{ "cells": [ { "cell_type": "markdown", "metadata": { "pycharm": {} }, "source": [ "\n", "*This notebook contains course material from [CBE40455](https://jckantor.github.io/CBE40455) by\n", "Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE40455.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": { "pycharm": {} }, "source": [ "\n", "< [Log-Optimal Growth and the Kelly Criterion](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/07.08-Log-Optimal-Growth-and-the-Kelly-Criterion.ipynb) | [Contents](toc.ipynb) | [Optimization in Google Sheets](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/08.00-Optimization-in-Google-Sheets.ipynb) >

\"Open

\"Download\"" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "3CtuFSz8tnBu", "pycharm": {} }, "source": [ "# Log-Optimal Portfolios" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "bpzKlSWAtnBv", "pycharm": {} }, "source": [ "This notebook demonstrates the Kelly criterion and other phenomena associated with log-optimal growth." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "fO1sP0ultnBv", "pycharm": {} }, "source": [ "## Initializations" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "Fe4021xvtnBw", "pycharm": {} }, "outputs": [], "source": [ "%matplotlib notebook\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import random" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "9jKiaekJtnBz", "pycharm": {} }, "source": [ "## Kelly's Criterion\n", "\n", "In a nutshell, Kelly's criterion is to choose strategies that maximize expected log return.\n", "\n", "$$\\max E[\\ln R]$$\n", "\n", "where $R$ is total return. As we learned, Kelly's criterion has properties useful in the context of long-term investments." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "WHpzlhzqtnB0", "pycharm": {} }, "source": [ "## Example 1. Maximizing Return for a Game with Arbitrary Odds\n", "\n", "Consider a game with two outcomes. For each \\$1 wagered, a successful outcome with probability $p$ returns $b+1$ dollars. An unsuccessful outcome returns nothing. What fraction $w$ of our portfolio should we wager on each turn of the game?\n", "\n", "![Kelly_Criterion_Fig2](https://github.com/jckantor/CBE40455/blob/master/notebooks/figures/Kelly_Criterion_Fig2.png?raw=true)\n", "\n", "There are two outcomes with returns\n", "\n", "\\begin{align*}\n", "R_1 & = w(b+1) + 1 - w = 1+wb & \\mbox{with probability }p\\\\\n", "R_2 & = 1-w & \\mbox{with probability }1-p\n", "\\end{align*}\n", "\n", "The expected log return becomes\n", "\n", "\\begin{align*}\n", "E[\\ln R] & = p \\ln R_1 + (1-p) \\ln R_2 \\\\\n", "& = p\\ln(1+ wb) + (1-p)\\ln(1-w)\n", "\\end{align*}\n", "\n", "Applying Kelly's criterion, we seek a value for $w$ that maximizes $E[\\ln R]$. Taking derivatives\n", "\n", "\\begin{align*}\n", "\\frac{\\partial E[\\ln R]}{\\partial w} = \\frac{pb}{1+w_{opt}b} - \\frac{1-p}{1-w_{opt}} & = 0\\\\\n", "\\end{align*}\n", "\n", "Solving for $w$\n", "\n", "$$w_{opt} = \\frac{p(b+1)-1}{b}$$\n", "\n", "The growth rate is then the value of $E[\\ln R]$ when $w = w_{opt}$, i.e., \n", "\n", "$$m = p\\ln(1+ w_{opt}b) + (1-p)\\ln(1-w_{opt})$$\n", "\n", "You can test how well this works in the following cell. Fix $p$ and $b$, and let the code do a Monte Carlo simulation to show how well Kelly's criterion works." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 295 }, "colab_type": "code", "executionInfo": { "elapsed": 3549, "status": "ok", "timestamp": 1557189274489, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "v4gExuy0tnB1", "outputId": "2dac60a3-0127-49a4-d674-41b1a9dba242", "pycharm": {} }, "outputs": [ { "data": { "image/png": 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gdhpU8wGqm7AaK0QlTMY9ikGfj108Ryf2KS6cJ+nustre5bQzwaIRUjImeT+p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\nEt/Hv3MXxbGRYUROO89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" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from numpy.random import uniform\n", "\n", "p = 0.5075\n", "b = 1\n", "\n", "# Kelly criterion\n", "w = (p*(b+1)-1)/b\n", "\n", "# optimal growth rate\n", "m = p*np.log(1+w*b) + (1-p)*np.log(1-w)\n", "\n", "# number of plays to double wealth\n", "K = int(np.log(2)/m)\n", "\n", "# monte carlo simulation and plotting\n", "for n in range(0,100):\n", " W = [1]\n", " for k in range(0,K):\n", " if uniform() <= p:\n", " W.append(W[-1]*(1+w*b))\n", " else:\n", " W.append(W[-1]*(1-w))\n", " plt.semilogy(W,alpha=0.2)\n", "plt.semilogy(np.linspace(0,K), np.exp(m*np.linspace(0,K)),'r',lw=3)\n", "plt.title('Kelly Criterion w = ' + str(round(w,4)))\n", "plt.xlabel('k')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "mKdhbYAJtnB5", "pycharm": {} }, "source": [ "## Example 2. Betting Wheel" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 286 }, "colab_type": "code", "executionInfo": { "elapsed": 640, "status": "ok", "timestamp": 1557189276268, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "P2M6ornJtnB6", "outputId": "208fda0b-356f-4076-fc83-7fe7d278e80e", "pycharm": {} }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:18: RuntimeWarning: divide by zero encountered in log\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "w1 = np.linspace(0,1)\n", "w2 = 0\n", "w3 = 0\n", "\n", "p1 = 1/2\n", "p2 = 1/3\n", "p3 = 1/6\n", "\n", "R1 = 1 + 2*w1 - w2 - w3\n", "R2 = 1 - w1 + w2 - w3\n", "R3 = 1 - w1 - w2 + 5*w3\n", "\n", "m = p1*np.log(R1) + p2*np.log(R2) + p3*np.log(R3)\n", "\n", "plt.plot(w1,m)\n", "plt.grid()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "8K_1ong5tnB9", "pycharm": {} }, "outputs": [], "source": [ "def wheel(w,N = 100):\n", " w1,w2,w3 = w\n", " " ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "G38Vjq_btnB_", "pycharm": {} }, "source": [ "## Example 3. Stock/Bond Portfolio in Continuous Time" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "GR1zwHQWtnCA", "pycharm": {} }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import pandas as pd\n", "import datetime\n", "from pandas_datareader import data, wb\n", "\n", "from scipy.stats import norm\n", "\n", "import requests\n", "\n", "def get_symbol(symbol):\n", " \"\"\"\n", " get_symbol(symbol) uses Yahoo to look up a stock trading symbol and \n", " return a description.\n", " \"\"\"\n", " url = \"http://d.yimg.com/autoc.finance.yahoo.com/autoc?query={}®ion=1&lang=en\".format(symbol)\n", " result = requests.get(url).json()\n", " for x in result['ResultSet']['Result']:\n", " if x['symbol'] == symbol:\n", " return x['name']" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 441 }, "colab_type": "code", "executionInfo": { "elapsed": 2338, "status": "ok", "timestamp": 1557189401187, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "QiT6Bs9ztnCD", "outputId": "fb72bda9-7f6d-4412-b211-25b2439c4309", "pycharm": {} }, "outputs": [ { "data": { "image/png": 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kNw8euLBXs1UYlFJYFaxPLeSpj7YAMLy7P3dOCmVcnyC6+3uclZzM40+zuKqO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\nC0MhBL++eiR/WHaQ2GA/Bkb4kxwRoFfU6Q5RTgdzh0ay92Qlv7t2FLdOT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" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "symbol = '^GSPC'\n", "\n", "# end date is today\n", "end = datetime.datetime.today().date()\n", "\n", "# start date is three years prior\n", "start = end-datetime.timedelta(1.5*365)\n", "\n", "# get stock price data\n", "S = data.DataReader(symbol,\"yahoo\",start,end)['Adj Close']\n", "rlin = (S - S.shift(1))/S.shift(1)\n", "rlog = np.log(S/S.shift(1))\n", "\n", "rlin = rlin.dropna()\n", "rlog = rlog.dropna()\n", "\n", "# plot data\n", "plt.figure(figsize=(10,6))\n", "plt.subplot(3,1,1)\n", "S.plot(title=get_symbol(symbol))\n", "plt.ylabel('Adjusted Close')\n", "plt.grid()\n", "\n", "plt.subplot(3,1,2)\n", "rlin.plot()\n", "plt.title('Linear Returns (daily)')\n", "plt.grid()\n", "plt.tight_layout()\n", "\n", "plt.subplot(3,1,3)\n", "rlog.plot()\n", "plt.title('Log Returns (daily)')\n", "plt.grid()\n", "plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 136 }, "colab_type": "code", "executionInfo": { "elapsed": 255, "status": "ok", "timestamp": 1557189402934, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "-_XEpBPYtnCG", "outputId": "a39bb47b-e6ce-4cf3-d851-1ae945221df7", "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Linear Returns\n", " mu = 0.00037731 (annualized = 9.51%)\n", "sigma = 0.00961646 (annualized = 15.27%)\n", "\n", "Log Returns\n", " nu = 0.00033089 (annualized = 8.34%)\n", "sigma = 0.00963609 (annualized = 15.30%)\n" ] } ], "source": [ "print('Linear Returns')\n", "mu,sigma = norm.fit(rlin)\n", "print(' mu = {0:12.8f} (annualized = {1:.2f}%)'.format(mu,100*252*mu))\n", "print('sigma = {0:12.8f} (annualized = {1:.2f}%)'.format(sigma,100*np.sqrt(252)*sigma))\n", "print()\n", "print('Log Returns')\n", "nu,sigma = norm.fit(rlog)\n", "print(' nu = {0:12.8f} (annualized = {1:.2f}%)'.format(nu,100*252*nu))\n", "print('sigma = {0:12.8f} (annualized = {1:.2f}%)'.format(sigma,100*np.sqrt(252)*sigma))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "3do-X8PjtnCJ", "pycharm": {} }, "outputs": [], "source": [ "mu = 252*mu\n", "nu = 252*nu\n", "sigma = np.sqrt(252)*sigma" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "executionInfo": { "elapsed": 231, "status": "ok", "timestamp": 1557189285964, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "5qy5uu1TtnCL", "outputId": "5fde9272-7bc1-4159-c1ba-61b7f20c3710", "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.4444444444444445 0.04888888888888889 0.6666666666666667\n" ] } ], "source": [ "rf = 0.04\n", "mu = 0.08\n", "sigma = 0.3\n", "\n", "w = (mu-rf)/sigma**2\n", "nu_opt = rf + (mu-rf)**2/2/sigma/sigma\n", "sigma_opt = np.sqrt(mu-rf)/sigma\n", "\n", "print(w,nu_opt,sigma_opt)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "3LHjeSGPtnCO", "pycharm": {} }, "source": [ "## Volatility Pumping" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "OMZvl5oftnCP", "pycharm": {} }, "source": [ "![Kelly_Criterion_Volatility_Pumping](https://github.com/jckantor/CBE40455/blob/master/notebooks/figures/Kelly_Criterion_Volatility_Pumping.png?raw=true)\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 695 }, "colab_type": "code", "executionInfo": { "elapsed": 1743, "status": "error", "timestamp": 1557189307891, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 240 }, "id": "UiFVuqh1tnCQ", "outputId": "62ad0b09-d8ba-4b84-803c-a8fed6a63546", "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Expected return = 0.004586\n" ] }, { "ename": "RuntimeError", "evalue": "ignored", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/units.py\u001b[0m in \u001b[0;36mget_converter\u001b[0;34m(self, x)\u001b[0m\n\u001b[1;32m 167\u001b[0m \u001b[0;31m# get_converter\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 168\u001b[0;31m \u001b[0;32mif\u001b[0m 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"\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/axis.py\u001b[0m in \u001b[0;36mupdate_units\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m 1465\u001b[0m \"\"\"\n\u001b[1;32m 1466\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1467\u001b[0;31m \u001b[0mconverter\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmunits\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mregistry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_converter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1468\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mconverter\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1469\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/units.py\u001b[0m in \u001b[0;36mget_converter\u001b[0;34m(self, x)\u001b[0m\n\u001b[1;32m 179\u001b[0m if (not isinstance(next_item, np.ndarray) or\n\u001b[1;32m 180\u001b[0m next_item.shape != x.shape):\n\u001b[0;32m--> 181\u001b[0;31m \u001b[0mconverter\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_converter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnext_item\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 182\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mconverter\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 183\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/units.py\u001b[0m in \u001b[0;36mget_converter\u001b[0;34m(self, x)\u001b[0m\n\u001b[1;32m 185\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mconverter\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 186\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 187\u001b[0;31m \u001b[0mthisx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msafe_first_element\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 188\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mTypeError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 189\u001b[0m \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/matplotlib/cbook/__init__.py\u001b[0m in \u001b[0;36msafe_first_element\u001b[0;34m(obj)\u001b[0m\n\u001b[1;32m 1633\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1634\u001b[0m \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1635\u001b[0;31m raise RuntimeError(\"matplotlib does not support generators \"\n\u001b[0m\u001b[1;32m 1636\u001b[0m \"as input\")\n\u001b[1;32m 1637\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0miter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mRuntimeError\u001b[0m: matplotlib does not support generators as input" ] }, { "data": { "image/png": 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" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "# payoffs for two states\n", "u = 1.059\n", "d = 1/u\n", "p = 0.54\n", "\n", "rf = 0.004\n", "\n", "K = 100\n", "\n", "ElnR = p*np.log(u) + (1-p)*np.log(d)\n", "print(\"Expected return = {:0.5}\".format(ElnR))\n", "\n", "\n", "Z = np.array([float(random.random() <= p) for _ in range(0,K)])\n", "R = d + (u-d)*Z\n", "S = np.cumprod(np.concatenate(([1],R)))\n", "\n", "\n", "ElnR = lambda alpha: p*np.log(alpha*u +(1-alpha)*np.exp(rf)) + \\\n", " (1-p)*np.log(alpha*d + (1-alpha)*np.exp(rf))\n", "\n", "a = np.linspace(0,1)\n", "\n", "plt.plot(a,map(ElnR,a))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "emKW95C3tnCU", "outputId": "fa2ad3fd-19ee-4f57-be9e-772b63534c88", "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.5\n" ] }, { "data": { "image/png": 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s0FjsOrfL2lBx4pJ9CtIBIytUUsqH9bw1zgaxEBERNSm5Jbm4WXkT/u7+9g7F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\nXkmevUOzmeKyYvl29Nuy43sd5dObn5b3b7hfer/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07i0emIrIzpYHQRo1Avr1qzgX8G4p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\nWlBpNBqNRqPR1JD/B/O+0qcfFVtMAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": { "tags": [] }, "output_type": "display_data" } ], "source": [ "from scipy.optimize import fminbound\n", "alpha = fminbound(lambda(alpha): -ElnR(alpha),0,1)\n", "print alpha\n", "\n", "#plt.plot(alpha, ElnR(alpha),'r.',ms=10)\n", "\n", "R = alpha*d + (1-alpha) + alpha*(u-d)*Z\n", "S2 = np.cumprod(np.concatenate(([1],R)))\n", "\n", "plt.figure(figsize=(10,4))\n", "plt.plot(range(0,K+1),S,range(0,K+1),S2)\n", "plt.legend(['Stock','Stock + Cash']);" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "Pj8JVV-ZtnCZ", "pycharm": {} }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "pycharm": {} }, "source": [ "\n", "< [Log-Optimal Growth and the Kelly Criterion](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/07.08-Log-Optimal-Growth-and-the-Kelly-Criterion.ipynb) | [Contents](toc.ipynb) | [Optimization in Google Sheets](http://nbviewer.jupyter.org/github/jckantor/CBE40455/blob/master/notebooks/08.00-Optimization-in-Google-Sheets.ipynb) >

\"Open

\"Download\"" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "07.08-Log-Optimal-Portfolios.ipynb", "provenance": [], "version": "0.3.2" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }