Chapter 10. Bet Sizing.ipynb

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  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set(palette='Set2')\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "from scipy.stats import norm\n",
    "\n",
    "from datetime import timedelta\n",
    "from pandas import Timestamp\n",
    "\n",
    "from sklearn.mixture import GaussianMixture\n",
    "\n",
    "from typing import Tuple\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import nbimporter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auxilary Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "def avg_active_signals_(signals: pd.DataFrame, molecule: np.ndarray) -> pd.Series:\n",
    "    '''\n",
    "    Auxilary function for averaging signals. At time loc, averages signal among those still active.\n",
    "    Signal is active if:\n",
    "        a) issued before or at loc AND\n",
    "        b) loc before signal's endtime, or endtime is still unknown (NaT).\n",
    "    \n",
    "        Parameters:\n",
    "            signals (pd.DataFrame): dataset with signals and t1\n",
    "            molecule (np.ndarray): dates of events on which weights are computed\n",
    "        \n",
    "        Returns:\n",
    "            out (pd.Series): series with average signals for each timestamp\n",
    "    '''\n",
    "    out = pd.Series()\n",
    "    for loc in molecule:\n",
    "        df0 = (signals.index.values <= loc) & ((loc < signals['t1']) | pd.isnull(signals['t1']))\n",
    "        act = signals[df0].index\n",
    "        if len(act) > 0:\n",
    "            out[loc] = signals.loc[act, 'signal'].mean()\n",
    "        else:\n",
    "            out[loc] = 0    # no signals active at this time\n",
    "    return out\n",
    "            \n",
    "\n",
    "def avg_active_signals(signals: pd.DataFrame) -> pd.Series:\n",
    "    '''\n",
    "    Computes the average signal among those active.\n",
    "    \n",
    "        Parameters:\n",
    "            signals (pd.DataFrame): dataset with signals and t1\n",
    "        \n",
    "        Returns:\n",
    "            out (pd.Series): series with average signals for each timestamp\n",
    "    '''\n",
    "    tPnts = set(signals['t1'].dropna().values)\n",
    "    tPnts = tPnts.union(signals.index.values)\n",
    "    tPnts = sorted(list(tPnts))\n",
    "    out = avg_active_signals_(signals=signals, molecule=tPnts)\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def discrete_signal(signal0: pd.Series, stepSize: float) -> pd.Series:\n",
    "    '''\n",
    "    Discretizes signals.\n",
    "    \n",
    "        Parameters:\n",
    "            signal0 (pd.Series): series with signals\n",
    "            stepSize (float): degree of discretization (must be in (0, 1])\n",
    "        \n",
    "        Returns:\n",
    "            signal1 (pd.Series): series with discretized signals\n",
    "    '''\n",
    "    signal1 = (signal0 / stepSize).round() * stepSize    # discretize\n",
    "    signal1[signal1 > 1] = 1    # cap\n",
    "    signal1[signal1 < -1] = -1    # floor\n",
    "    return signal1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# no multithreading\n",
    "def get_signal(\n",
    "    events: pd.DataFrame, stepSize: float, prob: pd.Series, pred: pd.Series, numClasses: int, **kargs\n",
    ") -> pd.Series:\n",
    "    '''\n",
    "    Gets signals from predictions. Includes averaging of active bets as well as discretizing final value.\n",
    "    \n",
    "        Parameters:\n",
    "            events (pd.DataFrame): dataframe with columns:\n",
    "                                       - t1: timestamp of the first barrier touch\n",
    "                                       - trgt: target that was used to generate the horizontal barriers\n",
    "                                       - side (optional): side of bets\n",
    "            stepSize (float): ---\n",
    "            prob (pd.Series): series with probabilities of given predictions\n",
    "            pred (pd.Series): series with predictions\n",
    "            numClasses (int): number of classes\n",
    "        \n",
    "        Returns:\n",
    "            signal1 (pd.Series): series with discretized signals\n",
    "    '''\n",
    "    if prob.shape[0] == 0:\n",
    "        return pd.Series()\n",
    "    signal0 = (prob - 1.0 / numClasses) / (prob * (1.0 - prob)) ** 0.5    # t-value\n",
    "    signal0 = pred * (2 * norm.cdf(signal0) - 1)    # signal = side * size\n",
    "    if 'side' in events:\n",
    "        signal0 *= events.loc[signal0.index, 'side']    # meta-labeling\n",
    "    df0 = signal0.to_frame('signal').join(events[['t1']], how='left')\n",
    "    df0 = avg_active_signals(df0)\n",
    "    signal1 = discrete_signal(signal0=df0, stepSize=stepSize)\n",
    "    return signal1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bet_size(x: float, w: float) -> float:\n",
    "    '''\n",
    "    Returns bet size given price divergence and sigmoid function coefficient.\n",
    "    \n",
    "        Parameters:\n",
    "            x (float): difference between forecast price and current price f_i - p_t\n",
    "            w (float): coefficient that regulates the width of the sigmoid function\n",
    "        \n",
    "        Returns:\n",
    "            (float): bet size\n",
    "    '''\n",
    "    return x * (w + x ** 2) ** (-0.5)\n",
    "\n",
    "\n",
    "def get_target_pos(w: float, f: float, mP: float, maxPos: float) -> float:\n",
    "    '''\n",
    "    Calculates target position size associated with forecast f.\n",
    "    \n",
    "        Parameters:\n",
    "            w (float): coefficient that regulates the width of the sigmoid function\n",
    "            f (float): forecast price\n",
    "            mP (float): current market price\n",
    "            maxPos (float): maximum absolute position size\n",
    "        \n",
    "        Returns:\n",
    "            (float): target position size\n",
    "    '''\n",
    "    return int(bet_size(w, f - mP) * maxPos)\n",
    "\n",
    "\n",
    "def inv_price(f: float, w: float, m: float) -> float:\n",
    "    '''\n",
    "    Calculates inverse function of bet size with respect to market price p_t.\n",
    "    \n",
    "        Parameters:\n",
    "            f (float): forecast price\n",
    "            w (float): coefficient that regulates the width of the sigmoid function\n",
    "            m (float): bet size\n",
    "            \n",
    "        Returns:\n",
    "            (float): inverse price function\n",
    "    '''\n",
    "    return f - m * (w / (1 - m**2)) ** 0.5\n",
    "\n",
    "\n",
    "def limit_price(tPos: float, pos: float, f: float, w: float, maxPos: float) -> float:\n",
    "    '''\n",
    "    Calculates breakeven limit price p̄ for the order size q̂_{i,t} − q_t to avoid realizing losses.\n",
    "    \n",
    "        Parameters:\n",
    "            tPos (float): target position\n",
    "            pos (float): current position\n",
    "            f (float): forecast price\n",
    "            w (float): coefficient that regulates the width of the sigmoid function\n",
    "            maxPos (float): maximum absolute position size\n",
    "        \n",
    "        Returns:\n",
    "            lP (float): limit price\n",
    "    '''\n",
    "    sgn = (1 if tPos >= pos else -1)\n",
    "    lP = 0\n",
    "    for j in range(abs(pos + sgn), abs(tPos + 1)):\n",
    "        lP += inv_price(f, w, j / float(maxPos))\n",
    "    lP /= tPos - pos\n",
    "    return lP\n",
    "\n",
    "\n",
    "def get_w(x: float, m: float):\n",
    "    '''\n",
    "    Calibrates sigmoid coefficient by calculating the inverse function of bet size with respect to w.\n",
    "    \n",
    "        Parameters:\n",
    "            x (float): difference between forecast price and current price f_i - p_t\n",
    "            m (float): bet size\n",
    "    '''\n",
    "    return x ** 2 * (m**(-2) - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calibrated w: 10.803324099723\n",
      "Target position: 94\n",
      "Limit price for order: 112.64745169441017\n"
     ]
    }
   ],
   "source": [
    "pos, maxPos, mP, f, wParams = 0, 100, 100, 115, {'divergence': 10, 'm': 0.95}\n",
    "w = get_w(wParams['divergence'], wParams['m'])    # calibrate w\n",
    "target_pos = get_target_pos(w, f, mP, maxPos)    # get target position\n",
    "lP = limit_price(target_pos, pos, f, w, maxPos)    # limit price for order\n",
    "\n",
    "print(f'Calibrated w: {w}')\n",
    "print(f'Target position: {target_pos}')\n",
    "print(f'Limit price for order: {lP}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Bet Size as a Function of the Maximum Predicted Probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I plot the bet size as a function of maximum predicted probability $\\tilde{p}$ given by expression\n",
    "$$m=2Z[z]-1,$$\n",
    "$$z=\\dfrac{\\tilde{p}-\\dfrac{1}{||X||}}{\\sqrt{\\tilde{p}(1-\\tilde{p})}}$$\n",
    "Here $||X||$ runs from $2$ to $10$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = np.linspace(0, 1, 1000)\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "for X_size in range(2, 11):\n",
    "    z = (p - 1 / X_size) / (p * (1 - p)) ** 0.5\n",
    "    ax.plot(p, 2 * norm.cdf(z) - 1, label=f'$||X||=${X_size}')\n",
    "ax.set_xlabel(r'Maximum Predicted Probability $\\tilde{p}$')\n",
    "ax.set_ylabel('Bet Size')\n",
    "ax.legend(loc='best')\n",
    "ax.set_title('Bet Size as a Function of Maximum Predicted Probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Bet Sizes & t1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As all the probabilities are between $0.5$ and $1$, we have to manually choose some positions to be short (otherwise they are all long). Let's choose every second position to be short. First we create a series of bet sizes for each of 10000 dates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1990-01-01    0.057322\n",
       "1990-01-02   -0.943288\n",
       "1990-01-03    0.327755\n",
       "1990-01-04   -0.569561\n",
       "1990-01-05    0.380620\n",
       "                ...   \n",
       "2017-05-14   -0.520364\n",
       "2017-05-15    0.856712\n",
       "2017-05-16   -0.048810\n",
       "2017-05-17    0.365394\n",
       "2017-05-18   -0.020484\n",
       "Freq: D, Length: 10000, dtype: float64"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = np.random.uniform(0.5, 1.0, size=10000)\n",
    "sides = np.array([(-1) ** i for i in range(10000)])\n",
    "z = (preds - 0.5) / (preds * (1 - preds)) ** 0.5\n",
    "bet_size = pd.Series(data=sides * (2 * norm.cdf(z) - 1), index=pd.date_range(start='1/1/1990', periods=10000))\n",
    "bet_size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we obtain random shifts to create the `t1` series and cpmbine it with bets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t1</th>\n",
       "      <th>signal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-01</th>\n",
       "      <td>1990-01-25</td>\n",
       "      <td>0.057322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>1990-01-16</td>\n",
       "      <td>-0.943288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>1990-01-17</td>\n",
       "      <td>0.327755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>1990-01-13</td>\n",
       "      <td>-0.569561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>1990-01-12</td>\n",
       "      <td>0.380620</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   t1    signal\n",
       "1990-01-01 1990-01-25  0.057322\n",
       "1990-01-02 1990-01-16 -0.943288\n",
       "1990-01-03 1990-01-17  0.327755\n",
       "1990-01-04 1990-01-13 -0.569561\n",
       "1990-01-05 1990-01-12  0.380620"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shifts = np.random.uniform(1, 25, size=10000).astype(int)\n",
    "shifts = pd.Series(data=shifts * timedelta(days=1) + pd.date_range(start='1/1/1990', periods=10000),\n",
    "                   index=pd.date_range(start='1/1/1990', periods=10000))\n",
    "signals = shifts.to_frame(name='t1')\n",
    "signals['signal'] = bet_size\n",
    "signals.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can calculate the average signal among those active:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1990-01-01    0.057322\n",
       "1990-01-02   -0.442983\n",
       "1990-01-03   -0.186070\n",
       "1990-01-04   -0.281943\n",
       "1990-01-05   -0.149431\n",
       "                ...   \n",
       "2017-05-27    0.426650\n",
       "2017-05-28    0.538434\n",
       "2017-06-01    0.734182\n",
       "2017-06-06    0.365394\n",
       "2017-06-10    0.000000\n",
       "Length: 10009, dtype: float64"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "avg_signals = avg_active_signals(signals)\n",
    "avg_signals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Concurrent Bets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maximum number of concurrent long and short bets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_num_conc_bets_by_date(date: Timestamp, signals: pd.DataFrame) -> Tuple[int, int]:\n",
    "    '''\n",
    "    Derives number of long and short concurrent bets by given date.\n",
    "    \n",
    "        Parameters:\n",
    "            date (Timestamp): date of signal\n",
    "            signals (pd.DataFrame): dataframe with signals\n",
    "            \n",
    "        Returns:\n",
    "            long, short (Tuple[int, int]): number of long and short concurrent bets\n",
    "    '''\n",
    "    long, short = 0, 0\n",
    "    for ind in pd.date_range(start=max(signals.index[0], date - timedelta(days=25)), end=date):\n",
    "        if ind <= date and signals.loc[ind]['t1'] >= date:\n",
    "            if signals.loc[ind]['signal'] >= 0:\n",
    "                long += 1\n",
    "            else:\n",
    "                short += 1\n",
    "    return long, short"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t1</th>\n",
       "      <th>signal</th>\n",
       "      <th>conc_long</th>\n",
       "      <th>conc_short</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-01</th>\n",
       "      <td>1990-01-25</td>\n",
       "      <td>0.057322</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>1990-01-16</td>\n",
       "      <td>-0.943288</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>1990-01-17</td>\n",
       "      <td>0.327755</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>1990-01-13</td>\n",
       "      <td>-0.569561</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>1990-01-12</td>\n",
       "      <td>0.380620</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-14</th>\n",
       "      <td>2017-05-18</td>\n",
       "      <td>-0.520364</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-15</th>\n",
       "      <td>2017-06-06</td>\n",
       "      <td>0.856712</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-16</th>\n",
       "      <td>2017-06-01</td>\n",
       "      <td>-0.048810</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-17</th>\n",
       "      <td>2017-06-10</td>\n",
       "      <td>0.365394</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-18</th>\n",
       "      <td>2017-05-28</td>\n",
       "      <td>-0.020484</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   t1    signal  conc_long  conc_short\n",
       "1990-01-01 1990-01-25  0.057322        1.0         0.0\n",
       "1990-01-02 1990-01-16 -0.943288        1.0         1.0\n",
       "1990-01-03 1990-01-17  0.327755        2.0         1.0\n",
       "1990-01-04 1990-01-13 -0.569561        2.0         2.0\n",
       "1990-01-05 1990-01-12  0.380620        3.0         2.0\n",
       "...               ...       ...        ...         ...\n",
       "2017-05-14 2017-05-18 -0.520364        5.0         6.0\n",
       "2017-05-15 2017-06-06  0.856712        6.0         6.0\n",
       "2017-05-16 2017-06-01 -0.048810        6.0         6.0\n",
       "2017-05-17 2017-06-10  0.365394        6.0         6.0\n",
       "2017-05-18 2017-05-28 -0.020484        6.0         6.0\n",
       "\n",
       "[10000 rows x 4 columns]"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for ind in signals.index:\n",
    "    signals.loc[ind, 'conc_long'], signals.loc[ind, 'conc_short'] = get_num_conc_bets_by_date(date=ind, signals=signals)\n",
    "signals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum number of concurrent long bets: 12.0\n",
      "Maximum number of concurrent short bets: 12.0\n"
     ]
    }
   ],
   "source": [
    "max_conc_long = signals['conc_long'].max()\n",
    "max_conc_short = signals['conc_short'].max()\n",
    "\n",
    "print(f'Maximum number of concurrent long bets: {max_conc_long}')\n",
    "print(f'Maximum number of concurrent short bets: {max_conc_short}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can derive the bet size another way - using the formula\n",
    "$$m_t=c_{t, l}\\dfrac{1}{\\overline{c}_l}-c_{t, s}\\dfrac{1}{\\overline{c}_s}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t1</th>\n",
       "      <th>signal</th>\n",
       "      <th>conc_long</th>\n",
       "      <th>conc_short</th>\n",
       "      <th>bet_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-01</th>\n",
       "      <td>1990-01-25</td>\n",
       "      <td>0.057322</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>1990-01-16</td>\n",
       "      <td>-0.943288</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>1990-01-17</td>\n",
       "      <td>0.327755</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>1990-01-13</td>\n",
       "      <td>-0.569561</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>1990-01-12</td>\n",
       "      <td>0.380620</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.083333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   t1    signal  conc_long  conc_short  bet_size\n",
       "1990-01-01 1990-01-25  0.057322        1.0         0.0  0.083333\n",
       "1990-01-02 1990-01-16 -0.943288        1.0         1.0  0.000000\n",
       "1990-01-03 1990-01-17  0.327755        2.0         1.0  0.083333\n",
       "1990-01-04 1990-01-13 -0.569561        2.0         2.0  0.000000\n",
       "1990-01-05 1990-01-12  0.380620        3.0         2.0  0.083333"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "signals['bet_size'] = signals['conc_long'] / max_conc_long - signals['conc_short'] / max_conc_short\n",
    "signals.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max bet size: 0.5833333333333334\n",
      "Min bet size: -0.6666666666666667\n"
     ]
    }
   ],
   "source": [
    "print(f'Max bet size: {signals.bet_size.max()}')\n",
    "print(f'Min bet size: {signals.bet_size.min()}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Bet Sizes Using Mixture of Two Gaussians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1990-01-01    1.0\n",
       "1990-01-02    0.0\n",
       "1990-01-03    1.0\n",
       "1990-01-04    0.0\n",
       "1990-01-05    1.0\n",
       "             ... \n",
       "2017-05-14   -1.0\n",
       "2017-05-15    0.0\n",
       "2017-05-16    0.0\n",
       "2017-05-17    0.0\n",
       "2017-05-18    0.0\n",
       "Freq: D, Length: 10000, dtype: float64"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = signals['conc_long'] - signals['conc_short']\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have to fit a mixture of two Gaussians on this series:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mixture = GaussianMixture(n_components=2).fit(c.values.reshape(-1, 1))\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "x = np.linspace(-10, 10, 1000).reshape(-1, 1)\n",
    "logprob = mixture.score_samples(x)\n",
    "pdf = np.exp(logprob)\n",
    "ax.plot(x, pdf, color='red', label='Gaussian Mixture')\n",
    "ax.hist(c.values, density=True, label='Histogram of c series')\n",
    "ax.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: this is indeed a **mixture** of 2 Gaussians, though they have close means and so it's hard to distinguish components by looking at the graphics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have to be able to calculate CDF of the fitted Gaussian mixture. We can calculate it simply as a cumulative sum of its PDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t1</th>\n",
       "      <th>signal</th>\n",
       "      <th>conc_long</th>\n",
       "      <th>conc_short</th>\n",
       "      <th>bet_size</th>\n",
       "      <th>bet_size_GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-01</th>\n",
       "      <td>1990-01-25</td>\n",
       "      <td>0.057322</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.083333</td>\n",
       "      <td>0.345229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>1990-01-16</td>\n",
       "      <td>-0.943288</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>1990-01-17</td>\n",
       "      <td>0.327755</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.083333</td>\n",
       "      <td>0.345229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>1990-01-13</td>\n",
       "      <td>-0.569561</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>1990-01-12</td>\n",
       "      <td>0.380620</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.083333</td>\n",
       "      <td>0.345229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-14</th>\n",
       "      <td>2017-05-18</td>\n",
       "      <td>-0.520364</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>-0.083333</td>\n",
       "      <td>-0.354456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-15</th>\n",
       "      <td>2017-06-06</td>\n",
       "      <td>0.856712</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-16</th>\n",
       "      <td>2017-06-01</td>\n",
       "      <td>-0.048810</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-17</th>\n",
       "      <td>2017-06-10</td>\n",
       "      <td>0.365394</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-05-18</th>\n",
       "      <td>2017-05-28</td>\n",
       "      <td>-0.020484</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   t1    signal  conc_long  conc_short  bet_size  bet_size_GM\n",
       "1990-01-01 1990-01-25  0.057322        1.0         0.0  0.083333     0.345229\n",
       "1990-01-02 1990-01-16 -0.943288        1.0         1.0  0.000000     0.000000\n",
       "1990-01-03 1990-01-17  0.327755        2.0         1.0  0.083333     0.345229\n",
       "1990-01-04 1990-01-13 -0.569561        2.0         2.0  0.000000     0.000000\n",
       "1990-01-05 1990-01-12  0.380620        3.0         2.0  0.083333     0.345229\n",
       "...               ...       ...        ...         ...       ...          ...\n",
       "2017-05-14 2017-05-18 -0.520364        5.0         6.0 -0.083333    -0.354456\n",
       "2017-05-15 2017-06-06  0.856712        6.0         6.0  0.000000     0.000000\n",
       "2017-05-16 2017-06-01 -0.048810        6.0         6.0  0.000000     0.000000\n",
       "2017-05-17 2017-06-10  0.365394        6.0         6.0  0.000000     0.000000\n",
       "2017-05-18 2017-05-28 -0.020484        6.0         6.0  0.000000     0.000000\n",
       "\n",
       "[10000 rows x 6 columns]"
      ]
     },
     "execution_count": 268,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = np.linspace(-15, 0, 1000).reshape(-1, 1)\n",
    "logprob = mixture.score_samples(x0)\n",
    "F_0 = np.exp(logprob).sum() * 15 / 1000    # have to normalize pdf\n",
    "for ind in signals.index:\n",
    "    x1 = np.linspace(-15, c[ind], 1000).reshape(-1, 1)\n",
    "    logprob = mixture.score_samples(x1)\n",
    "    F_c = np.exp(logprob).sum() * (c[ind] + 15) / 1000\n",
    "    if c[ind] >= 0:\n",
    "        signals.loc[ind, 'bet_size_GM'] = (F_c - F_0) / (1 - F_0)\n",
    "    else:\n",
    "        signals.loc[ind, 'bet_size_GM'] = (F_c - F_0) / F_0\n",
    "\n",
    "signals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can notice that bet sizes according to Gaussian mixture and method using concurrent bets agree on the side of the bet. However, GM produces bigger absolute bets meaning higher confidence in each bet."
   ]
  }
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