lab_204.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Backtesting: EW vs CW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import edhec_risk_kit_204 as erk\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "ind49_rets = erk.get_ind_returns(weighting=\"vw\", n_inds=49)[\"1974\":]\n",
    "ind49_mcap = erk.get_ind_market_caps(49, weights=True)[\"1974\":]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we'll develop a basic infrastructure to backtest various portfolio construction techniques and compare them. Here we'll start with something quite simple and straightforward - we'll write trivially simple weight-optimizers for Equally Weighted and Cap Weighted portfolios and compare them. Obviously, there are no Covariance estimates required for either one of these weighting schemes. In following sessions we'll enhance these optimizers to use more complex weighting schemes that will rely on covariance estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def weight_ew(r):\n",
    "    \"\"\"\n",
    "    Returns the weights of the EW portfolio based on the asset returns \"r\" as a DataFrame\n",
    "    \"\"\"\n",
    "    n = len(r.columns)\n",
    "    return pd.Series(1/n, index=r.columns)\n",
    "\n",
    "def backtest_ws(r, estimation_window=60, weighting=weight_ew):\n",
    "    \"\"\"\n",
    "    Backtests a given weighting scheme, given some parameters:\n",
    "    r : asset returns to use to build the portfolio\n",
    "    estimation_window: the window to use to estimate parameters\n",
    "    weighting: the weighting scheme to use, must be a function that takes \"r\", and a variable number of keyword-value arguments\n",
    "    \"\"\"\n",
    "    n_periods = r.shape[0]\n",
    "    windows = [(start, start+estimation_window) for start in range(n_periods-estimation_window+1)]\n",
    "    # windows is a list of tuples which gives us the (integer) location of the start and stop (non inclusive)\n",
    "    # for each estimation window\n",
    "    weights = [weighting(r.iloc[win[0]:win[1]]) for win in windows]\n",
    "    # List -> DataFrame\n",
    "    weights = pd.DataFrame(weights, index=r.iloc[estimation_window-1:].index, columns=r.columns)\n",
    "    # return weights\n",
    "    returns = (weights * r).sum(axis=\"columns\",  min_count=1) #mincount is to generate NAs if all inputs are NAs\n",
    "    return returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ewr = backtest_ws(ind49_rets, weighting=weight_ew)\n",
    "ewi = (1+ewr).cumprod()\n",
    "ewi.plot(figsize=(12,6), title=\"49 Industries - Equally Weighted\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's add capweighting. We'll need to compute capweights, which we've already been provided through the marketcap file. We can refactor the code we've developed in the past to add a convenience function to our toolkit. Note the use of `**kwargs` to be able to take a variable number of keyword arguments to the function so that we can call any weighting function and let that weighting function take care of whatever arguments it needs. We'll have to refactor `weight_ew` with this new signature, but thats the only change (for now) for `weight_ew`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def weight_ew(r, **kwargs):\n",
    "    \"\"\"\n",
    "    Returns the weights of the EW portfolio based on the asset returns \"r\" as a DataFrame\n",
    "    \"\"\"\n",
    "    n = len(r.columns)\n",
    "    return pd.Series(1/n, index=r.columns)\n",
    "\n",
    "def weight_cw(r, cap_weights, **kwargs):\n",
    "    \"\"\"\n",
    "    Returns the weights of the CW portfolio based on the time series of capweights\n",
    "    \"\"\"\n",
    "    return cap_weights.loc[r.index[0]]\n",
    "\n",
    "def backtest_ws(r, estimation_window=60, weighting=weight_ew, **kwargs):\n",
    "    \"\"\"\n",
    "    Backtests a given weighting scheme, given some parameters:\n",
    "    r : asset returns to use to build the portfolio\n",
    "    estimation_window: the window to use to estimate parameters\n",
    "    weighting: the weighting scheme to use, must be a function that takes \"r\", and a variable number of keyword-value arguments\n",
    "    \"\"\"\n",
    "    n_periods = r.shape[0]\n",
    "    # return windows\n",
    "    windows = [(start, start+estimation_window) for start in range(n_periods-estimation_window+1)]\n",
    "    weights = [weighting(r.iloc[win[0]:win[1]], **kwargs) for win in windows]\n",
    "    # convert list of weights to DataFrame\n",
    "    weights = pd.DataFrame(weights, index=r.iloc[estimation_window-1:].index, columns=r.columns)\n",
    "    # return weights\n",
    "    returns = (weights * r).sum(axis=\"columns\",  min_count=1) #mincount is to generate NAs if all inputs are NAs\n",
    "    return returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1974-01         NaN\n",
       "1974-02         NaN\n",
       "1974-03         NaN\n",
       "1974-04         NaN\n",
       "1974-05         NaN\n",
       "1974-06         NaN\n",
       "1974-07         NaN\n",
       "1974-08         NaN\n",
       "1974-09         NaN\n",
       "1974-10         NaN\n",
       "1974-11         NaN\n",
       "1974-12         NaN\n",
       "1975-01         NaN\n",
       "1975-02         NaN\n",
       "1975-03         NaN\n",
       "1975-04         NaN\n",
       "1975-05         NaN\n",
       "1975-06         NaN\n",
       "1975-07         NaN\n",
       "1975-08         NaN\n",
       "1975-09         NaN\n",
       "1975-10         NaN\n",
       "1975-11         NaN\n",
       "1975-12         NaN\n",
       "1976-01         NaN\n",
       "1976-02         NaN\n",
       "1976-03         NaN\n",
       "1976-04         NaN\n",
       "1976-05         NaN\n",
       "1976-06         NaN\n",
       "             ...   \n",
       "2016-07    0.038460\n",
       "2016-08    0.006097\n",
       "2016-09    0.004589\n",
       "2016-10   -0.020099\n",
       "2016-11    0.049931\n",
       "2016-12    0.017752\n",
       "2017-01    0.018496\n",
       "2017-02    0.035646\n",
       "2017-03    0.000464\n",
       "2017-04    0.010200\n",
       "2017-05    0.006189\n",
       "2017-06    0.007868\n",
       "2017-07    0.019176\n",
       "2017-08   -0.001567\n",
       "2017-09    0.029797\n",
       "2017-10    0.017194\n",
       "2017-11    0.034155\n",
       "2017-12    0.015368\n",
       "2018-01    0.053914\n",
       "2018-02   -0.041096\n",
       "2018-03   -0.018399\n",
       "2018-04    0.006246\n",
       "2018-05    0.020322\n",
       "2018-06    0.007748\n",
       "2018-07    0.034714\n",
       "2018-08    0.031083\n",
       "2018-09    0.003468\n",
       "2018-10   -0.070352\n",
       "2018-11    0.020936\n",
       "2018-12   -0.094909\n",
       "Freq: M, Length: 540, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ewr = backtest_ws(ind49_rets)\n",
    "cwr = backtest_ws(ind49_rets, weighting=weight_cw, cap_weights=ind49_mcap)\n",
    "cwr\n",
    "#btr = pd.DataFrame({\"EW\": ewr, \"CW\": cwr})\n",
    "#(1+btr).cumprod().plot(figsize=(12,5), title=\"49 Industries - CapWeighted vs Equally Weighted\")\n",
    "#erk.summary_stats(btr.dropna())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Improving EW with CapWeight Tethering\n",
    "\n",
    "Often in practice, we'll want to implement some sort of a modification of a pure strategy. For instance, although Equal Weight portfolios are popular, they'll be constrained in some way - for instance to match the sector weights of the cap-weighted benchmark or to make sure that microcap stocks are not overweighted. The motivation for doing so could be to make a portfolio more tradeable (e.g. some microcaps may not have the liquidity) or to improve the tracking error to the Cap-Weighted index.\n",
    "\n",
    "As an illustration of how that can be achieved, we enhance our simple `weight_ew` allocator to (i) drop microcap stocks beyond a particular threshold, and (ii) impose a constraint that ensures that the maximum weight assigned to any stock is no more than some multiple of the weight it would be in a cap-weighted portfolio.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def weight_ew(r, cap_weights=None, max_cw_mult=None, microcap_threshold=None, **kwargs):\n",
    "    \"\"\"\n",
    "    Returns the weights of the EW portfolio based on the asset returns \"r\" as a DataFrame\n",
    "    If supplied a set of capweights and a capweight tether, it is applied and reweighted \n",
    "    \"\"\"\n",
    "    n = len(r.columns)\n",
    "    ew = pd.Series(1/n, index=r.columns)\n",
    "    if cap_weights is not None:\n",
    "        cw = cap_weights.loc[r.index[0]] # starting cap weight\n",
    "        ## exclude microcaps\n",
    "        if microcap_threshold is not None and microcap_threshold > 0:\n",
    "            microcap = cw < microcap_threshold\n",
    "            ew[microcap] = 0\n",
    "            ew = ew/ew.sum()\n",
    "        #limit weight to a multiple of capweight\n",
    "        if max_cw_mult is not None and max_cw_mult > 0:\n",
    "            ew = np.minimum(ew, cw*max_cw_mult)\n",
    "            ew = ew/ew.sum() #reweight\n",
    "    return ew\n",
    "\n",
    "def weight_cw(r, cap_weights, **kwargs):\n",
    "    \"\"\"\n",
    "    Returns the weights of the CW portfolio based on the time series of capweights\n",
    "    \"\"\"\n",
    "    w = cap_weights.loc[r.index[0]]\n",
    "    return w/w.sum()\n",
    "\n",
    "def backtest_ws(r, estimation_window=60, weighting=weight_ew, **kwargs):\n",
    "    \"\"\"\n",
    "    Backtests a given weighting scheme, given some parameters:\n",
    "    r : asset returns to use to build the portfolio\n",
    "    estimation_window: the window to use to estimate parameters\n",
    "    weighting: the weighting scheme to use, must be a function that takes \"r\", and a variable number of keyword-value arguments\n",
    "    \"\"\"\n",
    "    n_periods = r.shape[0]\n",
    "    # return windows\n",
    "    windows = [(start, start+estimation_window) for start in range(n_periods-estimation_window+1)]\n",
    "    weights = [weighting(r.iloc[win[0]:win[1]], **kwargs) for win in windows]\n",
    "    # convert to DataFrame\n",
    "    weights = pd.DataFrame(weights, index=r.iloc[estimation_window-1:].index, columns=r.columns)\n",
    "    returns = (weights * r).sum(axis=\"columns\",  min_count=1) #mincount is to generate NAs if all inputs are NAs\n",
    "    return returns\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
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       "        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>Annualized Return</th>\n",
       "      <th>Annualized Vol</th>\n",
       "      <th>Skewness</th>\n",
       "      <th>Kurtosis</th>\n",
       "      <th>Cornish-Fisher VaR (5%)</th>\n",
       "      <th>Historic CVaR (5%)</th>\n",
       "      <th>Sharpe Ratio</th>\n",
       "      <th>Max Drawdown</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>EW</th>\n",
       "      <td>0.123921</td>\n",
       "      <td>0.160660</td>\n",
       "      <td>-0.759092</td>\n",
       "      <td>6.659028</td>\n",
       "      <td>0.071404</td>\n",
       "      <td>0.102331</td>\n",
       "      <td>0.568799</td>\n",
       "      <td>-0.528292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EW-Tethered</th>\n",
       "      <td>0.125572</td>\n",
       "      <td>0.156923</td>\n",
       "      <td>-0.752967</td>\n",
       "      <td>6.187433</td>\n",
       "      <td>0.069778</td>\n",
       "      <td>0.099191</td>\n",
       "      <td>0.592597</td>\n",
       "      <td>-0.530654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CW</th>\n",
       "      <td>0.120165</td>\n",
       "      <td>0.147544</td>\n",
       "      <td>-0.717960</td>\n",
       "      <td>5.562648</td>\n",
       "      <td>0.065636</td>\n",
       "      <td>0.093769</td>\n",
       "      <td>0.594625</td>\n",
       "      <td>-0.515999</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Annualized Return  Annualized Vol  Skewness  Kurtosis  \\\n",
       "EW                    0.123921        0.160660 -0.759092  6.659028   \n",
       "EW-Tethered           0.125572        0.156923 -0.752967  6.187433   \n",
       "CW                    0.120165        0.147544 -0.717960  5.562648   \n",
       "\n",
       "             Cornish-Fisher VaR (5%)  Historic CVaR (5%)  Sharpe Ratio  \\\n",
       "EW                          0.071404            0.102331      0.568799   \n",
       "EW-Tethered                 0.069778            0.099191      0.592597   \n",
       "CW                          0.065636            0.093769      0.594625   \n",
       "\n",
       "             Max Drawdown  \n",
       "EW              -0.528292  \n",
       "EW-Tethered     -0.530654  \n",
       "CW              -0.515999  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ewr = backtest_ws(ind49_rets)\n",
    "ewtr = backtest_ws(ind49_rets, cap_weights=ind49_mcap, max_cw_mult=5, microcap_threshold=.005)\n",
    "cwr = backtest_ws(ind49_rets, weighting=weight_cw, cap_weights=ind49_mcap)\n",
    "btr = pd.DataFrame({\"EW\": ewr, \"EW-Tethered\": ewtr, \"CW\": cwr})\n",
    "(1+btr).cumprod().plot(figsize=(12,5))\n",
    "erk.summary_stats(btr.dropna())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Don't forget to add the code we've just developed to the toolkit, we're going to use it in future sessions!\n",
    "\n",
    "## A Final Note ...\n",
    "\n",
    "One of the motivations of adding the tethering constraint is to improve tracking error to the cap-weighted portfolio. Let's see if we did manage to achieve that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.23402341787849118, 0.15661830578201005)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "erk.tracking_error(ewr, cwr),erk.tracking_error(ewtr, cwr)"
   ]
  },
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