Module 3 - Regression - Beta Calculation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Module 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This module would introduce us to the Regression related inferences to be drawn from the data.\n",
    "\n",
    "Regression is basically a statistical approach to find the relationship between variables. In machine learning, this is used to predict the outcome of an event based on the relationship between variables obtained from the data-set. More often than not, we utilize linear regression to come up with an ideal inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Query 3.1 \n",
    "Import the file 'gold.csv', which is contains the data about last 2 years price action of Indian(MCX) gold standard. Explore the dataframe. You'd see 2 unique columns - 'Pred' and 'new'.\n",
    "\n",
    "One of the 2 columns is a linear combination of the OHLC prices with varying coefficients while the other is a polynomial fucntion of the same inputs. Also, one of the 2 columns is partially filled.\n",
    "\n",
    ">Using linear regression, find the coefficients of the inputs and using the same trained model, complete the\n",
    "      entire column.\n",
    "      \n",
    ">Also, try to fit the other column as well using a new linear regression model. Check if the predicitons are \n",
    "      accurate.\n",
    "      Mention which column is a linear function and which is a polynomial function.\n",
    "      (Hint: Plotting a histogram & distplot helps in recognizing the  discrepencies in prediction, if any.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import r2_score\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"Datasets/GOLD.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date          0\n",
       "Price         0\n",
       "Open          0\n",
       "High          0\n",
       "Low           0\n",
       "Vol.          0\n",
       "Change %      0\n",
       "Pred        101\n",
       "new           0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['Price','Open','High','Low']].head(411)\n",
    "Y = df['Pred'].head(411)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "lin = LinearRegression() \n",
    "fit_r = lin.fit(X,Y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  3., -1., -4.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit_r.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_find = df[['Price','Open','High','Low']].tail(101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = lin.predict(X_find)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Pred'][411:] = Y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Date        0\n",
       "Price       0\n",
       "Open        0\n",
       "High        0\n",
       "Low         0\n",
       "Vol.        0\n",
       "Change %    0\n",
       "Pred        0\n",
       "new         0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best degree 2 with RMSE 0.035447612447046445\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#In this section, We are gonna find out the best degree for the Polynomial Regression Model.\n",
    "X = df[['Price','Open','High','Low']]\n",
    "y = df['new']\n",
    "x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.3)\n",
    "\n",
    "rmses = []\n",
    "degrees = np.arange(1, 10)\n",
    "min_rmse, min_deg = 1e10, 0\n",
    "\n",
    "for deg in degrees:\n",
    "\n",
    "    # Train features\n",
    "    poly_features = PolynomialFeatures(degree=deg, include_bias=False)\n",
    "    x_poly_train = poly_features.fit_transform(x_train)\n",
    "\n",
    "    # Linear regression\n",
    "    poly_reg = LinearRegression()\n",
    "    poly_reg.fit(x_poly_train, y_train)\n",
    "\n",
    "    # Compare with test data\n",
    "    x_poly_test = poly_features.fit_transform(x_test)\n",
    "    poly_predict = poly_reg.predict(x_poly_test)\n",
    "    poly_mse = mean_squared_error(y_test, poly_predict)\n",
    "    poly_rmse = np.sqrt(poly_mse)\n",
    "    rmses.append(poly_rmse)\n",
    "    \n",
    "        # Cross-validation of degree\n",
    "    if min_rmse > poly_rmse:\n",
    "        min_rmse = poly_rmse\n",
    "        min_deg = deg\n",
    "\n",
    "# Plot and present results\n",
    "print('Best degree {} with RMSE {}'.format(min_deg, min_rmse))\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(degrees, rmses)\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('Degree')\n",
    "ax.set_ylabel('RMSE')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = PolynomialFeatures(degree = 2)#Used Best Degree According to Graph\n",
    "X_poly = poly.fit_transform(df[['Price','Open','High','Low']])\n",
    "y = df['new']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_poly, y, test_size=0.3, random_state=0)\n",
    "lin2 = LinearRegression()\n",
    "poly.fit(X_train, y_train) \n",
    "lin2.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00000000e+00,  1.01149014e+00, -1.00038387e+00,  1.00514610e+00,\n",
       "       -1.01629689e+00,  4.01317582e-07, -1.02074780e-06,  3.25053322e-05,\n",
       "       -3.26601524e-05, -6.36851878e-07,  8.12007559e-07,  1.49803886e-06,\n",
       "       -5.70511253e-08, -3.33750698e-05,  3.25346911e-05])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin2.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly.fit(X_test) \n",
    "y_pred_1 = lin2.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999902555504"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_test, y_pred_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f8d522ef198>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(y_pred_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f8d4ff9cac8>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CAPM CAPM Analysis and Beta Calculation using regression -\n",
    "CAPM(Capital Asset Pricing Model) attempts to price securities by examining the relationship that exists between expected returns and risk.\n",
    "\n",
    "The Beta of an asset is a measure of the sensitivity of its returns relative to a market benchmark (usually a market index). How sensitive/insensitive is the returns of an asset to the overall market returns (usually a market index like S&P 500 index). What happens when the market jumps, does the returns of the asset jump accordingly or jump somehow?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Query 3.2 \n",
    "Import the stock of your choosing AND the Nifty index.\n",
    "Using linear regression (OLS), calculate -\n",
    ">The daily Beta value for the past 3 months. (Daily= Daily returns)\n",
    "\n",
    ">The monthly Beta value. (Monthly= Monthly returns)\n",
    "\n",
    "Refrain from using the (covariance(x,y)/variance(x)) formula.<BR>\n",
    "Attempt the question using regression.(Regression Reference)<BR>\n",
    "Were the Beta values more or less than 1 ? What if it was negative ?<BR>\n",
    "Discuss. Include a brief writeup in the bottom of your jupyter notebook with your inferences from the Beta values and regression results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#My all previous work is based on GMR. So, I have choosen GMR for this too.\n",
    "df2 = pd.read_csv(\"Datasets/MID_CAP/GMRINFRA.csv\",parse_dates=True,index_col='Date')\n",
    "df3 = pd.read_csv(\"Datasets/Nifty50.csv\",parse_dates=True,index_col='Date')\n",
    "daily_prices = pd.concat([df2['Close Price'], df3['Close']], axis=1)\n",
    "daily_prices.columns = ['GMR', 'Nifty']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              GMR    Nifty\n",
      "Date                      \n",
      "2017-05-15  17.55  9445.40\n",
      "2017-05-16  17.40  9512.25\n",
      "2017-05-17  17.30  9525.75\n",
      "2017-05-18  16.75  9429.45\n",
      "2017-05-19  16.95  9427.90\n",
      "                 GMR     Nifty\n",
      "Date                          \n",
      "2017-05-16 -0.008547  0.007078\n",
      "2017-05-17 -0.005747  0.001419\n",
      "2017-05-18 -0.031792 -0.010109\n",
      "2017-05-19  0.011940 -0.000164\n",
      "2017-05-22 -0.008850  0.001098\n"
     ]
    }
   ],
   "source": [
    "print(daily_prices.head())\n",
    "\n",
    "# calculate daily returns\n",
    "daily_returns = daily_prices.pct_change(1)\n",
    "clean_daily_returns = daily_returns.dropna(axis=0)  # drop first missing row\n",
    "print(clean_daily_returns.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    GMR   R-squared:                       0.207\n",
      "Model:                            OLS   Adj. R-squared:                  0.205\n",
      "Method:                 Least Squares   F-statistic:                     127.9\n",
      "Date:                Wed, 31 Jul 2019   Prob (F-statistic):           1.61e-26\n",
      "Time:                        23:23:26   Log-Likelihood:                 1083.7\n",
      "No. Observations:                 493   AIC:                            -2163.\n",
      "Df Residuals:                     491   BIC:                            -2155.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.0005      0.001     -0.425      0.671      -0.003       0.002\n",
      "Nifty          1.9044      0.168     11.311      0.000       1.574       2.235\n",
      "==============================================================================\n",
      "Omnibus:                       84.185   Durbin-Watson:                   2.095\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              300.010\n",
      "Skew:                           0.744   Prob(JB):                     7.14e-66\n",
      "Kurtosis:                       6.520   Cond. No.                         139.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# split dependent and independent variable\n",
    "\n",
    "X = clean_daily_returns['Nifty']\n",
    "y = clean_daily_returns['GMR']\n",
    "\n",
    "# Add a constant to the independent value\n",
    "X1 = sm.add_constant(X)\n",
    "\n",
    "# make regression model \n",
    "model = sm.OLS(y, X1)\n",
    "\n",
    "# fit model and print results\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta for all days in dataset: 1.904384093358036\n"
     ]
    }
   ],
   "source": [
    "print(\"Beta for all days in dataset: {}\" .format(results.params[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta for 3 months as per daily returns: 1.635273088999384\n"
     ]
    }
   ],
   "source": [
    "#Beta calculation for 3 months - 63 Days(as per Financial Markets)\n",
    "X = clean_daily_returns['Nifty'].tail(63)\n",
    "y = clean_daily_returns['GMR'].tail(63)\n",
    "X1 = sm.add_constant(X) \n",
    "model = sm.OLS(y, X1)\n",
    "results = model.fit()\n",
    "print(\"Beta for 3 months as per daily returns: {}\" .format(results.params[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Monthly Beta Calculation \n",
    "monthly_returns = daily_returns.copy()\n",
    "monthly_returns = monthly_returns+1\n",
    "monthly_returns = monthly_returns.dropna(axis=0)\n",
    "monthly_returns['Year'] = pd.DatetimeIndex(monthly_returns.index).year\n",
    "monthly_returns['Month'] = pd.DatetimeIndex(monthly_returns.index).month\n",
    "monthly_returns = monthly_returns.groupby(['Month','Year']).prod()\n",
    "monthly_returns = monthly_returns - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monthly Beta value for GMRINFRA: 1.9971306457455724\n"
     ]
    }
   ],
   "source": [
    "X = monthly_returns['Nifty']\n",
    "Y = monthly_returns['GMR']\n",
    "X1 = sm.add_constant(X)\n",
    "model = sm.OLS(Y, X1)\n",
    "results = model.fit()\n",
    "print(\"Monthly Beta value for GMRINFRA: {}\" .format(results.params[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion:\n",
    "\n",
    "> Beta values are greater than 1 for GMRINFRA for every parameter. \n",
    "\n",
    "> Beta Values greater than 1 implies that Stock is Volatile. At various points, I have found out that GMRINFRA is a volatile stock. Performance of GMRINFRA is not appropriate for the investment.\n",
    "\n",
    "> Stock market can't be risk free. Lower Beta Values implies of lower risk rate. Lower Beta also means lower volatility rate. \n",
    "\n",
    "> Thinking of market with Zero Risk & Zero Volatility, that will call for Zero beta value. What you see is not necessarily true. This proverb is for this situation,  your zero-beta investment actually loses if it pays interest at less than the rate of inflation.\n",
    "\n",
    "> Negative Beta implicates investtment is  moving in opposite direction from stock market. When the market rises, a negative-beta investment generally falls. When the market falls, the negative-beta investment will tend to rise. A negative beta coefficient does not really mean non attendance of hazard. Rather, negative beta methods your speculation offers a support against genuine market downturns. In the event that the market keeps rising, nonetheless, a negative-beta speculation is losing cash through circumstance hazard – the loss of the opportunity to make higher returns – and expansion chance, in which a low rate of return does not keep pace with swelling.\n",
    "\n",
    "> Regression Results - A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also tends to increase. A negative coefficient suggests that as the independent variable increases, the dependent variable tends to decrease."
   ]
  }
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