{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "12bfc759",
   "metadata": {},
   "source": [
    "---\n",
    "title: Betting Against Volatility\n",
    "summary: Long low-volatility names, short high-volatility names — the low-risk anomaly.\n",
    "tags: [low-volatility, defensive, anomaly]\n",
    "---\n",
    "\n",
    "# Betting Against Volatility\n",
    "\n",
    "One of the most stubborn anomalies: **low-volatility stocks earn as much or more than high-volatility\n",
    "ones**, on a risk-adjusted basis — the opposite of what the textbook risk-return tradeoff predicts.\n",
    "Leverage-constrained investors overpay for exciting, high-vol names. We lean the other way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a18b929",
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    import convexpi.lab  # noqa\n",
    "except ImportError:\n",
    "    import subprocess, sys\n",
    "    subprocess.run([sys.executable, \"-m\", \"pip\", \"install\", \"-q\", \"convexpi-lab\"])\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "print(\"ready\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68e642ee",
   "metadata": {},
   "source": [
    "## The idea\n",
    "\n",
    "`vol_1m` is each stock's recent volatility (high = risky). We want to be **long low vol / short high\n",
    "vol**, so we sort on the *negative* of the signal — high score = calm stock."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9df3e042",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from convexpi.lab import Strategy\n",
    "\n",
    "def _long_short(signal, frac=0.2):\n",
    "    \"\"\"Dollar-neutral long/short: long the top `frac`, short the bottom `frac`, equal-weighted.\"\"\"\n",
    "    s = np.nan_to_num(np.asarray(signal, dtype=float))\n",
    "    n = len(s); k = max(1, int(n * frac))\n",
    "    order = np.argsort(s)\n",
    "    w = np.zeros(n); w[order[-k:]] = 1.0 / k; w[order[:k]] = -1.0 / k\n",
    "    return w\n",
    "\n",
    "class MyStrategy(Strategy):\n",
    "    \"\"\"Long low-volatility names, short high-volatility names.\"\"\"\n",
    "    def on_day(self, day, features, prices, portfolio):\n",
    "        vol = features.get(\"vol_1m\", np.zeros(len(prices)))\n",
    "        return _long_short(-np.nan_to_num(vol), frac=0.2)   # negate: long the calmest"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b976d115",
   "metadata": {},
   "source": [
    "## Out-of-sample evaluation\n",
    "\n",
    "Train on the first half of a synthetic market, evaluate on the held-out second half — the same discipline as the leaderboard."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb1027ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "from convexpi.lab import SyntheticMarket, Grader\n",
    "market = SyntheticMarket(n_stocks=80, n_days=1800, seed=1)\n",
    "report = Grader(market).evaluate(MyStrategy())\n",
    "print(f\"in-sample Sharpe    : {report.is_sharpe:+.2f}\")\n",
    "print(f\"out-of-sample Sharpe: {report.oos_sharpe:+.2f}\")\n",
    "print(f\"overfitting ratio   : {report.overfitting_ratio:+.2f}\")\n",
    "oos = report.oos_result.daily_returns\n",
    "fig, ax = plt.subplots(figsize=(8, 3))\n",
    "ax.plot(np.cumprod(1 + oos)); ax.set_title(\"Out-of-sample equity curve\"); ax.set_ylabel(\"growth of $1\")\n",
    "plt.tight_layout(); plt.show()\n",
    "\n",
    "print(\"The low-vol leg is defensive — it tends to shine in drawdowns.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efaa1804",
   "metadata": {},
   "source": [
    "## What I'd try next\n",
    "\n",
    "- True **betting-against-beta** rescales each leg to equal beta (see the library's `frazzini_pedersen_bab` replication).\n",
    "- Combine low-vol with **quality** — calm *and* profitable.\n",
    "- Check whether the edge is just a sector tilt (utilities/staples) in disguise."
   ]
  }
 ],
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