Capital Asset Pricing Model.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pandas import ExcelWriter\n",
    "from pandas import ExcelFile\n",
    "import pandas_datareader as pdr\n",
    "from pandas_datareader import data, wb\n",
    "from datetime import date\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Open</th>\n",
       "      <th>Close</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4-Jan-16</td>\n",
       "      <td>32.290001</td>\n",
       "      <td>32.369999</td>\n",
       "      <td>32.580002</td>\n",
       "      <td>32.040001</td>\n",
       "      <td>8951900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5-Jan-16</td>\n",
       "      <td>32.98</td>\n",
       "      <td>32.889999</td>\n",
       "      <td>33.439999</td>\n",
       "      <td>32.5</td>\n",
       "      <td>12256800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6-Jan-16</td>\n",
       "      <td>32.349998</td>\n",
       "      <td>31.530001</td>\n",
       "      <td>32.5</td>\n",
       "      <td>31.16</td>\n",
       "      <td>11233600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7-Jan-16</td>\n",
       "      <td>30.74</td>\n",
       "      <td>30.280001</td>\n",
       "      <td>30.950001</td>\n",
       "      <td>29.879999</td>\n",
       "      <td>16132600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8-Jan-16</td>\n",
       "      <td>30.67</td>\n",
       "      <td>29.629999</td>\n",
       "      <td>30.700001</td>\n",
       "      <td>29.57</td>\n",
       "      <td>9961800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "       Date       Open      Close       High        Low    Volume\n",
       "0  4-Jan-16  32.290001  32.369999  32.580002  32.040001   8951900\n",
       "1  5-Jan-16      32.98  32.889999  33.439999       32.5  12256800\n",
       "2  6-Jan-16  32.349998  31.530001       32.5      31.16  11233600\n",
       "3  7-Jan-16      30.74  30.280001  30.950001  29.879999  16132600\n",
       "4  8-Jan-16      30.67  29.629999  30.700001      29.57   9961800"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=pd.read_csv(\"NVDA.csv\", decimal = ',')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Modelling CAPM and calculating alpha and beta from historical values.\n",
    "'''\n",
    "Download monthly prices of NVIDIA and S&P 500 index from 2016 to 2018\n",
    "CSV file downloaded from Yahoo File\n",
    "start period: 02/11/2016 \n",
    "end period: 30/11/2018\n",
    "period format: DD/MM/YEAR\n",
    "'''\n",
    "\n",
    "df_nvda = pdr.get_data_yahoo('NVDA', '2016-01-04', '2018-08-30')\n",
    "\n",
    "#Collect data on the market from S&P 500 StockPrice data --- GSPC\n",
    "df_gspc = pdr.get_data_yahoo('^GSPC', '2016-01-04', '2018-08-30')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
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       "      <th>Close</th>\n",
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       "      <th>Adj Close</th>\n",
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       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>32.580002</td>\n",
       "      <td>32.040001</td>\n",
       "      <td>32.290001</td>\n",
       "      <td>32.369999</td>\n",
       "      <td>8951900.0</td>\n",
       "      <td>31.724598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>33.439999</td>\n",
       "      <td>32.500000</td>\n",
       "      <td>32.980000</td>\n",
       "      <td>32.889999</td>\n",
       "      <td>12256800.0</td>\n",
       "      <td>32.234219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>32.500000</td>\n",
       "      <td>31.160000</td>\n",
       "      <td>32.349998</td>\n",
       "      <td>31.530001</td>\n",
       "      <td>11233600.0</td>\n",
       "      <td>30.901340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-07</th>\n",
       "      <td>30.950001</td>\n",
       "      <td>29.879999</td>\n",
       "      <td>30.740000</td>\n",
       "      <td>30.280001</td>\n",
       "      <td>16132600.0</td>\n",
       "      <td>29.676266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-08</th>\n",
       "      <td>30.700001</td>\n",
       "      <td>29.570000</td>\n",
       "      <td>30.670000</td>\n",
       "      <td>29.629999</td>\n",
       "      <td>9961800.0</td>\n",
       "      <td>29.039225</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                 High        Low       Open      Close      Volume  Adj Close\n",
       "Date                                                                         \n",
       "2016-01-04  32.580002  32.040001  32.290001  32.369999   8951900.0  31.724598\n",
       "2016-01-05  33.439999  32.500000  32.980000  32.889999  12256800.0  32.234219\n",
       "2016-01-06  32.500000  31.160000  32.349998  31.530001  11233600.0  30.901340\n",
       "2016-01-07  30.950001  29.879999  30.740000  30.280001  16132600.0  29.676266\n",
       "2016-01-08  30.700001  29.570000  30.670000  29.629999   9961800.0  29.039225"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_nvda.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Open</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Adj Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>2038.199951</td>\n",
       "      <td>1989.680054</td>\n",
       "      <td>2038.199951</td>\n",
       "      <td>2012.660034</td>\n",
       "      <td>4304880000</td>\n",
       "      <td>2012.660034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>2021.939941</td>\n",
       "      <td>2004.170044</td>\n",
       "      <td>2013.780029</td>\n",
       "      <td>2016.709961</td>\n",
       "      <td>3706620000</td>\n",
       "      <td>2016.709961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>2011.709961</td>\n",
       "      <td>1979.050049</td>\n",
       "      <td>2011.709961</td>\n",
       "      <td>1990.260010</td>\n",
       "      <td>4336660000</td>\n",
       "      <td>1990.260010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-07</th>\n",
       "      <td>1985.319946</td>\n",
       "      <td>1938.829956</td>\n",
       "      <td>1985.319946</td>\n",
       "      <td>1943.089966</td>\n",
       "      <td>5076590000</td>\n",
       "      <td>1943.089966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-08</th>\n",
       "      <td>1960.400024</td>\n",
       "      <td>1918.459961</td>\n",
       "      <td>1945.969971</td>\n",
       "      <td>1922.030029</td>\n",
       "      <td>4664940000</td>\n",
       "      <td>1922.030029</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "                   High          Low         Open        Close      Volume  \\\n",
       "Date                                                                         \n",
       "2016-01-04  2038.199951  1989.680054  2038.199951  2012.660034  4304880000   \n",
       "2016-01-05  2021.939941  2004.170044  2013.780029  2016.709961  3706620000   \n",
       "2016-01-06  2011.709961  1979.050049  2011.709961  1990.260010  4336660000   \n",
       "2016-01-07  1985.319946  1938.829956  1985.319946  1943.089966  5076590000   \n",
       "2016-01-08  1960.400024  1918.459961  1945.969971  1922.030029  4664940000   \n",
       "\n",
       "              Adj Close  \n",
       "Date                     \n",
       "2016-01-04  2012.660034  \n",
       "2016-01-05  2016.709961  \n",
       "2016-01-06  1990.260010  \n",
       "2016-01-07  1943.089966  \n",
       "2016-01-08  1922.030029  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gspc.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# joining the closing prices of the two datasets \n",
    "monthly_prices = pd.concat([df_nvda['Open'], df_gspc['Open']], axis=1)\n",
    "monthly_prices.columns = ['NVDA', '^GSPC']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>NVDA</th>\n",
       "      <th>^GSPC</th>\n",
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       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>32.290001</td>\n",
       "      <td>2038.199951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>32.980000</td>\n",
       "      <td>2013.780029</td>\n",
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       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>32.349998</td>\n",
       "      <td>2011.709961</td>\n",
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       "    <tr>\n",
       "      <th>2016-01-07</th>\n",
       "      <td>30.740000</td>\n",
       "      <td>1985.319946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-08</th>\n",
       "      <td>30.670000</td>\n",
       "      <td>1945.969971</td>\n",
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      "text/plain": [
       "                 NVDA        ^GSPC\n",
       "Date                              \n",
       "2016-01-04  32.290001  2038.199951\n",
       "2016-01-05  32.980000  2013.780029\n",
       "2016-01-06  32.349998  2011.709961\n",
       "2016-01-07  30.740000  1985.319946\n",
       "2016-01-08  30.670000  1945.969971"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_prices.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>NVDA</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>0.021369</td>\n",
       "      <td>-0.011981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>-0.019103</td>\n",
       "      <td>-0.001028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-07</th>\n",
       "      <td>-0.049768</td>\n",
       "      <td>-0.013118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-08</th>\n",
       "      <td>-0.002277</td>\n",
       "      <td>-0.019820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-11</th>\n",
       "      <td>-0.032931</td>\n",
       "      <td>-0.010201</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                NVDA     ^GSPC\n",
       "Date                          \n",
       "2016-01-05  0.021369 -0.011981\n",
       "2016-01-06 -0.019103 -0.001028\n",
       "2016-01-07 -0.049768 -0.013118\n",
       "2016-01-08 -0.002277 -0.019820\n",
       "2016-01-11 -0.032931 -0.010201"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate monthly returns\n",
    "# Percentage change between the current and a prior element.\n",
    "#Computes the percentage change from the immediately previous row by default. \n",
    "#This is useful in comparing the percentage of change in a time series of elements.\n",
    "\n",
    "monthly_returns = monthly_prices.pct_change(1)  # 1 used to denote Periods to shift for forming percent change.\n",
    "clean_monthly_returns = monthly_returns.dropna(axis=0)  # drop first missing row\n",
    "clean_monthly_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Ordinary Least Square (OLS)Regression with Statsmodels.\n",
    "# split dependent and independent variable\n",
    "X = clean_monthly_returns['^GSPC']\n",
    "y = clean_monthly_returns['NVDA']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   NVDA   R-squared:                       0.222\n",
      "Model:                            OLS   Adj. R-squared:                  0.221\n",
      "Method:                 Least Squares   F-statistic:                     190.9\n",
      "Date:                Sun, 15 Dec 2019   Prob (F-statistic):           2.24e-38\n",
      "Time:                        19:05:22   Log-Likelihood:                 1585.5\n",
      "No. Observations:                 671   AIC:                            -3167.\n",
      "Df Residuals:                     669   BIC:                            -3158.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0026      0.001      2.911      0.004       0.001       0.004\n",
      "^GSPC          1.7689      0.128     13.816      0.000       1.517       2.020\n",
      "==============================================================================\n",
      "Omnibus:                       76.428   Durbin-Watson:                   2.057\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              534.569\n",
      "Skew:                           0.174   Prob(JB):                    8.31e-117\n",
      "Kurtosis:                       7.359   Cond. No.                         145.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\gadep\\OneDrive\\Anakonda\\lib\\site-packages\\numpy\\core\\fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "# 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": "markdown",
   "metadata": {},
   "source": [
    "The coefficient value for (^GSPC) is 1.6134. If the Beta value provided by Yahoo! Finance is anywhere as close to this figure, then our regression model and attempt to replicate how Yahoo! Finance calculates Beta values is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.768894307438861\n"
     ]
    }
   ],
   "source": [
    "# alternatively scipy linear regression\n",
    "\n",
    "#https://finance.yahoo.com/quote/NVDA/\n",
    "\n",
    "from scipy import stats\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(X, y)\n",
    "\n",
    "print(slope)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "##model 2\n",
    "\n",
    "def capm(start_date, end_date, ticker1, ticker2):\n",
    "    df = pdr.get_data_yahoo(ticker1, start_date, end_date)\n",
    "    dfb = pdr.get_data_yahoo(ticker2, start_date, end_date)\n",
    "    df.head()\n",
    "    dfb.head()\n",
    "# create a time-series\n",
    "    rts = df.resample('M').last()\n",
    "    rbts = dfb.resample('M').last()\n",
    "    dfsm = pd.DataFrame({'s_open' : rts['Open'], 'b_open' : rbts['Open']}, index=rts.index)\n",
    "\n",
    "# compute returns\n",
    "    dfsm[['s_returns', 'b_returns']] = dfsm[['s_open','b_open']]/dfsm[['s_open','b_open']].shift(1) -1\n",
    "    dfsm = dfsm.dropna()\n",
    "\n",
    "    covmat = np.cov(dfsm[\"s_returns\"], dfsm[\"b_returns\"])\n",
    "\n",
    "# calculate measures now\n",
    "    beta = covmat[0,1]/covmat[1,1]\n",
    "    alpha = np.mean(dfsm[\"s_returns\"])-beta*np.mean(dfsm[\"b_returns\"])\n",
    "\n",
    "# r_squared     = 1.0 - SS_res/SS_tot\n",
    "    y = beta * dfsm[\"b_returns\"] + alpha\n",
    "    SS_res = np.sum(np.power(y - dfsm[\"s_returns\"],2))\n",
    "    SS_tot = covmat[0,0]*(len(dfsm) - 1) # SS_tot is sample_variance*(n-1)\n",
    "\n",
    "    r_squared = 1.0 - SS_res/SS_tot\n",
    "# Volatility for the full time and 1-year momentum\n",
    "    volatility = np.sqrt(covmat[0,0])\n",
    "    momentum = np.prod(1+dfsm[\"s_returns\"].tail(12).values) - 1.0\n",
    "\n",
    "\n",
    "    prd = 12.0 # used monthly returns; 12 periods to annualize\n",
    "    alpha = alpha*prd\n",
    "    volatility = volatility*np.sqrt(prd)\n",
    "\n",
    "    print (\"Beta, alpha, r_squared, volatility, momentum:\")\n",
    "    print (beta, alpha, r_squared, volatility, momentum)\n",
    "\n",
    "    %pylab\n",
    "    fig,ax = plt.subplots(1,figsize=(20,10))\n",
    "    ax.scatter(dfsm[\"b_returns\"], dfsm['s_returns'], label=\"Data points\")\n",
    "    beta,alpha = np.polyfit(dfsm[\"b_returns\"], dfsm['s_returns'], deg=1)\n",
    "    ax.plot(dfsm[\"b_returns\"], beta*dfsm[\"b_returns\"] + alpha, color='red', label=\"CAPM line\")\n",
    "\n",
    "\n",
    "    plt.title('Capital Asset Pricing Model, finding alphas and betas')\n",
    "    plt.xlabel('Market return $R_m$', fontsize=14)\n",
    "    plt.ylabel('Stock return $R_i$')\n",
    "#     plt.text(0.05, 0.05, r'$R_i = \\beta * R_m + \\alpha$', fontsize=14)\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "    return beta, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta, alpha, r_squared, volatility, momentum:\n",
      "2.166974886131238 0.61859069010838 0.1871663849759383 0.4010004992275091 0.6636636636636639\n",
      "Using matplotlib backend: Qt5Agg\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "beta, y = capm('2016-01-04', '2018-08-30','NVDA', '^GSPC')"
   ]
  }
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