17a_backtest_sbbg.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Backtesting estimation strategies (stocks, corp bonds, govt bonds, gold)\n",
    "\n",
    "We will compare the following four estimation strategies.  We will locate along the capital allocation line, so that all portfolios have the same expected return as the 1/N portfolio  (which is the cross-sectional average of the historical average returns).\n",
    "- Est-All\n",
    "- Est-SD-Corr\n",
    "- Est-SD\n",
    "- Est-None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import plotly.graph_objects as go\n",
    "from scipy.optimize import minimize\n",
    "from cvxopt import matrix\n",
    "from cvxopt.solvers import qp as Solver, options as SolverOptions"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TBills</th>\n",
       "      <th>S&amp;P 500</th>\n",
       "      <th>Gold</th>\n",
       "      <th>Corporates</th>\n",
       "      <th>Treasuries</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</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>1968</th>\n",
       "      <td>0.053383</td>\n",
       "      <td>0.108149</td>\n",
       "      <td>0.192439</td>\n",
       "      <td>0.048451</td>\n",
       "      <td>0.032746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1969</th>\n",
       "      <td>0.066667</td>\n",
       "      <td>-0.082414</td>\n",
       "      <td>-0.160667</td>\n",
       "      <td>-0.020252</td>\n",
       "      <td>-0.050140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970</th>\n",
       "      <td>0.063917</td>\n",
       "      <td>0.035611</td>\n",
       "      <td>0.061630</td>\n",
       "      <td>0.056496</td>\n",
       "      <td>0.167547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1971</th>\n",
       "      <td>0.043325</td>\n",
       "      <td>0.142212</td>\n",
       "      <td>0.166934</td>\n",
       "      <td>0.140015</td>\n",
       "      <td>0.097869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1972</th>\n",
       "      <td>0.040725</td>\n",
       "      <td>0.187554</td>\n",
       "      <td>0.483265</td>\n",
       "      <td>0.114091</td>\n",
       "      <td>0.028184</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        TBills   S&P 500      Gold  Corporates  Treasuries\n",
       "Year                                                      \n",
       "1968  0.053383  0.108149  0.192439    0.048451    0.032746\n",
       "1969  0.066667 -0.082414 -0.160667   -0.020252   -0.050140\n",
       "1970  0.063917  0.035611  0.061630    0.056496    0.167547\n",
       "1971  0.043325  0.142212  0.166934    0.140015    0.097869\n",
       "1972  0.040725  0.187554  0.483265    0.114091    0.028184"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('https://www.dropbox.com/s/6o4wb38za6g514q/sbbg.csv?dl=1',index_col=['Year'])\n",
    "df.head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create optimization functions for tangency, global minimum variance, and capital allocation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tangency(means, cov, rf):\n",
    "    n = len(means)\n",
    "    def f(w):\n",
    "        mn = w @ means\n",
    "        sd = np.sqrt(w @ cov @ w)\n",
    "        return -(mn - rf) / sd\n",
    "    # Initial guess (equal-weighted)\n",
    "    w0 = (1/n)*np.ones(n)\n",
    "    # Constraint: fully-invested portfolio\n",
    "    A = np.ones(n)\n",
    "    b = 1\n",
    "    cons = [{\"type\": \"eq\", \"fun\": lambda x: A @ x - b}]\n",
    "    # No short-sale constraint\n",
    "    bnds = [(None, None) for i in range(n)] \n",
    "    # Optimization\n",
    "    TOL = 10**(-10)\n",
    "    wgts = minimize(f, w0, bounds=bnds, constraints=cons, options={'ftol':TOL}).x\n",
    "    return wgts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gmv(means, cov):\n",
    "    n = len(means)\n",
    "    Q = matrix(cov, tc=\"d\")\n",
    "    p = matrix(np.zeros(n), (n, 1), tc=\"d\")\n",
    "    # No short-sale constraint    \n",
    "    G = matrix(np.zeros((n,n)), tc=\"d\")\n",
    "    h = matrix(np.zeros(n), (n, 1), tc=\"d\")\n",
    "    # Constraint: fully-invested portfolio\n",
    "    A = matrix(np.ones(n), (1, n), tc=\"d\")\n",
    "    b = matrix([1], (1, 1), tc=\"d\")\n",
    "    sol = Solver(Q, p, G, h, A, b)\n",
    "    wgts = np.array(sol[\"x\"]).flatten() if sol[\"status\"] == \"optimal\" else np.array(n * [np.nan])\n",
    "    return wgts\n",
    "SolverOptions['show_progress'] = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def capital_allocation(mean, sd, rf, target_expret):\n",
    "    ''' locate on CAL to match a target expected return'''\n",
    "    return (target_expret - rf) / (mean - rf)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimate inputs on rolling windows"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Estimation window\n",
    "WINDOW = 20\n",
    "\n",
    "# Define the risky asset list\n",
    "RISKY_ASSETS = ['S&P 500', 'Gold', 'Corporates', 'Treasuries']\n",
    "\n",
    "# Number of risky assets\n",
    "n = len(RISKY_ASSETS)\n",
    "\n",
    "# Length of out-of-sample window\n",
    "T = len(df)-WINDOW"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standardize column names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rf</th>\n",
       "      <th>r0</th>\n",
       "      <th>r1</th>\n",
       "      <th>r2</th>\n",
       "      <th>r3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</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>1968</th>\n",
       "      <td>0.053383</td>\n",
       "      <td>0.108149</td>\n",
       "      <td>0.192439</td>\n",
       "      <td>0.048451</td>\n",
       "      <td>0.032746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1969</th>\n",
       "      <td>0.066667</td>\n",
       "      <td>-0.082414</td>\n",
       "      <td>-0.160667</td>\n",
       "      <td>-0.020252</td>\n",
       "      <td>-0.050140</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            rf        r0        r1        r2        r3\n",
       "Year                                                  \n",
       "1968  0.053383  0.108149  0.192439  0.048451  0.032746\n",
       "1969  0.066667 -0.082414 -0.160667 -0.020252 -0.050140"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asset_list = [str(i) for i in range(n)]\n",
    "ret_list   = ['r' + asset for asset in asset_list]\n",
    "df.columns = ['rf'] + ret_list\n",
    "df.head(2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimate expected returns and standard deviations based on historical rolling windows\n",
    "\n",
    "- Note: rolling command includes current year in calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "for asset in asset_list:\n",
    "    df['mn' + asset]=df['r'+asset].rolling(WINDOW).mean()\n",
    "    df['sd' + asset]=df['r'+asset].rolling(WINDOW).std()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimate correlations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>r0</th>\n",
       "      <th>r1</th>\n",
       "      <th>r2</th>\n",
       "      <th>r3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</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 rowspan=\"4\" valign=\"top\">2020</th>\n",
       "      <th>r0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.070275</td>\n",
       "      <td>0.475592</td>\n",
       "      <td>-0.602105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r1</th>\n",
       "      <td>0.070275</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.556898</td>\n",
       "      <td>0.264032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r2</th>\n",
       "      <td>0.475592</td>\n",
       "      <td>0.556898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.134618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r3</th>\n",
       "      <td>-0.602105</td>\n",
       "      <td>0.264032</td>\n",
       "      <td>-0.134618</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">2021</th>\n",
       "      <th>r0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.027444</td>\n",
       "      <td>0.412879</td>\n",
       "      <td>-0.647386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r1</th>\n",
       "      <td>-0.027444</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.585691</td>\n",
       "      <td>0.313510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r2</th>\n",
       "      <td>0.412879</td>\n",
       "      <td>0.585691</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.065506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r3</th>\n",
       "      <td>-0.647386</td>\n",
       "      <td>0.313510</td>\n",
       "      <td>-0.065506</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               r0        r1        r2        r3\n",
       "Year                                           \n",
       "2020 r0  1.000000  0.070275  0.475592 -0.602105\n",
       "     r1  0.070275  1.000000  0.556898  0.264032\n",
       "     r2  0.475592  0.556898  1.000000 -0.134618\n",
       "     r3 -0.602105  0.264032 -0.134618  1.000000\n",
       "2021 r0  1.000000 -0.027444  0.412879 -0.647386\n",
       "     r1 -0.027444  1.000000  0.585691  0.313510\n",
       "     r2  0.412879  0.585691  1.000000 -0.065506\n",
       "     r3 -0.647386  0.313510 -0.065506  1.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrs = df[ret_list].rolling(WINDOW, min_periods=WINDOW).corr()\n",
    "corrs.tail(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>rf</th>\n",
       "      <th>r0</th>\n",
       "      <th>r1</th>\n",
       "      <th>r2</th>\n",
       "      <th>r3</th>\n",
       "      <th>mn0</th>\n",
       "      <th>sd0</th>\n",
       "      <th>mn1</th>\n",
       "      <th>sd1</th>\n",
       "      <th>mn2</th>\n",
       "      <th>sd2</th>\n",
       "      <th>mn3</th>\n",
       "      <th>sd3</th>\n",
       "      <th>c01</th>\n",
       "      <th>c02</th>\n",
       "      <th>c03</th>\n",
       "      <th>c12</th>\n",
       "      <th>c13</th>\n",
       "      <th>c23</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1968</td>\n",
       "      <td>0.053383</td>\n",
       "      <td>0.108149</td>\n",
       "      <td>0.192439</td>\n",
       "      <td>0.048451</td>\n",
       "      <td>0.032746</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1969</td>\n",
       "      <td>0.066667</td>\n",
       "      <td>-0.082414</td>\n",
       "      <td>-0.160667</td>\n",
       "      <td>-0.020252</td>\n",
       "      <td>-0.050140</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1970</td>\n",
       "      <td>0.063917</td>\n",
       "      <td>0.035611</td>\n",
       "      <td>0.061630</td>\n",
       "      <td>0.056496</td>\n",
       "      <td>0.167547</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1971</td>\n",
       "      <td>0.043325</td>\n",
       "      <td>0.142212</td>\n",
       "      <td>0.166934</td>\n",
       "      <td>0.140015</td>\n",
       "      <td>0.097869</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1972</td>\n",
       "      <td>0.040725</td>\n",
       "      <td>0.187554</td>\n",
       "      <td>0.483265</td>\n",
       "      <td>0.114091</td>\n",
       "      <td>0.028184</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1973</td>\n",
       "      <td>0.070317</td>\n",
       "      <td>-0.143080</td>\n",
       "      <td>0.734930</td>\n",
       "      <td>0.043180</td>\n",
       "      <td>0.036587</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1974</td>\n",
       "      <td>0.078300</td>\n",
       "      <td>-0.259018</td>\n",
       "      <td>0.670379</td>\n",
       "      <td>-0.043807</td>\n",
       "      <td>0.019886</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1975</td>\n",
       "      <td>0.057750</td>\n",
       "      <td>0.369951</td>\n",
       "      <td>-0.252000</td>\n",
       "      <td>0.110500</td>\n",
       "      <td>0.036053</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1976</td>\n",
       "      <td>0.049742</td>\n",
       "      <td>0.238310</td>\n",
       "      <td>-0.040642</td>\n",
       "      <td>0.197528</td>\n",
       "      <td>0.159846</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1977</td>\n",
       "      <td>0.052692</td>\n",
       "      <td>-0.069797</td>\n",
       "      <td>0.230769</td>\n",
       "      <td>0.099547</td>\n",
       "      <td>0.012900</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1978</td>\n",
       "      <td>0.071883</td>\n",
       "      <td>0.065093</td>\n",
       "      <td>0.355676</td>\n",
       "      <td>0.031376</td>\n",
       "      <td>-0.007776</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1979</td>\n",
       "      <td>0.100692</td>\n",
       "      <td>0.185195</td>\n",
       "      <td>1.334076</td>\n",
       "      <td>-0.020091</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1980</td>\n",
       "      <td>0.114342</td>\n",
       "      <td>0.317352</td>\n",
       "      <td>0.125000</td>\n",
       "      <td>-0.033157</td>\n",
       "      <td>-0.029897</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1981</td>\n",
       "      <td>0.140250</td>\n",
       "      <td>-0.047024</td>\n",
       "      <td>-0.321459</td>\n",
       "      <td>0.084624</td>\n",
       "      <td>0.081992</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1982</td>\n",
       "      <td>0.106142</td>\n",
       "      <td>0.204191</td>\n",
       "      <td>0.120000</td>\n",
       "      <td>0.290525</td>\n",
       "      <td>0.328145</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1983</td>\n",
       "      <td>0.086108</td>\n",
       "      <td>0.223372</td>\n",
       "      <td>-0.148438</td>\n",
       "      <td>0.161943</td>\n",
       "      <td>0.032002</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1984</td>\n",
       "      <td>0.095225</td>\n",
       "      <td>0.061461</td>\n",
       "      <td>-0.190039</td>\n",
       "      <td>0.156192</td>\n",
       "      <td>0.137334</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1985</td>\n",
       "      <td>0.074792</td>\n",
       "      <td>0.312351</td>\n",
       "      <td>0.058252</td>\n",
       "      <td>0.238626</td>\n",
       "      <td>0.257125</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1986</td>\n",
       "      <td>0.059783</td>\n",
       "      <td>0.184946</td>\n",
       "      <td>0.195413</td>\n",
       "      <td>0.214855</td>\n",
       "      <td>0.242842</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1987</td>\n",
       "      <td>0.057750</td>\n",
       "      <td>0.058127</td>\n",
       "      <td>0.244564</td>\n",
       "      <td>0.022898</td>\n",
       "      <td>-0.049605</td>\n",
       "      <td>0.104627</td>\n",
       "      <td>0.164522</td>\n",
       "      <td>0.193004</td>\n",
       "      <td>0.390017</td>\n",
       "      <td>0.094677</td>\n",
       "      <td>0.095289</td>\n",
       "      <td>0.077017</td>\n",
       "      <td>0.106371</td>\n",
       "      <td>-0.227893</td>\n",
       "      <td>0.479432</td>\n",
       "      <td>0.313243</td>\n",
       "      <td>-0.404730</td>\n",
       "      <td>-0.228507</td>\n",
       "      <td>0.844393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1988</td>\n",
       "      <td>0.066675</td>\n",
       "      <td>0.165372</td>\n",
       "      <td>-0.156937</td>\n",
       "      <td>0.151151</td>\n",
       "      <td>0.082236</td>\n",
       "      <td>0.107488</td>\n",
       "      <td>0.165083</td>\n",
       "      <td>0.175535</td>\n",
       "      <td>0.397790</td>\n",
       "      <td>0.099812</td>\n",
       "      <td>0.095434</td>\n",
       "      <td>0.079492</td>\n",
       "      <td>0.105861</td>\n",
       "      <td>-0.238915</td>\n",
       "      <td>0.488099</td>\n",
       "      <td>0.314679</td>\n",
       "      <td>-0.421166</td>\n",
       "      <td>-0.226353</td>\n",
       "      <td>0.836720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1989</td>\n",
       "      <td>0.081117</td>\n",
       "      <td>0.314752</td>\n",
       "      <td>-0.022309</td>\n",
       "      <td>0.157897</td>\n",
       "      <td>0.176936</td>\n",
       "      <td>0.127347</td>\n",
       "      <td>0.164925</td>\n",
       "      <td>0.182453</td>\n",
       "      <td>0.392808</td>\n",
       "      <td>0.108719</td>\n",
       "      <td>0.091886</td>\n",
       "      <td>0.090846</td>\n",
       "      <td>0.103374</td>\n",
       "      <td>-0.329593</td>\n",
       "      <td>0.457772</td>\n",
       "      <td>0.294991</td>\n",
       "      <td>-0.520394</td>\n",
       "      <td>-0.318253</td>\n",
       "      <td>0.823853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1990</td>\n",
       "      <td>0.074933</td>\n",
       "      <td>-0.030645</td>\n",
       "      <td>-0.024938</td>\n",
       "      <td>0.061401</td>\n",
       "      <td>0.062354</td>\n",
       "      <td>0.124034</td>\n",
       "      <td>0.167510</td>\n",
       "      <td>0.178125</td>\n",
       "      <td>0.394681</td>\n",
       "      <td>0.108965</td>\n",
       "      <td>0.091746</td>\n",
       "      <td>0.085586</td>\n",
       "      <td>0.101932</td>\n",
       "      <td>-0.305934</td>\n",
       "      <td>0.460649</td>\n",
       "      <td>0.329037</td>\n",
       "      <td>-0.513592</td>\n",
       "      <td>-0.301964</td>\n",
       "      <td>0.867061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1991</td>\n",
       "      <td>0.053750</td>\n",
       "      <td>0.302348</td>\n",
       "      <td>-0.096164</td>\n",
       "      <td>0.178535</td>\n",
       "      <td>0.150045</td>\n",
       "      <td>0.132041</td>\n",
       "      <td>0.172186</td>\n",
       "      <td>0.164970</td>\n",
       "      <td>0.399430</td>\n",
       "      <td>0.110891</td>\n",
       "      <td>0.092830</td>\n",
       "      <td>0.088195</td>\n",
       "      <td>0.102926</td>\n",
       "      <td>-0.329747</td>\n",
       "      <td>0.480878</td>\n",
       "      <td>0.349241</td>\n",
       "      <td>-0.527434</td>\n",
       "      <td>-0.317074</td>\n",
       "      <td>0.870710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1992</td>\n",
       "      <td>0.034317</td>\n",
       "      <td>0.074937</td>\n",
       "      <td>-0.058008</td>\n",
       "      <td>0.121723</td>\n",
       "      <td>0.093616</td>\n",
       "      <td>0.126410</td>\n",
       "      <td>0.172117</td>\n",
       "      <td>0.137906</td>\n",
       "      <td>0.395042</td>\n",
       "      <td>0.111272</td>\n",
       "      <td>0.092859</td>\n",
       "      <td>0.091466</td>\n",
       "      <td>0.101954</td>\n",
       "      <td>-0.339725</td>\n",
       "      <td>0.478439</td>\n",
       "      <td>0.362883</td>\n",
       "      <td>-0.537753</td>\n",
       "      <td>-0.297959</td>\n",
       "      <td>0.879991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1993</td>\n",
       "      <td>0.029975</td>\n",
       "      <td>0.099671</td>\n",
       "      <td>0.173476</td>\n",
       "      <td>0.164315</td>\n",
       "      <td>0.142110</td>\n",
       "      <td>0.138547</td>\n",
       "      <td>0.160263</td>\n",
       "      <td>0.109834</td>\n",
       "      <td>0.369507</td>\n",
       "      <td>0.117329</td>\n",
       "      <td>0.092132</td>\n",
       "      <td>0.096743</td>\n",
       "      <td>0.101694</td>\n",
       "      <td>-0.241858</td>\n",
       "      <td>0.442176</td>\n",
       "      <td>0.334447</td>\n",
       "      <td>-0.508431</td>\n",
       "      <td>-0.266799</td>\n",
       "      <td>0.879710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1994</td>\n",
       "      <td>0.042467</td>\n",
       "      <td>0.013259</td>\n",
       "      <td>-0.020863</td>\n",
       "      <td>-0.013192</td>\n",
       "      <td>-0.080367</td>\n",
       "      <td>0.152161</td>\n",
       "      <td>0.134151</td>\n",
       "      <td>0.075272</td>\n",
       "      <td>0.345889</td>\n",
       "      <td>0.118860</td>\n",
       "      <td>0.089531</td>\n",
       "      <td>0.091730</td>\n",
       "      <td>0.107960</td>\n",
       "      <td>-0.026641</td>\n",
       "      <td>0.332696</td>\n",
       "      <td>0.350916</td>\n",
       "      <td>-0.374622</td>\n",
       "      <td>-0.180012</td>\n",
       "      <td>0.911998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1995</td>\n",
       "      <td>0.054900</td>\n",
       "      <td>0.371952</td>\n",
       "      <td>0.010980</td>\n",
       "      <td>0.201562</td>\n",
       "      <td>0.234808</td>\n",
       "      <td>0.152261</td>\n",
       "      <td>0.134323</td>\n",
       "      <td>0.088421</td>\n",
       "      <td>0.337695</td>\n",
       "      <td>0.123413</td>\n",
       "      <td>0.091380</td>\n",
       "      <td>0.101668</td>\n",
       "      <td>0.111649</td>\n",
       "      <td>0.039023</td>\n",
       "      <td>0.411259</td>\n",
       "      <td>0.491734</td>\n",
       "      <td>-0.391726</td>\n",
       "      <td>-0.220212</td>\n",
       "      <td>0.917988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1996</td>\n",
       "      <td>0.050058</td>\n",
       "      <td>0.226810</td>\n",
       "      <td>-0.044350</td>\n",
       "      <td>0.047926</td>\n",
       "      <td>0.014286</td>\n",
       "      <td>0.151686</td>\n",
       "      <td>0.133959</td>\n",
       "      <td>0.088235</td>\n",
       "      <td>0.337770</td>\n",
       "      <td>0.115933</td>\n",
       "      <td>0.091117</td>\n",
       "      <td>0.094390</td>\n",
       "      <td>0.112399</td>\n",
       "      <td>0.040523</td>\n",
       "      <td>0.361432</td>\n",
       "      <td>0.449218</td>\n",
       "      <td>-0.359321</td>\n",
       "      <td>-0.192239</td>\n",
       "      <td>0.920646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1997</td>\n",
       "      <td>0.050608</td>\n",
       "      <td>0.331037</td>\n",
       "      <td>-0.217427</td>\n",
       "      <td>0.118349</td>\n",
       "      <td>0.099391</td>\n",
       "      <td>0.171728</td>\n",
       "      <td>0.128970</td>\n",
       "      <td>0.065825</td>\n",
       "      <td>0.342649</td>\n",
       "      <td>0.116873</td>\n",
       "      <td>0.091036</td>\n",
       "      <td>0.098714</td>\n",
       "      <td>0.110751</td>\n",
       "      <td>0.024497</td>\n",
       "      <td>0.359730</td>\n",
       "      <td>0.403952</td>\n",
       "      <td>-0.351115</td>\n",
       "      <td>-0.175646</td>\n",
       "      <td>0.927849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1998</td>\n",
       "      <td>0.047767</td>\n",
       "      <td>0.283380</td>\n",
       "      <td>-0.006051</td>\n",
       "      <td>0.079455</td>\n",
       "      <td>0.149214</td>\n",
       "      <td>0.182642</td>\n",
       "      <td>0.128707</td>\n",
       "      <td>0.047739</td>\n",
       "      <td>0.336027</td>\n",
       "      <td>0.119277</td>\n",
       "      <td>0.089277</td>\n",
       "      <td>0.106564</td>\n",
       "      <td>0.108343</td>\n",
       "      <td>0.057683</td>\n",
       "      <td>0.304267</td>\n",
       "      <td>0.385727</td>\n",
       "      <td>-0.315366</td>\n",
       "      <td>-0.139607</td>\n",
       "      <td>0.905275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1999</td>\n",
       "      <td>0.046383</td>\n",
       "      <td>0.208854</td>\n",
       "      <td>0.011828</td>\n",
       "      <td>0.008432</td>\n",
       "      <td>-0.082542</td>\n",
       "      <td>0.183825</td>\n",
       "      <td>0.128841</td>\n",
       "      <td>-0.018373</td>\n",
       "      <td>0.145923</td>\n",
       "      <td>0.120703</td>\n",
       "      <td>0.087136</td>\n",
       "      <td>0.102101</td>\n",
       "      <td>0.114344</td>\n",
       "      <td>0.125244</td>\n",
       "      <td>0.299311</td>\n",
       "      <td>0.348684</td>\n",
       "      <td>0.022290</td>\n",
       "      <td>0.103370</td>\n",
       "      <td>0.916728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>2000</td>\n",
       "      <td>0.058167</td>\n",
       "      <td>-0.090318</td>\n",
       "      <td>-0.062575</td>\n",
       "      <td>0.093297</td>\n",
       "      <td>0.166553</td>\n",
       "      <td>0.163442</td>\n",
       "      <td>0.138491</td>\n",
       "      <td>-0.027752</td>\n",
       "      <td>0.142204</td>\n",
       "      <td>0.127026</td>\n",
       "      <td>0.079650</td>\n",
       "      <td>0.111924</td>\n",
       "      <td>0.110791</td>\n",
       "      <td>0.090568</td>\n",
       "      <td>0.450795</td>\n",
       "      <td>0.348378</td>\n",
       "      <td>0.138667</td>\n",
       "      <td>0.169336</td>\n",
       "      <td>0.895974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>2001</td>\n",
       "      <td>0.033883</td>\n",
       "      <td>-0.118498</td>\n",
       "      <td>0.014121</td>\n",
       "      <td>0.078192</td>\n",
       "      <td>0.055722</td>\n",
       "      <td>0.159868</td>\n",
       "      <td>0.144978</td>\n",
       "      <td>-0.010973</td>\n",
       "      <td>0.124409</td>\n",
       "      <td>0.126704</td>\n",
       "      <td>0.079843</td>\n",
       "      <td>0.110610</td>\n",
       "      <td>0.111319</td>\n",
       "      <td>-0.112440</td>\n",
       "      <td>0.451505</td>\n",
       "      <td>0.362036</td>\n",
       "      <td>0.081868</td>\n",
       "      <td>0.151961</td>\n",
       "      <td>0.898256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2002</td>\n",
       "      <td>0.016025</td>\n",
       "      <td>-0.219660</td>\n",
       "      <td>0.239602</td>\n",
       "      <td>0.121779</td>\n",
       "      <td>0.151164</td>\n",
       "      <td>0.138675</td>\n",
       "      <td>0.167402</td>\n",
       "      <td>-0.004993</td>\n",
       "      <td>0.133573</td>\n",
       "      <td>0.118267</td>\n",
       "      <td>0.069920</td>\n",
       "      <td>0.101761</td>\n",
       "      <td>0.099526</td>\n",
       "      <td>-0.322240</td>\n",
       "      <td>0.406194</td>\n",
       "      <td>0.259764</td>\n",
       "      <td>-0.035109</td>\n",
       "      <td>0.089929</td>\n",
       "      <td>0.864946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>2003</td>\n",
       "      <td>0.010108</td>\n",
       "      <td>0.283558</td>\n",
       "      <td>0.217360</td>\n",
       "      <td>0.135320</td>\n",
       "      <td>0.003753</td>\n",
       "      <td>0.141685</td>\n",
       "      <td>0.169533</td>\n",
       "      <td>0.013297</td>\n",
       "      <td>0.137873</td>\n",
       "      <td>0.116936</td>\n",
       "      <td>0.069295</td>\n",
       "      <td>0.100349</td>\n",
       "      <td>0.100761</td>\n",
       "      <td>-0.210852</td>\n",
       "      <td>0.399561</td>\n",
       "      <td>0.228072</td>\n",
       "      <td>0.023765</td>\n",
       "      <td>-0.032458</td>\n",
       "      <td>0.872131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>2004</td>\n",
       "      <td>0.013717</td>\n",
       "      <td>0.107428</td>\n",
       "      <td>0.049730</td>\n",
       "      <td>0.098886</td>\n",
       "      <td>0.044907</td>\n",
       "      <td>0.143983</td>\n",
       "      <td>0.168697</td>\n",
       "      <td>0.025285</td>\n",
       "      <td>0.129427</td>\n",
       "      <td>0.114070</td>\n",
       "      <td>0.068769</td>\n",
       "      <td>0.095727</td>\n",
       "      <td>0.101094</td>\n",
       "      <td>-0.269381</td>\n",
       "      <td>0.422300</td>\n",
       "      <td>0.244119</td>\n",
       "      <td>0.072884</td>\n",
       "      <td>-0.007880</td>\n",
       "      <td>0.870481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>2005</td>\n",
       "      <td>0.031467</td>\n",
       "      <td>0.048345</td>\n",
       "      <td>0.171233</td>\n",
       "      <td>0.049175</td>\n",
       "      <td>0.028675</td>\n",
       "      <td>0.130783</td>\n",
       "      <td>0.165120</td>\n",
       "      <td>0.030934</td>\n",
       "      <td>0.133348</td>\n",
       "      <td>0.104598</td>\n",
       "      <td>0.063560</td>\n",
       "      <td>0.084305</td>\n",
       "      <td>0.094596</td>\n",
       "      <td>-0.310192</td>\n",
       "      <td>0.380223</td>\n",
       "      <td>0.186422</td>\n",
       "      <td>-0.001129</td>\n",
       "      <td>-0.065822</td>\n",
       "      <td>0.849698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>2006</td>\n",
       "      <td>0.047267</td>\n",
       "      <td>0.156126</td>\n",
       "      <td>0.239181</td>\n",
       "      <td>0.070484</td>\n",
       "      <td>0.019610</td>\n",
       "      <td>0.129342</td>\n",
       "      <td>0.164748</td>\n",
       "      <td>0.033123</td>\n",
       "      <td>0.136511</td>\n",
       "      <td>0.097379</td>\n",
       "      <td>0.058365</td>\n",
       "      <td>0.073143</td>\n",
       "      <td>0.087833</td>\n",
       "      <td>-0.312039</td>\n",
       "      <td>0.376445</td>\n",
       "      <td>0.162864</td>\n",
       "      <td>-0.165840</td>\n",
       "      <td>-0.240703</td>\n",
       "      <td>0.823229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>2007</td>\n",
       "      <td>0.043533</td>\n",
       "      <td>0.054847</td>\n",
       "      <td>0.315872</td>\n",
       "      <td>0.031504</td>\n",
       "      <td>0.102099</td>\n",
       "      <td>0.129178</td>\n",
       "      <td>0.164824</td>\n",
       "      <td>0.036688</td>\n",
       "      <td>0.143096</td>\n",
       "      <td>0.097809</td>\n",
       "      <td>0.057816</td>\n",
       "      <td>0.080729</td>\n",
       "      <td>0.083098</td>\n",
       "      <td>-0.310916</td>\n",
       "      <td>0.377659</td>\n",
       "      <td>0.130281</td>\n",
       "      <td>-0.178213</td>\n",
       "      <td>-0.093990</td>\n",
       "      <td>0.756636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>2008</td>\n",
       "      <td>0.013650</td>\n",
       "      <td>-0.365523</td>\n",
       "      <td>0.034071</td>\n",
       "      <td>-0.050657</td>\n",
       "      <td>0.201013</td>\n",
       "      <td>0.102633</td>\n",
       "      <td>0.198083</td>\n",
       "      <td>0.046239</td>\n",
       "      <td>0.135675</td>\n",
       "      <td>0.087719</td>\n",
       "      <td>0.065160</td>\n",
       "      <td>0.086667</td>\n",
       "      <td>0.087347</td>\n",
       "      <td>-0.246674</td>\n",
       "      <td>0.548606</td>\n",
       "      <td>-0.068452</td>\n",
       "      <td>-0.091499</td>\n",
       "      <td>-0.099448</td>\n",
       "      <td>0.483892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>2009</td>\n",
       "      <td>0.001500</td>\n",
       "      <td>0.259352</td>\n",
       "      <td>0.276301</td>\n",
       "      <td>0.233295</td>\n",
       "      <td>-0.111167</td>\n",
       "      <td>0.099863</td>\n",
       "      <td>0.195329</td>\n",
       "      <td>0.061169</td>\n",
       "      <td>0.143915</td>\n",
       "      <td>0.091489</td>\n",
       "      <td>0.071324</td>\n",
       "      <td>0.072262</td>\n",
       "      <td>0.095090</td>\n",
       "      <td>-0.139551</td>\n",
       "      <td>0.539006</td>\n",
       "      <td>-0.208140</td>\n",
       "      <td>0.111815</td>\n",
       "      <td>-0.220825</td>\n",
       "      <td>0.141851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>2010</td>\n",
       "      <td>0.001367</td>\n",
       "      <td>0.148211</td>\n",
       "      <td>0.277400</td>\n",
       "      <td>0.083478</td>\n",
       "      <td>0.084629</td>\n",
       "      <td>0.108806</td>\n",
       "      <td>0.193121</td>\n",
       "      <td>0.076286</td>\n",
       "      <td>0.150138</td>\n",
       "      <td>0.092593</td>\n",
       "      <td>0.071004</td>\n",
       "      <td>0.073376</td>\n",
       "      <td>0.095098</td>\n",
       "      <td>-0.141625</td>\n",
       "      <td>0.530309</td>\n",
       "      <td>-0.213064</td>\n",
       "      <td>0.084673</td>\n",
       "      <td>-0.206182</td>\n",
       "      <td>0.139191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>2011</td>\n",
       "      <td>0.000525</td>\n",
       "      <td>0.020984</td>\n",
       "      <td>0.116469</td>\n",
       "      <td>0.125845</td>\n",
       "      <td>0.160353</td>\n",
       "      <td>0.094737</td>\n",
       "      <td>0.188473</td>\n",
       "      <td>0.086918</td>\n",
       "      <td>0.144715</td>\n",
       "      <td>0.089958</td>\n",
       "      <td>0.068583</td>\n",
       "      <td>0.073891</td>\n",
       "      <td>0.095562</td>\n",
       "      <td>-0.087189</td>\n",
       "      <td>0.479930</td>\n",
       "      <td>-0.282518</td>\n",
       "      <td>0.179596</td>\n",
       "      <td>-0.149667</td>\n",
       "      <td>0.113933</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2012</td>\n",
       "      <td>0.000858</td>\n",
       "      <td>0.158906</td>\n",
       "      <td>0.056843</td>\n",
       "      <td>0.101247</td>\n",
       "      <td>0.029716</td>\n",
       "      <td>0.098936</td>\n",
       "      <td>0.188943</td>\n",
       "      <td>0.092660</td>\n",
       "      <td>0.140889</td>\n",
       "      <td>0.088935</td>\n",
       "      <td>0.068236</td>\n",
       "      <td>0.070696</td>\n",
       "      <td>0.095936</td>\n",
       "      <td>-0.099776</td>\n",
       "      <td>0.487047</td>\n",
       "      <td>-0.287036</td>\n",
       "      <td>0.209398</td>\n",
       "      <td>-0.135399</td>\n",
       "      <td>0.104494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2013</td>\n",
       "      <td>0.000583</td>\n",
       "      <td>0.321451</td>\n",
       "      <td>-0.277945</td>\n",
       "      <td>-0.010559</td>\n",
       "      <td>-0.091046</td>\n",
       "      <td>0.110025</td>\n",
       "      <td>0.195387</td>\n",
       "      <td>0.070089</td>\n",
       "      <td>0.161860</td>\n",
       "      <td>0.080191</td>\n",
       "      <td>0.069265</td>\n",
       "      <td>0.059039</td>\n",
       "      <td>0.100842</td>\n",
       "      <td>-0.212993</td>\n",
       "      <td>0.385217</td>\n",
       "      <td>-0.353438</td>\n",
       "      <td>0.305533</td>\n",
       "      <td>0.045584</td>\n",
       "      <td>0.163268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>2014</td>\n",
       "      <td>0.000325</td>\n",
       "      <td>0.135244</td>\n",
       "      <td>-0.001873</td>\n",
       "      <td>0.103849</td>\n",
       "      <td>0.107462</td>\n",
       "      <td>0.116124</td>\n",
       "      <td>0.194107</td>\n",
       "      <td>0.071039</td>\n",
       "      <td>0.161353</td>\n",
       "      <td>0.086043</td>\n",
       "      <td>0.065819</td>\n",
       "      <td>0.068430</td>\n",
       "      <td>0.095796</td>\n",
       "      <td>-0.233105</td>\n",
       "      <td>0.370352</td>\n",
       "      <td>-0.412477</td>\n",
       "      <td>0.271462</td>\n",
       "      <td>-0.007510</td>\n",
       "      <td>0.072588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2015</td>\n",
       "      <td>0.000525</td>\n",
       "      <td>0.013789</td>\n",
       "      <td>-0.114238</td>\n",
       "      <td>-0.006975</td>\n",
       "      <td>0.012843</td>\n",
       "      <td>0.098216</td>\n",
       "      <td>0.185597</td>\n",
       "      <td>0.064778</td>\n",
       "      <td>0.166164</td>\n",
       "      <td>0.075616</td>\n",
       "      <td>0.063013</td>\n",
       "      <td>0.057332</td>\n",
       "      <td>0.088050</td>\n",
       "      <td>-0.181982</td>\n",
       "      <td>0.297610</td>\n",
       "      <td>-0.600901</td>\n",
       "      <td>0.390278</td>\n",
       "      <td>0.060062</td>\n",
       "      <td>-0.072737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>2016</td>\n",
       "      <td>0.003175</td>\n",
       "      <td>0.117731</td>\n",
       "      <td>0.091174</td>\n",
       "      <td>0.103651</td>\n",
       "      <td>0.006906</td>\n",
       "      <td>0.092762</td>\n",
       "      <td>0.183207</td>\n",
       "      <td>0.071554</td>\n",
       "      <td>0.164232</td>\n",
       "      <td>0.078402</td>\n",
       "      <td>0.062956</td>\n",
       "      <td>0.056963</td>\n",
       "      <td>0.088255</td>\n",
       "      <td>-0.159784</td>\n",
       "      <td>0.321897</td>\n",
       "      <td>-0.592642</td>\n",
       "      <td>0.381690</td>\n",
       "      <td>0.038918</td>\n",
       "      <td>-0.097121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>2017</td>\n",
       "      <td>0.009308</td>\n",
       "      <td>0.216055</td>\n",
       "      <td>0.118540</td>\n",
       "      <td>0.097239</td>\n",
       "      <td>0.028017</td>\n",
       "      <td>0.087013</td>\n",
       "      <td>0.177036</td>\n",
       "      <td>0.088352</td>\n",
       "      <td>0.149653</td>\n",
       "      <td>0.077347</td>\n",
       "      <td>0.062426</td>\n",
       "      <td>0.053394</td>\n",
       "      <td>0.087892</td>\n",
       "      <td>-0.029329</td>\n",
       "      <td>0.301099</td>\n",
       "      <td>-0.663491</td>\n",
       "      <td>0.494450</td>\n",
       "      <td>0.091303</td>\n",
       "      <td>-0.120562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>2018</td>\n",
       "      <td>0.019392</td>\n",
       "      <td>-0.042269</td>\n",
       "      <td>-0.011454</td>\n",
       "      <td>-0.027626</td>\n",
       "      <td>-0.000167</td>\n",
       "      <td>0.070731</td>\n",
       "      <td>0.172954</td>\n",
       "      <td>0.088082</td>\n",
       "      <td>0.149837</td>\n",
       "      <td>0.071993</td>\n",
       "      <td>0.066683</td>\n",
       "      <td>0.045925</td>\n",
       "      <td>0.085639</td>\n",
       "      <td>0.033691</td>\n",
       "      <td>0.340620</td>\n",
       "      <td>-0.747918</td>\n",
       "      <td>0.518403</td>\n",
       "      <td>0.152453</td>\n",
       "      <td>-0.073249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>2019</td>\n",
       "      <td>0.015500</td>\n",
       "      <td>0.312117</td>\n",
       "      <td>0.188312</td>\n",
       "      <td>0.153295</td>\n",
       "      <td>0.096356</td>\n",
       "      <td>0.075894</td>\n",
       "      <td>0.178739</td>\n",
       "      <td>0.096906</td>\n",
       "      <td>0.150306</td>\n",
       "      <td>0.079236</td>\n",
       "      <td>0.067280</td>\n",
       "      <td>0.054870</td>\n",
       "      <td>0.080716</td>\n",
       "      <td>0.098746</td>\n",
       "      <td>0.447711</td>\n",
       "      <td>-0.662079</td>\n",
       "      <td>0.522730</td>\n",
       "      <td>0.133829</td>\n",
       "      <td>-0.128985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>2020</td>\n",
       "      <td>0.000900</td>\n",
       "      <td>0.180232</td>\n",
       "      <td>0.241694</td>\n",
       "      <td>0.104115</td>\n",
       "      <td>0.113319</td>\n",
       "      <td>0.089421</td>\n",
       "      <td>0.175710</td>\n",
       "      <td>0.112120</td>\n",
       "      <td>0.148704</td>\n",
       "      <td>0.079777</td>\n",
       "      <td>0.067442</td>\n",
       "      <td>0.052208</td>\n",
       "      <td>0.077659</td>\n",
       "      <td>0.070275</td>\n",
       "      <td>0.475592</td>\n",
       "      <td>-0.602105</td>\n",
       "      <td>0.556898</td>\n",
       "      <td>0.264032</td>\n",
       "      <td>-0.134618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>2021</td>\n",
       "      <td>0.000600</td>\n",
       "      <td>0.284689</td>\n",
       "      <td>-0.037544</td>\n",
       "      <td>0.009334</td>\n",
       "      <td>-0.044160</td>\n",
       "      <td>0.109581</td>\n",
       "      <td>0.173717</td>\n",
       "      <td>0.109536</td>\n",
       "      <td>0.150928</td>\n",
       "      <td>0.076334</td>\n",
       "      <td>0.069261</td>\n",
       "      <td>0.047214</td>\n",
       "      <td>0.080578</td>\n",
       "      <td>-0.027444</td>\n",
       "      <td>0.412879</td>\n",
       "      <td>-0.647386</td>\n",
       "      <td>0.585691</td>\n",
       "      <td>0.313510</td>\n",
       "      <td>-0.065506</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year        rf        r0        r1        r2        r3       mn0  \\\n",
       "0   1968  0.053383  0.108149  0.192439  0.048451  0.032746       NaN   \n",
       "1   1969  0.066667 -0.082414 -0.160667 -0.020252 -0.050140       NaN   \n",
       "2   1970  0.063917  0.035611  0.061630  0.056496  0.167547       NaN   \n",
       "3   1971  0.043325  0.142212  0.166934  0.140015  0.097869       NaN   \n",
       "4   1972  0.040725  0.187554  0.483265  0.114091  0.028184       NaN   \n",
       "5   1973  0.070317 -0.143080  0.734930  0.043180  0.036587       NaN   \n",
       "6   1974  0.078300 -0.259018  0.670379 -0.043807  0.019886       NaN   \n",
       "7   1975  0.057750  0.369951 -0.252000  0.110500  0.036053       NaN   \n",
       "8   1976  0.049742  0.238310 -0.040642  0.197528  0.159846       NaN   \n",
       "9   1977  0.052692 -0.069797  0.230769  0.099547  0.012900       NaN   \n",
       "10  1978  0.071883  0.065093  0.355676  0.031376 -0.007776       NaN   \n",
       "11  1979  0.100692  0.185195  1.334076 -0.020091  0.006707       NaN   \n",
       "12  1980  0.114342  0.317352  0.125000 -0.033157 -0.029897       NaN   \n",
       "13  1981  0.140250 -0.047024 -0.321459  0.084624  0.081992       NaN   \n",
       "14  1982  0.106142  0.204191  0.120000  0.290525  0.328145       NaN   \n",
       "15  1983  0.086108  0.223372 -0.148438  0.161943  0.032002       NaN   \n",
       "16  1984  0.095225  0.061461 -0.190039  0.156192  0.137334       NaN   \n",
       "17  1985  0.074792  0.312351  0.058252  0.238626  0.257125       NaN   \n",
       "18  1986  0.059783  0.184946  0.195413  0.214855  0.242842       NaN   \n",
       "19  1987  0.057750  0.058127  0.244564  0.022898 -0.049605  0.104627   \n",
       "20  1988  0.066675  0.165372 -0.156937  0.151151  0.082236  0.107488   \n",
       "21  1989  0.081117  0.314752 -0.022309  0.157897  0.176936  0.127347   \n",
       "22  1990  0.074933 -0.030645 -0.024938  0.061401  0.062354  0.124034   \n",
       "23  1991  0.053750  0.302348 -0.096164  0.178535  0.150045  0.132041   \n",
       "24  1992  0.034317  0.074937 -0.058008  0.121723  0.093616  0.126410   \n",
       "25  1993  0.029975  0.099671  0.173476  0.164315  0.142110  0.138547   \n",
       "26  1994  0.042467  0.013259 -0.020863 -0.013192 -0.080367  0.152161   \n",
       "27  1995  0.054900  0.371952  0.010980  0.201562  0.234808  0.152261   \n",
       "28  1996  0.050058  0.226810 -0.044350  0.047926  0.014286  0.151686   \n",
       "29  1997  0.050608  0.331037 -0.217427  0.118349  0.099391  0.171728   \n",
       "30  1998  0.047767  0.283380 -0.006051  0.079455  0.149214  0.182642   \n",
       "31  1999  0.046383  0.208854  0.011828  0.008432 -0.082542  0.183825   \n",
       "32  2000  0.058167 -0.090318 -0.062575  0.093297  0.166553  0.163442   \n",
       "33  2001  0.033883 -0.118498  0.014121  0.078192  0.055722  0.159868   \n",
       "34  2002  0.016025 -0.219660  0.239602  0.121779  0.151164  0.138675   \n",
       "35  2003  0.010108  0.283558  0.217360  0.135320  0.003753  0.141685   \n",
       "36  2004  0.013717  0.107428  0.049730  0.098886  0.044907  0.143983   \n",
       "37  2005  0.031467  0.048345  0.171233  0.049175  0.028675  0.130783   \n",
       "38  2006  0.047267  0.156126  0.239181  0.070484  0.019610  0.129342   \n",
       "39  2007  0.043533  0.054847  0.315872  0.031504  0.102099  0.129178   \n",
       "40  2008  0.013650 -0.365523  0.034071 -0.050657  0.201013  0.102633   \n",
       "41  2009  0.001500  0.259352  0.276301  0.233295 -0.111167  0.099863   \n",
       "42  2010  0.001367  0.148211  0.277400  0.083478  0.084629  0.108806   \n",
       "43  2011  0.000525  0.020984  0.116469  0.125845  0.160353  0.094737   \n",
       "44  2012  0.000858  0.158906  0.056843  0.101247  0.029716  0.098936   \n",
       "45  2013  0.000583  0.321451 -0.277945 -0.010559 -0.091046  0.110025   \n",
       "46  2014  0.000325  0.135244 -0.001873  0.103849  0.107462  0.116124   \n",
       "47  2015  0.000525  0.013789 -0.114238 -0.006975  0.012843  0.098216   \n",
       "48  2016  0.003175  0.117731  0.091174  0.103651  0.006906  0.092762   \n",
       "49  2017  0.009308  0.216055  0.118540  0.097239  0.028017  0.087013   \n",
       "50  2018  0.019392 -0.042269 -0.011454 -0.027626 -0.000167  0.070731   \n",
       "51  2019  0.015500  0.312117  0.188312  0.153295  0.096356  0.075894   \n",
       "52  2020  0.000900  0.180232  0.241694  0.104115  0.113319  0.089421   \n",
       "53  2021  0.000600  0.284689 -0.037544  0.009334 -0.044160  0.109581   \n",
       "\n",
       "         sd0       mn1       sd1       mn2       sd2       mn3       sd3  \\\n",
       "0        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "1        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "2        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "3        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "4        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "5        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "6        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "7        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "8        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "9        NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "10       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "11       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "12       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "13       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "14       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "15       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "16       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "17       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "18       NaN       NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "19  0.164522  0.193004  0.390017  0.094677  0.095289  0.077017  0.106371   \n",
       "20  0.165083  0.175535  0.397790  0.099812  0.095434  0.079492  0.105861   \n",
       "21  0.164925  0.182453  0.392808  0.108719  0.091886  0.090846  0.103374   \n",
       "22  0.167510  0.178125  0.394681  0.108965  0.091746  0.085586  0.101932   \n",
       "23  0.172186  0.164970  0.399430  0.110891  0.092830  0.088195  0.102926   \n",
       "24  0.172117  0.137906  0.395042  0.111272  0.092859  0.091466  0.101954   \n",
       "25  0.160263  0.109834  0.369507  0.117329  0.092132  0.096743  0.101694   \n",
       "26  0.134151  0.075272  0.345889  0.118860  0.089531  0.091730  0.107960   \n",
       "27  0.134323  0.088421  0.337695  0.123413  0.091380  0.101668  0.111649   \n",
       "28  0.133959  0.088235  0.337770  0.115933  0.091117  0.094390  0.112399   \n",
       "29  0.128970  0.065825  0.342649  0.116873  0.091036  0.098714  0.110751   \n",
       "30  0.128707  0.047739  0.336027  0.119277  0.089277  0.106564  0.108343   \n",
       "31  0.128841 -0.018373  0.145923  0.120703  0.087136  0.102101  0.114344   \n",
       "32  0.138491 -0.027752  0.142204  0.127026  0.079650  0.111924  0.110791   \n",
       "33  0.144978 -0.010973  0.124409  0.126704  0.079843  0.110610  0.111319   \n",
       "34  0.167402 -0.004993  0.133573  0.118267  0.069920  0.101761  0.099526   \n",
       "35  0.169533  0.013297  0.137873  0.116936  0.069295  0.100349  0.100761   \n",
       "36  0.168697  0.025285  0.129427  0.114070  0.068769  0.095727  0.101094   \n",
       "37  0.165120  0.030934  0.133348  0.104598  0.063560  0.084305  0.094596   \n",
       "38  0.164748  0.033123  0.136511  0.097379  0.058365  0.073143  0.087833   \n",
       "39  0.164824  0.036688  0.143096  0.097809  0.057816  0.080729  0.083098   \n",
       "40  0.198083  0.046239  0.135675  0.087719  0.065160  0.086667  0.087347   \n",
       "41  0.195329  0.061169  0.143915  0.091489  0.071324  0.072262  0.095090   \n",
       "42  0.193121  0.076286  0.150138  0.092593  0.071004  0.073376  0.095098   \n",
       "43  0.188473  0.086918  0.144715  0.089958  0.068583  0.073891  0.095562   \n",
       "44  0.188943  0.092660  0.140889  0.088935  0.068236  0.070696  0.095936   \n",
       "45  0.195387  0.070089  0.161860  0.080191  0.069265  0.059039  0.100842   \n",
       "46  0.194107  0.071039  0.161353  0.086043  0.065819  0.068430  0.095796   \n",
       "47  0.185597  0.064778  0.166164  0.075616  0.063013  0.057332  0.088050   \n",
       "48  0.183207  0.071554  0.164232  0.078402  0.062956  0.056963  0.088255   \n",
       "49  0.177036  0.088352  0.149653  0.077347  0.062426  0.053394  0.087892   \n",
       "50  0.172954  0.088082  0.149837  0.071993  0.066683  0.045925  0.085639   \n",
       "51  0.178739  0.096906  0.150306  0.079236  0.067280  0.054870  0.080716   \n",
       "52  0.175710  0.112120  0.148704  0.079777  0.067442  0.052208  0.077659   \n",
       "53  0.173717  0.109536  0.150928  0.076334  0.069261  0.047214  0.080578   \n",
       "\n",
       "         c01       c02       c03       c12       c13       c23  \n",
       "0        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "1        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "2        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "3        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "4        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "5        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "6        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "7        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "8        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "9        NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "10       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "11       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "12       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "13       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "14       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "15       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "16       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "17       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "18       NaN       NaN       NaN       NaN       NaN       NaN  \n",
       "19 -0.227893  0.479432  0.313243 -0.404730 -0.228507  0.844393  \n",
       "20 -0.238915  0.488099  0.314679 -0.421166 -0.226353  0.836720  \n",
       "21 -0.329593  0.457772  0.294991 -0.520394 -0.318253  0.823853  \n",
       "22 -0.305934  0.460649  0.329037 -0.513592 -0.301964  0.867061  \n",
       "23 -0.329747  0.480878  0.349241 -0.527434 -0.317074  0.870710  \n",
       "24 -0.339725  0.478439  0.362883 -0.537753 -0.297959  0.879991  \n",
       "25 -0.241858  0.442176  0.334447 -0.508431 -0.266799  0.879710  \n",
       "26 -0.026641  0.332696  0.350916 -0.374622 -0.180012  0.911998  \n",
       "27  0.039023  0.411259  0.491734 -0.391726 -0.220212  0.917988  \n",
       "28  0.040523  0.361432  0.449218 -0.359321 -0.192239  0.920646  \n",
       "29  0.024497  0.359730  0.403952 -0.351115 -0.175646  0.927849  \n",
       "30  0.057683  0.304267  0.385727 -0.315366 -0.139607  0.905275  \n",
       "31  0.125244  0.299311  0.348684  0.022290  0.103370  0.916728  \n",
       "32  0.090568  0.450795  0.348378  0.138667  0.169336  0.895974  \n",
       "33 -0.112440  0.451505  0.362036  0.081868  0.151961  0.898256  \n",
       "34 -0.322240  0.406194  0.259764 -0.035109  0.089929  0.864946  \n",
       "35 -0.210852  0.399561  0.228072  0.023765 -0.032458  0.872131  \n",
       "36 -0.269381  0.422300  0.244119  0.072884 -0.007880  0.870481  \n",
       "37 -0.310192  0.380223  0.186422 -0.001129 -0.065822  0.849698  \n",
       "38 -0.312039  0.376445  0.162864 -0.165840 -0.240703  0.823229  \n",
       "39 -0.310916  0.377659  0.130281 -0.178213 -0.093990  0.756636  \n",
       "40 -0.246674  0.548606 -0.068452 -0.091499 -0.099448  0.483892  \n",
       "41 -0.139551  0.539006 -0.208140  0.111815 -0.220825  0.141851  \n",
       "42 -0.141625  0.530309 -0.213064  0.084673 -0.206182  0.139191  \n",
       "43 -0.087189  0.479930 -0.282518  0.179596 -0.149667  0.113933  \n",
       "44 -0.099776  0.487047 -0.287036  0.209398 -0.135399  0.104494  \n",
       "45 -0.212993  0.385217 -0.353438  0.305533  0.045584  0.163268  \n",
       "46 -0.233105  0.370352 -0.412477  0.271462 -0.007510  0.072588  \n",
       "47 -0.181982  0.297610 -0.600901  0.390278  0.060062 -0.072737  \n",
       "48 -0.159784  0.321897 -0.592642  0.381690  0.038918 -0.097121  \n",
       "49 -0.029329  0.301099 -0.663491  0.494450  0.091303 -0.120562  \n",
       "50  0.033691  0.340620 -0.747918  0.518403  0.152453 -0.073249  \n",
       "51  0.098746  0.447711 -0.662079  0.522730  0.133829 -0.128985  \n",
       "52  0.070275  0.475592 -0.602105  0.556898  0.264032 -0.134618  \n",
       "53 -0.027444  0.412879 -0.647386  0.585691  0.313510 -0.065506  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add to dataframe\n",
    "corr_list = []\n",
    "for j, asset in enumerate(asset_list):\n",
    "    for k in range(j+1,n):\n",
    "        df['c'+asset+str(k)]=corrs.loc[(slice(None),'r'+asset),'r'+str(k)].values\n",
    "# Reset index to ease looping over years\n",
    "df = df.reset_index()\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save a copy of the data\n",
    "data = df.copy()\n",
    "\n",
    "# Create dataframe to store the results for each strategy\n",
    "results = pd.DataFrame(dtype=float, \n",
    "    columns=['sr','avg_ret','sd_ret'], \n",
    "    index = ['est_all', 'est_sd_corr', 'est_sd','est_none'])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Est-All"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "df = data.copy()\n",
    "\n",
    "# Make lists of means, sds, weights columns\n",
    "mn_list = ['mn'+asset for asset in asset_list]\n",
    "sd_list = ['sd'+asset for asset in asset_list] \n",
    "wgt_list = ['wgt'+asset for asset in asset_list] \n",
    "\n",
    "# Initialize empty columns for risky asset weights, risky portfolio return, CAL location, CAL portfolio return\n",
    "for wgt in wgt_list:\n",
    "    df[wgt] = np.nan\n",
    "df['risky_ret'] = np.nan\n",
    "df['wgt_risky'] = np.nan \n",
    "df['port_ret']  = np.nan\n",
    "\n",
    "# Choose optimal portfolios each time period\n",
    "for i in np.arange(WINDOW,WINDOW+T):\n",
    "    # Pull estimation inputs at each point in time\n",
    "    means = df[mn_list].iloc[i-1].values\n",
    "    sds   = df[sd_list].iloc[i-1].values\n",
    "    C  = np.identity(n)\n",
    "    for j, asset in enumerate(asset_list):\n",
    "        for k in range(j+1,n):\n",
    "            C[j, k] = C[k, j] = df.loc[i-1,'c'+asset+str(k)]  \n",
    "    cov = np.diag(sds) @ C @ np.diag(sds)\n",
    "\n",
    "    # Pull current period returns\n",
    "    rf = df.loc[i,'rf']\n",
    "    rets = df.loc[i,ret_list].values\n",
    "\n",
    "    ##### Note: all portfolio weights considered to be beginning of period weights\n",
    "    ##### (so multiply by contemporaneous realized returns)\n",
    "    wgts = tangency(means,cov,rf)\n",
    "    df.loc[i,wgt_list] = wgts\n",
    "    df.loc[i,'risky_ret'] = wgts @ rets\n",
    "\n",
    "    # Capital allocation and overall portfolio return\n",
    "    risky_expret = wgts @ means\n",
    "    risky_sd     = np.sqrt(wgts @ cov @ wgts)\n",
    "    target       = means.mean()\n",
    "    df.loc[i,'wgt_risky'] = capital_allocation(risky_expret, risky_sd, rf, target)\n",
    "    df.loc[i,'port_ret']  = rf + df.loc[i,'wgt_risky']*(df.loc[i,'risky_ret'] -rf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>Year</th>\n",
       "      <th>wgt0</th>\n",
       "      <th>wgt1</th>\n",
       "      <th>wgt2</th>\n",
       "      <th>wgt3</th>\n",
       "      <th>rf</th>\n",
       "      <th>risky_ret</th>\n",
       "      <th>wgt_risky</th>\n",
       "      <th>port_ret</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1988</td>\n",
       "      <td>0.046741</td>\n",
       "      <td>0.230671</td>\n",
       "      <td>1.734061</td>\n",
       "      <td>-1.011472</td>\n",
       "      <td>0.066675</td>\n",
       "      <td>0.150454</td>\n",
       "      <td>0.734038</td>\n",
       "      <td>0.128172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1989</td>\n",
       "      <td>0.008168</td>\n",
       "      <td>0.254833</td>\n",
       "      <td>2.250273</td>\n",
       "      <td>-1.513275</td>\n",
       "      <td>0.081117</td>\n",
       "      <td>0.084443</td>\n",
       "      <td>0.500912</td>\n",
       "      <td>0.082783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1990</td>\n",
       "      <td>0.125408</td>\n",
       "      <td>0.194271</td>\n",
       "      <td>1.330005</td>\n",
       "      <td>-0.649684</td>\n",
       "      <td>0.074933</td>\n",
       "      <td>0.032465</td>\n",
       "      <td>0.844489</td>\n",
       "      <td>0.039069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1991</td>\n",
       "      <td>0.058111</td>\n",
       "      <td>0.187457</td>\n",
       "      <td>1.680626</td>\n",
       "      <td>-0.926193</td>\n",
       "      <td>0.053750</td>\n",
       "      <td>0.160623</td>\n",
       "      <td>0.776417</td>\n",
       "      <td>0.136728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1992</td>\n",
       "      <td>0.064038</td>\n",
       "      <td>0.174833</td>\n",
       "      <td>1.523487</td>\n",
       "      <td>-0.762359</td>\n",
       "      <td>0.034317</td>\n",
       "      <td>0.108731</td>\n",
       "      <td>0.856921</td>\n",
       "      <td>0.098084</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year      wgt0      wgt1      wgt2      wgt3        rf  risky_ret  \\\n",
       "20  1988  0.046741  0.230671  1.734061 -1.011472  0.066675   0.150454   \n",
       "21  1989  0.008168  0.254833  2.250273 -1.513275  0.081117   0.084443   \n",
       "22  1990  0.125408  0.194271  1.330005 -0.649684  0.074933   0.032465   \n",
       "23  1991  0.058111  0.187457  1.680626 -0.926193  0.053750   0.160623   \n",
       "24  1992  0.064038  0.174833  1.523487 -0.762359  0.034317   0.108731   \n",
       "\n",
       "    wgt_risky  port_ret  \n",
       "20   0.734038  0.128172  \n",
       "21   0.500912  0.082783  \n",
       "22   0.844489  0.039069  \n",
       "23   0.776417  0.136728  \n",
       "24   0.856921  0.098084  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "df_est_all = df.copy()\n",
    "df[['Year']+wgt_list+['rf','risky_ret','wgt_risky','port_ret']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Avg return of Est-All:\t  0.0766\n",
      "SD(return) of Est-All:\t  0.0651\n",
      "Sharpe ratio of Est-All:  0.7452\n"
     ]
    }
   ],
   "source": [
    "avg_ret = df.port_ret.mean()\n",
    "sd_ret  = df.port_ret.std()\n",
    "avg_rf  = df.rf.mean()\n",
    "sr = (avg_ret - avg_rf)/sd_ret\n",
    "print(f'Avg return of Est-All:\\t {avg_ret: .4f}')\n",
    "print(f'SD(return) of Est-All:\\t {sd_ret: .4f}')\n",
    "print(f'Sharpe ratio of Est-All: {sr: .4f}')\n",
    "\n",
    "# Save results\n",
    "results.loc['est_all','avg_ret'] = avg_ret\n",
    "results.loc['est_all','sd_ret']  = sd_ret\n",
    "results.loc['est_all','sr']      = sr"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Est-SD-Corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "df = data.copy()\n",
    "\n",
    "# Initialize empty columns for risky asset weights, risky portfolio return, CAL location, CAL portfolio return\n",
    "for wgt in wgt_list:\n",
    "    df[wgt] = np.nan\n",
    "df['risky_ret'] = np.nan\n",
    "df['wgt_risky'] = np.nan \n",
    "df['port_ret']  = np.nan\n",
    "\n",
    "# Choose optimal portfolios each time period\n",
    "for i in np.arange(WINDOW,WINDOW+T):\n",
    "    # Pull estimation inputs at each point in time\n",
    "    means = df[mn_list].iloc[i-1].values\n",
    "    sds   = df[sd_list].iloc[i-1].values\n",
    "    C  = np.identity(n)\n",
    "    for j, asset in enumerate(asset_list):\n",
    "        for k in range(j+1,n):\n",
    "            C[j, k] = C[k, j] = df.loc[i-1,'c'+asset+str(k)]  \n",
    "    cov = np.diag(sds) @ C @ np.diag(sds)\n",
    "\n",
    "    # Pull current period returns\n",
    "    rf = df.loc[i,'rf']\n",
    "    rets = df.loc[i,ret_list].values\n",
    "\n",
    "    ##### Note: all portfolio weights considered to be beginning of period weights\n",
    "    ##### (so multiply by contemporaneous realized returns)\n",
    "    wgts = gmv(means,cov)                                       # <------------ different\n",
    "    df.loc[i,wgt_list] = wgts\n",
    "    df.loc[i,'risky_ret'] = wgts @ rets\n",
    "\n",
    "    # Capital allocation and overall portfolio return\n",
    "    risky_expret = wgts @ (np.ones(n)*means.mean())             # <------------ different\n",
    "    risky_sd     = np.sqrt(wgts @ cov @ wgts)\n",
    "    target       = means.mean()\n",
    "    df.loc[i,'wgt_risky'] = capital_allocation(risky_expret, risky_sd, rf, target)\n",
    "    df.loc[i,'port_ret']  = rf + df.loc[i,'wgt_risky']*(df.loc[i,'risky_ret'] -rf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>Year</th>\n",
       "      <th>wgt0</th>\n",
       "      <th>wgt1</th>\n",
       "      <th>wgt2</th>\n",
       "      <th>wgt3</th>\n",
       "      <th>rf</th>\n",
       "      <th>risky_ret</th>\n",
       "      <th>wgt_risky</th>\n",
       "      <th>port_ret</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1988</td>\n",
       "      <td>0.058566</td>\n",
       "      <td>0.127085</td>\n",
       "      <td>0.864139</td>\n",
       "      <td>-0.049790</td>\n",
       "      <td>0.066675</td>\n",
       "      <td>0.116261</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.116261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1989</td>\n",
       "      <td>0.053563</td>\n",
       "      <td>0.127204</td>\n",
       "      <td>0.868483</td>\n",
       "      <td>-0.049250</td>\n",
       "      <td>0.081117</td>\n",
       "      <td>0.142438</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.142438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1990</td>\n",
       "      <td>0.072808</td>\n",
       "      <td>0.138003</td>\n",
       "      <td>0.841629</td>\n",
       "      <td>-0.052440</td>\n",
       "      <td>0.074933</td>\n",
       "      <td>0.042734</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.042734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1991</td>\n",
       "      <td>0.049981</td>\n",
       "      <td>0.141893</td>\n",
       "      <td>1.036918</td>\n",
       "      <td>-0.228793</td>\n",
       "      <td>0.053750</td>\n",
       "      <td>0.152264</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.152264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1992</td>\n",
       "      <td>0.041519</td>\n",
       "      <td>0.144520</td>\n",
       "      <td>1.061836</td>\n",
       "      <td>-0.247875</td>\n",
       "      <td>0.034317</td>\n",
       "      <td>0.100772</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.100772</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year      wgt0      wgt1      wgt2      wgt3        rf  risky_ret  \\\n",
       "20  1988  0.058566  0.127085  0.864139 -0.049790  0.066675   0.116261   \n",
       "21  1989  0.053563  0.127204  0.868483 -0.049250  0.081117   0.142438   \n",
       "22  1990  0.072808  0.138003  0.841629 -0.052440  0.074933   0.042734   \n",
       "23  1991  0.049981  0.141893  1.036918 -0.228793  0.053750   0.152264   \n",
       "24  1992  0.041519  0.144520  1.061836 -0.247875  0.034317   0.100772   \n",
       "\n",
       "    wgt_risky  port_ret  \n",
       "20        1.0  0.116261  \n",
       "21        1.0  0.142438  \n",
       "22        1.0  0.042734  \n",
       "23        1.0  0.152264  \n",
       "24        1.0  0.100772  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "df_est_sd_corr = df.copy()\n",
    "df[['Year']+wgt_list+['rf','risky_ret','wgt_risky','port_ret']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Avg return of Est-SD-Corr:\t  0.0855\n",
      "SD(return) of Est-SD-Corr:\t  0.0673\n",
      "Sharpe ratio of Est-SD-Corr:\t  0.8534\n"
     ]
    }
   ],
   "source": [
    "avg_ret = df.port_ret.mean()\n",
    "sd_ret  = df.port_ret.std()\n",
    "avg_rf  = df.rf.mean()\n",
    "sr = (avg_ret - avg_rf)/sd_ret\n",
    "print(f'Avg return of Est-SD-Corr:\\t {avg_ret: .4f}')\n",
    "print(f'SD(return) of Est-SD-Corr:\\t {sd_ret: .4f}')\n",
    "print(f'Sharpe ratio of Est-SD-Corr:\\t {sr: .4f}')\n",
    "\n",
    "# Save results\n",
    "results.loc['est_sd_corr','avg_ret'] = avg_ret\n",
    "results.loc['est_sd_corr','sd_ret']  = sd_ret\n",
    "results.loc['est_sd_corr','sr']      = sr\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Est-SD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "df = data.copy()\n",
    "\n",
    "# Initialize empty columns for risky asset weights, risky portfolio return, CAL location, CAL portfolio return\n",
    "for wgt in wgt_list:\n",
    "    df[wgt] = np.nan\n",
    "df['risky_ret'] = np.nan\n",
    "df['wgt_risky'] = np.nan \n",
    "df['port_ret']  = np.nan\n",
    "\n",
    "# Choose optimal portfolios each time period\n",
    "for i in np.arange(WINDOW,WINDOW+T):\n",
    "    # Pull estimation inputs at each point in time\n",
    "    means = df[mn_list].iloc[i-1].values\n",
    "    sds   = df[sd_list].iloc[i-1].values\n",
    "    C  = np.identity(n)                                         # <------------ different\n",
    "    cov = np.diag(sds) @ C @ np.diag(sds)\n",
    "\n",
    "    # Pull current period returns\n",
    "    rf = df.loc[i,'rf']\n",
    "    rets = df.loc[i,ret_list].values\n",
    "\n",
    "    ##### Note: all portfolio weights considered to be beginning of period weights\n",
    "    ##### (so multiply by contemporaneous realized returns)\n",
    "    wgts = gmv(means,cov)                                       # <------------ different\n",
    "    df.loc[i,wgt_list] = wgts\n",
    "    df.loc[i,'risky_ret'] = wgts @ rets\n",
    "\n",
    "    # Capital allocation and overall portfolio return\n",
    "    risky_expret = wgts @ (np.ones(n)*means.mean())             # <------------ different\n",
    "    risky_sd     = np.sqrt(wgts @ cov @ wgts)\n",
    "    target       = means.mean()\n",
    "    df.loc[i,'wgt_risky'] = capital_allocation(risky_expret, risky_sd, rf, target)\n",
    "    df.loc[i,'port_ret']  = rf + df.loc[i,'wgt_risky']*(df.loc[i,'risky_ret'] -rf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>wgt0</th>\n",
       "      <th>wgt1</th>\n",
       "      <th>wgt2</th>\n",
       "      <th>wgt3</th>\n",
       "      <th>rf</th>\n",
       "      <th>risky_ret</th>\n",
       "      <th>wgt_risky</th>\n",
       "      <th>port_ret</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1988</td>\n",
       "      <td>0.152645</td>\n",
       "      <td>0.027162</td>\n",
       "      <td>0.455033</td>\n",
       "      <td>0.365160</td>\n",
       "      <td>0.066675</td>\n",
       "      <td>0.119788</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.119788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1989</td>\n",
       "      <td>0.151601</td>\n",
       "      <td>0.026109</td>\n",
       "      <td>0.453626</td>\n",
       "      <td>0.368664</td>\n",
       "      <td>0.081117</td>\n",
       "      <td>0.183990</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.183990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1990</td>\n",
       "      <td>0.144025</td>\n",
       "      <td>0.025389</td>\n",
       "      <td>0.463993</td>\n",
       "      <td>0.366593</td>\n",
       "      <td>0.074933</td>\n",
       "      <td>0.046301</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.046301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1991</td>\n",
       "      <td>0.138614</td>\n",
       "      <td>0.024969</td>\n",
       "      <td>0.462080</td>\n",
       "      <td>0.374337</td>\n",
       "      <td>0.053750</td>\n",
       "      <td>0.178174</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.178174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1992</td>\n",
       "      <td>0.134681</td>\n",
       "      <td>0.025028</td>\n",
       "      <td>0.463370</td>\n",
       "      <td>0.376921</td>\n",
       "      <td>0.034317</td>\n",
       "      <td>0.100329</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.100329</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year      wgt0      wgt1      wgt2      wgt3        rf  risky_ret  \\\n",
       "20  1988  0.152645  0.027162  0.455033  0.365160  0.066675   0.119788   \n",
       "21  1989  0.151601  0.026109  0.453626  0.368664  0.081117   0.183990   \n",
       "22  1990  0.144025  0.025389  0.463993  0.366593  0.074933   0.046301   \n",
       "23  1991  0.138614  0.024969  0.462080  0.374337  0.053750   0.178174   \n",
       "24  1992  0.134681  0.025028  0.463370  0.376921  0.034317   0.100329   \n",
       "\n",
       "    wgt_risky  port_ret  \n",
       "20        1.0  0.119788  \n",
       "21        1.0  0.183990  \n",
       "22        1.0  0.046301  \n",
       "23        1.0  0.178174  \n",
       "24        1.0  0.100329  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "df_est_sd = df.copy()\n",
    "df[['Year']+wgt_list+['rf','risky_ret','wgt_risky','port_ret']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Avg return of Est-SD:\t  0.0860\n",
      "SD(return) of Est-SD:\t  0.0656\n",
      "Sharpe ratio of Est-SD:\t  0.8825\n"
     ]
    }
   ],
   "source": [
    "avg_ret = df.port_ret.mean()\n",
    "sd_ret  = df.port_ret.std()\n",
    "avg_rf  = df.rf.mean()\n",
    "sr = (avg_ret - avg_rf)/sd_ret\n",
    "print(f'Avg return of Est-SD:\\t {avg_ret: .4f}')\n",
    "print(f'SD(return) of Est-SD:\\t {sd_ret: .4f}')\n",
    "print(f'Sharpe ratio of Est-SD:\\t {sr: .4f}')\n",
    "\n",
    "# Save results\n",
    "results.loc['est_sd','avg_ret'] = avg_ret\n",
    "results.loc['est_sd','sd_ret']  = sd_ret\n",
    "results.loc['est_sd','sr']      = sr\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Est-None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "df = data.copy()\n",
    "\n",
    "# Initialize empty columns for risky asset weights, risky portfolio return, CAL location, CAL portfolio return\n",
    "for wgt in wgt_list:\n",
    "    df[wgt] = np.nan\n",
    "df['risky_ret'] = np.nan\n",
    "df['wgt_risky'] = np.nan \n",
    "df['port_ret']  = np.nan\n",
    "\n",
    "# Choose optimal portfolios each time period\n",
    "for i in np.arange(WINDOW,WINDOW+T):\n",
    "    # Pull estimation inputs at each point in time\n",
    "    means = df[mn_list].iloc[i-1].values\n",
    "    sds   = df[sd_list].iloc[i-1].values\n",
    "    means = np.ones(n)*means.mean()                             # <------------ different\n",
    "    sds   = np.ones(n)*sds.mean()                               # <------------ different\n",
    "    C  = np.identity(n)                                         # <------------ different\n",
    "    cov = np.diag(sds) @ C @ np.diag(sds)\n",
    "\n",
    "    # Pull current period returns\n",
    "    rf = df.loc[i,'rf']\n",
    "    rets = df.loc[i,ret_list].values\n",
    "\n",
    "    ##### Note: all portfolio weights considered to be beginning of period weights\n",
    "    ##### (so multiply by contemporaneous realized returns)\n",
    "    wgts = gmv(means,cov)                                       # <------------ different\n",
    "    df.loc[i,wgt_list] = wgts\n",
    "    df.loc[i,'risky_ret'] = wgts @ rets\n",
    "\n",
    "    # Capital allocation and overall portfolio return\n",
    "    risky_expret = wgts @ (np.ones(n)*means.mean())             # <------------ different\n",
    "    risky_sd     = np.sqrt(wgts @ cov @ wgts)\n",
    "    target       = means.mean()\n",
    "    df.loc[i,'wgt_risky'] = capital_allocation(risky_expret, risky_sd, rf, target)\n",
    "    df.loc[i,'port_ret']  = rf + df.loc[i,'wgt_risky']*(df.loc[i,'risky_ret'] -rf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>wgt0</th>\n",
       "      <th>wgt1</th>\n",
       "      <th>wgt2</th>\n",
       "      <th>wgt3</th>\n",
       "      <th>rf</th>\n",
       "      <th>risky_ret</th>\n",
       "      <th>wgt_risky</th>\n",
       "      <th>port_ret</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1988</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.066675</td>\n",
       "      <td>0.060455</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.060455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1989</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.081117</td>\n",
       "      <td>0.156819</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.156819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1990</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.074933</td>\n",
       "      <td>0.017043</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.017043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1991</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.053750</td>\n",
       "      <td>0.133691</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.133691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1992</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.034317</td>\n",
       "      <td>0.058067</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.058067</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year  wgt0  wgt1  wgt2  wgt3        rf  risky_ret  wgt_risky  port_ret\n",
       "20  1988  0.25  0.25  0.25  0.25  0.066675   0.060455        1.0  0.060455\n",
       "21  1989  0.25  0.25  0.25  0.25  0.081117   0.156819        1.0  0.156819\n",
       "22  1990  0.25  0.25  0.25  0.25  0.074933   0.017043        1.0  0.017043\n",
       "23  1991  0.25  0.25  0.25  0.25  0.053750   0.133691        1.0  0.133691\n",
       "24  1992  0.25  0.25  0.25  0.25  0.034317   0.058067        1.0  0.058067"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "df_est_none = df.copy()\n",
    "df[['Year']+wgt_list+['rf','risky_ret','wgt_risky','port_ret']].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Avg return of Est-None:\t\t  0.0825\n",
      "SD(return) of Est-None:\t\t  0.0663\n",
      "Sharpe ratio of Est-None:\t  0.8207\n"
     ]
    }
   ],
   "source": [
    "avg_ret = df.port_ret.mean()\n",
    "sd_ret  = df.port_ret.std()\n",
    "avg_rf  = df.rf.mean()\n",
    "sr = (avg_ret - avg_rf)/sd_ret\n",
    "print(f'Avg return of Est-None:\\t\\t {avg_ret: .4f}')\n",
    "print(f'SD(return) of Est-None:\\t\\t {sd_ret: .4f}')\n",
    "print(f'Sharpe ratio of Est-None:\\t {sr: .4f}')\n",
    "\n",
    "# Save results\n",
    "results.loc['est_none','avg_ret'] = avg_ret\n",
    "results.loc['est_none','sd_ret']  = sd_ret\n",
    "results.loc['est_none','sr']      = sr\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sr</th>\n",
       "      <th>avg_ret</th>\n",
       "      <th>sd_ret</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>est_all</th>\n",
       "      <td>0.7452</td>\n",
       "      <td>0.0766</td>\n",
       "      <td>0.0651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>est_sd_corr</th>\n",
       "      <td>0.8534</td>\n",
       "      <td>0.0855</td>\n",
       "      <td>0.0673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>est_sd</th>\n",
       "      <td>0.8825</td>\n",
       "      <td>0.0860</td>\n",
       "      <td>0.0656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>est_none</th>\n",
       "      <td>0.8207</td>\n",
       "      <td>0.0825</td>\n",
       "      <td>0.0663</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "                 sr  avg_ret  sd_ret\n",
       "est_all      0.7452   0.0766  0.0651\n",
       "est_sd_corr  0.8534   0.0855  0.0673\n",
       "est_sd       0.8825   0.0860  0.0656\n",
       "est_none     0.8207   0.0825  0.0663"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.round(4)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "label_dict = {'est_all': 'estimate all inputs',\n",
    "            'est_sd_corr': 'estimate covariance matrix only',\n",
    "            'est_sd': 'estimate standard deviations only',\n",
    "            'est_none': 'equal weights'}\n",
    "\n",
    "xaxis_label_dict = {'est_all': 'Est-All',\n",
    "            'est_sd_corr': 'Est-SD-Corr',\n",
    "            'est_sd': 'Est-SD',\n",
    "            'est_none': 'Est-None',}\n",
    "results = results.reset_index()\n",
    "results['label'] = results['index'].apply(lambda x: label_dict[x])\n",
    "results['xaxis_label'] = results['index'].apply(lambda x: xaxis_label_dict[x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
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           "bgcolor": "#E5ECF6",
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          },
          "title": {
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          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
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           "zerolinewidth": 2
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          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
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       }
      }
     },
     "metadata": {},
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   ],
   "source": [
    "string = \"Strategy: %{customdata[0]} <br>\"\n",
    "string += \"Sharpe ratio: %{y:0.3f}<br>\"\n",
    "string += \"Average return: %{customdata[1]:0.1%}<br>\"\n",
    "string += \"SD(return): %{customdata[2]:0.1%}<br>\"\n",
    "string += \"<extra></extra>\"\n",
    "\n",
    "fig = go.Figure()\n",
    "fig.add_trace(go.Bar(x=results['xaxis_label'], y=results['sr'], customdata=results[['label','avg_ret','sd_ret']], hovertemplate=string))\n",
    "fig.layout.yaxis[\"title\"] = \"Sharpe ratio\"\n",
    "fig.layout.xaxis[\"title\"] = \"Strategy\"\n",
    "fig.show()"
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