25c_attribution_analysis.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Attribution Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pandas_datareader import DataReader as pdr\n",
    "import yfinance as yf\n",
    "import plotly.graph_objects as go\n",
    "import statsmodels.api as sm\n",
    "pd.options.display.float_format = '{:.4f}'.format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to pull returns\n",
    "def returns(ticker):\n",
    "    ret = yf.download(ticker, start='2000-01-01', end='2022-12-31', progress=False)\n",
    "    ret.index = ret.index.to_period('D')\n",
    "    ret = ret[\"Adj Close\"].resample(\"M\").last()\n",
    "    ret = ret.pct_change()\n",
    "    ret.name = ticker\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\bbcx-investments-quarto\\quarto\\venv\\lib\\site-packages\\pandas\\core\\arrays\\datetimes.py:1162: UserWarning: Converting to PeriodArray/Index representation will drop timezone information.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Date\n",
       "2014-10       NaN\n",
       "2014-11    0.0103\n",
       "2014-12   -0.0209\n",
       "2015-01    0.0040\n",
       "2015-02    0.0627\n",
       "            ...  \n",
       "2022-08   -0.0720\n",
       "2022-09   -0.0991\n",
       "2022-10    0.0146\n",
       "2022-11   -0.0209\n",
       "2022-12   -0.1665\n",
       "Freq: M, Name: ARKK, Length: 99, dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pull data\n",
    "TICKER = 'ARKK'\n",
    "\n",
    "# Pull the data from Yahoo\n",
    "df = returns(TICKER)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ARKK</th>\n",
       "      <th>Mkt-RF</th>\n",
       "      <th>SMB</th>\n",
       "      <th>HML</th>\n",
       "      <th>RF</th>\n",
       "      <th>Mom</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>2014-10</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.0252</td>\n",
       "      <td>0.0420</td>\n",
       "      <td>-0.0181</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>-0.0006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-11</th>\n",
       "      <td>0.0103</td>\n",
       "      <td>0.0255</td>\n",
       "      <td>-0.0206</td>\n",
       "      <td>-0.0309</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12</th>\n",
       "      <td>-0.0209</td>\n",
       "      <td>-0.0006</td>\n",
       "      <td>0.0249</td>\n",
       "      <td>0.0227</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-01</th>\n",
       "      <td>0.0040</td>\n",
       "      <td>-0.0311</td>\n",
       "      <td>-0.0055</td>\n",
       "      <td>-0.0358</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-02</th>\n",
       "      <td>0.0627</td>\n",
       "      <td>0.0613</td>\n",
       "      <td>0.0061</td>\n",
       "      <td>-0.0186</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>-0.0282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-08</th>\n",
       "      <td>-0.0720</td>\n",
       "      <td>-0.0377</td>\n",
       "      <td>0.0137</td>\n",
       "      <td>0.0030</td>\n",
       "      <td>0.0019</td>\n",
       "      <td>0.0199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-09</th>\n",
       "      <td>-0.0991</td>\n",
       "      <td>-0.0935</td>\n",
       "      <td>-0.0079</td>\n",
       "      <td>0.0006</td>\n",
       "      <td>0.0019</td>\n",
       "      <td>0.0347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-10</th>\n",
       "      <td>0.0146</td>\n",
       "      <td>0.0783</td>\n",
       "      <td>0.0009</td>\n",
       "      <td>0.0805</td>\n",
       "      <td>0.0023</td>\n",
       "      <td>0.0387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-11</th>\n",
       "      <td>-0.0209</td>\n",
       "      <td>0.0460</td>\n",
       "      <td>-0.0340</td>\n",
       "      <td>0.0138</td>\n",
       "      <td>0.0029</td>\n",
       "      <td>-0.0201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12</th>\n",
       "      <td>-0.1665</td>\n",
       "      <td>-0.0641</td>\n",
       "      <td>-0.0068</td>\n",
       "      <td>0.0132</td>\n",
       "      <td>0.0033</td>\n",
       "      <td>0.0452</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>99 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           ARKK  Mkt-RF     SMB     HML     RF     Mom\n",
       "Date                                                  \n",
       "2014-10     NaN  0.0252  0.0420 -0.0181 0.0000 -0.0006\n",
       "2014-11  0.0103  0.0255 -0.0206 -0.0309 0.0000  0.0069\n",
       "2014-12 -0.0209 -0.0006  0.0249  0.0227 0.0000  0.0112\n",
       "2015-01  0.0040 -0.0311 -0.0055 -0.0358 0.0000  0.0384\n",
       "2015-02  0.0627  0.0613  0.0061 -0.0186 0.0000 -0.0282\n",
       "...         ...     ...     ...     ...    ...     ...\n",
       "2022-08 -0.0720 -0.0377  0.0137  0.0030 0.0019  0.0199\n",
       "2022-09 -0.0991 -0.0935 -0.0079  0.0006 0.0019  0.0347\n",
       "2022-10  0.0146  0.0783  0.0009  0.0805 0.0023  0.0387\n",
       "2022-11 -0.0209  0.0460 -0.0340  0.0138 0.0029 -0.0201\n",
       "2022-12 -0.1665 -0.0641 -0.0068  0.0132 0.0033  0.0452\n",
       "\n",
       "[99 rows x 6 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add factors\n",
    "ff3 = pdr('F-F_Research_Data_Factors','famafrench', start=1900)[0]/100\n",
    "Mom = pdr('F-F_Momentum_Factor','famafrench', start=1900)[0]/100\n",
    "Mom.columns = ['Mom']\n",
    "ff = ff3.join(Mom)\n",
    "df = pd.merge(df, ff, how='left', left_index=True, right_index=True)\n",
    "df"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Run Fama-French-Carhart performance model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.786\n",
      "Model:                            OLS   Adj. R-squared:                  0.777\n",
      "Method:                 Least Squares   F-statistic:                     85.61\n",
      "Date:                Tue, 11 Apr 2023   Prob (F-statistic):           2.51e-30\n",
      "Time:                        13:49:41   Log-Likelihood:                 166.50\n",
      "No. Observations:                  98   AIC:                            -323.0\n",
      "Df Residuals:                      93   BIC:                            -310.1\n",
      "Df Model:                           4                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.0026      0.005     -0.553      0.582      -0.012       0.007\n",
      "Mkt-RF         1.4535      0.110     13.163      0.000       1.234       1.673\n",
      "SMB            0.9113      0.186      4.889      0.000       0.541       1.281\n",
      "HML           -0.9318      0.132     -7.047      0.000      -1.194      -0.669\n",
      "Mom           -0.0488      0.146     -0.334      0.739      -0.339       0.241\n",
      "==============================================================================\n",
      "Omnibus:                        3.435   Durbin-Watson:                   2.025\n",
      "Prob(Omnibus):                  0.180   Jarque-Bera (JB):                2.846\n",
      "Skew:                           0.293   Prob(JB):                        0.241\n",
      "Kurtosis:                       3.594   Cond. No.                         42.1\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "ff4 = sm.OLS(df[TICKER]-df['RF'], sm.add_constant(df[['Mkt-RF','SMB','HML','Mom']]),missing='drop').fit()\n",
    "print(ff4.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    -0.0026\n",
       "Mkt-RF    1.4535\n",
       "SMB       0.9113\n",
       "HML      -0.9318\n",
       "Mom      -0.0488\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefs = ff4.params\n",
    "coefs"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Attribution analysis using FFC model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df.dropna()\n",
    "cum_rets = pd.DataFrame(dtype=float, columns = [TICKER,'active','mkt','SMB','HML','Mom'],index=df.index)\n",
    "cum_rets[TICKER] = (1 + df[TICKER]).cumprod()\n",
    "cum_rets['mkt']  = (1 + df.RF + coefs['Mkt-RF']*df['Mkt-RF']).cumprod()\n",
    "cum_rets['SMB']  = (1 + coefs['SMB']*df['SMB']).cumprod()\n",
    "cum_rets['HML']  = (1 + coefs['HML']*df['HML']).cumprod()\n",
    "cum_rets['Mom']  = (1 + coefs['Mom']*df['Mom']).cumprod()\n",
    "cum_rets['active']=(1 + coefs['const'] + ff4.resid).cumprod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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   "source": [
    "# Scatter plot with returns due to each source\n",
    "fig = go.Figure()\n",
    "for c in cum_rets.columns:\n",
    "    trace  = go.Scatter(x=cum_rets.index.astype(str), y=cum_rets[c], mode=\"lines\", name = c)\n",
    "    fig.add_trace(trace)\n",
    "\n",
    "# Formatting\n",
    "fig.update_yaxes(title='Cumulative Return',tickformat=\".2f\")\n",
    "fig.update_layout(legend=dict(yanchor=\"top\", y =0.99, xanchor=\"left\", x=0.01),yaxis_type=\"log\")\n",
    "fig.show()"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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