3.1_reinforcement_trading_offline_simple.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import jit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a trading system model $F_{t}(\\theta)$, the goal is to adjust the parameters $\\theta$ in order to maximise $U_{t}$ (wealth)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $$ \\frac{dU_{T}(\\theta)}{d\\theta} = \n",
    "\\sum \\limits _{t=1} ^ {T} \n",
    "\\frac{dU_{T}}{dR_{t}} \n",
    "\\{ \\frac{dR_{t}}{dF_{t}} \\frac{dF_{t}}{d\\theta} + \\frac{dR_{t}}{dF_{t-1}} \\frac{dF_{t-1}}{d\\theta}  \\}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where:\n",
    "* $U$ = wealth function (Sharpe ratio / Sterling ratio)\n",
    "* $R_{t}$ = realised returns \n",
    "* $r_{t}$ = asset returns\n",
    "* $F_{t}$ = position  \n",
    "* $\\theta$ = model weights\n",
    "* $\\delta$ = transaction costs\n",
    "* $\\mu$ = max position (multiplied by $F_{t}$ which goes from -1 to 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### References\n",
    "\n",
    "* J. Moody and M. Saffell, \"Learning to trade via direct reinforcement,\" in IEEE Transactions on Neural Networks, vol. 12, no. 4, pp. 875-889, July 2001, doi: 10.1109/72.935097.\n",
    "\n",
    "* https://teddykoker.com/2019/06/trading-with-reinforcement-learning-in-python-part-ii-application/\n",
    "* http://cs229.stanford.edu/proj2006/Molina-StockTradingWithRecurrentReinforcementLearning.pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load derivative functions from standalone notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run 3_reinforcement_trading_offline_simple_derivs.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM_RETURNS = M = 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate positions based on $tanh(\\theta \\cdot state)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "State takes the form: $[1, R_{t}, R_{t-1}, ..., R_{t-M}, F_{t-1}]$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def positions(r, theta):\n",
    "    '''\n",
    "    Apply weights to state to determine positisons\n",
    "    '''\n",
    "    \n",
    "    T = len(r)\n",
    "    Ft = np.zeros(T)\n",
    "    for t in range(M, T):\n",
    "        state = np.concatenate([ [1], r[t - M:t], [Ft[t-1]] ])\n",
    "        Ft[t] = np.tanh(np.dot(theta, state))\n",
    "        \n",
    "    return Ft"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### TODO: returns are based on zscores, fees are absolute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def returns(Ft, r, delta):\n",
    "    '''\n",
    "    Calculate realised returns based on positions and fees\n",
    "    '''\n",
    "    T = len(r)\n",
    "    R = (Ft[0:T-1] * r[1:T]) - delta * (np.abs(Ft[1:T] - Ft[0:T-1]))\n",
    "    return np.concatenate((np.array([0]), R))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(rets, theta, delta, moving_avg_n):\n",
    "    Ft = positions(rets, theta) \n",
    "    R = returns(Ft, rets, delta) \n",
    "   \n",
    "    # I don't think i need to calc this for all time here, \n",
    "    # just N where n = (1/N)\n",
    "    A = get_A(R, moving_avg_n)\n",
    "    DD2 = get_DD2(R, moving_avg_n)\n",
    "    \n",
    "    return _gradient(rets, theta, R, Ft, A, DD2, delta), DDR(R[:-1], R[:1])\n",
    "    \n",
    "def _gradient(rets, theta, R, Ft, A, DD2, delta):\n",
    "    T = len(rets)\n",
    "    grad = np.zeros(M + 2)\n",
    "    dFtdTheta_prev = np.zeros(M + 2)\n",
    "    \n",
    "    for t in range(M, T):\n",
    "        state = np.concatenate( (np.array([1]), rets[t - M:t], np.array([Ft[t-1]]) ))\n",
    "        \n",
    "        # Derivative functions are defined in 3_reinforcement_trading_simple_derivs.ipynb\n",
    "        dRdFt = get_dRdFt(delta, Ft, t)\n",
    "\n",
    "        dFtdTheta = get_dFtdTheta(Ft, t, state, theta, dFtdTheta_prev)\n",
    "        \n",
    "        dRdFtp = get_dRdFtp(rets, delta, Ft, t)\n",
    "\n",
    "        dUdR = ddr_auto(R[min(t-25, 0):t], R[t])#get_dUdR(A, t, R, DD2)\n",
    "        \n",
    "        inner = ((dRdFt*dFtdTheta) + (dRdFtp*dFtdTheta_prev))\n",
    "\n",
    "        grad_delta = dUdR * inner\n",
    "        grad = grad + np.nan_to_num(grad_delta)\n",
    "        \n",
    "        dFtdTheta_prev = dFtdTheta\n",
    "  \n",
    "    return grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Main"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "epochs = 250\n",
    "tick_sample_n = 700\n",
    "lr = 0.05\n",
    "best_weights = np.zeros(M+2)\n",
    "delta = 0.02\n",
    "\n",
    "moving_avg_n = 1/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2019-01-07 19:57:30 -> 2019-01-07 22:05:22'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv('~/Downloads/coinbaseGBP.csv', \n",
    "             names=['_dt', 'price', 'size'])\n",
    "\n",
    "df['dt'] = pd.to_datetime(df['_dt'],unit='s')\n",
    "df = df.set_index('dt').drop(columns=['_dt'])\n",
    "\n",
    "df['ret'] = np.log(df.price) - np.log(df.price.shift(1))\n",
    "\n",
    "df = df.tail(tick_sample_n)\n",
    "\n",
    "display('{} -> {}'.format(df.index[0], df.index[-1]))\n",
    "\n",
    "# TODO: Rolling Z-Score\n",
    "rets_z = stats.zscore(df.ret.values)\n",
    "rets = np.tanh(rets_z/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.03550669,  0.04026647, -0.14444841, -0.5487993 , -0.32584427,\n",
       "       -0.12545008, -0.12036871,  0.14900055, -0.59143941, -0.1591881 ])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def xavier_weights_init(n):\n",
    "    return (np.random.randn(1, n) * np.sqrt(1/(n-1)))[0]\n",
    "\n",
    "theta = xavier_weights_init(M+2)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss: -0.0289749838411808\n",
      "loss: 0.09169968217611313\n",
      "loss: 0.15329015254974365\n",
      "loss: 0.1782471239566803\n",
      "loss: 0.19290967285633087\n",
      "loss: 0.18377934396266937\n",
      "loss: 0.19171522557735443\n",
      "loss: 0.17331057786941528\n",
      "loss: 0.16738010942935944\n",
      "loss: 0.1719541698694229\n",
      "loss: 0.1744432896375656\n",
      "loss: 0.17604510486125946\n",
      "loss: 0.1774604469537735\n",
      "loss: 0.17787235975265503\n",
      "loss: 0.1795313060283661\n",
      "loss: 0.18026413023471832\n",
      "loss: 0.17961430549621582\n",
      "loss: 0.18104977905750275\n",
      "loss: 0.18060219287872314\n",
      "loss: 0.1823214590549469\n",
      "loss: 0.18232767283916473\n",
      "loss: 0.1847740262746811\n",
      "loss: 0.1850517988204956\n",
      "loss: 0.18591716885566711\n",
      "loss: 0.18640828132629395\n",
      "CPU times: user 3min 13s, sys: 22.4 s, total: 3min 35s\n",
      "Wall time: 3min 15s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "loss_history = []\n",
    "for i in range(0, epochs):\n",
    "    g, loss = gradient(rets, theta, delta, moving_avg_n)\n",
    "    theta = theta + (lr * g)\n",
    "    \n",
    "    loss_history.append(loss)\n",
    "    if loss == max(loss_history):\n",
    "        best_theta = theta\n",
    "        \n",
    "    if i % 10 == 0:\n",
    "        print('loss: {}'.format(loss))\n",
    "        \n",
    "theta = best_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_history = [l.item() for l in loss_history]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda3/envs/py36/lib/python3.6/site-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  FutureWarning\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(range(0, len(loss_history)), loss_history)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Ft = positions(rets, theta)\n",
    "Rt = returns(Ft, rets, delta)\n",
    "\n",
    "# TODO: These are zscores of log returns, convert back to normal returns\n",
    "realised_returns = returns(Ft, rets, delta)\n",
    "pd.Series(realised_returns).cumsum().plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda3/envs/py36/lib/python3.6/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(realised_returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Positions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda3/envs/py36/lib/python3.6/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(Ft)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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