fall-of-genius-trader.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "29ddfddf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:08:25.298874Z",
     "start_time": "2022-09-16T17:08:24.292778Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "plt.rcParams[\"figure.figsize\"] = (20,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96c34d69",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-12T20:23:05.159081Z",
     "start_time": "2022-09-12T20:23:05.134890Z"
    }
   },
   "source": [
    "Let's say ~~you think~~ you're a genius.\n",
    "- You have $100 starting capital.\n",
    "- You can always find bets with 60/40 % chance of doubling/halving (+100%/-50%).\n",
    "\n",
    "This is great, but there's a catch: you are poor af. You just want to escape poverty, so you know you will YOLO 60%+ of your capital on each bet.\n",
    "\n",
    "**Should you start trading? \n",
    "The answer is No.** Life is not a coin flip.\n",
    "\n",
    "As long as you bet (>60%) more than your odds (60%), you will lose everything.\n",
    "\n",
    "This is a mathematical fact via the [Kelly Criterion](https://en.wikipedia.org/wiki/Kelly_criterion).\n",
    "But it's an extremely unintuitive concept. So, below are 1000 (Monte Carlo) simulations that demonstrate the certainty.\n",
    "\n",
    "---\n",
    "\n",
    "Most traders find out they're [highly regarded](https://www.reddit.com/r/wallstreetbets/comments/wtxwen/highly_regarded/) when it's too late. They go on losing streaks and the leverage only accelerate on the urge to make back the money.\n",
    "\n",
    "> Your grandmother does not analyze smoking as a single-period event, but as an activity of smoking. Risk-taking (trading) is an activity, not a single event.\n",
    "\n",
    "*- [Nassim Taleb](https://www.youtube.com/watch?v=91IOwS0gf3g).*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df286da3",
   "metadata": {},
   "source": [
    "## All roads lead to financial ruin.\n",
    "1000 simulations with the above conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b3f4cf40",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:08:25.306342Z",
     "start_time": "2022-09-16T17:08:25.300296Z"
    },
    "code_folding": [
     6
    ]
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "num_simulations = 1000\n",
    "max_num_bets = 1000\n",
    "win_probability = []\n",
    "end_balance = []\n",
    "kelly_bets = [[.61,.6]]\n",
    "def random_num(chance_of_winning=.5):\n",
    "    chance_of_winning = chance_of_winning * 100\n",
    "    num = random.randint(1, 100)\n",
    "    if num <= chance_of_winning:\n",
    "        same_num = True\n",
    "    else:\n",
    "        same_num = False\n",
    "    return same_num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dfb30341",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:08:27.750050Z",
     "start_time": "2022-09-16T17:08:25.377166Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "list_overall_end_balance = []\n",
    "\n",
    "for n, x in enumerate(kelly_bets):\n",
    "    win_probability = []\n",
    "    end_balance = []\n",
    "    for i in range(num_simulations):\n",
    "        bet = x[0]\n",
    "        chance_of_winning = x[1]\n",
    "        balance = [100]\n",
    "        num_bets = [0]\n",
    "        num_wins = 0\n",
    "        while num_bets[-1] < max_num_bets:\n",
    "            same = random_num(chance_of_winning)\n",
    "            if same:\n",
    "                balance.append(balance[-1] * (1+bet))\n",
    "                num_wins += 1\n",
    "            else:\n",
    "                balance.append(balance[-1] * (1-bet))\n",
    "            num_bets.append(num_bets[-1] + 1)\n",
    "        win_probability.append(num_wins/num_bets[-1])\n",
    "        end_balance.append(balance[-1])    \n",
    "        plt.title(\"All good trades (60%+) leads to $0.\", fontsize=20)\n",
    "        plt.xlabel(\"Trade #\", fontsize=20)\n",
    "        plt.ylabel(\"Account Balance $\", fontsize=20)\n",
    "        plt.plot(num_bets, balance)\n",
    "    overall_end_balance = sum(end_balance)/len(end_balance)\n",
    "    list_overall_end_balance.append(overall_end_balance)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "74983460",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:08:27.755269Z",
     "start_time": "2022-09-16T17:08:27.751794Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "highest end balance: $7.02e-10 ($0.0000000007020803271948798315132758323449824883200065528399136383086442947387695312500000000000000000)\n",
      "lowest end balance: $7.69e-71 ($0.0000000000000000000000000000000000000000000000000000000000000000000000769167937318915647272310498921)\n",
      "average end balance: $7.88e-13 ($0.0000000000007875125041409818356167967033067249537931636682586145070672500878572463989257812500000000)\n",
      "all cases: financially irrecoverable.\n"
     ]
    }
   ],
   "source": [
    "average_end_balance = sum(end_balance)/len(end_balance)\n",
    "print(\"highest end balance: ${:.2e} (${:.100f})\".format(max(end_balance), max(end_balance)))\n",
    "print(\"lowest end balance: ${:.2e} (${:.100f})\".format(min(end_balance), min(end_balance)))\n",
    "print(\"average end balance: ${:.2e} (${:.100f})\".format(average_end_balance, average_end_balance))\n",
    "print(\"all cases: financially irrecoverable.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "492d86c9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:09:58.807102Z",
     "start_time": "2022-09-16T17:09:58.802747Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# print(\"plot: all 1000 end balances\")\n",
    "# plt.plot(np.arange(0,len(end_balance)),end_balance)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "902c818b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T16:54:30.943648Z",
     "start_time": "2022-09-16T16:54:30.924316Z"
    }
   },
   "source": [
    "## The optimal bet\n",
    "\n",
    "What's the optimal bet for 60% odds? Much smaller than you probably guessed. ([wiki](https://en.wikipedia.org/wiki/Kelly_criterion))\n",
    "![kelly criterion formula](kelly-criterion-formula.svg) \n",
    "\n",
    "- f = the fraction of the current bankroll to wager.\n",
    "- p = the probability of a win.\n",
    "- q = the probability of a loss | q = 1-p\n",
    "- b = the proportion of the bet gained with a win\n",
    "\n",
    "f = 60% - (40%/100%) = 20%\n",
    "**The optimal bet is 20% of bankroll.**\n",
    "\n",
    "1000 simulations, using 20% of bankroll. (Instead of 61%.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a45e8323",
   "metadata": {},
   "source": [
    "![kelly-criterion-visualized.jpg](kelly-criterion-visualized.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dca02c86",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:08:50.116186Z",
     "start_time": "2022-09-16T17:08:50.104537Z"
    }
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "num_simulations = 1000\n",
    "max_num_bets = 1000\n",
    "win_probability = []\n",
    "end_balance = []\n",
    "kelly_bets = [[.2,.6]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "abc70706",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:28:11.278488Z",
     "start_time": "2022-09-16T17:28:08.688683Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "list_overall_win_probability = []\n",
    "list_overall_end_balance = []\n",
    "\n",
    "for n, x in enumerate(kelly_bets):\n",
    "    win_probability = []\n",
    "    end_balance = []\n",
    "    for i in range(num_simulations):\n",
    "        bet = x[0]\n",
    "        chance_of_winning = x[1]\n",
    "        balance = [100]\n",
    "        num_bets = [0]\n",
    "        num_wins = 0\n",
    "        while num_bets[-1] < max_num_bets:\n",
    "            same = random_num(chance_of_winning)\n",
    "            if same:\n",
    "                balance.append(balance[-1] * (1+bet))\n",
    "                num_wins += 1\n",
    "            else:\n",
    "                balance.append(balance[-1] * (1-bet))    \n",
    "            num_bets.append(num_bets[-1] + 1)\n",
    "        win_probability.append(num_wins/num_bets[-1])\n",
    "        end_balance.append(balance[-1])    \n",
    "        plt.title(\"Impossible trades lead to riches.\", fontsize=20)\n",
    "        plt.xlabel(\"Trade #\", fontsize=20)\n",
    "        plt.ylabel(\"Account Balance $\", fontsize=20)\n",
    "        plt.plot(num_bets, balance)\n",
    "    overall_end_balance = sum(end_balance)/len(end_balance)\n",
    "    list_overall_end_balance.append(overall_end_balance)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "18300c4d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:28:26.875111Z",
     "start_time": "2022-09-16T17:28:26.855969Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "highest end balance: $1.20e+20 ($119558141466334396416)\n",
      "lowest end balance: $2.58e+01 ($26)\n",
      "average end balance: $1.63e+17 ($163425299699914336)\n"
     ]
    }
   ],
   "source": [
    "average_end_balance = sum(end_balance)/len(end_balance)\n",
    "print(\"highest end balance: ${:.2e} (${:.0f})\".format(max(end_balance), max(end_balance)))\n",
    "print(\"lowest end balance: ${:.2e} (${:.0f})\".format(min(end_balance), min(end_balance)))\n",
    "print(\"average end balance: ${:.2e} (${:.0f})\".format(average_end_balance, average_end_balance))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae45cd5f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-09-16T17:28:42.709998Z",
     "start_time": "2022-09-16T17:28:42.684565Z"
    }
   },
   "source": [
    "**all cases: impossible.** You're not gonna find a 60% odd bet consistently in an unknowable future, my guy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2823eda2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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