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
-}
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+================================ Switzerland =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Switzerland R-squared: 0.631
+Model: OLS Adj. R-squared: 0.628
+Method: Least Squares F-statistic: 202.0
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.50e-27
+Time: 22:49:09 Log-Likelihood: 273.35
+No. Observations: 120 AIC: -542.7
+Df Residuals: 118 BIC: -537.1
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0032 0.002 1.404 0.163 -0.001 0.008
+MSCI World 0.6919 0.049 14.214 0.000 0.596 0.788
+==============================================================================
+Omnibus: 1.468 Durbin-Watson: 1.809
+Prob(Omnibus): 0.480 Jarque-Bera (JB): 1.024
+Skew: -0.018 Prob(JB): 0.599
+Kurtosis: 3.451 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Germany =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Germany R-squared: 0.726
+Model: OLS Adj. R-squared: 0.724
+Method: Least Squares F-statistic: 312.7
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 5.74e-35
+Time: 22:49:09 Log-Likelihood: 227.65
+No. Observations: 120 AIC: -451.3
+Df Residuals: 118 BIC: -445.7
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0021 0.003 0.632 0.529 -0.005 0.009
+MSCI World 1.2598 0.071 17.683 0.000 1.119 1.401
+==============================================================================
+Omnibus: 14.964 Durbin-Watson: 2.272
+Prob(Omnibus): 0.001 Jarque-Bera (JB): 30.839
+Skew: -0.472 Prob(JB): 2.01e-07
+Kurtosis: 5.297 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ UK =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: UK R-squared: 0.826
+Model: OLS Adj. R-squared: 0.824
+Method: Least Squares F-statistic: 559.2
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.37e-46
+Time: 22:49:09 Log-Likelihood: 303.42
+No. Observations: 120 AIC: -602.8
+Df Residuals: 118 BIC: -597.3
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0007 0.002 0.369 0.712 -0.003 0.004
+MSCI World 0.8960 0.038 23.647 0.000 0.821 0.971
+==============================================================================
+Omnibus: 5.877 Durbin-Watson: 2.333
+Prob(Omnibus): 0.053 Jarque-Bera (JB): 5.334
+Skew: -0.458 Prob(JB): 0.0695
+Kurtosis: 3.477 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Sweden =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Sweden R-squared: 0.652
+Model: OLS Adj. R-squared: 0.649
+Method: Least Squares F-statistic: 220.9
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 8.32e-29
+Time: 22:49:09 Log-Likelihood: 194.41
+No. Observations: 120 AIC: -384.8
+Df Residuals: 118 BIC: -379.3
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0029 0.004 0.659 0.511 -0.006 0.012
+MSCI World 1.3969 0.094 14.864 0.000 1.211 1.583
+==============================================================================
+Omnibus: 12.053 Durbin-Watson: 2.158
+Prob(Omnibus): 0.002 Jarque-Bera (JB): 34.968
+Skew: 0.058 Prob(JB): 2.55e-08
+Kurtosis: 5.642 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Norway =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Norway R-squared: 0.555
+Model: OLS Adj. R-squared: 0.551
+Method: Least Squares F-statistic: 146.9
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.85e-22
+Time: 22:49:09 Log-Likelihood: 182.68
+No. Observations: 120 AIC: -361.4
+Df Residuals: 118 BIC: -355.8
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0101 0.005 2.069 0.041 0.000 0.020
+MSCI World 1.2562 0.104 12.122 0.000 1.051 1.461
+==============================================================================
+Omnibus: 27.978 Durbin-Watson: 1.688
+Prob(Omnibus): 0.000 Jarque-Bera (JB): 57.320
+Skew: -0.955 Prob(JB): 3.57e-13
+Kurtosis: 5.796 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ France =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: France R-squared: 0.786
+Model: OLS Adj. R-squared: 0.784
+Method: Least Squares F-statistic: 434.0
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.41e-41
+Time: 22:49:09 Log-Likelihood: 269.52
+No. Observations: 120 AIC: -535.0
+Df Residuals: 118 BIC: -529.5
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0021 0.002 0.892 0.374 -0.003 0.007
+MSCI World 1.0470 0.050 20.833 0.000 0.947 1.147
+==============================================================================
+Omnibus: 2.279 Durbin-Watson: 2.394
+Prob(Omnibus): 0.320 Jarque-Bera (JB): 2.014
+Skew: -0.045 Prob(JB): 0.365
+Kurtosis: 3.628 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Italy =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Italy R-squared: 0.630
+Model: OLS Adj. R-squared: 0.627
+Method: Least Squares F-statistic: 201.2
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.89e-27
+Time: 22:49:09 Log-Likelihood: 235.38
+No. Observations: 120 AIC: -466.8
+Df Residuals: 118 BIC: -461.2
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0014 0.003 0.446 0.657 -0.005 0.008
+MSCI World 0.9476 0.067 14.186 0.000 0.815 1.080
+==============================================================================
+Omnibus: 8.166 Durbin-Watson: 2.093
+Prob(Omnibus): 0.017 Jarque-Bera (JB): 15.022
+Skew: -0.169 Prob(JB): 0.000547
+Kurtosis: 4.700 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Spain =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Spain R-squared: 0.646
+Model: OLS Adj. R-squared: 0.643
+Method: Least Squares F-statistic: 215.0
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.38e-28
+Time: 22:49:09 Log-Likelihood: 230.99
+No. Observations: 120 AIC: -458.0
+Df Residuals: 118 BIC: -452.4
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0066 0.003 2.034 0.044 0.000 0.013
+MSCI World 1.0159 0.069 14.662 0.000 0.879 1.153
+==============================================================================
+Omnibus: 0.012 Durbin-Watson: 2.125
+Prob(Omnibus): 0.994 Jarque-Bera (JB): 0.120
+Skew: 0.012 Prob(JB): 0.942
+Kurtosis: 2.847 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Netherlands =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Netherlands R-squared: 0.763
+Model: OLS Adj. R-squared: 0.761
+Method: Least Squares F-statistic: 380.5
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.01e-38
+Time: 22:49:09 Log-Likelihood: 249.86
+No. Observations: 120 AIC: -495.7
+Df Residuals: 118 BIC: -490.2
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0018 0.003 0.665 0.508 -0.004 0.007
+MSCI World 1.1548 0.059 19.506 0.000 1.038 1.272
+==============================================================================
+Omnibus: 3.142 Durbin-Watson: 2.120
+Prob(Omnibus): 0.208 Jarque-Bera (JB): 2.607
+Skew: -0.339 Prob(JB): 0.272
+Kurtosis: 3.247 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Austria =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Austria R-squared: 0.372
+Model: OLS Adj. R-squared: 0.367
+Method: Least Squares F-statistic: 69.89
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.43e-13
+Time: 22:49:09 Log-Likelihood: 172.24
+No. Observations: 120 AIC: -340.5
+Df Residuals: 118 BIC: -334.9
+Df Model: 1
+Covariance Type: nonrobust
+==============================================================================
+ coef std err t P>|t| [0.025 0.975]
+------------------------------------------------------------------------------
+const 0.0061 0.005 1.153 0.251 -0.004 0.017
+MSCI World 0.9451 0.113 8.360 0.000 0.721 1.169
+==============================================================================
+Omnibus: 42.561 Durbin-Watson: 1.424
+Prob(Omnibus): 0.000 Jarque-Bera (JB): 193.645
+Skew: -1.099 Prob(JB): 8.92e-43
+Kurtosis: 8.822 Cond. No. 21.3
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+================================ Switzerland =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Switzerland R-squared: 0.674
+Model: OLS Adj. R-squared: 0.662
+Method: Least Squares F-statistic: 59.37
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 4.25e-27
+Time: 22:49:09 Log-Likelihood: 280.69
+No. Observations: 120 AIC: -551.4
+Df Residuals: 115 BIC: -537.4
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0035 0.002 1.565 0.120 -0.001 0.008
+FX USD/EUR 0.2081 0.075 2.759 0.007 0.059 0.358
+EUR 10Y Rate 0.0626 0.052 1.206 0.230 -0.040 0.165
+CRB Index -0.1146 0.048 -2.383 0.019 -0.210 -0.019
+MSCI World 0.7431 0.053 14.017 0.000 0.638 0.848
+==============================================================================
+Omnibus: 4.731 Durbin-Watson: 1.689
+Prob(Omnibus): 0.094 Jarque-Bera (JB): 4.503
+Skew: 0.314 Prob(JB): 0.105
+Kurtosis: 3.711 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Germany =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Germany R-squared: 0.807
+Model: OLS Adj. R-squared: 0.800
+Method: Least Squares F-statistic: 120.4
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 3.73e-40
+Time: 22:49:09 Log-Likelihood: 248.73
+No. Observations: 120 AIC: -487.5
+Df Residuals: 115 BIC: -473.5
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0019 0.003 0.655 0.514 -0.004 0.008
+FX USD/EUR 0.5952 0.098 6.046 0.000 0.400 0.790
+EUR 10Y Rate 0.1419 0.068 2.094 0.038 0.008 0.276
+CRB Index -0.1684 0.063 -2.684 0.008 -0.293 -0.044
+MSCI World 1.3622 0.069 19.686 0.000 1.225 1.499
+==============================================================================
+Omnibus: 16.175 Durbin-Watson: 2.404
+Prob(Omnibus): 0.000 Jarque-Bera (JB): 40.147
+Skew: -0.438 Prob(JB): 1.92e-09
+Kurtosis: 5.695 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ UK =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: UK R-squared: 0.839
+Model: OLS Adj. R-squared: 0.834
+Method: Least Squares F-statistic: 150.0
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.16e-44
+Time: 22:49:09 Log-Likelihood: 308.22
+No. Observations: 120 AIC: -606.4
+Df Residuals: 115 BIC: -592.5
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0005 0.002 0.279 0.781 -0.003 0.004
+FX USD/EUR 0.1063 0.060 1.772 0.079 -0.013 0.225
+EUR 10Y Rate 0.0983 0.041 2.381 0.019 0.017 0.180
+CRB Index 0.0334 0.038 0.875 0.384 -0.042 0.109
+MSCI World 0.8620 0.042 20.452 0.000 0.779 0.946
+==============================================================================
+Omnibus: 7.626 Durbin-Watson: 2.411
+Prob(Omnibus): 0.022 Jarque-Bera (JB): 7.234
+Skew: -0.550 Prob(JB): 0.0269
+Kurtosis: 3.489 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Sweden =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Sweden R-squared: 0.696
+Model: OLS Adj. R-squared: 0.685
+Method: Least Squares F-statistic: 65.68
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 8.24e-29
+Time: 22:49:09 Log-Likelihood: 202.46
+No. Observations: 120 AIC: -394.9
+Df Residuals: 115 BIC: -381.0
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0018 0.004 0.424 0.673 -0.007 0.010
+FX USD/EUR 0.5744 0.145 3.968 0.000 0.288 0.861
+EUR 10Y Rate 0.0408 0.100 0.409 0.683 -0.157 0.238
+CRB Index -0.0427 0.092 -0.463 0.644 -0.226 0.140
+MSCI World 1.4895 0.102 14.639 0.000 1.288 1.691
+==============================================================================
+Omnibus: 22.814 Durbin-Watson: 2.313
+Prob(Omnibus): 0.000 Jarque-Bera (JB): 94.146
+Skew: 0.465 Prob(JB): 3.60e-21
+Kurtosis: 7.238 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Norway =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Norway R-squared: 0.747
+Model: OLS Adj. R-squared: 0.738
+Method: Least Squares F-statistic: 84.70
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.31e-33
+Time: 22:49:09 Log-Likelihood: 216.51
+No. Observations: 120 AIC: -423.0
+Df Residuals: 115 BIC: -409.1
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0065 0.004 1.735 0.085 -0.001 0.014
+FX USD/EUR 0.9059 0.129 7.036 0.000 0.651 1.161
+EUR 10Y Rate 0.3405 0.089 3.843 0.000 0.165 0.516
+CRB Index 0.4185 0.082 5.098 0.000 0.256 0.581
+MSCI World 1.1142 0.091 12.311 0.000 0.935 1.293
+==============================================================================
+Omnibus: 15.924 Durbin-Watson: 1.868
+Prob(Omnibus): 0.000 Jarque-Bera (JB): 33.019
+Skew: -0.509 Prob(JB): 6.76e-08
+Kurtosis: 5.360 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ France =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: France R-squared: 0.852
+Model: OLS Adj. R-squared: 0.847
+Method: Least Squares F-statistic: 165.6
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 9.55e-47
+Time: 22:49:09 Log-Likelihood: 291.60
+No. Observations: 120 AIC: -573.2
+Df Residuals: 115 BIC: -559.3
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0014 0.002 0.676 0.500 -0.003 0.005
+FX USD/EUR 0.4732 0.069 6.872 0.000 0.337 0.610
+EUR 10Y Rate 0.0582 0.047 1.228 0.222 -0.036 0.152
+CRB Index -0.0556 0.044 -1.266 0.208 -0.143 0.031
+MSCI World 1.1211 0.048 23.160 0.000 1.025 1.217
+==============================================================================
+Omnibus: 12.951 Durbin-Watson: 2.605
+Prob(Omnibus): 0.002 Jarque-Bera (JB): 29.042
+Skew: 0.342 Prob(JB): 4.94e-07
+Kurtosis: 5.311 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Italy =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Italy R-squared: 0.706
+Model: OLS Adj. R-squared: 0.696
+Method: Least Squares F-statistic: 68.97
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.16e-29
+Time: 22:49:09 Log-Likelihood: 249.08
+No. Observations: 120 AIC: -488.2
+Df Residuals: 115 BIC: -474.2
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const -0.0005 0.003 -0.161 0.873 -0.006 0.005
+FX USD/EUR 0.5203 0.098 5.301 0.000 0.326 0.715
+EUR 10Y Rate -0.0382 0.068 -0.566 0.573 -0.172 0.096
+CRB Index 0.0835 0.063 1.335 0.185 -0.040 0.207
+MSCI World 1.0161 0.069 14.727 0.000 0.879 1.153
+==============================================================================
+Omnibus: 17.824 Durbin-Watson: 2.452
+Prob(Omnibus): 0.000 Jarque-Bera (JB): 76.127
+Skew: -0.185 Prob(JB): 2.95e-17
+Kurtosis: 6.884 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Spain =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Spain R-squared: 0.737
+Model: OLS Adj. R-squared: 0.727
+Method: Least Squares F-statistic: 80.38
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.13e-32
+Time: 22:49:09 Log-Likelihood: 248.77
+No. Observations: 120 AIC: -487.5
+Df Residuals: 115 BIC: -473.6
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0057 0.003 1.964 0.052 -4.98e-05 0.011
+FX USD/EUR 0.5245 0.098 5.330 0.000 0.330 0.719
+EUR 10Y Rate -0.0898 0.068 -1.325 0.188 -0.224 0.044
+CRB Index -0.1187 0.063 -1.893 0.061 -0.243 0.006
+MSCI World 1.1800 0.069 17.060 0.000 1.043 1.317
+==============================================================================
+Omnibus: 2.041 Durbin-Watson: 2.419
+Prob(Omnibus): 0.360 Jarque-Bera (JB): 1.545
+Skew: 0.162 Prob(JB): 0.462
+Kurtosis: 3.451 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Netherlands =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Netherlands R-squared: 0.806
+Model: OLS Adj. R-squared: 0.799
+Method: Least Squares F-statistic: 119.4
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 5.33e-40
+Time: 22:49:09 Log-Likelihood: 261.80
+No. Observations: 120 AIC: -513.6
+Df Residuals: 115 BIC: -499.7
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0011 0.003 0.428 0.669 -0.004 0.006
+FX USD/EUR 0.4316 0.088 4.889 0.000 0.257 0.606
+EUR 10Y Rate 0.0570 0.061 0.939 0.350 -0.063 0.177
+CRB Index -0.0364 0.056 -0.647 0.519 -0.148 0.075
+MSCI World 1.2156 0.062 19.588 0.000 1.093 1.339
+==============================================================================
+Omnibus: 1.008 Durbin-Watson: 2.216
+Prob(Omnibus): 0.604 Jarque-Bera (JB): 0.703
+Skew: -0.179 Prob(JB): 0.704
+Kurtosis: 3.110 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+================================ Austria =================================
+ OLS Regression Results
+==============================================================================
+Dep. Variable: Austria R-squared: 0.607
+Model: OLS Adj. R-squared: 0.593
+Method: Least Squares F-statistic: 44.37
+Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.75e-22
+Time: 22:49:09 Log-Likelihood: 200.34
+No. Observations: 120 AIC: -390.7
+Df Residuals: 115 BIC: -376.7
+Df Model: 4
+Covariance Type: nonrobust
+================================================================================
+ coef std err t P>|t| [0.025 0.975]
+--------------------------------------------------------------------------------
+const 0.0020 0.004 0.468 0.641 -0.007 0.011
+FX USD/EUR 1.1376 0.147 7.721 0.000 0.846 1.429
+EUR 10Y Rate 0.1561 0.101 1.540 0.126 -0.045 0.357
+CRB Index 0.3184 0.094 3.391 0.001 0.132 0.504
+MSCI World 0.9502 0.104 9.176 0.000 0.745 1.155
+==============================================================================
+Omnibus: 6.503 Durbin-Watson: 1.871
+Prob(Omnibus): 0.039 Jarque-Bera (JB): 11.138
+Skew: -0.004 Prob(JB): 0.00382
+Kurtosis: 4.492 Cond. No. 35.2
+==============================================================================
+
+Notes:
+[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
+
+
+
+
+
+
+
+
+
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": {
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"title": {
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],
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}
},
"title": {
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"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": {