{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# the Phat Distribution #\n", "\n", "## In Search of Two Tails ##\n", "\n", "Many phenomena are understood to exhibit fat tails: insurance losses, wealth distribution, [rainfall](https://hess.copernicus.org/articles/17/851/2013/hess-17-851-2013.pdf), etc. These are one-tailed phenomenom (usually bounded by zero) for which many potential distributions are applicable: Weibull, Levy, Frechet, Paretos I-IV, the generalized Pareto, the Extreme Value distribution etc.\n", "\n", "For two-tailed phenomenon, such as financial asset returns, there are only two, and decidedly imperfect, candidates:\n", "\n", "+ Levy-Stable Distribion \n", " + the Levy-Stable is bounded in the range $\\alpha \\in (0, 2]$ with $\\alpha = 2$ being the Gaussian distribution. Thus, the Levy-Stable *only* exhibits fat tails with tail index $\\alpha < 2$ and undefined variance.\n", " + Unfortunately, equity returns in particular are known to have both a [second moment](https://fan.princeton.edu/fan/FinEcon/chap1.pdf) AND [fat tails](https://papers.tinbergen.nl/98017.pdf), meaning $\\alpha > 2$, which the Levy-Stable does not support.\n", "+ Student's T\n", " + the Student's T is the most popular distribution for modelling asset returns as it does exhibit fat tails and it is power law-*like*.\n", " + unfortunately, the Student's T only *tends* toward a power law in the extreme tails and so can still heavily underestimate unlikely events.\n", " + also, the Student's T is symmetric and cannot accomodate different tail indices in either tail. Nor can the skewed Student's T, which is asymmetric, but accepts only a single tail index.\n", "\n", "*we should note that an asymmetric Student's T has* [been proposed](https://www.sciencedirect.com/science/article/abs/pii/S0304407610000266) *to address this.*\n", "\n", "As a result of the seeming intractability of this problem, academics and risk managers often opt for a non-parametric or \"tail-only\" approach.\n", "\n", "+ For instance, [Papenbrock et al. 2016](references.ipynb) and many others use the generalized Pareto to focus solely on VaR.\n", "+ [Nystrom and Skoglund (2002)](references.ipynb) proposed two-pareto tails with a Gaussian kernel density in the body.\n", "\n", "These models are useful, no doubt, but perhaps we can do better." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## the Double Pareto ##\n", "\n", "The simplest approach to two-tailed power laws is two combine two Paretos, reflecting one so that it is left-tailed.\n", "\n", "*Note: going forward we will generally use the term \"Pareto\" to refer to the \"Generalized Pareto\"*" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2\n", "\n", "import seaborn as sns; sns.set(style = 'whitegrid')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true, "tags": [ "hide_input" ] }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import phat as ph\n", "\n", "dbl = ph.dists.DBLGP()\n", "shape = 2\n", "x = np.linspace(-10, 10,1000)\n", "\n", "fig, (ax1,ax2) = plt.subplots(1,2,figsize=(18,6))\n", "\n", "ax1.plot(x, dbl.cdf(x, shape))\n", "ax2.plot(x, dbl.pdf(x, shape))\n", "\n", "ax2.set_xlabel('x')\n", "ax2.set_ylabel('P(X" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy.stats as scist\n", "\n", "fig, (ax1, ax2) = plt.subplots(1,2,figsize=(18,6))\n", "\n", "xp = np.linspace(0,10,500)\n", "\n", "ax1.plot(xp, scist.genpareto.cdf(xp, shape), label='Right Pareto')\n", "ax1.plot(-xp, scist.genpareto.sf(xp, shape), label='Left Pareto')\n", "ax1.plot(x, dbl.cdf(x, shape), c='C4', label='DBLGP')\n", "\n", "qs = np.linspace(0,1,200)\n", "ax2.plot(qs, scist.genpareto.ppf(qs, shape), label='Right Pareto')\n", "ax2.plot(qs, -scist.genpareto.isf(qs, shape), label='Left Pareto')\n", "ax2.plot(qs, dbl.ppf(qs, shape), c='C4', label='DBLGP')\n", "\n", "ax2.set_yscale('symlog')\n", "ax2.set_ylim((-10000,10000))\n", "\n", "ax1.legend()\n", "ax2.legend()\n", "\n", "ax1.set_xlabel('x')\n", "ax1.set_ylabel('P(X" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import yfinance as yf\n", "\n", "sp = yf.download('^GSPC')\n", "sp_ret = sp.Close.pct_change()[1:]\n", "\n", "dbl = ph.dists.DBLGP()\n", "shape = .18\n", "loc = .005\n", "scale = .006\n", "\n", "x = np.linspace(-.1, .1, 101)\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(10,6))\n", "\n", "\n", "ax.plot(x, dbl.pdf(x, shape, scale=scale), lw=2, label='Double Pareto')\n", "ax.plot(x, scist.t(1/.18, scale=.006).pdf(x), lw=2, c='C2', label='T')\n", "counts, bins, _ = ax.hist(\n", " sp_ret, \n", " bins=np.linspace(-.1,.1,101), \n", " color='C1',\n", " density=True,\n", " alpha=.5,\n", " label='S&P 500 Daily Returns'\n", ")\n", "\n", "ax.set_title(\"Double Pareto vs Student's T\")\n", "\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, the double Pareto is a tighter fit in the tails, but it underestimates the shoulders and significantly overestimates the peak." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## the CarBen Hybrid ##\n", "\n", "As we saw above, the double Pareto performs well in the tails but is a poor model of returns in the body. One approach to addressing this issue is to just ignore it. Taleb would say all the impact is in the tails anyway, so the action in the body can simply be ignored. Fine, but if we can improve the performance in the body, this *should* improve our modelling.\n", "\n", "Another approach is to combine two distributions: one for the body and one for the tail. [Carreau and Bengio (2009)](references.ipynb) propose an approach for grafting a generalized Pareto distribution onto the tail of a Gaussian. The resulting Carben hybrid is a one-tailed distribution, with properties as follows:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. described by 5 parameters\n", " + $\\mu$ and $\\sigma$ for the Gaussian\n", " + $a$, $b$, and $\\xi$ representing location, scale, and shape of the Pareto tail\n", " + as we'll see, two necessary equalities reduces the number of free parameters to 3\n", "\n", "2. the junction point between the two distributions is the location parameter, $m$, of the Pareto tail, such that:\n", "\n", "$$ \n", "f(X=a) = g(X=0) \n", "$$\n", "\n", "where:\n", "\n", "$$\n", "f(X) \\text{ is Gaussian}, g(X) \\text{ is Pareto}, and\n", "\\\\a = \\text{location of Pareto tail}\n", "$$\n", "\n", "3. the derivatives of each distribution at the junction point are also equal:\n", "\n", "$$ \n", "f'(X=a) = g'(X=0) \n", "$$\n", "\n", "4. from (2) and (3) above, the location and scale parameters of the Pareto are (see Carreau for derivation):\n", "\n", "$$\n", "b = \\frac{\\sigma(1 + \\xi)}{\\sqrt{W(z)}}\n", "\\\\a = \\mu + \\sigma\\sqrt{W(z)}\n", "$$\n", "where:\n", "$$\n", "W(z) \\text{ is the Lambert W function, and } z = \\omega e^{\\omega}\n", "$$\n", "\n", "So, we have just the following free parameters to estimate:\n", "\n", "+ for the gaussian: $\\mu$ and $\\sigma$\n", "+ for the generalized Pareto: $\\xi$, which is $= 1/\\alpha$, or the inverse of the tail index \n", "\n", "5. a scaling factor, $1 / \\gamma$, is applied to both distributions such that the probabilities sum to 1. This scaling is also equivalent to the survival function in tail:\n", "\n", "$$ 1 / \\gamma = P(X > a) $$\n", "\n", "$\\gamma$ is computed directly as detailed in [Carreau and Bengio (2008)](#references.ipynb):\n", "\n", "$$ \\gamma = 1 + \\frac{1}{2}(1 + Erf(\\sqrt{W(z) / 2})) $$\n", "\n", "where: $$ Erf \\text{ is the error function}$$\n", "\n", "Thus, the PDF for the Carben is given as:\n", "\n", "$$\n", "f_{\\textit{right}}(x) = \\left\\{ \\begin{array}{ll}\n", " \\frac{1}{\\gamma} f_{\\mu,\\sigma}(x) & \\text{if } x\\leq a \\\\\n", " \\frac{1}{\\gamma} g_{\\xi,a,b}(x) & \\text{if } x > a\\\\\n", "\\end{array} \\right.\n", "$$\n", "where: \n", "\n", "$$f_{\\mu,\\sigma} \\text{ is the Guassian and } g_{\\xi,a,b} \\text{ is the generalized Pareto}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we show the statistical functions for the Carben with parameters:\n", "\n", "+ $\\xi = 1/4$ (equivalent to $\\alpha = 4$)\n", "+ $a = 0$\n", "+ $b = 1$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [ "hide_input" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "shape, mean, sig = 1/4, 0, 1\n", "x = np.linspace(-3, 5, 1000)\n", "dist = ph.dists.CarBenHybrid(shape, mean, sig)\n", "\n", "fig, ((ax1,ax2), (ax3, ax4)) = plt.subplots(2,2,figsize=(18,12))\n", "\n", "tailprops = dict(ls='--', lw=2, alpha=.5)\n", "ax1.plot(x, dist.pdf(x), label='CarBen')\n", "ax1.plot(x, dist.body.pdf(x), label='Guassian', **tailprops)\n", "ax1.plot(x[x>dist.a], dist.tail.pdf(x[x>dist.a]), label='Pareto', **tailprops)\n", "\n", "paramtxt = r'$\\mu, \\sigma$ = ' + f'{dist.mu:.0f}, {dist.sig:.0f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\epsilon$ = ' + f'{dist.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$a$ = ' + f'{dist.a:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$b$ = ' + f'{1 / dist.b:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\alpha$ = ' + f'{1 / dist.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\gamma = $' + f'{dist.gamma:.2f}'\n", "ax1.text(\n", " .02,.69, paramtxt,\n", " transform=ax1.transAxes,\n", " bbox=dict(boxstyle='round', ec='.8', fc='w')\n", ")\n", "\n", "txt = 'Junction Point\\n' + r'$x = a$' \n", "arrowprops = dict(\n", " arrowstyle=\"-|>\", connectionstyle=\"arc3,rad=-.2\", fc='black', ec='black'\n", ")\n", "ax1.annotate(\n", " txt, xy=(dist.a, dist.tail.pdf(dist.a)), xytext=(dist.a*4, dist.tail.pdf(dist.a)),\n", " arrowprops=arrowprops\n", ")\n", "ax1.annotate(\n", " txt, xy=(dist.a, dist.pdf(dist.a)), xytext=(dist.a*4, dist.tail.pdf(dist.a)),\n", " arrowprops=arrowprops\n", ")\n", "\n", "txt = r'$P(X > m) = \\frac{1}{\\gamma}$ = ' + f'{1 / dist.gamma:.2f}'\n", "ax1.text(\n", " dist.a*2, dist.pdf(dist.a)/8, txt,\n", " bbox=dict(boxstyle='square', ec='w', fc='w', alpha=.8)\n", ")\n", "ax1.fill_between(x[x>dist.a], dist.pdf(x[x>dist.a]), alpha=.8)\n", "ax1.grid(False)\n", "ax2.plot(x, dist.cdf(x), label='CarBen')\n", "ax2.plot(x, dist.body.cdf(x), label='Guassian', **tailprops)\n", "ax2.plot(x, dist.tail.cdf(x), label='Pareto', **tailprops)\n", "\n", "ax3.plot(x, dist.sf(x), label='CarBen')\n", "ax3.plot(x, dist.body.sf(x), label='Guassian', **tailprops)\n", "ax3.plot(x, dist.tail.sf(x), label='Pareto', **tailprops)\n", "\n", "q = np.linspace(0,.99,101)\n", "ax4.plot(q, dist.ppf(q), label='CarBen')\n", "ax4.plot(q, dist.body.ppf(q), label='Guassian', **tailprops)\n", "ax4.plot(q, dist.tail.ppf(q), label='Pareto', **tailprops)\n", "\n", "ax1.legend()\n", "ax2.legend()\n", "ax3.legend()\n", "ax4.legend()\n", "\n", "ax1.set_xlabel('x')\n", "ax1.set_ylabel('f(x)', loc='top', rotation='horizontal')\n", "\n", "ax2.set_xlabel('x')\n", "ax2.set_ylabel('P(Xx)', loc='top', rotation='horizontal')\n", "\n", "ax4.set_xlabel('P(X" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5, 3, 1000)\n", "\n", "dist = ph.dists.CarBenHybrid(-shape, mean, sig)\n", "\n", "fig, ((ax1,ax2), (ax3, ax4)) = plt.subplots(2,2,figsize=(18,12))\n", "\n", "tailprops = dict(ls='--', lw=2, alpha=.5)\n", "ax1.plot(x, dist.pdf(x), label='CarBen')\n", "ax1.plot(x, dist.body.pdf(x), label='Guassian', **tailprops)\n", "ax1.plot(x[x\", connectionstyle=\"arc3,rad=.4\", fc='black', ec='black'\n", ")\n", "ax1.annotate(\n", " txt, xy=(dist.a, dist.tail.pdf(-dist.a)), xytext=(dist.a*6, dist.tail.pdf(-dist.a)),\n", " arrowprops=arrowprops\n", ")\n", "ax1.annotate(\n", " txt, xy=(dist.a, dist.pdf(-dist.a)), xytext=(dist.a*6, dist.tail.pdf(-dist.a)),\n", " arrowprops=arrowprops\n", ")\n", "txt = r'$P(x < a) = \\frac{1}{\\gamma}$ = ' + f'{1 / dist.gamma:.2f}'\n", "ax1.text(\n", " dist.a*8, dist.pdf(dist.a)/8, txt,\n", " bbox=dict(boxstyle='square', ec='w', fc='w', alpha=.8)\n", ")\n", "ax1.fill_between(x[xx)', loc='top', rotation='horizontal')\n", "\n", "ax4.set_xlabel('x')\n", "ax4.set_ylabel('P(X" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ((ax1,ax2), (ax3,ax4)) = plt.subplots(2,2,figsize=(18,12))\n", "\n", "ax1.plot(x, dist1.pdf(x), alpha=.5)\n", "x_body = np.linspace(dist1.left.a, dist1.right.a, 100)\n", "x_left = np.linspace(x[0], dist1.left.a, 100)\n", "x_right = np.linspace(dist1.right.a, x[-1], 100)\n", "ax1.plot(x_body, dist1.pdf(x_body), c='C1', ls='--', label='Gaussian Body')\n", "ax1.plot(x_left, dist1.pdf(x_left), c='C2', ls='--', label='Left Paretian')\n", "ax1.plot(x_right, dist1.pdf(x_right), c='C4', ls='--', label='Right Paretian')\n", "\n", "ax1.axvline(\n", " dist1.left.a, .825, .925, \n", " c='r', lw=1, label=r'$x = a_l$')\n", "ax1.axvline(dist1.right.a, .825, .925, c='r', lw=1, label=r'$x = a_r$')\n", "\n", "paramtxt = 'Body'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\mu, \\sigma$ = ' + f'{dist1.mu:.0f}, {dist1.sig:.0f}'\n", "\n", "ax1.text(\n", " .5, .5, paramtxt, ha='center',\n", " transform=ax1.transAxes,\n", " bbox=dict(boxstyle='round', ec='.8', fc='w')\n", ")\n", "\n", "paramtxt = r'Left Tail$_{}$'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\epsilon_{l}$ = ' + f'{dist1.xi_l:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$a_l$ = ' + f'{dist1.left.a:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$b_l$ = ' + f'{1 / dist1.left.b:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\alpha_l$ = ' + f'{1 / dist1.left.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\gamma_l = $' + f'{dist1.right.gamma:.2f}'\n", "\n", "ax1.text(\n", " .02,.3, paramtxt,\n", " transform=ax1.transAxes,\n", " bbox=dict(boxstyle='round', ec='.8', fc='w')\n", ")\n", "paramtxt = r'Right Tail$_{}$'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\epsilon_r$ = ' + f'{dist1.right.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$a_r$ = ' + f'{dist1.right.a:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$b_r$ = ' + f'{1 / dist1.right.b:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\alpha_r$ = ' + f'{1 / dist1.right.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\gamma_r = $' + f'{dist1.right.gamma:.2f}'\n", "\n", "ax1.text(\n", " .98,.3, paramtxt, ha='right',\n", " transform=ax1.transAxes,\n", " bbox=dict(boxstyle='round', ec='.8', fc='w')\n", ")\n", "ax1.set_xlabel('x')\n", "ax1.set_ylabel('f(x)', loc='top', rotation='horizontal')\n", "\n", "ax1.legend()\n", "ax1.set_title('PDF - Phat')\n", "\n", "tailprops = dict(ls='--', lw=2, alpha=.5)\n", "ax2.plot(x, dist1.cdf(x), label='Phat')\n", "ax2.plot(x, dist1.left.cdf(x), label='Left CarBen', **tailprops)\n", "ax2.plot(x, dist1.right.cdf(x), label='Right CarBen', **tailprops)\n", "\n", "ax3.plot(x, dist1.sf(x), label='Phat')\n", "ax3.plot(x, dist1.left.sf(x), label='Left CarBen', **tailprops)\n", "ax3.plot(x, dist1.right.sf(x), label='Right CarBen', **tailprops)\n", "\n", "q = np.linspace(0,.999,1000)\n", "ax4.plot(q, dist1.ppf(q), label='Phat')\n", "ax4.plot(q, dist1.left.ppf(q), label='Left CarBen', **tailprops)\n", "ax4.plot(q, dist1.right.ppf(q), label='Right CarBen', **tailprops)\n", "\n", "ax1.legend()\n", "ax2.legend()\n", "ax3.legend()\n", "ax4.legend()\n", "\n", "ax1.set_xlabel('x')\n", "ax1.set_ylabel('f(x)', loc='top', rotation='horizontal')\n", "\n", "ax2.set_xlabel('x')\n", "ax2.set_ylabel('P(Xx)', loc='top', rotation='horizontal')\n", "\n", "ax4.set_xlabel('P(X" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mean, sig = -5, 2\n", "x = np.linspace(-10+mean, 10+mean, 100)\n", "shape_l1, shape_r = 1/2, 1/2\n", "dist1 = ph.Phat(mean, sig, shape_l1, shape_r)\n", "shape_l2, shape_r = 1/2, 1/20\n", "dist2 = ph.Phat(mean, sig, shape_l2, shape_r,)\n", "\n", "fig, ((ax1,ax2), (ax3,ax4)) = plt.subplots(2,2,figsize=(18,12))\n", "\n", "ax1.plot(x, dist1.pdf(x), label='Fatter Right')\n", "ax1.plot(x, dist2.pdf(x), label='Thinner Right')\n", "\n", "paramtxt = r'Fatter Right$_{}$'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\epsilon_{l}$ = ' + f'{dist1.right.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$a_l$ = ' + f'{dist1.right.a:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$b_l$ = ' + f'{1 / dist1.right.b:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\alpha_l$ = ' + f'{1 / dist1.right.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\gamma_l = $' + f'{dist1.right.gamma:.2f}'\n", "\n", "ax1.text(\n", " .02,.975, paramtxt, va='top',\n", " transform=ax1.transAxes,\n", " bbox=dict(boxstyle='round', ec='.8', fc='w')\n", ")\n", "paramtxt = r'Thinner Right$_{}$'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\epsilon_{l}$ = ' + f'{dist2.right.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$a_l$ = ' + f'{dist2.right.a:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$b_l$ = ' + f'{1 / dist2.right.b:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\alpha_l$ = ' + f'{1 / dist2.right.xi:.2f}'\n", "paramtxt += '\\n'\n", "paramtxt += r'$\\gamma_l = $' + f'{dist2.right.gamma:.2f}'\n", "\n", "ax1.text(\n", " .02,.2, paramtxt, va='bottom',\n", " transform=ax1.transAxes,\n", " bbox=dict(boxstyle='round', ec='.8', fc='w')\n", ")\n", "\n", "ax2.plot(x, dist1.cdf(x))\n", "ax2.plot(x, dist1.cdf(x))\n", "\n", "ax3.plot(x, dist1.sf(x))\n", "ax3.plot(x, dist2.sf(x))\n", "\n", "q = np.linspace(0,.999,1000)\n", "ax4.plot(q, dist1.ppf(q))\n", "ax4.plot(q, dist2.ppf(q))\n", "\n", "ax1.legend()\n", "\n", "ax1.set_xlabel('x')\n", "ax1.set_ylabel('f(x)', loc='top', rotation='horizontal')\n", "\n", "ax2.set_xlabel('x')\n", "ax2.set_ylabel('P(Xx)', loc='top', rotation='horizontal')\n", "\n", "ax4.set_xlabel('x')\n", "ax4.set_ylabel('P(X