sharpe_difference_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis Testing of the Sharpe Ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When one is evaluating various portfolio optimization methods based on historical performance, one has to have an idea about what constitues a significant difference between Sharpe ratios. To make this process a little more rigorous I'm presenting here several statistical tests."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Jobson and Korkie \n",
    "\n",
    "If returns of portfolio $ p $ and $q$ can be assumed $iid$ multivariate Gaussian i.e.\n",
    "\n",
    "$\\left(\\begin{array}{c}{R_{p, t}} \\\\ {R_{q, t}}\\end{array}\\right) \\stackrel{i i d}{\\sim} \\mathrm{N}\\left(\\left(\\begin{array}{c}{\\mu_{p}} \\\\ {\\mu_{q}}\\end{array}\\right),\\left(\\begin{array}{cc}{\\sigma_{p}^{2}} & {\\sigma_{p q}} \\\\ {\\sigma_{p q}} & {\\sigma_{q}^{2}}\\end{array}\\right)\\right)$\n",
    "\n",
    "Define two vector containing the parameters and their sample estimates:\n",
    "\n",
    "$\\boldsymbol{m}=\\left(\\begin{array}{cccc}{\\mu_{p}} & {\\mu_{q}} & {\\sigma_{p}^{2}} & {\\sigma_{q}^{2}}\\end{array}\\right)^{\\prime}, \\quad \\widehat{\\boldsymbol{m}}=\\left(\\begin{array}{cccc}{\\widehat{\\mu}_{p}} & {\\widehat{\\mu}_{q}} & {\\widehat{\\sigma}_{p}^{2}} & {\\widehat{\\sigma}_{q}^{2}}\\end{array}\\right)^{\\prime}$\n",
    "\n",
    "Then \n",
    "\n",
    "$\\sqrt{T}(\\boldsymbol{\\widehat{m}}-\\boldsymbol{m}) \\stackrel{d}{\\rightarrow} \\mathrm{N}(\\mathbf{0}, \\boldsymbol{V})$\n",
    "\n",
    "where\n",
    "\n",
    "$V=\\left(\\begin{array}{cccc}{\\sigma_{p}^{2}} & {\\sigma_{p q}} & {0} & {0} \\\\ {\\sigma_{p q}} & {\\sigma_{q}^{2}} & {0} & {0} \\\\ {0} & {0} & {2 \\sigma_{p}^{4}} & {2 \\sigma_{p q}^{2}} \\\\ {0} & {0} & {2 \\sigma_{p q}^{2}} & {2 \\sigma_{q}^{4}}\\end{array}\\right)$\n",
    "\n",
    "Further define the Sharpe ratio as the vector function\n",
    "\n",
    "$\\boldsymbol{\\theta}(\\boldsymbol{m})=\\left(\\begin{array}{cc}{\\theta_{p}\\left(\\mu_{p}, \\sigma_{p}^{2}\\right)} & {\\left.\\theta_{q}\\left(\\mu_{q}, \\sigma_{q}^{2}\\right)\\right)^{\\prime}=\\left(\\begin{array}{cc}{\\frac{\\mu_{p}}{\\sigma_{p}}} & {\\frac{\\mu_{q}}{\\sigma_{q}}}\\end{array}\\right)^{\\prime}}\\end{array}\\right.$\n",
    "\n",
    "with Jacobian\n",
    "\n",
    "$\\begin{aligned} \\boldsymbol{D}=\\left(\\begin{array}{ccc}{\\frac{\\partial \\theta_{p}}{\\partial \\mu_{p}}} & {\\frac{\\partial \\theta_{p}}{\\partial \\mu_{q}}} & {\\frac{\\partial \\theta_{p}}{\\partial \\sigma_{p}^{2}}} & {\\frac{\\partial \\theta_{p}}{\\partial \\sigma_{q}^{2}}} \\\\ {\\frac{\\partial \\theta_{q}}{\\partial \\mu_{p}}} & {\\frac{\\partial \\theta_{q}}{\\partial \\mu_{q}}} & {\\frac{\\partial \\theta_{q}}{\\partial \\sigma_{p}^{2}}} & {\\frac{\\partial \\theta_{q}}{\\partial \\sigma_{q}^{2}}}\\end{array}\\right) &=\\left(\\begin{array}{cccc}{\\frac{1}{\\sigma_{p}}} & {0} & {-\\frac{\\mu_{p}}{2 \\sigma_{p}^{3}}} & {0} \\\\ {0} & {\\frac{1}{\\sigma_{q}}} & {0} & {-\\frac{\\mu_{q}}{2 \\sigma_{q}^{3}}}\\end{array}\\right) \\\\ &=\\left(\\begin{array}{cccc}{\\frac{1}{\\sigma_{p}}} & {0} & {-\\frac{\\theta_{p}}{2 \\sigma_{p}^{2}}} & {0} \\\\ {0} & {\\frac{1}{\\sigma_{q}}} & {0} & {-\\frac{\\theta_{q}}{2 \\sigma_{q}^{2}}}\\end{array}\\right) \\end{aligned}$\n",
    "\n",
    "and its sample estimate\n",
    "\n",
    "$\\widehat{\\boldsymbol{\\theta}}=\\boldsymbol{\\theta}(\\widehat{\\boldsymbol{m}})=\\left(\\begin{array}{cc}{\\widehat{\\theta}_{p}} & {\\widehat{\\theta}_{q}}\\end{array}\\right)=\\left(\\begin{array}{cc}{\\frac{\\widehat{\\mu}_{p}}{\\widehat{\\sigma}_{p}^{2}}} & {\\frac{\\widehat{\\boldsymbol{\\mu}}_{q}}{\\widehat{\\sigma}_{q}^{2}}}\\end{array}\\right)$\n",
    "\n",
    "Then\n",
    "\n",
    "$\\sqrt{T}(\\boldsymbol{\\theta}(\\widehat{\\boldsymbol{m}})-\\boldsymbol{\\theta}(\\boldsymbol{m})) \\stackrel{d}{\\rightarrow} \\mathrm{N}(\\mathbf{0}, \\boldsymbol{\\Psi})$\n",
    "\n",
    "where $\\operatorname{Corr}\\left(R_{p}, R_{q}\\right)=\\varrho_{p q}=\\sigma_{p q} / \\sigma_{p} \\sigma_{q}$\n",
    "\n",
    "and \n",
    "$\\Psi=D \\Sigma D^{\\prime}$\n",
    "\n",
    "$=\\left(\\begin{array}{cccc}{\\frac{1}{\\sigma_{p}}} & {0} & {-\\frac{\\theta_{p}}{2 \\sigma_{p}^{2}}} & {0} \\\\ {0} & {\\frac{1}{\\sigma_{q}}} & {0} & {-\\frac{\\theta_{q}}{2 \\sigma_{q}^{2}}}\\end{array}\\right)\\left(\\begin{array}{cccc}{\\sigma_{p}^{2}} & {\\sigma_{p q}} & {0} & {0} \\\\ {\\sigma_{p q}} & {\\sigma_{q}^{2}} & {0} & {0} \\\\ {0} & {0} & {2 \\sigma_{p}^{4}} & {2 \\sigma_{p q}^{2}} \\\\ {0} & {0} & {2 \\sigma_{p q}^{2}} & {2 \\sigma_{q}^{4}}\\end{array}\\right)\\left(\\begin{array}{cc}{\\frac{1}{\\sigma_{p}}} & {0} \\\\ {0} & {\\frac{1}{\\sigma q}} \\\\ {-\\frac{\\theta_{p}}{2 \\sigma_{p}^{2}}} & {0} \\\\ {0} & {-\\frac{\\theta_{q}}{2 \\sigma_{q}^{2}}}\\end{array}\\right)$\n",
    "\n",
    "$=\\left(\\begin{array}{cc}{1+\\frac{\\theta_{p}^{2}}{2}} & {\\varrho_{p q}+\\frac{\\varrho_{p q}^{2} \\theta_{p} \\theta_{q}}{2}} \\\\ {\\varrho_{p q}+\\frac{\\rho_{p q}^{2} \\theta_{p} \\theta_{q}}{2}} & {1+\\frac{\\theta_{q}^{2}}{2}}\\end{array}\\right)$\n",
    "\n",
    "The asymptotic variance based on sample estimates is \n",
    "\n",
    "$\\widehat{\\operatorname{AsyVar}}\\left(\\hat{\\theta}_{p}-\\widehat{\\theta}_{q}\\right)=\\widehat{\\operatorname{AsyVar}}\\left(\\widehat{\\theta}_{p}\\right)+\\widehat{\\operatorname{AsyVar}}\\left(\\widehat{\\theta}_{q}\\right)-2 \\widehat{\\operatorname{AsyCov}}\\left(\\widehat{\\theta}_{p}, \\widehat{\\theta}_{q}\\right)$\n",
    "\n",
    "\n",
    "$=T^{-1}\\left\\{2\\left(1-\\widehat{\\varrho}_{p q}\\right)+\\frac{1}{2}\\left(\\widehat{\\theta}_{p}^{2}+\\widehat{\\theta}_{q}^{2}-2 \\widehat{\\theta}_{p} \\widehat{\\theta}_{q} \\widehat{\\varrho}_{p q}^{2}\\right)\\right\\}$\n",
    "\n",
    "Now the hypothesis $H_{0} : \\theta_{p}=\\theta_{q}$ can be based on $t=\\frac{\\widehat{\\theta}_{p}-\\widehat{\\theta}_{q}}{\\sqrt{\\widehat{\\operatorname{Asy} \\operatorname{Var}}\\left(\\widehat{\\theta}_{p}-\\widehat{\\theta}_{q}\\right)}} \\stackrel{d}{\\rightarrow} \\mathrm{N}(0,1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac34860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.0436\n",
      "percentage false H0 rejected at alpha = 0.05:  0.9334\n"
     ]
    }
   ],
   "source": [
    "from src import hypothesis\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "plt.style.use('seaborn')\n",
    "\n",
    "\n",
    "t_stat = []\n",
    "p_val = []\n",
    "t_stat2 = []\n",
    "p_val2 = []\n",
    "n = 12\n",
    "MC = 5000\n",
    "for i in range(MC):\n",
    "    returns_1 = np.random.normal(2, 1, n)\n",
    "    returns_2 = np.random.normal(2, 1, n)\n",
    "    returns_3 = np.random.normal(0.1, 1, n)\n",
    "    \n",
    "    outcome_tn = hypothesis.jobson_korkie(returns_1, returns_2)\n",
    "    t_stat.append(outcome_tn['t_statistic'])\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "    outcome_fn = hypothesis.jobson_korkie(returns_1, returns_3)\n",
    "    t_stat2.append(outcome_fn['t_statistic'])\n",
    "    p_val2.append(outcome_fn['p_value'])\n",
    "\n",
    "    \n",
    "plt.hist(t_stat, bins=50, alpha=0.5)\n",
    "plt.hist(t_stat2, bins=50, alpha=0.5)\n",
    "plt.title('t-stat histogram: true null vs. false null')\n",
    "plt.xlabel = 't-statistic'\n",
    "plt.ylabel = 'frequency'\n",
    "plt.show()\n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)\n",
    "\n",
    "p_val2 = np.array(p_val2)\n",
    "rejection_pct2 = len(p_val2[p_val2<alpha])/n\n",
    "print(f'percentage false H0 rejected at alpha = {alpha}: ', rejection_pct2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ahv3WDdJX3A0qR+qSVBBDXZIKYvlFGkD3Pby16fojXzC+wC1Rv3GkLkkFMdQlqSCGuiQVxFCXpIIY6pJUEK9+GULfuuWBXjdBUpc4UpekghjqklQQQ12SCmKoS1JBDHVJKoihLkkF8ZLGwn1l/X1s376r183omvsnN/a6CVJfmVOoR8QrgI9l5skR8UJgHbAXuAd4d2Y+ExFnA+cAe4DVmXltl9osSZrBrKEeER8EzgS216suBS7KzJsjYg1wekTcDpwLHAcsA26NiBsys9whotSHZpqSt5mXHXVYF1uiXpnLSP1+4M3AlfXPq4Dv1svXA6cCk8BtdYjviojNwNFAy7+Nx8eXs2TJ4nbaPauJibGu7HcQjY4u7XUTumZk5/wqiCMjVhwbLV/g90Y//172c9vmY9Z3eGZeHRFHNKxalJl76+VtwArgEOCJhm2m1re0deuOubd0HiYmxtiyZVtX9j2ISq6p757cM+dtR0aWsHv33LcfBjsW+L3Rr7+Xg5YZrT6A2rn65ZmG5THgceDJenn6eknSAmon1H8YESfXy6cBtwB3AidGxLKIWAEcRXUSVZK0gNopMP4BsDYiDgbuBa7KzMmIuIwq4A8CLszMpzvYTkkFuO6BDfute/3KU3vQknLNKdQz80HghHr5J8BJTbZZC6ztZOMkSfPjHaWSVBBDXZIKYqhLUkEMdUkqiKEuSQUx1CWpIIa6JBXEUJekgjhlnQaGX4ghzc5QL8S3bnmg6fqSp92VtD/LL5JUEEfqknrKSb46y1BXX7J+LrXH8oskFcRQl6SCGOqSVBBDXZIKYqhLUkEMdUkqiKEuSQXxOvUBM9N0AJIEhro0tO7e/HN2796z3/ojXzDeg9aoUwx1SX3HqQPaZ01dkgpiqEtSQQx1SSqINXVJA8E6+9w4UpekgjhS72Neky5pvgx1LSi//ELqLssvklQQQ12SCtJ2+SUifgA8Wf/4d8CfAuuAvcA9wLsz85kDbaAkae7aCvWIWAYsysyTG9Z9G7goM2+OiDXA6cA1HWmlJGlO2h2pHwMsj4gN9T4uAFYB360fvx44lVlCfXx8OUuWLG6zCa1NTIx1Zb8LaXR0aV/tpxNGdvb23PzIiNcGNGrWH8v76P0ym07+npeQGdB+qO8ALgEuB15EFeKLMnNv/fg2YMVsO9m6dUebh29tYmKMLVu2dWXfC2n79l0HvI/R0aUd2U+n7J7cf1bAhTIysqTprITDaqb+2NFH75fZdOr3fNAyo9UHULuh/hNgcx3iP4mIx6hG6lPGgMfb3LckqU3thvrbgZcAvx8RvwYcAmyIiJMz82bgNOCmzjRRg8pr0gfTfQ9v3W+dc6wPjnZD/S+AdRFxK9XVLm8Hfg6sjYiDgXuBqzrTREm91izoofdh32w+GBjuOWHaCvXM/AXwu00eOunAmjOcnA5AUqd485EkFcRQl6SCGOqSVBDvxJBUnGH+Qg1H6pJUEENdkgpiqEtSQayp64B556jUPwx1SW2b6U7TZnp99+mwsPwiSQUx1CWpIJZfFpBzvEjqNkfqklQQQ12SCmKoS1JBrKlLWhD9+kUbpTHUNS/eaCT1N0NdUk/5naidZah3iZcvSuoFQ10zstQiDR5D/QA5Ipc6rxsnVYflizO8pFGSCuJIXdLQmhq9L//ZUnZs3wUM/ujdUG9iGEsq1s+lSrMyTTP9Gv6WXySpIIa6JBXE8ssQstQilctQL9y9O+9g9+SeXjdD6gjnj5nd0IR6s5OfbzpxZQ9aIkndMzShLkmd1K83MxnqA2immvhvLH75ArdE6g8zlWWaKb1U09FQj4iDgM8BxwC7gLMyc3MnjzGbb93yAKOjS9le30gw6OZzUrPZtiMH+bktDZNO/8a/CViWma+MiBOATwCnd/gYHdPLm4y8AkUaHgtZqul0qL8a+A5AZt4REcd1eP/PGsa7PiV1Tynzui/au3dvx3YWEZcDV2fm9fXPDwMrM9Nr6iRpAXT6jtIngbHG/RvokrRwOh3qtwGvA6hr6nd3eP+SpBY6XVO/BjglIr4HLALe1uH9S5Ja6GhNXZLUW87SKEkFMdQlqSCGuiQVpOh7yCPiSOD7wKGZ+XSv29MLEbEC+O/AIcDBwPmZeXtvW7Ww+mH6in4RESPAFcARwFJgdWZ+u6eN6rGI+BVgE3BKZt7X6/YcqGJH6hFxCNU0BWVMAtO+84EbM/Mk4PeAz/a2OT3x7PQVwIep3hfD6gzgscw8EXgt8Oc9bk9P1R9yXwB29rotnVJkqEfEIuCLwAXAjh43p9c+SfWmheovs2H8i+U501cAXZu+YgB8A7i4Xl4EDPvNgZcAa4D/2+uGdMrAl18i4j8C75u2+iHgq5n5o4joQat6Y4a+eFtmboyIw6jKMO9d+Jb13CHAEw0/T0bEkmG82zkznwKIiDHgKuCi3raodyLi94Atmbk+Iv6w1+3plCKvU4+IzcDf1z+eANyZmf+ih03qqYh4CfBV4P1T8/IMk4i4FLgjM79e//z3mfmPe9ysnomIw6luFPxcZl7R6/b0SkT8NbC3/vdS4CfAGzPz0Z427AAN/Ei9mcx84dRyRDwI9P7rSHokIn6T6k/uf5eZP+p1e3rkNuANwNeHffqKiDgU2AC8JzNv7HV7eqlxoBcRNwPvHPRAh0JDXc/xUWAZ8Om6FPVEZvbtHPdd4vQV+1wAjAMXR8RUbf20zCzmROGwK7L8IknDqsirXyRpWBnqklQQQ12SCmKoS1JBDHVJKoihLkkFMdQlqSD/H1BAAWG9AhZnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1c139b00>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.1006\n",
      "percentage false H0 rejected at alpha = 0.05:  0.2328\n"
     ]
    }
   ],
   "source": [
    "\n",
    "t_stat = []\n",
    "p_val = []\n",
    "t_stat2 = []\n",
    "p_val2 = []\n",
    "n = 12\n",
    "MC = 5000\n",
    "for i in range(MC):\n",
    "    returns_1 = np.random.standard_t(2, n) + 1\n",
    "    returns_2 = np.random.standard_t(2, n) + 1\n",
    "    returns_3 = np.random.standard_t(2, n) + 0.1\n",
    "    \n",
    "    outcome_tn = hypothesis.jobson_korkie(returns_1, returns_2)\n",
    "    t_stat.append(outcome_tn['t_statistic'])\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "    outcome_fn = hypothesis.jobson_korkie(returns_1, returns_3)\n",
    "    t_stat2.append(outcome_fn['t_statistic'])\n",
    "    p_val2.append(outcome_fn['p_value'])\n",
    "\n",
    "    \n",
    "plt.hist(t_stat, bins=50, alpha=0.5)\n",
    "plt.hist(t_stat2, bins=50, alpha=0.5)\n",
    "plt.title('t-stat histogram: true null vs. false null')\n",
    "plt.xlabel = 't-statistic'\n",
    "plt.ylabel = 'frequency'\n",
    "plt.show()\n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)\n",
    "\n",
    "p_val2 = np.array(p_val2)\n",
    "rejection_pct2 = len(p_val2[p_val2<alpha])/n\n",
    "print(f'percentage false H0 rejected at alpha = {alpha}: ', rejection_pct2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multivariate_t_rvs(m, S, df=np.inf, n=1):\n",
    "    '''generate random variables of multivariate t distribution\n",
    "    Parameters\n",
    "    ----------\n",
    "    m : array_like\n",
    "        mean of random variable, length determines dimension of random variable\n",
    "    S : array_like\n",
    "        square array of covariance  matrix\n",
    "    df : int or float\n",
    "        degrees of freedom\n",
    "    n : int\n",
    "        number of observations, return random array will be (n, len(m))\n",
    "    Returns\n",
    "    -------\n",
    "    rvs : ndarray, (n, len(m))\n",
    "        each row is an independent draw of a multivariate t distributed\n",
    "        random variable\n",
    "    '''\n",
    "    m = np.asarray(m)\n",
    "    d = len(m)\n",
    "    if df == np.inf:\n",
    "        x = 1.\n",
    "    else:\n",
    "        x = np.random.chisquare(df, n)/df\n",
    "    z = np.random.multivariate_normal(np.zeros(d),S,(n,))\n",
    "    return m + z/np.sqrt(x)[:,None]   # same output format as random.multivariate_normal\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1be7b908>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.3462\n"
     ]
    }
   ],
   "source": [
    "\n",
    "t_stat = []\n",
    "p_val = []\n",
    "n = 120\n",
    "MC = 5000\n",
    "for i in range(MC):\n",
    "    returns =  multivariate_t_rvs([2, 2], np.array([[1, 0.5], [0.5, 1]]), df=2, n=n)\n",
    "    returns_1  = returns[:,0]\n",
    "    returns_2 = returns[:,1]\n",
    "    \n",
    "    outcome_tn = hypothesis.jobson_korkie(returns_1, returns_2)\n",
    "    t_stat.append(outcome_tn['t_statistic'])\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "\n",
    "plt.hist(t_stat, bins=50, alpha=0.5)\n",
    "plt.title('t-stat histogram: true null')\n",
    "plt.xlabel = 't-statistic'\n",
    "plt.ylabel = 'frequency'\n",
    "plt.show()\n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ledoit and Wolf Bootstrap\n",
    "\n",
    "Ledoit and Wolf (2008) suggest to use the bootstrap to better approximate the quantiles of the t statistic in finite samples.\n",
    "Assuming returns are iid i.e. $\\left\\{\\boldsymbol{R}_{t}\\right\\}_{t=1}^{T}=\\left\\{\\left(R_{p t}, R_{q t}\\right)^{\\prime}\\right\\}$\n",
    "\n",
    "#### Step 1\n",
    "\n",
    "From the full sample compute \n",
    "\n",
    "$$\\widehat{\\Delta}=\\widehat{\\theta}_{p}-\\widehat{\\theta}_{q}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\widehat{\\sigma}_{\\widehat{\\Delta}}=\\sqrt{\\boldsymbol{\\widehat{\\delta}} \\boldsymbol{\\widehat{V}} \\boldsymbol{\\widehat{\\delta}^{\\prime}} / T}$$\n",
    "\n",
    "with\n",
    "\n",
    "$$\\begin{aligned} \\widehat{\\boldsymbol{\\delta}} &=\\left(\\begin{array}{cccc}{\\frac{\\partial \\Delta}{\\partial \\mu_{p}}} & {\\frac{\\partial \\Delta}{\\partial \\mu_{q}}} & {\\frac{\\partial \\Delta}{\\partial \\sigma_{p}^{2}}} & {\\frac{\\partial \\Delta}{\\partial \\sigma_{q}^{2}}}\\end{array}\\right) \\\\ &=\\left(\\begin{array}{ccc}{\\frac{1}{\\widehat{\\sigma}_{p}}} & {-\\frac{1}{\\widehat{\\sigma}_{q}}} & {-\\frac{\\widehat{\\mu}_{p}}{2 \\widehat{\\sigma}_{p}^{3}}} & {\\frac{\\widehat{\\mu}_{q}}{2 \\widehat{\\sigma}_{q}^{3}}}\\end{array}\\right) \\end{aligned}$$\n",
    "\n",
    "and \n",
    "\n",
    "$$\\widehat{\\boldsymbol{V}}=T^{-1} \\sum_{t=1}^{T} \\widehat{\\boldsymbol{g}}_{t} \\widehat{\\boldsymbol{g}}_{t}^{\\prime}$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\\widehat{\\boldsymbol{g}}_{t}=\\left(\\begin{array}{c}{R_{t, p}-\\widehat{\\mu}_{p}} \\\\ {R_{t, q}-\\widehat{\\mu}_{q}} \\\\ {\\left(R_{p, t}-\\widehat{\\mu}_{p}\\right)^{2}-\\widehat{\\sigma}_{p}^{2}} \\\\ {\\left(R_{q, t}-\\widehat{\\mu}_{q}\\right)^{2}-\\widehat{\\sigma}_{q}^{2}}\\end{array}\\right)$$\n",
    "\n",
    "Then the t-statistic is \n",
    "\n",
    "$$t_{\\widehat{\\Delta}}=\\widehat{\\Delta} / \\widehat{\\sigma}_{\\widehat{\\Delta}}$$\n",
    "\n",
    "#### Step 2\n",
    "\n",
    "Draw a bootstrap sample $\\left\\{\\boldsymbol{R}_{t}^{*}\\right\\}_{t=1}^{T}=\\left\\{\\left(R_{p, t}^{*}, R_{q, t}^{*}\\right)^{\\prime}\\right\\}_{t=1}^{T}$ from the empirical distribution of the sample, i.e. the bivariate distribution which puts probability $1/T$ on each observed return pair $\\left(R_{p, t}, R_{q, t}\\right)^{\\prime}, t=1, \\ldots, T$.\n",
    "\n",
    "#### Step 3\n",
    "Compute a bootstrap replication of the t-statistic, i.e. from the bootstrap\n",
    "sample, compute the statistics of step 1\n",
    "\n",
    "$$\\widehat{\\Delta}^{\\star}=\\widehat{\\theta}_{p}^{\\star}-\\widehat{\\theta}_{q}^{\\star}$$\n",
    "\n",
    "\n",
    "$$\\widehat{\\sigma}_{\\widehat{\\Delta}^{\\star}}^{\\star}=\\sqrt{\\widehat{\\boldsymbol{\\delta}}^{\\star} \\widehat{\\boldsymbol{V}}^{\\star} \\widehat{\\boldsymbol{\\delta}}^{\\star^{\\prime}}} / T$$\n",
    "\n",
    "\n",
    "$$t_{\\widehat{\\Delta}^{\\star}}^{\\star}=\\frac{\\widehat{\\Delta}^{\\star}-\\widehat{\\Delta}}{\\widehat{\\sigma}_{\\widehat{\\Delta}^{\\star}}^{\\star}}$$\n",
    "\n",
    "#### Step 4\n",
    "Repeat steps 2 and 3 $B$ times, thus producing a sample of $B$ bootstrap replications\n",
    "$\\left\\{t_{\\widehat{\\Delta}^{\\star}}^{\\star, b}\\right\\}_{b=1, \\ldots, B}=\\left\\{t_{\\widehat{\\Delta}^{\\star}}^{\\star, 1}, \\ldots, t_{\\widehat{\\Delta}^{\\star}}^{\\star, B}\\right\\}$\n",
    "\n",
    "#### Step 5\n",
    "Let $z_{\\left|t^{\\star}\\right|, 1-\\alpha}^{\\star}$ denote the $(1-\\alpha)$-quantile of \n",
    "$\\left\\{\\left|t_{\\widehat{\\Delta}^{\\star}}^{\\star, b}\\right|\\right\\}_{b=1, \\ldots, B}=\\left\\{\\left|\\widehat{\\Delta}^{\\star, b}-\\widehat{\\Delta}\\right| / \\widehat{\\sigma}_{\\widehat{\\Delta}^{\\star}}^{\\star, b}\\right\\}_{b=1, \\ldots, B}$\n",
    "\n",
    "Then the symmetric bootstrap $(1-\\alpha)$-confidence interval is \n",
    "$$\\widehat{\\Delta} \\pm z_{\\left|t^{\\star}\\right|, 1-\\alpha}^{\\star} \\widehat{\\sigma}_{\\widehat{\\Delta}}$$\n",
    "\n",
    "with $\\widehat{\\sigma}_{\\widehat{\\Delta}}$ from step 1.\n",
    "\n",
    "The null $H_{0} : \\Delta=\\theta_{p}-\\theta_{q}=0$ is rejected at level $\\alpha$ if the confidence interval does not contain zero.\n",
    "\n",
    "The p-value is $$p=\\frac{\\#\\left\\{\\left|t_{\\widehat{\\Delta}^{\\star}}^{\\star, b}\\right| \\geq\\left|t_{\\widehat{\\Delta}}\\right|\\right\\}+1}{B+1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.052\n",
      "percentage false H0 rejected at alpha = 0.05:  0.14\n"
     ]
    }
   ],
   "source": [
    "p_val = []\n",
    "p_val2 = []\n",
    "\n",
    "n = 12*10\n",
    "MC = 500\n",
    "for i in range(MC):\n",
    "    returns_1 = np.random.normal(0, 1, n)\n",
    "    returns_2 = np.random.normal(0, 1, n)\n",
    "    returns_3 = np.random.normal(0.1, 1, n)\n",
    "    \n",
    "    outcome_tn = hypothesis.ledoit_wolf_bootstrap(returns_1, returns_2, n_bootstraps=100, alpha=0.05)\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "    outcome_fn = hypothesis.ledoit_wolf_bootstrap(returns_1, returns_3, n_bootstraps=100, alpha=0.05)\n",
    "    p_val2.append(outcome_fn['p_value'])\n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)\n",
    "\n",
    "p_val2 = np.array(p_val2)\n",
    "rejection_pct2 = len(p_val2[p_val2<alpha])/n\n",
    "print(f'percentage false H0 rejected at alpha = {alpha}: ', rejection_pct2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.054\n",
      "percentage false H0 rejected at alpha = 0.05:  0.084\n"
     ]
    }
   ],
   "source": [
    "p_val = []\n",
    "p_val2 = []\n",
    "\n",
    "n = 12*10\n",
    "MC = 500\n",
    "for i in range(MC):\n",
    "    returns_1 = np.random.standard_t(2, n) \n",
    "    returns_2 = np.random.standard_t(2, n) \n",
    "    returns_3 = np.random.standard_t(2, n) + 0.1\n",
    "\n",
    "    outcome_tn = hypothesis.ledoit_wolf_bootstrap(returns_1, returns_2, n_bootstraps=500, alpha=0.05)\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "    outcome_fn = hypothesis.ledoit_wolf_bootstrap(returns_1, returns_3, n_bootstraps=500, alpha=0.05)\n",
    "    p_val2.append(outcome_fn['p_value'])\n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)\n",
    "\n",
    "p_val2 = np.array(p_val2)\n",
    "rejection_pct2 = len(p_val2[p_val2<alpha])/n\n",
    "print(f'percentage false H0 rejected at alpha = {alpha}: ', rejection_pct2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [04:49<00:00,  6.91it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.1015\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from  tqdm import tqdm\n",
    "\n",
    "\n",
    "p_val = []\n",
    "\n",
    "n = 12*10\n",
    "MC = 2000\n",
    "for i in tqdm(range(MC)):\n",
    "    returns =  multivariate_t_rvs([1, 1], np.array([[1, 0.5], [0.5, 1]]), df=2, n=n)\n",
    "    returns_1  = returns[:,0]\n",
    "    returns_2 =returns[:,1]\n",
    "\n",
    "    outcome_tn = hypothesis.ledoit_wolf_bootstrap(returns_1, returns_2, n_bootstraps=500, alpha=0.05, b=12)\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1c1395c0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(p_val, alpha=0.5, bins=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [01:10<00:00,  7.10it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.094\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1c8256d8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from src import hypothesis\n",
    "from  tqdm import tqdm\n",
    "from statsmodels.tsa.arima_process import ArmaProcess\n",
    "\n",
    "AR = ArmaProcess((1,-0.3,),(1,))\n",
    "sim1 = AR.generate_sample(nsample=n)\n",
    "sim2 = AR.generate_sample(nsample=n)\n",
    "\n",
    "plt.plot(sim1)\n",
    "plt.plot(sim2)\n",
    "\n",
    "p_val = []\n",
    "\n",
    "n = 12*10\n",
    "MC = 500\n",
    "for i in tqdm(range(MC)):\n",
    "    returns_1 = AR.generate_sample(nsample=n)\n",
    "    returns_2 = AR.generate_sample(nsample=n)\n",
    "\n",
    "    outcome_tn = hypothesis.ledoit_wolf_bootstrap(returns_1, returns_2, n_bootstraps=500, alpha=0.05, b=12)\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [00:50<00:00,  9.92it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.146\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1c8252b0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from src import hypothesis\n",
    "from  tqdm import tqdm\n",
    "from statsmodels.tsa.arima_process import ArmaProcess\n",
    "\n",
    "AR = ArmaProcess((1,-0.3,),(1,))\n",
    "sim1 = AR.generate_sample(nsample=n)\n",
    "sim2 = AR.generate_sample(nsample=n)\n",
    "\n",
    "plt.plot(sim1)\n",
    "plt.plot(sim2)\n",
    "\n",
    "p_val = []\n",
    "\n",
    "n = 12*10\n",
    "MC = 500\n",
    "for i in tqdm(range(MC)):\n",
    "    returns_1 = AR.generate_sample(nsample=n)\n",
    "    returns_2 = AR.generate_sample(nsample=n)\n",
    "\n",
    "    outcome_tn = hypothesis.ledoit_wolf_bootstrap(returns_1, returns_2, n_bootstraps=500, alpha=0.05, b=1)\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:01<00:00, 2711.61it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "percentage true H0 rejected at alpha = 0.05:  0.1596\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1c79b4a8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from src import hypothesis\n",
    "from  tqdm import tqdm\n",
    "from statsmodels.tsa.arima_process import ArmaProcess\n",
    "\n",
    "AR = ArmaProcess((1,-0.3,),(1,))\n",
    "sim1 = AR.generate_sample(nsample=n)\n",
    "sim2 = AR.generate_sample(nsample=n)\n",
    "\n",
    "plt.plot(sim1)\n",
    "plt.plot(sim2)\n",
    "\n",
    "p_val = []\n",
    "\n",
    "n = 12*10\n",
    "MC = 5000\n",
    "for i in tqdm(range(MC)):\n",
    "    returns_1 = AR.generate_sample(nsample=n)\n",
    "    returns_2 = AR.generate_sample(nsample=n)\n",
    "\n",
    "    outcome_tn = hypothesis.jobson_korkie(returns_1, returns_2)\n",
    "    p_val.append(outcome_tn['p_value'])\n",
    "    \n",
    "\n",
    "alpha = 0.05\n",
    "n = len(p_val)\n",
    "p_val = np.array(p_val)\n",
    "rejection_pct = len(p_val[p_val<alpha])/n\n",
    "print(f'percentage true H0 rejected at alpha = {alpha}: ', rejection_pct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}