CAPM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "50b949cf",
   "metadata": {},
   "source": [
    "# Capital asset pricing model\n",
    "\n",
    "### helps to calculate expected return of the stock\n",
    "\n",
    "\n",
    "#### The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared to its expected return."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e232006",
   "metadata": {},
   "source": [
    "# Utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "303a735e",
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -U yfinance requests pandas fredapi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "96700daa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import yfinance as yf\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import requests\n",
    "import io\n",
    "\n",
    "from fredapi import Fred\n",
    "from datetime import datetime, timedelta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6be5e4d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def three_month_yield_us_tresuries(start, end):\n",
    "    fred = Fred(api_key='')\n",
    "    return pd.DataFrame(fred.get_series('DGS3MO', observation_start=start, observation_end=end), columns=['value'])\n",
    "\n",
    "def capm(risk_free_rate, beta, expected_return):\n",
    "    return risk_free_rate + beta * (expected_return - risk_free_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49b43f92",
   "metadata": {},
   "source": [
    "# Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "39d9935f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Start date: 07/02/2017 End date: 06/02/2022\n"
     ]
    }
   ],
   "source": [
    "market = \"SPY\"\n",
    "stock = \"AAPL\"\n",
    "historical_data_years = 5\n",
    "tickers = [market, stock]\n",
    "\n",
    "start = datetime.now() - timedelta(days = 365 * historical_data_years)\n",
    "end = datetime.now()\n",
    "print('Start date:', start.strftime(\"%d/%m/%Y\"), 'End date:', end.strftime(\"%d/%m/%Y\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be53b3a2",
   "metadata": {},
   "source": [
    "# Stock and market price right now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6c837304",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  2 of 2 completed\n",
      "Adj Close stock price now: {'SPY': 448.70001220703125, 'AAPL': 172.38999938964844}\n"
     ]
    }
   ],
   "source": [
    "live_prices = yf.download(tickers=tickers, period='1d', interval='1d')\n",
    "live_prices = [live_prices['Adj Close'][ticker][0] for ticker in tickers]\n",
    "print(\"Adj Close stock price now:\", dict(zip(tickers, live_prices)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69d86f99",
   "metadata": {},
   "source": [
    "# Historical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "04e30917",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "Risk free rate: 0.010778959999999999\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "</style>\n",
       "<table id=\"T_b872c\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_b872c_level0_col0\" class=\"col_heading level0 col0\" >tickers</th>\n",
       "      <th id=\"T_b872c_level0_col1\" class=\"col_heading level0 col1\" >starting_date</th>\n",
       "      <th id=\"T_b872c_level0_col2\" class=\"col_heading level0 col2\" >observations(days)</th>\n",
       "      <th id=\"T_b872c_level0_col3\" class=\"col_heading level0 col3\" >annual_return_avg</th>\n",
       "      <th id=\"T_b872c_level0_col4\" class=\"col_heading level0 col4\" >daily_return_avg</th>\n",
       "      <th id=\"T_b872c_level0_col5\" class=\"col_heading level0 col5\" >variance</th>\n",
       "      <th id=\"T_b872c_level0_col6\" class=\"col_heading level0 col6\" >std</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_b872c_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_b872c_row0_col0\" class=\"data row0 col0\" >SPY</td>\n",
       "      <td id=\"T_b872c_row0_col1\" class=\"data row0 col1\" >02/06/2017</td>\n",
       "      <td id=\"T_b872c_row0_col2\" class=\"data row0 col2\" >1260</td>\n",
       "      <td id=\"T_b872c_row0_col3\" class=\"data row0 col3\" >17.07%</td>\n",
       "      <td id=\"T_b872c_row0_col4\" class=\"data row0 col4\" >0.07%</td>\n",
       "      <td id=\"T_b872c_row0_col5\" class=\"data row0 col5\" >3.62%</td>\n",
       "      <td id=\"T_b872c_row0_col6\" class=\"data row0 col6\" >19.03%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b872c_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_b872c_row1_col0\" class=\"data row1 col0\" >AAPL</td>\n",
       "      <td id=\"T_b872c_row1_col1\" class=\"data row1 col1\" >02/06/2017</td>\n",
       "      <td id=\"T_b872c_row1_col2\" class=\"data row1 col2\" >1260</td>\n",
       "      <td id=\"T_b872c_row1_col3\" class=\"data row1 col3\" >39.30%</td>\n",
       "      <td id=\"T_b872c_row1_col4\" class=\"data row1 col4\" >0.16%</td>\n",
       "      <td id=\"T_b872c_row1_col5\" class=\"data row1 col5\" >9.38%</td>\n",
       "      <td id=\"T_b872c_row1_col6\" class=\"data row1 col6\" >30.62%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x127b406d0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stock_info = {\n",
    "    'tickers': tickers, \n",
    "    'starting_date': [], \n",
    "    'observations(days)': [], \n",
    "    'annual_return_avg': [], \n",
    "    'daily_return_avg': [], \n",
    "    'variance': [],\n",
    "}\n",
    "price_hist = {}\n",
    "\n",
    "sns.set(rc = {'figure.figsize': (16,8)})\n",
    "\n",
    "for ticker in tickers:\n",
    "    tmp = yf.download(ticker, start=start, end=end)\n",
    "    tmp['daily_change'] = tmp['Adj Close'].pct_change()\n",
    "    stock_info['starting_date'].append(tmp.index[0])\n",
    "    stock_info['annual_return_avg'].append(tmp['daily_change'].mean() * 252)\n",
    "    stock_info['daily_return_avg'].append(tmp['daily_change'].mean())\n",
    "    stock_info['variance'].append(tmp['daily_change'].var() * 252)\n",
    "    stock_info['observations(days)'].append(len(tmp))\n",
    "    price_hist[ticker] = tmp['daily_change']\n",
    "    sns.lineplot(x=tmp.index, y='Adj Close', data=tmp, markers=True, label=ticker)\n",
    "    \n",
    "price_hist = pd.DataFrame.from_dict(price_hist)\n",
    "\n",
    "three_month_yield = three_month_yield_us_tresuries(start, end)\n",
    "risk_free_rate = three_month_yield['value'].mean() / 100\n",
    "print(\"Risk free rate:\", risk_free_rate)\n",
    "\n",
    "df = pd.DataFrame.from_dict(stock_info)\n",
    "df['std'] = df['variance'].apply(np.sqrt)\n",
    "df['starting_date'] = df['starting_date'].dt.strftime('%m/%d/%Y')\n",
    "df.style.format({\n",
    "    'annual_return_avg': '{:,.2%}'.format,\n",
    "    'daily_return_avg': '{:,.2%}'.format,\n",
    "    'variance': '{:,.2%}'.format, \n",
    "    'std': '{:,.2%}'.format},\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aedb4d35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SPY</th>\n",
       "      <th>AAPL</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>2017-02-06</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-02-07</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-02-08</th>\n",
       "      <td>0.13</td>\n",
       "      <td>0.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-02-09</th>\n",
       "      <td>0.59</td>\n",
       "      <td>0.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-02-10</th>\n",
       "      <td>0.39</td>\n",
       "      <td>-0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-01-31</th>\n",
       "      <td>1.80</td>\n",
       "      <td>2.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-02-01</th>\n",
       "      <td>0.68</td>\n",
       "      <td>-0.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-02-02</th>\n",
       "      <td>0.97</td>\n",
       "      <td>0.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-02-03</th>\n",
       "      <td>-2.35</td>\n",
       "      <td>-1.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-02-04</th>\n",
       "      <td>0.47</td>\n",
       "      <td>-0.17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1260 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             SPY  AAPL\n",
       "Date                  \n",
       "2017-02-06   NaN   NaN\n",
       "2017-02-07  0.00  0.95\n",
       "2017-02-08  0.13  0.39\n",
       "2017-02-09  0.59  0.72\n",
       "2017-02-10  0.39 -0.23\n",
       "...          ...   ...\n",
       "2022-01-31  1.80  2.61\n",
       "2022-02-01  0.68 -0.10\n",
       "2022-02-02  0.97  0.70\n",
       "2022-02-03 -2.35 -1.67\n",
       "2022-02-04  0.47 -0.17\n",
       "\n",
       "[1260 rows x 2 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected_returns = (price_hist * 100).round(2)\n",
    "expected_returns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cac05f3",
   "metadata": {},
   "source": [
    "#### Beta might be considered as a slope of the line (k param) in line equation:\n",
    "$y = kx + b$\n",
    "\n",
    "# CAPM\n",
    "$ER_i=R_f+\\beta_i(ER_m-R_f)$, where\n",
    "\n",
    "- $ER_i$ - expected return of investment\n",
    "- $R_i$ - risk free rate\n",
    "- $B_i$ - beta of the investment\n",
    "- $(ER_m-R_f)$ - market risk premium "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "96ad3bcd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta: 1.235467572492615\n",
      "CAPM of stock: 0.208328523168931\n",
      "\n",
      "Expected stock price in a year: 208.3037533715868\n"
     ]
    }
   ],
   "source": [
    "beta = (price_hist.cov() / price_hist[market].var()).loc[stock, market]\n",
    "print(\"Beta:\", beta)\n",
    "\n",
    "annual_return = df.where(df['tickers'] == market).dropna()['annual_return_avg'][0]\n",
    "CAPM_stock = capm(risk_free_rate, beta, annual_return)\n",
    "print(\"CAPM of stock:\", CAPM_stock)\n",
    "print(\"\\nExpected stock price in a year:\", dict(zip(tickers, live_prices))[stock] * (1 + CAPM_stock))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a9820e9",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "- https://www.investopedia.com/terms/c/capm.asp\n",
    "\n",
    "- https://fred.stlouisfed.org/series/DGS3MO\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}