468 0.641 -0.007 0.011\n", - "FX USD/EUR 1.1376 0.147 7.721 0.000 0.846 1.429\n", - "EUR 10Y Rate 0.1561 0.101 1.540 0.126 -0.045 0.357\n", - "CRB Index 0.3184 0.094 3.391 0.001 0.132 0.504\n", - "MSCI World 0.9502 0.104 9.176 0.000 0.745 1.155\n", - "==============================================================================\n", - "Omnibus: 6.503 Durbin-Watson: 1.871\n", - "Prob(Omnibus): 0.039 Jarque-Bera (JB): 11.138\n", - "Skew: -0.004 Prob(JB): 0.00382\n", - "Kurtosis: 4.492 Cond. No. 35.2\n", - "==============================================================================\n", - "\n", - "Notes:\n", - "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" - ] - } - ], - "source": [ - "for country in returnsMSCI.columns[1:]:\n", - " y = returnsMSCI[country]\n", - " X = returnsFactors[['FX USD/EUR', 'EUR 10Y Rate' ,'CRB Index', 'MSCI World']]\n", - " # Add a constant to the independent variable\n", - " X = sm.add_constant(X)\n", - "\n", - " model = sm.OLS(y, X).fit()\n", - " print(f\"\\n\\n{\"=\"*32} {country} {\"=\"*33}\")\n", - " print(model.summary())" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "env", - "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": "3.12.4" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebook.html b/notebook.html new file mode 100644 index 0000000..9678b10 --- /dev/null +++ b/notebook.html @@ -0,0 +1,8963 @@ + + + + + +notebook + + + + + + + + + + + + +
+ + + + + + + + + + + +
+ + diff --git a/case1.ipynb b/notebook.ipynb similarity index 79% rename from case1.ipynb rename to notebook.ipynb index 48e574b..5d1dd50 100644 --- a/case1.ipynb +++ b/notebook.ipynb @@ -1,8 +1,30 @@ { "cells": [ + { + "cell_type": "markdown", + "id": "5e76f051", + "metadata": {}, + "source": [ + "# ICM25\n", + "\n", + "Analysis of the long-term evolution of international equity markets (average returns, volatilities, long-term correlations) and economic risks of European stock markets.\n", + "\n", + "## Case 1: Analyzing 25 years of stock market returns\n", + "\n", + "Analysis of the **longterm evolution of international equity markets**, i.e.\n", + "- Average returns\n", + "- Volatilities\n", + "- Long-term correlations between markets\n", + "- Correlation regimes\n", + "\n", + "Data set ([Case1.csv](./data/Case1.csv)) includes 16 stock market indices in local currencies covering developed markets in North America, Europe and Asia-Pacific\n", + "- Monthly stock market data starting on December 31, 1992, and ending on February 28, 2018\n", + "- Indexed to ”100” at the beginning of the period" + ] + }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -14,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 3, "id": "e6fb4fc0", "metadata": {}, "outputs": [], @@ -10950,7 +10972,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 5, "id": "922755b0", "metadata": {}, "outputs": [ @@ -11961,7 +11983,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 6, "id": "5b3cffde", "metadata": {}, "outputs": [ @@ -14028,7 +14050,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 7, "id": "0c06cadb", "metadata": {}, "outputs": [ @@ -15310,7 +15332,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 8, "id": "9ed4ed19", "metadata": {}, "outputs": [ @@ -15659,6 +15681,8 @@ ], "layout": { "coloraxis": { + "cmax": 1, + "cmin": 0, "colorscale": [ [ 0, @@ -16603,290 +16627,290 @@ "z": [ [ 1, - 0.8320540166593678, - 0.9185240149429265, - 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0.5195711069608441, + 0.8247814667384304, + 0.7170642126388511, + 0.6275546327547749, + 0.5149816762111132 ], [ 0.5891932638811348, - 0.7281840640417876, - 0.6984360278295774, - 0.8422643122637129, - 0.6740237181657197 + 0.704267316695557, + 0.8007340701823165, + 0.857879700559443, + 0.786300289588607, + 0.6740237181657197, + 0.5236526915521025 ], [ 0.605368665365416, - 0.6927726594076025, - 0.5983129275583013, - 0.7362624275162716, - 0.6360239525545529 + 0.6622632895789733, + 0.7634737923355192, + 0.8154373368169103, + 0.6781870251778219, + 0.6360239525545529, + 0.5443224956603798 ], [ 0.6496278308461678, - 0.6157935929369659, - 0.5876875841994723, - 0.8150484433216322, - 0.5562416231560933 + 0.6100576835836632, + 0.664905176238756, + 0.82582269961162, + 0.707838607275431, + 0.5562416231560933, + 0.1568539753529496 ], [ 0.6048363453974878, - 0.5765660643184528, - 0.4435075434410774, - 0.7762859955224912, - 0.5038971290674578 + 0.5982388094093647, + 0.6711043821114737, + 0.7481411975743241, + 0.6930266093034455, + 0.5038971290674578, + 0.37370274208977533 ], [ 0.5620662430667941, - 0.5314439847347631, - 0.5868420649945726, - 0.7801064880356211, - 0.5158664719800952 + 0.5605655466850232, + 0.620489005425513, + 0.8098399439136472, + 0.6858958059889538, + 0.5158664719800952, + 0.3228108382664206 ], [ 0.3490581753471797, - 0.5012985044154611, - 0.489864041952172, - 0.7399685062938098, - 0.5279241737170683 + 0.5277143553993453, + 0.5240770378730752, + 0.7645273194980245, + 0.5916679561446208, + 0.5279241737170683, + 0.4169001123158391 ] ] } ], "layout": { "coloraxis": { + "cmax": 1, + "cmin": 0, "colorscale": [ [ 0, @@ -22541,17 +25083,764 @@ "source": [ "correlation_matrix_avg = pd.DataFrame()\n", "\n", - "for year in range(1993, 2018, 5):\n", - " returns_sub = returns[returns['Year'].between(year, year+4)]\n", + "time_delta = 4\n", + "for year in range(1993, 2018, time_delta):\n", + " returns_sub = returns[returns['Year'].between(year, year+time_delta)]\n", " correlation_matrix = returns_sub.drop(columns=['Date', 'Year']).corr()\n", - " correlation_matrix_avg[f'{year}-{year + 4}'] = correlation_matrix.mean()\n", + " correlation_matrix_avg[f'{year}-{year + time_delta}'] = correlation_matrix.mean()\n", "\n", - " fig = px.imshow(correlation_matrix, text_auto=True, title=f'Correlation Matrix ({year}-{year + 4})', color_continuous_scale='RdBu_r')\n", + " fig = px.imshow(correlation_matrix, text_auto=True, title=f'Correlation Matrix ({year}-{year + time_delta})', color_continuous_scale='RdBu_r', zmin=0, zmax=1)\n", " fig.show()\n", "\n", - "fig = px.imshow(correlation_matrix_avg, text_auto=True, title='Average correlation over sub-periods', color_continuous_scale='RdBu_r')\n", + "fig = px.imshow(correlation_matrix_avg, text_auto=True, title='Average correlation over sub-periods', color_continuous_scale='RdBu_r', zmin=0, zmax=1)\n", "fig.show()" ] + }, + { + "cell_type": "markdown", + "id": "708c05de", + "metadata": {}, + "source": [ + "## Case 2: Rational asset pricing and multifactor models\n", + "\n", + "Data set ([Case2Factors.csv](./data/Case2Factors.csv) and [Case2MSCI.csv](./data/Case2MSCI.csv)) include monthly total return index data over the 1st decade of the 21st century, from January 2000 to December 2009, denominated in EUR for 10 European stock markets and 4 global risk factors.\n", + "\n", + "[Case2.py](./case2.py) analyzes the **relationships between the returns of the stock markets and the changes of the global factors** using the following regressions for each market:\n", + "- **Market return on the MSCI World index return** (_single factor model_)\n", + "- **Market return on the 4 global factors** (_4-factor model_)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "76f622cf", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import statsmodels.api as sm" + ] + }, + { + "cell_type": "markdown", + "id": "6a855aed", + "metadata": {}, + "source": [ + "Prepare MSCI world return data (Switzerland, Germany, France, UK, Japan, USA)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "18258252", + "metadata": {}, + "outputs": [], + "source": [ + "dataMSCI = pd.read_csv('data/Case2MSCI.csv')\n", + "# print(dataMSCI.info())\n", + "# print(dataMSCI.describe())\n", + "dataMSCI['Date'] = pd.to_datetime(dataMSCI['Date'])\n", + "\n", + "returnsMSCI = dataMSCI.copy()\n", + "for index in dataMSCI.columns[1:]:\n", + " for i in range(1, len(dataMSCI[index])):\n", + " returnsMSCI.loc[i, index] = np.log(dataMSCI.loc[i, index] / dataMSCI.loc[i - 1, index])\n", + "\n", + "# First row needs to be removed as it is 100% return\n", + "returnsMSCI = returnsMSCI.drop(0)\n", + "\n", + "# print(returnsMSCI.info())\n", + "# print(returnsMSCI.head())" + ] + }, + { + "cell_type": "markdown", + "id": "723b70dc", + "metadata": {}, + "source": [ + "Prepare global factors return data (MSCI World, CRB Index, EUR 10Y Rate, FX USD/EUR)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "745b56bb", + "metadata": {}, + "outputs": [], + "source": [ + "dataFactors = pd.read_csv('data/Case2Factors.csv')\n", + "# print(dataFactors.info())\n", + "# print(dataFactors.describe())\n", + "dataFactors['Date'] = pd.to_datetime(dataFactors['Date'])\n", + "\n", + "returnsFactors = dataFactors.copy()\n", + "for index in dataFactors.columns[1:]:\n", + " for i in range(1, len(dataFactors[index])):\n", + " returnsFactors.loc[i, index] = np.log(dataFactors.loc[i, index] / dataFactors.loc[i - 1, index])\n", + "\n", + "# First row needs to be removed as it is 100% return\n", + "returnsFactors = returnsFactors.drop(0)\n", + "\n", + "# print(returnsFactors.info())\n", + "# print(returnsFactors.head())" + ] + }, + { + "cell_type": "markdown", + "id": "ee4a07ee", + "metadata": {}, + "source": [ + "Market return on the MSCI World index return (single factor model)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "a232b027", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "================================ Switzerland =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Switzerland R-squared: 0.631\n", + "Model: OLS Adj. R-squared: 0.628\n", + "Method: Least Squares F-statistic: 202.0\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.50e-27\n", + "Time: 22:48:25 Log-Likelihood: 273.35\n", + "No. Observations: 120 AIC: -542.7\n", + "Df Residuals: 118 BIC: -537.1\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0032 0.002 1.404 0.163 -0.001 0.008\n", + "MSCI World 0.6919 0.049 14.214 0.000 0.596 0.788\n", + "==============================================================================\n", + "Omnibus: 1.468 Durbin-Watson: 1.809\n", + "Prob(Omnibus): 0.480 Jarque-Bera (JB): 1.024\n", + "Skew: -0.018 Prob(JB): 0.599\n", + "Kurtosis: 3.451 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Germany =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Germany R-squared: 0.726\n", + "Model: OLS Adj. R-squared: 0.724\n", + "Method: Least Squares F-statistic: 312.7\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 5.74e-35\n", + "Time: 22:48:25 Log-Likelihood: 227.65\n", + "No. Observations: 120 AIC: -451.3\n", + "Df Residuals: 118 BIC: -445.7\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0021 0.003 0.632 0.529 -0.005 0.009\n", + "MSCI World 1.2598 0.071 17.683 0.000 1.119 1.401\n", + "==============================================================================\n", + "Omnibus: 14.964 Durbin-Watson: 2.272\n", + "Prob(Omnibus): 0.001 Jarque-Bera (JB): 30.839\n", + "Skew: -0.472 Prob(JB): 2.01e-07\n", + "Kurtosis: 5.297 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ UK =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: UK R-squared: 0.826\n", + "Model: OLS Adj. R-squared: 0.824\n", + "Method: Least Squares F-statistic: 559.2\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.37e-46\n", + "Time: 22:48:25 Log-Likelihood: 303.42\n", + "No. Observations: 120 AIC: -602.8\n", + "Df Residuals: 118 BIC: -597.3\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0007 0.002 0.369 0.712 -0.003 0.004\n", + "MSCI World 0.8960 0.038 23.647 0.000 0.821 0.971\n", + "==============================================================================\n", + "Omnibus: 5.877 Durbin-Watson: 2.333\n", + "Prob(Omnibus): 0.053 Jarque-Bera (JB): 5.334\n", + "Skew: -0.458 Prob(JB): 0.0695\n", + "Kurtosis: 3.477 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Sweden =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Sweden R-squared: 0.652\n", + "Model: OLS Adj. R-squared: 0.649\n", + "Method: Least Squares F-statistic: 220.9\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 8.32e-29\n", + "Time: 22:48:25 Log-Likelihood: 194.41\n", + "No. Observations: 120 AIC: -384.8\n", + "Df Residuals: 118 BIC: -379.3\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0029 0.004 0.659 0.511 -0.006 0.012\n", + "MSCI World 1.3969 0.094 14.864 0.000 1.211 1.583\n", + "==============================================================================\n", + "Omnibus: 12.053 Durbin-Watson: 2.158\n", + "Prob(Omnibus): 0.002 Jarque-Bera (JB): 34.968\n", + "Skew: 0.058 Prob(JB): 2.55e-08\n", + "Kurtosis: 5.642 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Norway =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Norway R-squared: 0.555\n", + "Model: OLS Adj. R-squared: 0.551\n", + "Method: Least Squares F-statistic: 146.9\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.85e-22\n", + "Time: 22:48:25 Log-Likelihood: 182.68\n", + "No. Observations: 120 AIC: -361.4\n", + "Df Residuals: 118 BIC: -355.8\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0101 0.005 2.069 0.041 0.000 0.020\n", + "MSCI World 1.2562 0.104 12.122 0.000 1.051 1.461\n", + "==============================================================================\n", + "Omnibus: 27.978 Durbin-Watson: 1.688\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 57.320\n", + "Skew: -0.955 Prob(JB): 3.57e-13\n", + "Kurtosis: 5.796 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ France =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: France R-squared: 0.786\n", + "Model: OLS Adj. R-squared: 0.784\n", + "Method: Least Squares F-statistic: 434.0\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.41e-41\n", + "Time: 22:48:25 Log-Likelihood: 269.52\n", + "No. Observations: 120 AIC: -535.0\n", + "Df Residuals: 118 BIC: -529.5\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0021 0.002 0.892 0.374 -0.003 0.007\n", + "MSCI World 1.0470 0.050 20.833 0.000 0.947 1.147\n", + "==============================================================================\n", + "Omnibus: 2.279 Durbin-Watson: 2.394\n", + "Prob(Omnibus): 0.320 Jarque-Bera (JB): 2.014\n", + "Skew: -0.045 Prob(JB): 0.365\n", + "Kurtosis: 3.628 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Italy =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Italy R-squared: 0.630\n", + "Model: OLS Adj. R-squared: 0.627\n", + "Method: Least Squares F-statistic: 201.2\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.89e-27\n", + "Time: 22:48:25 Log-Likelihood: 235.38\n", + "No. Observations: 120 AIC: -466.8\n", + "Df Residuals: 118 BIC: -461.2\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0014 0.003 0.446 0.657 -0.005 0.008\n", + "MSCI World 0.9476 0.067 14.186 0.000 0.815 1.080\n", + "==============================================================================\n", + "Omnibus: 8.166 Durbin-Watson: 2.093\n", + "Prob(Omnibus): 0.017 Jarque-Bera (JB): 15.022\n", + "Skew: -0.169 Prob(JB): 0.000547\n", + "Kurtosis: 4.700 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Spain =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Spain R-squared: 0.646\n", + "Model: OLS Adj. R-squared: 0.643\n", + "Method: Least Squares F-statistic: 215.0\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.38e-28\n", + "Time: 22:48:25 Log-Likelihood: 230.99\n", + "No. Observations: 120 AIC: -458.0\n", + "Df Residuals: 118 BIC: -452.4\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0066 0.003 2.034 0.044 0.000 0.013\n", + "MSCI World 1.0159 0.069 14.662 0.000 0.879 1.153\n", + "==============================================================================\n", + "Omnibus: 0.012 Durbin-Watson: 2.125\n", + "Prob(Omnibus): 0.994 Jarque-Bera (JB): 0.120\n", + "Skew: 0.012 Prob(JB): 0.942\n", + "Kurtosis: 2.847 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Netherlands =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Netherlands R-squared: 0.763\n", + "Model: OLS Adj. R-squared: 0.761\n", + "Method: Least Squares F-statistic: 380.5\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.01e-38\n", + "Time: 22:48:25 Log-Likelihood: 249.86\n", + "No. Observations: 120 AIC: -495.7\n", + "Df Residuals: 118 BIC: -490.2\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0018 0.003 0.665 0.508 -0.004 0.007\n", + "MSCI World 1.1548 0.059 19.506 0.000 1.038 1.272\n", + "==============================================================================\n", + "Omnibus: 3.142 Durbin-Watson: 2.120\n", + "Prob(Omnibus): 0.208 Jarque-Bera (JB): 2.607\n", + "Skew: -0.339 Prob(JB): 0.272\n", + "Kurtosis: 3.247 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Austria =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Austria R-squared: 0.372\n", + "Model: OLS Adj. R-squared: 0.367\n", + "Method: Least Squares F-statistic: 69.89\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.43e-13\n", + "Time: 22:48:25 Log-Likelihood: 172.24\n", + "No. Observations: 120 AIC: -340.5\n", + "Df Residuals: 118 BIC: -334.9\n", + "Df Model: 1 \n", + "Covariance Type: nonrobust \n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "const 0.0061 0.005 1.153 0.251 -0.004 0.017\n", + "MSCI World 0.9451 0.113 8.360 0.000 0.721 1.169\n", + "==============================================================================\n", + "Omnibus: 42.561 Durbin-Watson: 1.424\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 193.645\n", + "Skew: -1.099 Prob(JB): 8.92e-43\n", + "Kurtosis: 8.822 Cond. No. 21.3\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" + ] + } + ], + "source": [ + "for country in returnsMSCI.columns[1:]:\n", + " y = returnsMSCI[country]\n", + " X = returnsFactors['MSCI World']\n", + " # Add a constant to the independent variable\n", + " X = sm.add_constant(X)\n", + "\n", + " model = sm.OLS(y, X).fit()\n", + " print(f\"\\n\\n{\"=\"*32} {country} {\"=\"*33}\")\n", + " print(model.summary())" + ] + }, + { + "cell_type": "markdown", + "id": "320da11d", + "metadata": {}, + "source": [ + "Market return on the 4 global factors (4-factor model)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "3f6585aa", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "================================ Switzerland =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Switzerland R-squared: 0.674\n", + "Model: OLS Adj. R-squared: 0.662\n", + "Method: Least Squares F-statistic: 59.37\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 4.25e-27\n", + "Time: 22:48:25 Log-Likelihood: 280.69\n", + "No. Observations: 120 AIC: -551.4\n", + "Df Residuals: 115 BIC: -537.4\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0035 0.002 1.565 0.120 -0.001 0.008\n", + "FX USD/EUR 0.2081 0.075 2.759 0.007 0.059 0.358\n", + "EUR 10Y Rate 0.0626 0.052 1.206 0.230 -0.040 0.165\n", + "CRB Index -0.1146 0.048 -2.383 0.019 -0.210 -0.019\n", + "MSCI World 0.7431 0.053 14.017 0.000 0.638 0.848\n", + "==============================================================================\n", + "Omnibus: 4.731 Durbin-Watson: 1.689\n", + "Prob(Omnibus): 0.094 Jarque-Bera (JB): 4.503\n", + "Skew: 0.314 Prob(JB): 0.105\n", + "Kurtosis: 3.711 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Germany =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Germany R-squared: 0.807\n", + "Model: OLS Adj. R-squared: 0.800\n", + "Method: Least Squares F-statistic: 120.4\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 3.73e-40\n", + "Time: 22:48:25 Log-Likelihood: 248.73\n", + "No. Observations: 120 AIC: -487.5\n", + "Df Residuals: 115 BIC: -473.5\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0019 0.003 0.655 0.514 -0.004 0.008\n", + "FX USD/EUR 0.5952 0.098 6.046 0.000 0.400 0.790\n", + "EUR 10Y Rate 0.1419 0.068 2.094 0.038 0.008 0.276\n", + "CRB Index -0.1684 0.063 -2.684 0.008 -0.293 -0.044\n", + "MSCI World 1.3622 0.069 19.686 0.000 1.225 1.499\n", + "==============================================================================\n", + "Omnibus: 16.175 Durbin-Watson: 2.404\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 40.147\n", + "Skew: -0.438 Prob(JB): 1.92e-09\n", + "Kurtosis: 5.695 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ UK =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: UK R-squared: 0.839\n", + "Model: OLS Adj. R-squared: 0.834\n", + "Method: Least Squares F-statistic: 150.0\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.16e-44\n", + "Time: 22:48:25 Log-Likelihood: 308.22\n", + "No. Observations: 120 AIC: -606.4\n", + "Df Residuals: 115 BIC: -592.5\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0005 0.002 0.279 0.781 -0.003 0.004\n", + "FX USD/EUR 0.1063 0.060 1.772 0.079 -0.013 0.225\n", + "EUR 10Y Rate 0.0983 0.041 2.381 0.019 0.017 0.180\n", + "CRB Index 0.0334 0.038 0.875 0.384 -0.042 0.109\n", + "MSCI World 0.8620 0.042 20.452 0.000 0.779 0.946\n", + "==============================================================================\n", + "Omnibus: 7.626 Durbin-Watson: 2.411\n", + "Prob(Omnibus): 0.022 Jarque-Bera (JB): 7.234\n", + "Skew: -0.550 Prob(JB): 0.0269\n", + "Kurtosis: 3.489 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Sweden =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Sweden R-squared: 0.696\n", + "Model: OLS Adj. R-squared: 0.685\n", + "Method: Least Squares F-statistic: 65.68\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 8.24e-29\n", + "Time: 22:48:25 Log-Likelihood: 202.46\n", + "No. Observations: 120 AIC: -394.9\n", + "Df Residuals: 115 BIC: -381.0\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0018 0.004 0.424 0.673 -0.007 0.010\n", + "FX USD/EUR 0.5744 0.145 3.968 0.000 0.288 0.861\n", + "EUR 10Y Rate 0.0408 0.100 0.409 0.683 -0.157 0.238\n", + "CRB Index -0.0427 0.092 -0.463 0.644 -0.226 0.140\n", + "MSCI World 1.4895 0.102 14.639 0.000 1.288 1.691\n", + "==============================================================================\n", + "Omnibus: 22.814 Durbin-Watson: 2.313\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 94.146\n", + "Skew: 0.465 Prob(JB): 3.60e-21\n", + "Kurtosis: 7.238 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Norway =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Norway R-squared: 0.747\n", + "Model: OLS Adj. R-squared: 0.738\n", + "Method: Least Squares F-statistic: 84.70\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.31e-33\n", + "Time: 22:48:25 Log-Likelihood: 216.51\n", + "No. Observations: 120 AIC: -423.0\n", + "Df Residuals: 115 BIC: -409.1\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0065 0.004 1.735 0.085 -0.001 0.014\n", + "FX USD/EUR 0.9059 0.129 7.036 0.000 0.651 1.161\n", + "EUR 10Y Rate 0.3405 0.089 3.843 0.000 0.165 0.516\n", + "CRB Index 0.4185 0.082 5.098 0.000 0.256 0.581\n", + "MSCI World 1.1142 0.091 12.311 0.000 0.935 1.293\n", + "==============================================================================\n", + "Omnibus: 15.924 Durbin-Watson: 1.868\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 33.019\n", + "Skew: -0.509 Prob(JB): 6.76e-08\n", + "Kurtosis: 5.360 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ France =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: France R-squared: 0.852\n", + "Model: OLS Adj. R-squared: 0.847\n", + "Method: Least Squares F-statistic: 165.6\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 9.55e-47\n", + "Time: 22:48:25 Log-Likelihood: 291.60\n", + "No. Observations: 120 AIC: -573.2\n", + "Df Residuals: 115 BIC: -559.3\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0014 0.002 0.676 0.500 -0.003 0.005\n", + "FX USD/EUR 0.4732 0.069 6.872 0.000 0.337 0.610\n", + "EUR 10Y Rate 0.0582 0.047 1.228 0.222 -0.036 0.152\n", + "CRB Index -0.0556 0.044 -1.266 0.208 -0.143 0.031\n", + "MSCI World 1.1211 0.048 23.160 0.000 1.025 1.217\n", + "==============================================================================\n", + "Omnibus: 12.951 Durbin-Watson: 2.605\n", + "Prob(Omnibus): 0.002 Jarque-Bera (JB): 29.042\n", + "Skew: 0.342 Prob(JB): 4.94e-07\n", + "Kurtosis: 5.311 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Italy =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Italy R-squared: 0.706\n", + "Model: OLS Adj. R-squared: 0.696\n", + "Method: Least Squares F-statistic: 68.97\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.16e-29\n", + "Time: 22:48:25 Log-Likelihood: 249.08\n", + "No. Observations: 120 AIC: -488.2\n", + "Df Residuals: 115 BIC: -474.2\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const -0.0005 0.003 -0.161 0.873 -0.006 0.005\n", + "FX USD/EUR 0.5203 0.098 5.301 0.000 0.326 0.715\n", + "EUR 10Y Rate -0.0382 0.068 -0.566 0.573 -0.172 0.096\n", + "CRB Index 0.0835 0.063 1.335 0.185 -0.040 0.207\n", + "MSCI World 1.0161 0.069 14.727 0.000 0.879 1.153\n", + "==============================================================================\n", + "Omnibus: 17.824 Durbin-Watson: 2.452\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 76.127\n", + "Skew: -0.185 Prob(JB): 2.95e-17\n", + "Kurtosis: 6.884 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Spain =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Spain R-squared: 0.737\n", + "Model: OLS Adj. R-squared: 0.727\n", + "Method: Least Squares F-statistic: 80.38\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.13e-32\n", + "Time: 22:48:25 Log-Likelihood: 248.77\n", + "No. Observations: 120 AIC: -487.5\n", + "Df Residuals: 115 BIC: -473.6\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0057 0.003 1.964 0.052 -4.98e-05 0.011\n", + "FX USD/EUR 0.5245 0.098 5.330 0.000 0.330 0.719\n", + "EUR 10Y Rate -0.0898 0.068 -1.325 0.188 -0.224 0.044\n", + "CRB Index -0.1187 0.063 -1.893 0.061 -0.243 0.006\n", + "MSCI World 1.1800 0.069 17.060 0.000 1.043 1.317\n", + "==============================================================================\n", + "Omnibus: 2.041 Durbin-Watson: 2.419\n", + "Prob(Omnibus): 0.360 Jarque-Bera (JB): 1.545\n", + "Skew: 0.162 Prob(JB): 0.462\n", + "Kurtosis: 3.451 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Netherlands =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Netherlands R-squared: 0.806\n", + "Model: OLS Adj. R-squared: 0.799\n", + "Method: Least Squares F-statistic: 119.4\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 5.33e-40\n", + "Time: 22:48:25 Log-Likelihood: 261.80\n", + "No. Observations: 120 AIC: -513.6\n", + "Df Residuals: 115 BIC: -499.7\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0011 0.003 0.428 0.669 -0.004 0.006\n", + "FX USD/EUR 0.4316 0.088 4.889 0.000 0.257 0.606\n", + "EUR 10Y Rate 0.0570 0.061 0.939 0.350 -0.063 0.177\n", + "CRB Index -0.0364 0.056 -0.647 0.519 -0.148 0.075\n", + "MSCI World 1.2156 0.062 19.588 0.000 1.093 1.339\n", + "==============================================================================\n", + "Omnibus: 1.008 Durbin-Watson: 2.216\n", + "Prob(Omnibus): 0.604 Jarque-Bera (JB): 0.703\n", + "Skew: -0.179 Prob(JB): 0.704\n", + "Kurtosis: 3.110 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "\n", + "\n", + "================================ Austria =================================\n", + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: Austria R-squared: 0.607\n", + "Model: OLS Adj. R-squared: 0.593\n", + "Method: Least Squares F-statistic: 44.37\n", + "Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.75e-22\n", + "Time: 22:48:25 Log-Likelihood: 200.34\n", + "No. Observations: 120 AIC: -390.7\n", + "Df Residuals: 115 BIC: -376.7\n", + "Df Model: 4 \n", + "Covariance Type: nonrobust \n", + "================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "--------------------------------------------------------------------------------\n", + "const 0.0020 0.004 0.468 0.641 -0.007 0.011\n", + "FX USD/EUR 1.1376 0.147 7.721 0.000 0.846 1.429\n", + "EUR 10Y Rate 0.1561 0.101 1.540 0.126 -0.045 0.357\n", + "CRB Index 0.3184 0.094 3.391 0.001 0.132 0.504\n", + "MSCI World 0.9502 0.104 9.176 0.000 0.745 1.155\n", + "==============================================================================\n", + "Omnibus: 6.503 Durbin-Watson: 1.871\n", + "Prob(Omnibus): 0.039 Jarque-Bera (JB): 11.138\n", + "Skew: -0.004 Prob(JB): 0.00382\n", + "Kurtosis: 4.492 Cond. No. 35.2\n", + "==============================================================================\n", + "\n", + "Notes:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" + ] + } + ], + "source": [ + "for country in returnsMSCI.columns[1:]:\n", + " y = returnsMSCI[country]\n", + " X = returnsFactors[['FX USD/EUR', 'EUR 10Y Rate' ,'CRB Index', 'MSCI World']]\n", + " # Add a constant to the independent variable\n", + " X = sm.add_constant(X)\n", + "\n", + " model = sm.OLS(y, X).fit()\n", + " print(f\"\\n\\n{\"=\"*32} {country} {\"=\"*33}\")\n", + " print(model.summary())" + ] } ], "metadata": {