notebook.ipynb

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   "metadata": {},
   "source": [
    "© Carlo Bortolan&nbsp;&middot;&nbsp;GitHub [carlobortolan](https://github.com/carlobortolan)&nbsp;&middot;&nbsp;contact via [carlobortolan@gmail.com](mailto:carlobortolan@gmail.com)\n",
    "\n",
    "---\n",
    "\n",
    "# [ICM25](https://github.com/carlobortolan/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": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import plotly.express as px"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "e6fb4fc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Metadata\n",
    "data = pd.read_csv('data/Case1.csv')\n",
    "# print(data.info())\n",
    "# print(data.describe())\n",
    "data['Date'] = pd.to_datetime(data['Date'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de3d7eb5",
   "metadata": {},
   "source": [
    "1. Display the long-term performance of the equity markets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "1c26349b",
   "metadata": {},
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    "2. Calculate mean returns and volatilities over the total period"
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    "returns = data.copy()\n",
    "for index in data.columns[1:]:\n",
    "    for i in range(1, len(data[index])):\n",
    "        returns.loc[i, index] = np.log(data.loc[i, index] / data.loc[i - 1, index])\n",
    "\n",
    "# First row needs to be removed as it is 100% return\n",
    "returns = returns.drop(0)\n",
    "\n",
    "# print(returns.info())\n",
    "# print(returns.head())\n",
    "\n",
    "# Mean and SD (volatility) of the returns\n",
    "results_list = []\n",
    "for index in returns.columns[1:]:\n",
    "    mean_return = math.exp(returns[index].mean()*12)-1\n",
    "    std_return = returns[index].std()*math.sqrt(12)\n",
    "    results_list.append({'Index': index, 'Mean Return p.a.': mean_return, 'Volatility': std_return})\n",
    "\n",
    "results = pd.DataFrame(results_list)\n",
    "results_melted = results.melt(id_vars='Index', value_vars=['Mean Return p.a.', 'Volatility'], var_name='Metric', value_name='Value')\n",
    "fig = px.bar(results_melted, x='Index', y='Value', color='Metric', barmode='group', title='Mean returns p.a. and volatilities')\n",
    "fig.show()"
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   "source": [
    "3. Calculate yearly returns for the stock markets\n"
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    "returns['Year'] = returns['Date'].dt.year\n",
    "grouped_returns = returns.drop(columns=['Date']).groupby('Year').sum().reset_index()\n",
    "\n",
    "fig = px.line(grouped_returns, x='Year', y=grouped_returns.columns[1:], title='Yearly returns for the stock markets')\n",
    "fig.show()"
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  {
   "cell_type": "markdown",
   "id": "390ea807",
   "metadata": {},
   "source": [
    "4. Calculate the correlations between the markets over the period 1993-2017\n"
   ]
  },
  {
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    "correlation_matrix = returns.drop(columns=['Date', 'Year']).corr()\n",
    "correlation_matrix.loc['Mean'] = correlation_matrix.mean(axis=1)\n",
    "\n",
    "fig = px.imshow(correlation_matrix, text_auto=True, title='Correlation Matrix (full)', color_continuous_scale='RdBu_r')\n",
    "fig.show()"
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   "source": [
    "5. Calculate the correlations for five sub-periods and analyze the correlation regimes\n",
    "- 1993-1997\n",
    "- 1998-2002\n",
    "- 2003-2007\n",
    "- 2008-2012\n",
    "- 2013-2017"
   ]
  },
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   "source": [
    "correlation_matrix_avg = pd.DataFrame()\n",
    "\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 + time_delta}'] = correlation_matrix.mean()\n",
    "\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', 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",
    "Case 2 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": 83,
   "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": 84,
   "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": 85,
   "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": 86,
   "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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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:                        23:18:55   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": 87,
   "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:                        23:18:55   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:                        23:18:56   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:                        23:18:56   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:                        23:18:56   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:                        23:18:56   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:                        23:18:56   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:                        23:18:56   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:                        23:18:56   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:                        23:18:56   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:                        23:18:56   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())"
   ]
  },
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    "---\n",
    "\n",
    "© Carlo Bortolan&nbsp;&middot;&nbsp;GitHub [carlobortolan](https://github.com/carlobortolan)&nbsp;&middot;&nbsp;contact via [carlobortolan@gmail.com](mailto:carlobortolan@gmail.com)"
   ]
  }
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