{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "sec0-title",
   "metadata": {},
   "source": [
    "# Comprehensive Stress Testing for a Multi-Asset ETF Portfolio\n",
    "\n",
    "This notebook walks through advanced stress-testing techniques using **pyvallocation**.\n",
    "We answer practical portfolio questions such as:\n",
    "\n",
    "- *What if equity spreads widen and then mean revert?*\n",
    "- *What if the 2020 COVID crash repeats?*\n",
    "- *What is the 95th-percentile max drawdown at 3-month vs 1-year horizon?*\n",
    "- *What if correlations break down (SPY-TLT hedge fails)?*\n",
    "- *How does the portfolio perform under bearish equity + rising rates?*\n",
    "\n",
    "**Assets**: SPY (US equity), TLT (long-term bonds), GLD (gold), DBC (commodities)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "sec0-setup",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:49.648430Z",
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     "shell.execute_reply": "2026-03-30T19:38:50.310589Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "from pyvallocation import (\n",
    "    PortfolioWrapper, FlexibleViewsProcessor,\n",
    "    stress_test, linear_map, kernel_focus_stress,\n",
    "    entropy_pooling_stress,\n",
    "    horizon_report, drawdown_quantile,\n",
    "    simulate_paths, performance_report,\n",
    ")\n",
    "np.random.seed(42)\n",
    "plt.rcParams.update({\"figure.dpi\": 100, \"axes.grid\": True})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "sec0-data",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.312197Z",
     "iopub.status.busy": "2026-03-30T19:38:50.312103Z",
     "iopub.status.idle": "2026-03-30T19:38:50.329250Z",
     "shell.execute_reply": "2026-03-30T19:38:50.328995Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Assets: ['DBC', 'GLD', 'SPY', 'TLT']  |  Weeks: 1006\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\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>DBC</th>\n",
       "      <th>GLD</th>\n",
       "      <th>SPY</th>\n",
       "      <th>TLT</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2025-05-09</th>\n",
       "      <td>0.017192</td>\n",
       "      <td>0.029300</td>\n",
       "      <td>-0.004279</td>\n",
       "      <td>-0.007781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-05-16</th>\n",
       "      <td>0.003309</td>\n",
       "      <td>-0.041931</td>\n",
       "      <td>0.051559</td>\n",
       "      <td>-0.008653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-05-23</th>\n",
       "      <td>0.010329</td>\n",
       "      <td>0.051370</td>\n",
       "      <td>-0.025724</td>\n",
       "      <td>-0.020487</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 DBC       GLD       SPY       TLT\n",
       "Date                                              \n",
       "2025-05-09  0.017192  0.029300 -0.004279 -0.007781\n",
       "2025-05-16  0.003309 -0.041931  0.051559 -0.008653\n",
       "2025-05-23  0.010329  0.051370 -0.025724 -0.020487"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Load ETF prices and compute weekly log returns ---\n",
    "_paths = [Path(d + \"examples/ETF_prices.csv\")\n",
    "          for d in [\"\", \"../\", \"../../\", \"../../../\"]]\n",
    "_csv = next((p for p in _paths if p.exists()), None)\n",
    "if _csv is None:\n",
    "    raise FileNotFoundError(\"ETF_prices.csv not found\")\n",
    "prices = pd.read_csv(_csv, index_col=\"Date\", parse_dates=True)\n",
    "weekly = prices.dropna(how=\"all\").ffill().resample(\"W-FRI\").last()\n",
    "log_returns = np.log(weekly).diff().dropna(how=\"all\").dropna()\n",
    "ASSETS = list(log_returns.columns)\n",
    "print(f\"Assets: {ASSETS}  |  Weeks: {len(log_returns)}\")\n",
    "log_returns.tail(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "sec0-tangency",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.330326Z",
     "iopub.status.busy": "2026-03-30T19:38:50.330263Z",
     "iopub.status.idle": "2026-03-30T19:38:50.506795Z",
     "shell.execute_reply": "2026-03-30T19:38:50.506568Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tangency weights:\n",
      "DBC    0.0000\n",
      "GLD    0.3335\n",
      "SPY    0.4032\n",
      "TLT    0.2633\n",
      "Name: Tangency Portfolio (rf=0.00%), dtype: float64\n",
      "\n",
      "Expected return: 0.0015  |  Risk: 0.0138\n"
     ]
    }
   ],
   "source": [
    "# --- Build a tangency portfolio from the MV frontier ---\n",
    "wrapper = PortfolioWrapper.from_moments(\n",
    "    log_returns.mean(), log_returns.cov()\n",
    ")\n",
    "frontier = wrapper.variance_frontier(num_portfolios=25)\n",
    "w_tangency, ret_t, risk_t = frontier.tangency(risk_free_rate=0.0)\n",
    "print(\"Tangency weights:\")\n",
    "print(w_tangency.round(4))\n",
    "print(f\"\\nExpected return: {ret_t:.4f}  |  Risk: {risk_t:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec1-title",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 1 -- Nominal Performance at Multiple Horizons\n",
    "\n",
    "We project the tangency portfolio across 1-month, 3-month, 6-month, and\n",
    "1-year horizons using bootstrapped scenarios and measure VaR/CVaR scaling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "sec1-horizon",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.507885Z",
     "iopub.status.busy": "2026-03-30T19:38:50.507824Z",
     "iopub.status.idle": "2026-03-30T19:38:50.543979Z",
     "shell.execute_reply": "2026-03-30T19:38:50.543769Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nominal horizon report:\n"
     ]
    },
    {
     "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>mean</th>\n",
       "      <th>stdev</th>\n",
       "      <th>VaR95</th>\n",
       "      <th>CVaR95</th>\n",
       "      <th>ENS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1m</th>\n",
       "      <td>0.0074</td>\n",
       "      <td>0.0284</td>\n",
       "      <td>0.0381</td>\n",
       "      <td>0.0546</td>\n",
       "      <td>5000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3m</th>\n",
       "      <td>0.0230</td>\n",
       "      <td>0.0512</td>\n",
       "      <td>0.0605</td>\n",
       "      <td>0.0865</td>\n",
       "      <td>5000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6m</th>\n",
       "      <td>0.0470</td>\n",
       "      <td>0.0752</td>\n",
       "      <td>0.0724</td>\n",
       "      <td>0.1014</td>\n",
       "      <td>5000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1y</th>\n",
       "      <td>0.0958</td>\n",
       "      <td>0.1101</td>\n",
       "      <td>0.0737</td>\n",
       "      <td>0.1158</td>\n",
       "      <td>5000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mean   stdev   VaR95  CVaR95     ENS\n",
       "1m  0.0074  0.0284  0.0381  0.0546  5000.0\n",
       "3m  0.0230  0.0512  0.0605  0.0865  5000.0\n",
       "6m  0.0470  0.0752  0.0724  0.1014  5000.0\n",
       "1y  0.0958  0.1101  0.0737  0.1158  5000.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Multi-horizon risk report ---\n",
    "w_arr = w_tangency.values\n",
    "hr_nominal = horizon_report(\n",
    "    w_arr, log_returns.values,\n",
    "    horizons=[4, 13, 26, 52],\n",
    "    n_simulations=5000, confidence=0.95, seed=42,\n",
    ")\n",
    "print(\"Nominal horizon report:\")\n",
    "hr_nominal.round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "sec1-chart",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-30T19:38:50.592012Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r4iYrkONIa9bGxe8dyyxD/D/krN9jbak7+EeCARYzjtx+UphFZKDM0/3Jefnll80fVI7kZ61lfAxy2bbKEYM7lg3wcZj15f15Sj9+RsXx+fKPlrv9b+m5554zp9vfe++9JNdjEB3/dWUwR1Z5AU9zch2r4b8j676u9pmnpFmmkJ6YfWZtLxv5WxhoTJgwIUWBLE/Pz5gxw15qwGCCWVhml7n95OpjrdIGd79YpRS/SLAcxcK6z6+++socK8e2YK4w4GR2nG3GHI8PvxTyGCVVQsNyF5bk8CxIfOxcYT1ffl74BYAdA+LPKOf4mHyvu1Nmwi9jfG7saOL4mjJQZhsyflHKaHxM1iPzfeL4GrCTAs9c8CxKarC2l19KeHxdfVm9leMncqtUWiDiJqs1FQcoUfxAlllJnmZnCyCu988//5jMIWvE3MXsJvs6Mrizso2usiMcwDJp0iS3tslMFDOrHMTFWjnHmb1Wr15tb8/jqryAgQgDaz5Xx+wSnx//oLHNEgeSMIvFFj0pOTXIWly+Vgx+OdDNquOLj4EC12FgzefCel8GhSxrsIIFZsLZp5V/SJmRYmsfBovMYPI2tiJiIMM/tmyFxS8MrJ/kdnhamhnT9MK+rBzI8uKLL5qsJUsbmBW2ssfuZACtIJUZL8d2a8zCMmPOmmzHswOu8MsJB+cwyGHtKktf+D5Iq5pRbpMt0NhuiYMgp0yZYr44ufNFgaf/WXfJLyI8djwjwOfK487nldRMcgzOeDwZoPILII8zBzjxfcD3Nr+kcQAl3y8sIeEXOm6T7bb4HmY/X2bLrV6rLCPia8T2UlyPASDfM66wzRzbRbHUg8/dar/FTHn8Hr0ZgXX3bPnHzzP7PjMTzjNFrA3n/yspGfTpePaH/w/wyyLPRvFi4WvD9/etHD+RW+Z2fwMRsbemql+/foLb2HLqxRdfNC2HwsLCbI0bN7atWbMm0VZOI0eOdPkYjz/+uC0gIMC0qXLl559/Nq2WTp48maJ937Vrl61v3762MmXKmFY5bEXEfRw3bpxTu6z4bce4r/Pnz09w+6pVq2x33nmnea7FihWzvfzyy6ZlF9dfunRpgvZbruzdu9c8V66TmE2bNtm6d+9uK1WqlGllxnZHbP+zYcOGBPvL17Ry5crm+RUsWNB233332TZu3Ghf58cff7TVrFnTFhoaal6H999/37QGit/GzN32W66el9VqyRFbX/Xo0cO85rlz5zbHmK8f15s+fbrNHXzeXN/xuK9cudIsu/vuuxOsH79NFa1evdq00+Lr49iKKyXPxRU+DttW8fjz9eVx4nGI30rOar+VWCs1tmvi/YKCgkzLsWeeecZ2/vz5ZJ8XTZ482Tw3vh/5OteoUcO8J48dO+a0Ht8DjRo1Muux/RQ/y99995399kuXLpljlSdPHrOv1mMl1pbqt99+M58ja3sdOnSwbd++3eXryPeBq9cjqRZ6xPditWrVEix39Vrw/dG7d29bgQIFzHHm6xB/n5P6Pyj+87T20dUl/mO7c/xS8lxE3OHHf249HBaRjMJm8qwTZYN98V6cPINZZrbOYn2nN2Pmj5ldDg5Mb8y8s947JTXGIuK7VFog4mVYl5fYqU7JnHjK2XFQGWs6eQqap7vr1Knj0X3zNiwD4UAqERFSICviZVgHJ96FA9sYzLKWkgPUOL0u65NZ75reXRN8BWszmcVmG7JBgwZ5endEJJNQICsiks6aNWtm+t7y1DtHzHPyAGZkOQhN3MPgn68ZW9txYJGICKlGVkRERES8kvrIioiIiIhXUiArIiIiIl5JNbIusJE6Z6lh8+j0ntZRRERERG5i1SsnvylWrFiCKZHjUyDrAoPYkiVLeno3RERERLKsw4cPo0SJEkmuo0DWBWsaP76A7PMoGY9zx3O+cmu6SfFuOp6+Q8fSt+h4+o4oHzqWERERJqHozrTKCmRdsMoJGMQqkPXcBzJbtmzm9ff2D6ToePoSHUvfouPpO6J88Fi6U96pwV4iIiIi4pUUyIqIiIiIV1IgKyIiIiJeSTWytyAmJsbUpEja4+saGBhopvPk65yRWFsUEBCQoY8pIiIiKadANpX9zU6cOIHw8HBP74pPv8ZFihQxnSM80cs3T5485vHVR1hERLKk8MNA5NnEb8+WH8jj+ValCmRTwQpiCxUqZEYIKthJn0kpLl26hBw5ciTbDDmtA+jIyEicOnXKXC9atGiGPbaIiEimCWLH1wWiryW+TmAI0G+jx4NZBbIpxNPcVhCbP39+T++OTwey169fR2hoaIYGshQWFmZ+MpjlcVaZgYiIZCmRZ5MOYom3cz0PB7Ia7JVCVk0sM7Hiu6zjqxpoERGRzEsZ2VRSOYFv0/EVEZEs5dpF4Nx+4Nxe4MBKeAsFsiIiIiJZwbVLwLl9ccEqf551+P3SSXgjBbIiIiIivuL6JeDM4XjB6o2ANblglZ0I8pUHQvMAexbBG6hG1oNiYm1Ys/cs5v111Pzk9fTSoUMHtGnTxuVtK1asMKfSt2zZkux2Hn/8cbMuL+y3WrZsWbz88sum32tSLl68iOeffx6lS5c2g6kaNWqE9evXJ7ptDrDKmzcv7rvvPvvt165dw2OPPWbmka5UqRJ+++03p/uPHDkSzz33XLLPQURExOszq8e3ANvmACtGAXOfRcBX7dH6n+cQNLIM8MndwKzHgSVvA399AxxafTOIZbBaoj5Q82Hg3teBLp8DfZcCrxwEXt4HPLkYaPY6vIUysh6yYOtxDPtpO45fuBkAFs0diqEdqqJN9bRv+dSnTx906dIFR44cQYkSJZxumzp1KurVq4eaNWu6tS0GxLwPB0Jt3LgRvXr1MsHn+++/n+h9nnzySWzduhVff/01ihUrhm+++QYtWrTA9u3bUbx48QTbZtcCBr8FChSw3zZ58mTzeGvWrMGvv/6KHj164OTJk+ax9+/fj08//RQbNmxI1esjIiKS+csAEs+s+gMIdcqslovLruYvf+P3G5ewPPAlCmQ9FMQ+880mxM+/nrhw1Syf+GidNA9m27dvj4IFC+KLL77AkCFD7MvZq3XWrFkmm3n27Fn069cPf/zxB86fP4/y5cvjtddeQ/fu3Z22FRISYiYLoJIlS5qAdPHixYkGsleuXMHs2bMxb948NGnSxCx766238NNPP2HixIl45513EmybgSw7BzD7avn333/RsWNHVKtWDeXKlcOgQYNw5swZ87yeeeYZ8/iO64uIiHhHsHojQE1xGUA5e7AanbsUVv17HI3aP4agnDeTQKnCbbNPbHJ9ZLmehymQTaMm+lei3JtGleUDQ3/cliCINdvhaHkGeT9uR+MKBRDgn/TI+bCgALdH13O61549e5pA9vXXX7ffj0Ese+MyWGVQW7duXbzyyismIPzll1/MqXwGtPXr13e5XWZZV69ebUoGEhMdHW0egz1hnfY/LAwrVzqPjFy2bJnp3cqygsaNG5vglIEq1apVy2R0GRgvXLjQTFbAjO23335rtv3AAw+49VqIiIh4LFh1HGSVkmCVPx2zq/Eyq7aoKIQfnA+E5r71fWZvWE52oJm9sgYGsVXfXJgm22IweyLiKmq8lXyR9fa3WyNbsPuH8IknnjCZ1+XLl+Oee+4xy3ganyUHuXPnNpeXXnrJvj7rTRkwzpw50ymQ/fnnn82MWwxQWbfKCQvGjx+f6OPmzJkTDRs2xPDhw1GlShUULlwY3333nSkRqFChglNZQefOnU3d7e7du002uF27dmY91sxy/1nHW7VqVRPAcr+YOX7zzTdNAMxM8/Tp003gPWXKFKeSBRERkYwPVtkN4EQqgtWyN4LVvPCYPCUzRaCaHAWyWUjlypXNICsGeQxk9+zZYwZ6vf322+Z2Zk3/97//mQDx6NGjZmYtBqrxJ3+49957TUnA5cuX8dFHH5lsL4PhpDCTykCUwSWD0jp16pgsMGteLQ8//LD9d6t84PbbbzdBavPmzc3gsgkTJjhtt3fv3ujfvz82b96MuXPn4u+//8YHH3xglrGcQUREJM2C1fP7gbN7Ux6shuW7EaBmsmDVByiQTQM8xc/sqDvW7T+Hx6c6j9Z35Yved6B+2XzJPm5qBn0x08qAkNlYZi+bNm1qbmO2duzYsRgzZgxq1KiB7Nmzm04DDGgdcbmVSWVQzFP+n3/+udl2Yvg4zAQz+I2IiDBlAd26dTPBamLKlCljMq8MuBnIxrd06VJs27YNn332mamXbdu2rdm3hx56KMkMsYiISPLBary6VbeDVcdBVgpW05sC2TTAelN3T/HfXbGg6U7AgV2u6mRZuVokd6hZL7ka2dRgkDdgwABMmzYNX331lRkkZdXLrlq1Cvfffz8effRRc50Drnbt2mVO5SeGZQUsAXjhhRdMFwHWvSaFgSYvLAlg2QKzp4lhVpgD0Bj0xsd2X88++6ypj2WGl9lk1ioTuynwuoiIiFvB6rkb11MarJrsqlWzqmDVExTIZjAGp2yxxe4EDB8dg1krbOXt6RHEEmtbmQkdPHiwyYyyd6ulYsWK+P77783gLQ62Gj16tGlvlVQgS127djUZUWZ5HWtsHTFoZaB52223mQwr12epA0sDiAPNhg0bZkoU2LWANbJch5nf1q0TZrtZb8sMLEsPiAPDuD63x2wsr4uISBZ1/fKNU/8KVn2dAlkPYGstttiK30e2SDr2kXXEEgCWAjAQZE9XCwdL7du3zwSOrIt96qmn0KlTJ1y4cCHJ7bFGlm27mF1lhpcZ1/i4DQbP7GObL18+E7C+++67pu6VmFXlQK4vv/wS4eHhZr9YxztixAjTkit+pwTW8f7111/2ZQ8++KCppb377rtNsMyMs4iIZIFg1R6wpjBYtdeqKlj1Zn4263ys2DFTyRH8DL7i9yXlKW023+fI+vjtpFKKrbhYM3vq4lUUyhlqamLTKxPrbVjWwOPA15/lCxktLY+zxJV7zJ8/33x5sr68iHfSsfQtmf54JghWHX5PUbBq1a36brAaldmPZRrFYZkuI8vT0RxkdOLECTNoaNy4cYn2LOXAHrZa4kj3gwcPmhHzHIzkiM38uT2uc/z4ccyZM8dkFTMjBq0Ny3u+mbCIiEimC1Z5uXg85cGqlV31wWBVMlkgO2PGDDNIaNKkSWjQoIEZLc/T2jt37jRN8eOLjIw0o9xZkzlw4ECX2+SoeAbEbPXEnqQiIiKSGYLV/Te6AChYFR8JZDmYqG/fvvYBPwxoOZsUWzq9+uqrCda/4447zIVc3U733XefuYiIiIiHgtX42dVkg9W8Di2rHIJVtq/KlnQrSsnaPBbIsjcpT/9zAJCFtZAtWrQwMzllJDb958WxNsOqN+HFEa+zrJg1nLxI+rBKt63XOqPxMfnYPN4ciCa3xvocxf88iffRsczix5PB6vkD8Du/D37n9sOPQet5/twHv2RqVm1heWHLGxec8qeNgar5WTbpzKrea1nusxmVgufgsUD2zJkzptcnpyt1xOs7duzI0H3hyHi2fopv0aJFCWa14gh9todiu6j4EwVI2rt48aJHHpfH9sqVK6bmmlPxStpYvHixp3dB0oiOpe8ez4CYa8h+/SSyX4u75Ljxk5ewqPNJbud6QHZcCimCyyGF7ZdLN35GBea4ueKlG5dDDH6TGbQlWe6zGRkZ6fa6Hh/slRkwK8xaXceMbMmSJdGqVSuXXQsOHz5s+rFqNHv6YTaUQWzOnDntEzZkJB5nTu7QpEkTHec0+nbN/1xbtmzp9aNpszodSx8RFWnKAGJP78Ke9YtxW/5A+F84kMrMalkgb3nz0y8sL3IC5iIZK8qHPpvWmfFMHchy6lGesmXDfUe8zoxnRmKf0vi9SolvhPhvBmaRGVixDMITbaGyCqucwHqtMxofk4/t6j0gqafX03foWHqB65EOg6qsQVY3algdalar8Z9jrmpWy7moWy0Lv2z57BP4SOYT5AOfzZTsv8cC2eDgYNStWxdLliyxt8di8MLrbK4vIiIiKQxWzSCrG7+7McAqNm9ZHL0SimLVGyOgYCV7sKoBVuItPFpawNP5vXr1Qr169UzvWLbfYvssq4tBz549Ubx4cVPDatUtbt++3f770aNHzexOPM3PqUyJtaucAtXCpvZch7NJlSpVyiPPU0REJO2DVXYDiJ9KjSc0T7zZq6zsajkTrMZERWHT/Pko0qQtArw8iydZk0cD2W7duuH06dNmkgNOiFC7dm0sWLDAPgDs0KFDTqeVjx07httvv91+/cMPPzSXpk2bmulJacOGDbj33nvt61i1rwyYv/jiiwx8diIiIikIVs/fmF41jYNVEV/m8cFeLCNIrJTACk4tZcqUsbdlSsw999yT7DoeF34YiDyb+O3Z8gN5SqbLQ/MLw7vvvmv69TKjzYkn+AWCM6TdfffdKFasGF566SWXfXqHDx+O8ePH48iRI8nWr/BYcfY14qCp8uXLY8CAAXjyySeTvN/evXvN469cudK0ROMEGXxMx+4Wjtu2MGtv7fOBAwdMNp/t3Vi+8tVXX5n7WNq3b2+y/l26dHHzVRMRSetg1apbTWmwGr9uVcGqZG0eD2SzHAax4+sC0Tf71iYQGAL025jmwSwDvMaNGyNPnjxmGt8aNWqYUY4LFy7Es88+a9qePfroo5g6dWqCQJZfDpjRZoDobhH222+/bSa8YBuNWbNmmd9ZKpLYhBUsK2GnCM7M9ttvv5kykQ8++AAdOnTA2rVrnbLz1rYt7G5gefHFF83jfP755xgyZIgJjL///nv7bHLcjoJYEcmwYPXcjespDVYds6sKVkVcUiCb0ZiJTSqIJd7O9dI4kP3vf/9rRuKvW7cO2bNnty+vVq2amdKX+vTpg7Fjx5qM6F133WVfZ/ny5di3b5+5ff369XjttdewefNmEwgzo/vRRx+hTp06To/H4NLqQPHKK6+YoJStQRILZFetWmWCbW6Xdc9sv8HgOX/+/Pj999/NZBmuth3fv//+a2aNq1ixIh5//HETyFJ4eLgJbLktEZFUU7AqkmkokE0LLGVgTz53RF9xfz3OoJKUoGzsT+XW5s6dO2fqj1lW4BjEWpilJWZpOQ0wpwl2DGSZpW3UqBEqV65sAkHWHI8bN85kakeNGoW2bdti9+7dTplRC7tRzJkzB+fPnzfdKhLDUgIG2o6t0NjDlRlUBtaOgex7771nSh04gK9Hjx4YOHCgmayCrIwus7uc1KJmzZpm+aBBg0zmmT2CRUTcClbtU60qWBXJjBTIpgUGsf8rlrbbnNIm+XVeOwYEJwxKXWEnBwadDESTw6wrs5gff/yxyYxyYgKemud1atasmdP6kydPNoEws7asP7UwC8sMKANUzo7FzhFJ1cjeeeedJsjm/d555x1TasD7s3fv8eM328j079/fZH+5vdWrV5sJLXg7s7DEAYD/+c9/TF0sg9hPPvnEzNDF7hXvv/8+HnroITMokIEun1NSwbWIZKVg9Ua9qlvBam6HWlUFqyKeokA2i0jJALju3bubDOfMmTNNyYFVV8ouE9akFQwwORjv1KlTJtBkHSy7TDhiBpSn9hlk8neWNlht0lwpWLCgqaV95plnTIDJx3z44YdN0OpYH+s4CxsDVQaiDFw54IvZXNbH/vzzz/Z1rEFjX375pQmQmTXeuXMn2rRpY4Lc5557zu3XRkR8JFjlJeJoCoLVeIOsFKyKZAoKZNMCT/EzO+qOE1vcy7Y+sQAoUjP5x3UT60V52p4DupLDaXkffPBBU07AQJY/mcVkdpZYVnD27FlTS1u6dGkTPDZs2ND09o0/exsDV14YoLJsgT2Dq1atmuhjM0vKzgUMkK9cuWLKANhJoVy5conep0GDBibjy/ra2267LcHt//vf/8x22cGAA8QYzHLAWufOnU2ZhAJZES8XdeXmjFVpEaxa2VUFqyKZngLZtMA6VTdP8SMwzP313N2mG3ganlnJCRMmmFPz8etkORDKqpO1ygvYyoyZTZ6+Z5cDx0FZ//d//2fqYunw4cM4c+ZMko/PgJQZXZYBzJs3L9n9ZRDMwV4MNBnUduzYMdF1WTLAjC1bibka+DVt2jSzDjF7zAFqxJ+8LiJeFqzGz67eSrDKqVjdHGsgIpmPAtkshEEs229xFjW2r+JpeWYy2Ulg4sSJJuizNGnSxGRS2W6LdbUc6OWY3f36669NdpXBJssG2Cs2OewjW716dVOfyvu6wuxvlSpV7J0K2B2BZQ5WpnXNmjX4888/zaQXLBHgdd7OtmF58+ZNUE7x1FNPmY4KVuDO5//pp5+iUqVKpr8syyhExIeCVXutqoJVkaxAgWxG42QH7BObXB9ZrpfGeHp+06ZNpnMBe62ydpV1qTzlzkDWEcsQWFbAQJJZVEfsz8oAkbWrzLTy1L3V4iopLCngKX7O5DZ//nyX67B2lY/HLgvsSMDHd6yJZRnD9OnT8dZbb5na17Jly5pA1nEdx0FonEjBcQAa78cuByxHYI0suxiIiLcGqw51qwpWRbIkP1umnwYr4zHLmDt3bly4cMHUizq6evUq9u/fbwIotobytpm9vAVbdvE48PV3HOiVUdLkOIsdyzj45YXlKO5OqCFefCzTI1i1BlgpWE1T+mz6jigfOpZJxWHxKSPrCQxSs3igKiJezgSrux2mWk1BsBqSG8gff6pVBasiknIKZEVEJJnMqjV71T4EnNmDVse2I2jzuaTvq2BVRDKAAlkRkazMRbAal13dD0QcSbA6C33CXAWr8QdZKVgVkQygQFZEJCsEq+cPOEy1mnSw6iResBqdpwxW7ziOhu0eRVCuwgpWRcSjFMiKiGSU9Bzo6RSsOtat7r9Rs5rEuF6XmdUb1+NlVm1RUTh/eH7cviqIFREPUyB7C6PqxXfp+Eq6BLHj6ybfeq/fxsSDWVfBqsmu7ktBsOqiblVlACLipRTIplBwcLBpB3Xs2DHTg5XX2XNV0j6Q5JS3bIOVke232I2Oj3v69GnzuDy+ImmCmdikglji7RHHgeuX0iZYdaxbVbAqIj5IgWwKMbhhb1FOJsBgVtIvoLxy5YqZMcwTXxSyZctmJmTwRA9byeKmtEz69kSDVQ6w0ul+EclaUhzIhoeHY86cOVixYgUOHjyIyMhIk5m8/fbb0bp1a6epTFMyderIkSNx4sQJ1KpVC+PGjTPTqLqybds2MzPUxo0bzeNz+tHnn3/+lraZUszSMcjh9K4xMTFpsk1J2Nj5jz/+MFPlZnRj54CAAAQGBirTLmkrNtr9dUNyuZ5qVcGqiEjqAllmHxlAfvvttyhWrJgJCmvXrm0yZpxOdOnSpfjwww9RunRpDB06FN26dXNruzNmzDDTi06aNMlMGzpmzBgTEHOq0kKFCiVYn4Ezp1rt2rWrmZo0LbaZGgxyGGB5++wZmRWDSX5R4Kxaeo3Fa10+A+xeDOxeCOxa7N59es4DyjZVsCoikpaBLDOuvXr1MpnQqlWrulyHp4Lnzp1rAsfDhw/jpZdeSna7o0ePRt++fdG7d29zncHnL7/8gilTpuDVV19NsP4dd9xhLuTq9tRsU0QkTXDG7xNbgF0MXBcCRzcmXdPqSmgeBbEiImkdyG7fvh358+dPch1mZ7t3724uZ88m0WLmBg6qYWA8ePBg+zLWJLZo0QJr1qxxd9fSfZsiIom6dgnYtywu68rs68XjzrcXqQFUagPkLQfMe8ZTeykikrUD2eSC2NSsf+bMGVNjWrhwYaflvL5jx44UPd6tbPPatWvmYomIiLDXafIiGc963fX6+wafO57n98N/z2L48XJwFfxirttvsgVlh61sE8RWaAlb+ZZArqJxNxz/G+4UyURFR/OFQmblc8cyi9Px9B1RPnQsU/IcUt21YPfu3aYu9tSpUwl6brKW1puMGDECw4YNS7B80aJFZvS6eM7ixW7WFYpX8Nbj6RcbjfyXd6Hwhb9QOOJv5LzmnHW9HFwIJ3PXwolctXE2R2XE+gcBXOX4ZgC8AGHXz6C5XxACbIn/Bx3jF4Slf/6NK8Fss5W5eeuxFNd0PH3HYh84lhwPla6B7KeffopnnnkGBQoUQJEiRZxGd/N3dwNZ3p+Dek6ePOm0nNe53dRIzTZZhsDBYY4Z2ZIlS6JVq1bIlStXqvZDbv3bGD+MLVu21GAvH+CVx/PSKfjtXRKXed2/FH7XLtpvsvkHwlbyTtgqtERshVYIzl8BJf38kNycXLH3NkNsMjN73Zu7BDIzrzyWkigdT98R5UPH0joznm6B7DvvvIN3330Xr7zyCm61jVXdunWxZMkSdOrUySxjdpfX+/Xrl2HbDAkJMZf41JXA83QMfEumPp48s3Tib2DXorh616ObnAdqZSsAVGwFVGoFv/LN4Bea2ywOSMljFCgLgBfvl6mPpaSYjqfvCPKBY5mS/U9VIHv+/HnT/iotMBPKbgj16tUzLb3Y8eDy5cv2jgM9e/ZE8eLFzel/azAXB55Zvx89ehR//fUXcuTIgQoVKri1TRERg1nWvUtvDtS65HwmB0VrxQ3UqtgaKHY7R456ak9FRCStAlkGsawfffrpp3Gr2G+W04GyHIGTF7A37YIFC+yDtQ4dOuQ0uxL72bIVmIW9a3lp2rQpli1b5tY2RSQL49SvbI3F4PXAKiDWoWY1OAdQ7h6gUuu47GvO1JU4iYhIJg5kmfl84403sHbtWtSoUSNBCrh///4p2h5P+Sd22t8KTi1lypQx05feyjZFJAuJvg4cWh1XMrBrAXBur/PtnC2LGddKrYDSjYHAhGVGIiLiQ4Hs5MmTzan85cuXm4sjDvZKaSArIpKmLp4Edt+odd27DLh+c6AW/AOB0o1ulgwUiCtJEhGRLBLI7t+/P+33RETkVgZqsdWVNVDrWFzLK7vshewDtVDuXiBU3UhERHxBqvvIWqzT/I4tuERE0t3VCGDf0hv1rouBy6ecb+fgLFMy0BooWlsDtUREfFCqA9mvvvoKI0eONBMjUKVKlTBo0CA89thjabl/IiI3ndkTV+fKrOvBNfEGauUEyt8bF7hWaAnk1OBOERFfl6pAdvTo0WawFwdTNW7c2CxbuXKl6WLAKWIHDhyY1vspIllR9DXg4KqbJQPn9jnfnr/CzYFapRoBgcGe2lMREfGWQHbcuHGYOHGi6fFq6dixI6pVq4a33npLgayIpN7FE3EDtVgysI8DtS7dvI1Tv5ZpfGOgVisgf3lP7qmIiHhjIHv8+HE0atQowXIu420iIikaqHVs083ersf/dr49R+EbA7Vax/V4DcnpqT0VERFf6SM7c+ZMvPbaa07LZ8yYgYoVK6bVvomIr7p6Adj7e1zJwB4O1DrtcKMfULzOzZKBIrU0UEtERNIukB02bJiZPeuPP/6w18iuWrUKS5YsMQGuiIgTmw05rh6D/9rxwN4lwCEO1Iq+eXtIrhsDtdrEDdTKUdCTeysiIr4cyHbp0gV//vknPvroI8ydO9csq1KlCtatW+c0fayIZGFRV4GDK03WNXDXQjQPPwD863B7gUo3SwZKNQQCnGcIFBERSbf2W3Xr1sU333yT2ruLiC+KOHZjoNaiuB6vUZFmMbtMx/gFwq/s3fBn1pUlA5waVkREJCMC2YiICOTKlcv+e1Ks9UTEx8XGAEc33ezteuIf59tzFjVZ1+hyzbFg11W07tAZ/kHKvIqISAYHsnnz5jUdCQoVKoQ8efK4nMmLs3xxeUxMTBrtnohkOlfC4+pcrYFakWcdbvQDStRzGKhVk9P+wRYVhZi98z240yIikqUD2d9//x358uUzvy9dujQ990lEMhNOQ316Z1zGlS2yDq0FbA5fVkNyAxWaxQWvFVsC2Qt4cm9FRCQLcTuQbdq0qf33smXLomTJkgmysszIHj58OG33UEQ8M1DrwIqbvV3DDznfXuC2uEFavJRsoIFaIiLiPYO9GMhaZQaOzp07Z25TaYGIF7pw9EbWdRGwf7l9oJYREAKUvftmyUDeMp7cUxERkdQHslYtbHyXLl1CaGhoajYpIp4YqHVkw83g9WT8gVrF4oJWdhko2wQIzu6pPRUREbn1QPaFF14wPxnEvvHGG8iWLZv9NmZh2Vu2du3aKdmkiGSkyHM3ZtRaCOz5DbhyzuFGP6Bk/Zu9XQtXNwO1REREfCKQ3bx5sz0j+88//yA4ONh+G3+vVasWXnrppbTfSxFJ/UCtU//ezLoe5kCt2Ju3h3KgVou4kgH+zJ7fk3srIiKSfoGs1a2gd+/eGDt2bJr1i50wYQJGjhyJEydOmGB43LhxqF+/fqLrz5o1y2SEDxw4gIoVK+L9999H27Zt7befPHkSr7zyChYtWoTw8HA0adLEbJPrivi8qCvA/hU3g9cL8QZqFaxys2SgRH0gINXzooiIiHhUqv6CTZ06Nc12YMaMGaZkYdKkSWjQoAHGjBmD1q1bY+fOnQkGk9Hq1avRvXt3jBgxAu3bt8e0adPQqVMnbNq0CdWrVzfZYl4PCgrCvHnzTLA9evRotGjRAtu3b0f27KrzEx8UfthhoNYfQPSVm7cFhsbVuLJkgJe8pT25pyIiIp4NZC9fvoz33nsPS5YswalTpxAb63CqEsC+ffvc3haDzL59+5osLzGg/eWXXzBlyhS8+uqrCdZnJrhNmzYYNGiQuT58+HAsXrwY48ePN/fdvXs31q5di61bt6JatWpmnYkTJ6JIkSL47rvv8OSTT6bmKYtkLjHRwJH1N4PXU9ucb89VIi7rypIBM1DrZj27iIhIlg5kGQwuX74cjz32GIoWLeqyg4E7rl+/jo0bN2Lw4MH2Zf7+/iZ7umbNGpf34XJr0JmFGdy5c+ea369du2Z+OnZP4DZDQkKwcuVKBbLi3QO19nBGrQVxA7Wuht+8zc8/rkzA6u1aqKoGaomIiM9LVSD766+/mqxp48aNb+nBz5w5Y7odFC5c2Gk5r+/YscPlfVhH62p9LqfKlSujVKlSJjj+5JNPTCnBRx99hCNHjpjet64w+LUCYIqIiDA/o6KizEUynvW6Z+nX3wzU2g7/PYvhx8vR9fBzGKhlC8sLW7lmiK3Q0vxEtriZ94zoaGQmOp6+Q8fSt+h4+o4oHzqWKXkOqQpk8+bNa5+uNrNhbewPP/yAPn36mH0MCAgwGd777rvP1M+6wnrbYcOGJVjOwWKOLcYk47FsJCsJiL2GAhe3o3DE3yh84S9ki3JsjwVcCC2Jk7lr4WSuWjifvQJsfgEAx3Jx2lgvkNWOpy/TsfQtOp6+Y7EPHMvISIcJedIjkGVd6ptvvokvv/zylgK9AgUKmECTXQYc8TprWl3h8uTWr1u3Lv766y9cuHDBlC8ULFjQDCSrV6+ey20ye+tYrsCMLKfgbdWqVZp1ZpCUfxvjh7Fly5bmy4lPu3AY/ruZdV0Ev4Mr4Rd91X6TLTAMtjJ3w1ahpcm8ZstdAmU5ux68S5Y6nj5Ox9K36Hj6jigfOpbWmfF0C2RHjRqFvXv3mlP6ZcqUSfCCsYOAO9h7lkEnB42x0wBx4Biv9+vXz+V9GjZsaG5//vnn7ct44Lg8vty5c5ufHAC2YcMGE4C7wvpZXuLj8/L2N4O388ljwIFah/+8OVDr9L/Ot+cuZR+o5Vf2bvgFhZnFAfB+Pnk8sygdS9+i4+k7gnzgWKZk/1MVyFpBZ1pgJrRXr14mW8resWy/xa4IVheDnj17onjx4ub0Pw0YMABNmzY1wXS7du0wffp0E6ROnjzZqc8ss7CsleXEDbwP95kZVhGPuHw2boAWg1czUOvCzdtYHlCywc3ergUra6CWiIhIegWyQ4cORVrp1q0bTp8+bUoVOGCLU9wuWLDAPqDr0KFDpuuApVGjRqZ37JAhQ/Daa6+ZSQ7YsYA9ZC0c1MUAmSUH7KrAYJgTKIhkGNZjn9wa12GAWVe2yoJDjXZYPqBiy7i+rhWaA2F5Pbm3IiIiXinVU/pwxqzvv//elBiwpysHVrGkgAEoM6gpwTKCxEoJli1blmBZ165dzSUx/fv3NxeRW5pgIPJs4rdnyw/kKem87PplYN/yuKzr7sVAxFHn2wvXuNnbtUQ9wN8XigVERES8LJDdsmWL6QTAGlROE8sJDRjIslsAM6hfffVV2u+pSEYGsePrAtE3W7IlEBgC9NsI2GLiMq4MXjktbIzDfYKyAWWbxvV1ZeY1d8q+4ImIiEg6BLI8bf/444/jgw8+QM6cOe3L27Ztix49eqRmkyKZBzOxSQWxxNu/aAeEH3Renqf0jcC1NVDmLiDo5sQcIiIikgkC2fXr15vJBuJjSYE1MYGIz2MQy4FapRreLBkoeJsGaomIiGTmQJatqlz1+Nq1a5fpFiCSJTQfCtR7AgjL4+k9ERERyZJutgNIgY4dO+Ltt9+2TyHm5+dnamNfeeUVdOnSJa33USRzKt9MQayIiIi3BbLs4Xrp0iUUKlQIV65cMX1dK1SoYOpl33333bTfSxERERGRtCgtYLcCzqa1cuVK08GAQW2dOnVMJwMRrxYbC6yZ4Om9EBERkfQKZA8fPoySJUvirrvuMhcRnxATBfz4HPDPTE/viYiIiKRXaUGZMmVMOcGnn36K8+fPp2YTIpnL9Uhg+iPA39/FfSz8k/mOxz6ynBRBREREvCsju2HDBjNNLAd8Pffcc2jTpg0effRRdOjQwXQ0EPEqkeeA7x4GDv8JBIYBD30JFKqa8pm9REREJPMHsrfffru5cEIETiHLoPapp55CbGwsOnfujClTpqT9noqkhwtHgW+6AKf/BUJzAz1mAaUaxN2mQFVERMT3SgssbLt17733mhKD3377DWXLlsWXX36Zdnsnkp7O7AamtI4LYnMWBXovuBnEioiIiG8HskeOHDFZ2dq1a6N+/frIkSMHJkzQiG/xAkc3xgWxFw4D+SsAfRYBhat6eq9EREQkvUsLOD0tywlWrVqFypUr45FHHsG8efNQunTp1GxOJGPt/R2Y/igQdRkodjvwyPdA9gKe3isRERHJiED2nXfeQffu3fHxxx+jVq1aqdmEiGdsnQ388B8gNgoodw/Q7RsgJKen90pEREQyKpDldLSsjxXxKn9OBn59GYANqNYZeGBSXBstERERyTqBLIPY8PBwrFu3DqdOnTLdChz17NkzrfZP5NbZbMCyEcDy9+Ou138KaPM+4H9LJeIiIiLijYHsTz/9ZOpiOTVtrly5nLKz/F2BrGQasTHALy8CG6fGXb/3daDJIL5RPb1nIiIicotSlZJ68cUX8cQTT5hAlplZzu5lXc6dO3er+ySSNqKvAbMevxHE+gHtRgNNX1YQKyIikpUD2aNHj6J///7Ili1bmuwEW3Zx2tvQ0FA0aNDAlCwkZdasWaZbAtevUaMG5s+f73Q7A+x+/fqhRIkSCAsLQ9WqVTFp0qQ02VfxElcj4iY6+PdHICAY6PoFcEcfT++ViIiIeDqQbd26tZmmNi3MmDEDL7zwAoYOHYpNmzaZLgjcPmtvXVm9erXpmNCnTx9s3rwZnTp1MpetW7fa1+H2FixYgG+++Qb//vsvnn/+eRPY/vjjj2myz5LJXToFfNEOOLACCM4Z116rWidP75WIiIhkhhrZdu3aYdCgQdi+fbvJiAYFBTnd3rFjR7e3NXr0aPTt2xe9e/c215k5/eWXX8w0t6+++mqC9ceOHYs2bdqYx6fhw4dj8eLFGD9+vD3rymC3V69euOeee8x1Tp/L3rfM9KZk38QLnT8AfP0AcG4fkK0A8OhsoFhtT++ViIiIZJZAloEnvf322wlu42CvmJgYt7Zz/fp1bNy4EYMHD7Yv8/f3R4sWLbBmzRqX9+FyZlwdMYM7d+5c+/VGjRqZ7CvreIsVK4Zly5Zh165d+Oijj1xu89q1a+ZiiYiIMD+joqLMRTKe9bqn6PU/uQ2B33WF3+VTsOUuheges4B85bmR9NtRSb/jKZmSjqVv0fH0HVE+dCxT8hxSFcjGb7eVWmfOnDFBb+HChZ2W8/qOHTtc3ufEiRMu1+dyy7hx40wWljWygYGBJjj+9NNP0aRJE5fbHDFiBIYNG5Zg+aJFi9KsDlhSh9l2d+S/tAMN9o2BX0wkLoSWxJqSL+Ha2p0AeBFvO56S+elY+hYdT9+x2AeOZWRkZPoGspkdA9m1a9earCynzf3jjz/w7LPPmuwss73xMSPsmOVlRrZkyZJo1aqVaS8mnvk2xg9jy5YtE5SuxOe3cz4C5oyCX8w1xJa8E9ke+hbNQ3Nn2L5K2h5Pydx0LH2LjqfviPKhY2mdGU/XQHb58uX48MMPzWAqYmcA1q3efffdbm+jQIECCAgIwMmTJ52W83qRIkVc3ofLk1r/ypUreO211zBnzhxTy0s1a9bEX3/9ZfbXVSAbEhJiLvHxjeDtbwZvl+wx2PQ18FN/wBYL3NYW/g9OgX9QWEbuoqSAPlO+Q8fSt+h4+o4gHziWKdn/VHUtYDcABoQ87c42XLywzVXz5s0xbdo0t7cTHByMunXrYsmSJU5lC7zesGFDl/fhcsf1id9ArPWtulaWEzhiwJxWJRGSSWbrWvkR8GO/uCC29qPAQ18DCmJFRESyjFRlZN9991188MEHGDhwoH0Zg1l2IGAXgR49eri9LZ7SZ4eBevXqoX79+hgzZgwuX75s72LAWcKKFy9u6lhpwIABaNq0KUaNGmUyrtOnTzetwCZPnmxuZykAb2d2mME1SwuYPf7qq6/M/okP4BeSRUOAtRPirjd+HmjxliY6EBERyWJSFcju27cPHTp0SLCcra14Wj8lunXrhtOnT+PNN980A7Zq165tesBaA7oOHTrklF1lRwJmfYcMGWIeq2LFiqZjQfXq1e3rMLhl3Sun0eVMYwxmGXw//fTTqXm6kpnERAHzngW2zIi73updoFE/T++ViIiIeEsgy4FQPL1foUIFp+W//fabuS2lOFkBL66wdVZ8Xbt2NZfEsF526lROSyo+5fplYGYvYM9iwD8QuH8CUOthT++ViIiIeFMg++KLL5pSAg6gYoaUVq1ahS+++MJMWCCS5iLPAdMeAo6sBwLDgIe+Aiq18vReiYiIiLcFss8884zJerJOdebMmWZZlSpVzHSz999/f1rvo2R1F44C33QGTu8AQvMAj8wCStb39F6JiIiIh6W6/dYDDzxgLiLp6sxu4LuuQMQRIGcx4LEfgEJVPL1XIiIikgmkqv3W+vXr8eeffyZYzmXsICCSFvJc3ovAr9rFBbH5KwJ9FimIFRERkVsLZDlL1uHDhxMsP3r0qLlN5Fb57VuKxnveg9+Vc0CxOsATC4E8KR9IKCIiIr4rVYHs9u3bUadOnQTLb7/9dnObyC3553sEzOiBwNhriC13L9DrJyB7fk/vlYiIiPhCIMvpXONPE0vHjx9HYGCqy25FgLWTgNl94BcbhSN57kTMQ98CITk8vVciIiLiK4Fsq1atzIQDFy5csC8LDw83ExS0bNkyLfdPstKUs7+/Ayx4xVyNqdcXG8s8DQQEe3rPREREsqyYWBvW7D2LeX8dNT95PTNJVfr0ww8/RJMmTcyMWSwnIPaU5WxcX3/9dVrvo/i62BjglxeAjV/EXW82BLF3DgB+/dXTeyYiIpJlLdh6HMN+2o7jF67alxXNHYqhHaqiTfWi8NpAtnjx4tiyZQu+/fZb/P333wgLC0Pv3r3RvXt3BAUFpf1eiu+Kugr88CTw70+Anz/QbjRQrzcQFeXpPRMREcnSQewz32xC/PzriQtXzfKJj9bJFMFsqgtas2fPjqeeeipt90aylqsXgOmPAAdWxJUQdPkcqNrR03slIiKSpcXE2kwm1lURAZf5Aeb2llWLIMCf1zxHI7PEMy6diput68Q/QHBOoPs0oGwTT++VSIb9kVi3/xxOXbyKQjlDUb9sPo//MRCR5MXG2hBjs5nPcKzNhmj+5DKH5ea2WNy4HosY/u6wvvW7ta51X27Hvr14t8etjxvb4+24ub4tbp2o6GjsPOSP7Yt2A35+Zpnj7ebxY24+Frdh314snJ7PucvXncoJXAWzvJ3/jzUs79muQgpkJeOd2w98/QBwfj+QvSDw6GygaC1P75VIhvCGmjPxbTYrSLLZcPV6NK5GAxeuRMH/OgOZWHsQZgVKtxJ4me3d+N2+PSuQihcAxg/MzHKnwMvxMZB0IHnjd8f9S/T5mNuQMPCLv782mxmXnLn5A0f3Z9ij8cu4pymQlYx1fAvwTRfg8ikgT2ngsTlA/vKe3iuRDOEtNWfeFozZs18x7mXLks2m2bNfzkFbgsDrRoYrqcDr5mNYgVdchi5BYOZWYOj4+FZgyEDRYV/jBV6uXpOEwVggsH6pZw6kD/HzAwL9/eDv52fOsATwZ0DcT3/ruv/NC0/CBPr7x93mD6fb7duwLje2YbYff1t+ccv8EIsjhw6hXNkyCAoMsK/v9Pg39sd6jMCAePt7Y5t7T1/CuN/3JPuceUbJ0xTISsY5sBL4rjtwLQIoXAN49HsgZxFP75VIpqk5e+vH7ahfNr/5PcnAK6nsV0qzaYncZj+NaQVNN4K2qJgY7N/vjzU/bofN5pdI0JbcaVSH06JuZMtcZesyWQcgn+IYLNl/twIf6/dEAi/H+9oDqfiBmRVIWeub60gQmLkMvBz2x+nxE+wvbqzvb//d7cAw0ecTF3hav8d/Pn6MZD0oKioK8+cfQNu2lW954D0/Y99vPGK+ZLv6qPGZFskdVxbllYEsp6flAStRooS5vm7dOkybNg1Vq1bVADBx7d+fge+fAGKuAaUbAw9PA8LyeHqvRDLMmr1nkq05OxFxFXWGL0bm5w+cPILMLEGg42cFHnGBjbuBTPKBFwMb3AykHDJczoGf68e4+fjO+3dLgZf9Nm4z8cCL27HFRGPxokVoe18bhAYHm2UiAf5+ptyJZ4r4jnAMZq13CG/PDLX9qQpke/ToYQLWxx57DCdOnDCTIFSrVs204+L1N998M+33VLzXxi+Bn58HbLFA5fZAl8+AoDBP75VIurp8LRqbD4Vj/YFz2HDwHNbvP5fibdw89egceCV76jFe4OUcyMQFXsmdWkwsWOLpy3179+K2ShURHBiQIPBKfUbOdeDl9Hxu7K87GTtxDzsdBvkDQQFxp7hFLCxzYrlT/Jr+Ipmspj9VgezWrVtRv3598/vMmTNRvXp1rFq1CosWLcLTTz+tQFbisBBr5Whgydtx129/DGg/BghQRYv4Hg562HjgPNYxcD1wHtuPR6RqBpyvn6iPRhUKmCDW06cqEz19eX032t5bXn3DRXxcm+pFTYutzNxlJTC1/5GFhISY33/77Td07BjX+7Ny5co4fvx42u6heCcW6i16HVj7f3HX73oBaP5mXDW8iA8MNNp35jI2HDiH9QfOm58HzkYmWK94njDcUSYv6pXJhzql8uKJL9bjZETSNWcMYjPTHwkRydoC/P083mIrzQNZlhFMmjQJ7dq1w+LFizF8+HCz/NixY8ifP+VPdsKECRg5cqQpS6hVqxbGjRtnz/i6MmvWLLzxxhs4cOAAKlasiPfffx9t27a1355YFuODDz7AoEGDUrx/kkLR14F5zwL/zIy73noE0PC/nt4rkVS7Hh2LbccumExrXKnAedNn0RH/26lcJJc9cK1XOi+K5XEuoXmro3fUnImIeItUBbIMHB944AETfPbq1csEn/Tjjz8mGYC6MmPGDLzwwgsmMG7QoAHGjBmD1q1bY+fOnShUqFCC9VevXm2mwh0xYgTat29vBpl16tQJmzZtMiUOFD8r/Ouvv6JPnz7o0qVLap6upMT1y8DMnsCe3wD/QKDTRKDmQ57eK5EUuXg1yl7fystfh8NxNSrWaZ2QQH/UKpnHKeOaOyzIJ2rORER8OpC95557cObMGURERCBv3rz25RwAli1bthRta/To0ejbty969+5trjOg/eWXXzBlyhS8+uqrCdYfO3Ys2rRpY8+sMhvMrPD48ePNfalIEeeWTvPmzcO9996LcuXKpebpirsizwHfdgWObgCCsgEPfQ1UbOHpvRJJFk/3m0zrjYzrv8cjErR3ypMtCPVK57MHrtWL50JIYIBP1pyJiPh0IHvlyhVTI2YFsQcPHsScOXNQpUoVk0111/Xr17Fx40YMHjzYvszf3x8tWrTAmjVrXN6Hy5nBdcTHnDt3rsv1T548aQLjL7/8MtH9uHbtmrlYGKBbtcC8iBsijiLwu67wO7MLtrC8iOn2HWzF68UNiU0F63XX6+8bMtPxZD/SvWcuY+PBcGw8eB4bDoXjyPkrCdYrmTcM9UrnQd3SeVG3VB6UK5DdeVS3LRZR8bK0KVGvVC4AvACxMdGIjYFXyEzHUm6djqfviPKhY5mS55CqQPb+++9H586dTYeC8PBwUxLA0avM0jLD+swzz7i1Ha4fExODwoULOy3n9R07dri8D+toXa3P5a4wgM2ZM6fZ38SwTGHYsGEJlrMLQ0ozzFlRjqtH0WjPSARFncOVoHxYXWYQLv19Cvh7/i1vm9l28R2eOJ7RscDhy8C+CD/suxh3iYx2zn76wYbi2YFyOW0ol8tmfuYOvsgiA+DUYew6BezK8D3P3PTZ9C06nr5jsQ8cy8jIhINn0zSQZT3qRx99ZH7//vvvTSC5efNmzJ4927TecjeQzQgsUXjkkUcQGpr4NGrMCDtmeZmRLVmyJFq1aoVcueIyJuKa39GNCJgxAH5R52HLXxGBPb5Hk1zF0+TbGD+M7FGsFj/eLyOPZ8SVKGw+zGxruMm2bjlyAdcYzToIDfJH7RK547KtpfOgdok8yBmqtnDu0GfTt+h4+o4oHzqW1plxdwSmNlJmltPKWjLbyZKAO++805QZuKtAgQIICAgwp/8d8Xr8OlcLl7u7/ooVK8ygMQ4oSwpbiVntxBzxjeDtb4Z0tfs3YOZjQFQkULwe/B6ZhaBsaTtdnY6Bb0mP43ks/IpTfevOkxcTzCWfP3sw6pXJizvYTaBMPlQrlss0gJfU02fTt+h4+o4gHziWKdn/VAWyFSpUMDWp7FywcOFCDBw40Cw/depUijKYwcHBqFu3LpYsWWI6D1BsbKy53q9fP5f3adiwobn9+eefty/jNxAuj+/zzz8327e6Kkga2jILmPs0EBsNlG8OdPsaCM7u6b0SH8f61t2nLtm7CTB4PRqesL61TP5sJmC940bwWrZA9kw5uYCIiNyaVAWyLB/gNLUMYJs1a2YPIpmdvf3221O0LZ7SZwuvevXqmdZdbL91+fJlexeDnj17onjx4qaOlQYMGICmTZti1KhRpo/t9OnTsWHDBkyePDlBWpr9ZrmepLG1E4EFNzpK1OgK3P9/QGCwp/dKfNDVqBj8c/SCPWjlxAMRV6Od1uFof2ZYrY4CdcvkNZ0ARETE96UqkH3wwQdx1113mX6tjtnO5s2bmyxtSnTr1g2nT582wTEHbNWuXRsLFiywD+g6dOiQKVuwNGrUyPSOHTJkCF577TUzIQKzw1YPWQsDXHZWYM9ZSSM8X/v7cGDFjS8HDZ4BWv+PrSY8vWfiI8Ijr5tOAtZsWaxvvR7jXN+aLTjA9Gy1SgVql8yD7CGqbxURyYpS/b8/a1J5OXLkiLleokSJFE+GYGEZQWKlBMuWLUuwrGvXruaSFPa05UXSSEw08MtAYNNXcdc53SynndXpWkklftFkWQAzretMxvUcdp28lGC9AjlC7CUCvFQpmhOBqm8VEZHUBrKsY33nnXfMaftLl+L+8HDw14svvojXX3/dKYMqPiDqKjC7D7DjZ8DPH2g/Bqjby9N7JV6GEwz8e/wi/joaYc+4Os5uZSlXMDvuKM1BWXHBa+n82VTfKiIiaRfIMljlQKr33nsPjRs3NstWrlyJt956C1evXsW7776bms1KZnT1AvBdD+DgSiAgBHjwc6BKB0/vlXhJfSundmXAum7/WazbF4Cra50nOgn090P14rnts2XVK50X+XMk7CAiIiKSZoEsJxn47LPP0LFjR/uymjVrmkFZ//3vfxXI+oqLJ4FvugAn/wFCcgHdvwPK3OXpvZJM6txlq741rqPA1qMXEBXj2AfLD9lDAlCXg7JKxwWurG8NC075NK8iIiKpDmTPnTuHypUrJ1jOZbxNfMC5fcDXDwDnDwDZCwGPzgaK1vT0Xkkmqm89fO5G/9aDDFzPY8+phPWthXKG4I6y+VCnZG5cPbwVT3RugbBQZVxFRMSDgSw7FYwfPx4ff/yx03IuU89WH3D8b+CbB4HLp4C8ZYDH5gD5ynl6r8SDomNisePERaeJB05dvJZgvYqFcjj1by2RN8zUt3LGmfnntmqQloiIeD6Q/eCDD0wP199++83eQ3bNmjU4fPgw5s+fn7Z7KBlr/wpgeg/gWgRQpAbwyGwgZ1wrNMk6Iq9Hm/rW9fvPm4zrpoPncfl6jNM6QQF+qMH61rIsFchnpnvNm139hEVEJJMHspyQYNeuXZgwYQJ27NhhlnGaWtbHFitWLK33UTLK9h+B2U8CMdeA0ncB3acBobk9vVeSAc5cumafcGD9wfPYdvQCotlmwEHOkEAz2YCZ5rV0XtQqmQehQapvFRERL+wjy4BVg7p8yMYvgJ8HArZYoHJ7oMvnQJBmR/LV+tYDZyNvlAnElQrsO3M5wXpFc4fe6N0aNzCrUuGcZhYtERERrwtkt2zZ4vZG2cFAvGi2rhUfAr+/E3e9Ti+g/UeAvzJtvlTfuv14XO/W9fvjBmeduXTdaR22ab2tcE5771YGrsXzhHlsn0VERNI0kOXUsRy0wWxOUrhOTIxzLZ1kUrGxwMLBwJ+T4q7f/RLQbIhm6/Jyl69FY/OhcHtHAf4eGa++NTjAH7VK5rYPzKpbKh9yZwvy2D6LiIikayC7f//+VD2AZFLR14G5zwBbv4+73uZ94M6nPb1XkgqnLl61dxLgT2ZfY+LVt+YOCzJ1rVbgykkIVN8qIiJZJpAtXbp0+u6JZJxrl4CZjwF7fwf8A4FOk4CaXT29V+IGnhFhPasZlHVjcBbrXeNj26u4EoG4UoEKBXPAX/WtIiKSVQPZtWvX4s4773Rr3cjISJPBrVat2q3sm6SHy2eBaV2BoxuBoGxAt6+BCi08vVeSiOvRsdh27MLNjOvB82YGLUesBKlcJJd9UBZ/Fs2t+lYREfF9bgeyjz32GMqVK4cnn3wSbdu2Rfbs2ROss337dnzzzTeYOnUq3n//fQWymU344bjZus7uBsLyAY/MAkrU8/ReiYOLV6Ow6VD4jYzrOdPL9WpUrNM6IYH+ZmpXK+Nap3Re5ApVfauIiGQ9bgeyDFInTpyIIUOGoEePHqhUqZJpwRUaGorz58+bfrKXLl3CAw88gEWLFqFGjRrpu+eSMqd2AN90BiKOArlKAI/9ABS8zdN7leWduHDVDMhixnXd/nPYcSIC8cpbkTdbkD3Typ/Vi+VGcKBmyBIREXE7kA0KCkL//v3NZcOGDVi5ciUOHjyIK1eumGlpBw4ciHvvvRf58uVL3z2WlDu8Dvi2K3A1HChwW1wQm7uEp/cqy4mNtWHv6Uv22tb1B8/h8LkrCdYrlS+bybTWv9EGq3zB7KYbiIiIiKTBhAj16tUzF/ECuxcDMx4Doq8AJe4AeswEsunLhrs4+p+ZUnYGKJQzFPXL5nN7UoBr0THYevSCPXBlfWt4ZJTTOtxU1WK5UK90PnupQOFcmohCREQkXWf2Ei/w9wxg3n+B2Oi4AV0PfQUEJ6xtFtcWbD2OYT9tx/ELV51muxraoSraVC+aYP0LV1jfeiPbeuA8/j4cjmvRzvWtYUEBuL1UHnupwO2l8iJHiD6GIiIiqZEp/oJOmDABI0eOxIkTJ0yZwrhx41C/fv1E1581axbeeOMNHDhwABUrVjQDyzgAzdG///6LV155BcuXL0d0dDSqVq2K2bNno1SpUsgS1kwAFr4W93uNh4BO/wcEaEBQSoLYZ77ZBJuLmlYun/hoHdQskcfeu5U/d568aCZKc5Q/e7DTbFnViuVCUIDqW0VERHwikJ0xYwZeeOEFTJo0CQ0aNMCYMWPQunVr7Ny5E4UKFUqw/urVq9G9e3eMGDEC7du3x7Rp09CpUyds2rQJ1atXN+vs3bsXd911F/r06YNhw4YhV65c2LZtmxmY5vMYSS0ZBqz8KO76nf8FWr0L+Ct4Skk5ATOxruaws5Y9++0mxLhYoWyB7GbiAatMgNdV3yoiIuKjgezo0aPRt29f9O7d21xnQPvLL79gypQpePXVVxOsP3bsWLRp0waDBg0y14cPH47Fixdj/Pjx5r70+uuvmwztBx98YL9f+fLl4fNiooGfBwCbv4m73nwocNdATTmbQqyJdSwncIVBLOtbaxR3mOa1dD4UzBmSYfspIiKS1aUqTXfkyJEkJ05w1/Xr17Fx40a0aHGzIb+/v7+5vmbNGpf34XLH9YkZXGv92NhYEwizPRiXM6vLTO/cuXPh06KuxM3WxSDWzx/oOA64+wUFsanAgV3ueK9LTczrdxfeaB9XM6sgVkRExAsysq1atTLtt+K32lq1ahXatWuH8PBwt7Zz5swZxMTEoHDhwk7LeZ19aV1hHa2r9bmcTp06ZfrZvvfee3jnnXdM/eyCBQvQuXNnLF26FE2bNk2wzWvXrpmLJSIiwvyMiooyl0zv6gUEzHwE/ofXwhYQgpgHPoXttrZ8AvBW1uvuidf/4pWb74WkFMsV7B3vjyx+PCVt6Vj6Fh1P3xHlQ8cyJc8hVYEsp6plMMvAMGfOnGbZH3/8gQ4dOuCtt96CJzEjS/fff7/pbUu1a9c2tbUsPXAVyLLelrW08XFih2zZsiEzC4kKR8M9I5H76mFE+Yfhz3IDcXYvC4XnwxewbCSjXI8BFh7xx5JjzGLzwiJYVxltG/IEA6e3r8X8fzNs93xCRh5PSV86lr5Fx9N3LPaBYxkZGZm+gexnn32GBx980ASuCxcuNEFix44dTQZ0wIABbm+nQIECCAgIwMmTJ52W83qRIkVc3ofLk1qf2wwMDDRdChxVqVLFZJFdGTx4sBlw5piRLVmypAnWOVAs0zq3D4HfdYXf1cOwZS8EdJ+JBoXjBrz5wrcxfhhbtmxpJuNIb3/uP4ch87bjwNm4D8/tJXNj8+EL9nDWEhfW+uGdzrXQuprzmQHJPMdT0o+OpW/R8fQdUT50LK0z4+kWyLKOdfr06aaMoFmzZtiyZYvJavbr1y9F2wkODkbdunWxZMkS03nAyqjyemLbatiwobn9+eefty/jgeNya5t33HGH6XrgaNeuXShdurTLbYaEhJhLfHwjZNo3w7G/gG8fBC6fBvKWhd9jcxCUryx8TXofg4irURgxfwe+W3fIXC+cKwTD76+OVtWKuOwjWySJPrKSvEz9mZIU0bH0LTqeviPIB45lSvbf7UCWwWp8LCNgK6xHH30UTZo0sa9Ts2ZNt3eAmdBevXqZmcLYO5btty5fvmzvYtCzZ08UL17cBMrEjC/LA0aNGmUCaQbUnDJ38uTJ9m2yo0G3bt3MPnHaXNbI/vTTT1i2bBl8wv4/gO96ANcvAkVqAo/OBnIkbFUmSVu07QTemLcVJyPiamJ7NCiFV++rjFyhcR8gBqstqxZJ9cxeIiIikr7cDmRZZ8p+mDaHju/W9U8++cQEkvydyziAy10MOE+fPo0333zTDNji4zDwtAZ0HTp0yGSALY0aNTK9Y4cMGYLXXnvNTIjAjgRWD1l64IEHTD0sg9/+/fvjtttuM5MhsLes19s+D5j9JBBzHShzN/DwNCA0E5c/ZEIMSt/6cRvm/xM3QJC9Xkd0roE7y+VPsC6D1oblEy4XERERLwpk9+/fn247wTKCxEoJXGVRu3btai5JeeKJJ8zFp2yYAvzMWl4bUKUD0PkzICgLTPKQRvhFa9bGI3j3l3/NdLIMUv/TpBz6N6+I0KAAT++eiIiIpFcgm1h9qWQAZsH/GAksfTfuet3eQLtRgL+CL3cdOhuJwXO2YNWes+Z69eK58H6XmqhWLLend01EREQyckKEL7/80kw6YHn55ZeRJ08ec9r/4MGDqd0XcYXtxH59+WYQ2+RloP1HCmLdFB0Ti0//2IdWY5abIDY0yB+vta2Muf9trCBWREQkKway//vf/xAWFmZ+54xanB6W08Gy9ZXVu1XSQPR14IcngXUcyOYH3DcSaPa6Zuty0/ZjEeg8cTXenf8vrkbFolH5/Fj4fBM81aQ8AgNS9dYXERGRTCRV7bcOHz6MChUqmN850Io9ZZ966ik0btwY99xzT1rvY9Z07RIw41Fg31LAPwh4YBJQ40FP75VXuBoVg3G/78Yny/chOtaGXKGBGNKuKrrWK2EGI4qIiEgWDmRz5MiBs2fPolSpUmb2K2sygdDQUFy5ciWt9zHruXwG+LYrcGwTEJQd6PY1UKG5p/fKK/y57ywG//AP9p25bK7fV70IhnWshkK5NChORETE16QqkOWsEU8++SRuv/12M9FA27ZtzfJt27ahTJkyab2Pvin8MBAZN/DIyaUTwC8vARcOA2H5gEe+B0rU9cQeehVObPD+rzvw7Z9xExsUyhmCt++vjjbVXc8QJyIiIlk0kJ0wYYLp48oSA/ZnzZ8/rs/mxo0bzQQJ4kYQO74uEB3XiD9RXb9UEOuGxdtP4o25W3EiIm4Gru71S+LV+6ogd5h3z2wiIiIi6RDIskMBB3jFN2zYsNRsLuthJja5IJY00UGSTl+8hrd+2oZfthw318vkz4YRnWtqAgMREZEsIkVT1HL2LM6y5Wq6WkcpmaJWJDUTG3y/8QjecZjYoO/d5fB8C01sICIikpWkaIpaTiFbqFChJKerTekUtSIpndjgtTn/YOWeM/aJDd7rXBPVi6snrIiISFaToilqCxYsaP9dJCPFxNowddV+jFq0C1eiYhAS6I+BLSvhybvKqiesiIhIFpWqKWqTmq5W7bckrf17PAKvzt6Cv49cMNcblsuPEZ1roEyB7J7eNREREfGgNEtlXbt2DaNGjULZsmXTapOSxUXFAqN/240O41aaIDZnaCDe61wD0/o2UBArIiIiKetawGD1rbfewuLFixEcHIyXX34ZnTp1wtSpU/H6668jICBAU9RKmlh/4Dw++DsAp67GlbG0qVYEb9+viQ1EREQklYHsm2++iU8++QQtWrTA6tWr0bVrV/Tu3Rtr167F6NGjzXUGs5KMbPmBwJCkW3Dxdq6XxVzkxAYLduCbtZzYwA8FcwRjeCdObFDU07smIiIi3hzIzpo1C1999RU6duyIrVu3mjZb0dHR+PvvvzWHfUrkKQn02+h6Zi8Lg1iul4X8tv0khjhMbNCwUCzGPdkYBXJl8/SuiYiIiLcHskeOHEHdunEzTbGnbEhIiCklUBCbCgxSs1igmpgzl67hrR+34ecbExuUzp8NwztWwfkdf2p2LhEREUmbQJb9YVkba79zYCBy5MiRkk2I2LHv8OxNR/HOL9sRHhk3scGTd5fF880rIdAvFvN3eHoPRURExGcCWQYejz/+uMnE0tWrV/H0008je3bnEeQ//PBD2u6l+JzD5+ImNlixO25ig6pFc+GDB29ObBDFlgUiIiIiadV+q1evXmZmr9y5c5vLo48+imLFitmvW5eUmjBhAsqUKYPQ0FA0aNAA69atS7ZWt3Llymb9GjVqYP78+U63M9hmuYPjpU2bNineL0mfiQ0+W7EPrT76wwSxnNjglTaVMa9fY83OJSIiIumXkWWbrbQ2Y8YMvPDCC5g0aZIJYseMGYPWrVtj586dJmiOj90SunfvjhEjRqB9+/aYNm2aaQG2adMmU7drYeDquL9WFlk8Z8eJCLwy+x/8fTjcXG9QNh/e61ITZdUTVkRERFLB43N7sm1X3759TRuvqlWrmoA2W7ZsmDJlisv1x44da4LUQYMGoUqVKhg+fDjq1KmD8ePHO63HwLVIkSL2S968eTPoGUl816JjMGrRTrT/eKUJYnOGBJqZub7re6eCWBEREfHOQPb69evYuHGj6Utr3yF/f3N9zZo1Lu/D5Y7rEzO48ddftmyZyejedttteOaZZ3D2bBKtriTdbDhwDm3HrsC43/cgOtaGVlUL47cXm6J7/VLw91e3CxEREcmg0oK0dubMGdMJoXDhwk7LeX3HDtdD1k+cOOFyfS63MGPbuXNnM13u3r178dprr+G+++4zwa6rCRs4YxkvloiICPMzKirKXCTlLl2LxqjFu/HtusOw2YACOYIxtH0VtK5ayNQsJ/e6Wrfr9fcNOp6+Q8fSt+h4+o4oHzqWKXkOHg1k08vDDz9s/52DwThxQ/ny5U2Wtnnz5gnWZ73tsGHDEixftGiRKXOQlNl23g8z9/kj/HpcxrVBwVh0KhOJ2IMb8evBlG2L0yGL79Dx9B06lr5Fx9N3LPaBYxkZGekdgWyBAgVMhvTkyZNOy3mdda2ucHlK1qdy5cqZx9qzZ4/LQHbw4MFmwJljRrZkyZJo1aoVcuXKlYpnljWdvXwd7/yyAz/viMuOl8wbhnfur4pG5fOn6tsYP4wtW7ZEUJAmRfB2Op6+Q8fSt+h4+o4oHzqW1pnxTB/IcnIFzhS2ZMkS03mAYmNjzfV+/fq5vE/Dhg3N7c8//7x9GQ8clyc1IxlrZIsWLerydg4Mc9XVgG8Eb38zZAT2F56z+SiG/7wd5yOjwNLXJ+8uh4EtKiEsOGEpR0roGPgWHU/foWPpW3Q8fUeQDxzLlOy/x0sLmAllf9p69eqhfv36pv3W5cuXTRcD6tmzJ4oXL25O/9OAAQPQtGlTjBo1Cu3atcP06dOxYcMGTJ482dx+6dIlUybQpUsXk6VljezLL7+MChUqmEFhkraOnOfEBlvxx67T5noVTmzQpSZqlFBPWBEREUlfHg9ku3XrhtOnT+PNN980A7Zq166NBQsW2Ad0HTp0yHQysDRq1Mj0jh0yZIgZxFWxYkXMnTvX3kOWpQpbtmzBl19+ifDwcDNhA0sE2KZLvWTTdmKDL1cfwIeLdiLyegyCA/0xoHlFPNWkHIICPN7VTURERLIAjweyxDKCxEoJOEArvq5du5qLK2FhYVi4cGGa76PctOvkRbz8/Rb8dWNig/qc2KBzDZQrmMPTuyYiIiJZSKYIZMV7JjaYsHQvJi7bg6gYm5nY4NW2ldH9DvWEFRERkYynQFbcsvHgOTO97J5Tl8z1llULY/j91VEkd6ind01ERESyKAWykuzEBiMX7MBXaw/aJzYY1rE62tYoYiY2EBEREfEUBbKSqKU7TuH1Of/g2IWr5nrXuiXwersqyJMt2NO7JiIiIqJAVhI6e+ka3v55O+b9dcxcL5kvDCMeqIm7Khbw9K6JiIiI2CmQFaeJDeb+dRRv/3RzYoM+d5XFwJaVkC1YbxURERHJXBSdiH1igyFzt2LZzriJDSoXyYn3u9RErZJ5PL1rIiIiIi4pkM3iOLHBV2sOYORCTWwgIiIi3kWBbBaf2OCV2Vuw+VDcxAZ3lMmL97rURHlNbCAiIiJeQIFsFp3Y4P+W7sX/3ZjYIEdIIF65rzIeqa+JDURERMR7KJDNYjYePI9XZ2/B7hsTG7SoUgjDO1VH0dxhnt41ERERkRRRIJtFXObEBgt34ss1B8zEBvmzB+OtjtXQvmZRTWwgIiIiXkmBbBawbCcnNtiKo+FXzPUudUpgSLsqyJtdExuIiIiI91Ig68POXb6Ot3/ahrk3JjYokTcM/3ugBppUKujpXRMRERG5ZQpkfXRigx//PoZhP203wSzHb/VuXBYvttLEBiIiIuI7FNX4GJYPDJnzD5bemNjgtsI58f6DNVFbExuIiIiIj1Eg6yNiY234eu1BfLBgBy5zYoMAfzzXrAL+07S8meRARERExNcokPUBu29MbLDpxsQG9UpzYoMaqFAop6d3TURERCTdKJD1YtejYzFx2V5MWLoH12NikT04AK9yYoMGpTWxgYiIiPi8THHOecKECShTpgxCQ0PRoEEDrFu3Lsn1Z82ahcqVK5v1a9Sogfnz5ye67tNPP236pI4ZMwa+ZPOh82g/bgU++m2XCWKbVS6ExS80xWMNyyiIFRERkSzB44HsjBkz8MILL2Do0KHYtGkTatWqhdatW+PUqVMu11+9ejW6d++OPn36YPPmzejUqZO5bN26NcG6c+bMwdq1a1GsWDH40sQGw37ahs4TV2PXyUtmYoOPu9+Oz3vVQ7E8mp1LREREsg6PB7KjR49G37590bt3b1StWhWTJk1CtmzZMGXKFJfrjx07Fm3atMGgQYNQpUoVDB8+HHXq1MH48eOd1jt69Ciee+45fPvttwgKCoIvWL7rNFp99AemroqbnatzneL47YWm6FirmGbnEhERkSzHozWy169fx8aNGzF48GD7Mn9/f7Ro0QJr1qxxeR8uZwbXETO4c+fOtV+PjY3FY489ZoLdatWqJbsf165dMxdLRESE+RkVFWUunnY+8jr+N38n5v593FwvnicUwztWxd0VC5jrmWEf05r1nHzxuWVFOp6+Q8fSt+h4+o4oHzqWKXkOHg1kz5w5g5iYGBQuXNhpOa/v2LHD5X1OnDjhcn0ut7z//vsIDAxE//793dqPESNGYNiwYQmWL1q0yGSHPYVZ181n/TB7vz8uRfvBDzY0KWpDu5KXcHH3OszfDZ+3ePFiT++CpCEdT9+hY+lbdDx9x2IfOJaRkZFZt2sBM7wsP2C9rbun25kRdszyMiNbsmRJtGrVCrly5UrHvQViYm3YcPA8Tl28hkI5Q0zrrAB/Pxy/cBVDf9qOpbvPmPUqFcqBdztVzTITG/DbGD+MLVu29JnSkKxMx9N36Fj6Fh1P3xHlQ8fSOjOe6QPZAgUKICAgACdPnnRazutFihRxeR8uT2r9FStWmIFipUqVst/OrO+LL75oOhccOHAgwTZDQkLMJT6+EdLzzbBg63EzjSyDVkuRXKG457aC+HnLcVy6Fm0mNujXrAKezqITG6T3MZCMpePpO3QsfYuOp+8I8oFjmZL992hkFBwcjLp162LJkiVO9a283rBhQ5f34XLH9YnfQKz1WRu7ZcsW/PXXX/YLuxawXnbhwoXILBjEPvPNJqcglk5EXMX09YdNEFu3dF780v8u9G9eMUsGsSIiIiKZurSAp/R79eqFevXqoX79+iZrevnyZdPFgHr27InixYubOlYaMGAAmjZtilGjRqFdu3aYPn06NmzYgMmTJ5vb8+fPby7xI3tmbG+77TZkBiwnYCbWlsQ6ucICMb3vnQhSACsiIiKSOQPZbt264fTp03jzzTfNgK3atWtjwYIF9gFdhw4dMp0MLI0aNcK0adMwZMgQvPbaa6hYsaLpWFC9enV4i3X7zyXIxMYXcSXa1M42LO8clIuIiIhIJglkqV+/fubiyrJlyxIs69q1q7m4y1VdrCedung1TdcTERERyYp03toDCuUMTdP1RERERLIiBbIeUL9sPhTNHYrEmoNxOW/neiIiIiLimgJZD2Cf2KEdqprf4wez1nXezvVERERExDUFsh7SpnpRTHy0Dorkdi4f4HUu5+0iIiIikskHe2VVDFZbVi1iuhhwYBdrYllOoEysiIiISPIUyHoYg1a12BIRERFJOZUWiIiIiIhXUiArIiIiIl5JgayIiIiIeCUFsiIiIiLilTTYywWbzWZ+RkREeHpXsqyoqChERkaaYxAUFOTp3ZFbpOPpO3QsfYuOp++I8qFjacVfVjyWFAWyLly8eNH8LFmypKd3RURERCTLxmO5c+dOch0/mzvhbhYTGxuLY8eOIWfOnPDzU09XT30b4xeJw4cPI1euXJ7eHblFOp6+Q8fSt+h4+o4IHzqWDE0ZxBYrVgz+/klXwSoj6wJftBIlSnh6NwQwH0Zv/0DKTTqevkPH0rfoePqOXD5yLJPLxFo02EtEREREvJICWRERERHxSgpkJVMKCQnB0KFDzU/xfjqevkPH0rfoePqOkCx6LDXYS0RERES8kjKyIiIiIuKVFMiKiIiIiFdSICsiIiIiXkmBrHjUH3/8gQ4dOpimx5x8Yu7cuU63s4T7zTffRNGiRREWFoYWLVpg9+7dHttfSdyIESNwxx13mIlEChUqhE6dOmHnzp1O61y9ehXPPvss8ufPjxw5cqBLly44efKkx/ZZXJs4cSJq1qxp70fZsGFD/Prrr/bbdRy923vvvWf+v33++efty3RMvcNbb71ljp3jpXLlyln6OCqQFY+6fPkyatWqhQkTJri8/YMPPsDHH3+MSZMm4c8//0T27NnRunVr82GVzGX58uXmP9C1a9di8eLFZt7vVq1amWNsGThwIH766SfMmjXLrM8Z9Dp37uzR/ZaEOCEMg52NGzdiw4YNaNasGe6//35s27bN3K7j6L3Wr1+PTz75xHxRcaRj6j2qVauG48eP2y8rV67M2seRXQtEMgO+HefMmWO/HhsbaytSpIht5MiR9mXh4eG2kJAQ23fffeehvRR3nTp1yhzT5cuX249dUFCQbdasWfZ1/v33X7POmjVrPLin4o68efPaPvvsMx1HL3bx4kVbxYoVbYsXL7Y1bdrUNmDAALNcx9R7DB061FarVi2Xt4Vn0eOojKxkWvv378eJEydMOYHjlHUNGjTAmjVrPLpvkrwLFy6Yn/ny5TM/md1jltbxePKUWKlSpXQ8M7GYmBhMnz7dZNZZYqDj6L14xqRdu3ZOx450TL0Ly+tYjleuXDk88sgjOHToUJY+joGe3gGRxDCIpcKFCzst53XrNsmcYmNjTf1d48aNUb16dbOMxyw4OBh58uRxWlfHM3P6559/TODKMh7W2s2ZMwdVq1bFX3/9pePohfhlZNOmTaa0ID59Nr0HEzlffPEFbrvtNlNWMGzYMNx9993YunVrlj2OCmRFJF0yP/yP1bF2S7wL/1AyaGVm/fvvv0evXr1MzZ14n8OHD2PAgAGmdj00NNTTuyO34L777rP/zjrnBg0aoHTp0pg5c6YZEJ0VqbRAMq0iRYqYn/FHXPK6dZtkPv369cPPP/+MpUuXmkFDFh6z69evIzw83Gl9Hc/MiZmdChUqoG7duqYjBQdljh07VsfRC/GU86lTp1CnTh0EBgaaC7+UcCAtf2fGTsfUO+XJkweVKlXCnj17suxnU4GsZFply5Y1H74lS5bYl0VERJjuBTzlKZkLx+sxiOUp6N9//90cP0cMiIKCgpyOJ9tzsb5Lx9M7ykWuXbum4+iFmjdvbkpFmGG3LvXq1TP1ldbvOqbe6dKlS9i7d69pUZlVP5sqLRCPfwj5TdJxgBf/Y+UAIRaos87ynXfeQcWKFU1g9MYbb5gid/YolcxXTjBt2jTMmzfP9JK1arI4QI+nvPizT58+eOGFF8zxZX/S5557zvwHe+edd3p698XB4MGDzSlMfgYvXrxojuuyZcuwcOFCHUcvxM+jVatuYStD9hq1luuYeoeXXnrJ9F5nOQFbaw0dOhQBAQHo3r171v1serptgmRtS5cuNa1B4l969eplb8H1xhtv2AoXLmzabjVv3ty2c+dOT++2uODqOPIydepU+zpXrlyx/fe//zWtnLJly2Z74IEHbMePH/fofktCTzzxhK106dK24OBgW8GCBc3nbtGiRfbbdRy9n2P7LdIx9Q7dunWzFS1a1Hw2ixcvbq7v2bMnSx9HP/7j6WBaRERERCSlVCMrIiIiIl5JgayIiIiIeCUFsiIiIiLilRTIioiIiIhXUiArIiIiIl5JgayIiIiIeCUFsiIiIiLilRTIioiIiIhXUiArIiIiIl5JgayISDo5cOAA/Pz88Ndff3l6V/DGG2/gqaee8tjjf/HFF8iTJ0+q7nvmzBkUKlQIR44cSfP9EhHvpkBWRLKsxx9/HJ06dUqwfNmyZSYADQ8Pv6XtlyxZEsePH0f16tXhSSdOnMDYsWPx+uuvwxsVKFAAPXv2xNChQz29KyKSySiQFRFJB9evX0dAQACKFCmCwMBAj+7LZ599hkaNGqF06dLwVr1798a3336Lc+fOeXpXRCQTUSArIuKG2bNno1q1aggJCUGZMmUwatQop9u5bPjw4SZzmCtXLnMaP35pATPAvB7/wgwwnT9/3tw/b968yJYtG+677z7s3r07wen5hQsXokqVKsiRIwfatGljsr5JmT59Ojp06GC//vPPP5vtxMTEmOvcP+7Hq6++al/nySefxKOPPmq/vnLlStx9990ICwszmeb+/fvj8uXL9tuvXbuGl156CcWLF0f27NnRoEED+/Ny5fTp06hXrx4eeOABc18+90ceeQQFCxY0j1GxYkVMnTrVvj5f+2LFimHOnDnJHCkRyUoUyIqIJGPjxo146KGH8PDDD+Off/7BW2+9ZWpOGVg6+vDDD1GrVi1s3rzZ3B4fT+8z6LQuAwYMMLWflStXtge6GzZswI8//og1a9bAZrOhbdu2iIqKsm8jMjLSPM7XX3+NP/74A4cOHTIBZGKYwdy+fbsJGi0MSC9evGj2k5YvX25O3zsGnlx2zz33mN/37t1rAuYuXbpgy5YtmDFjhgls+/XrZ1+fv3OfGTRzna5du5r7OAbilsOHD5t9YMnF999/b74c8PXifv7666/4999/MXHiRLNPjurXr48VK1Ykc7REJEuxiYhkUb169bIFBATYsmfP7nQJDQ218b/H8+fPm/V69Ohha9mypdN9Bw0aZKtatar9eunSpW2dOnVyWmf//v1mO5s3b07w2LNnzzaPs3LlSnN9165dZt1Vq1bZ1zlz5owtLCzMNnPmTHN96tSpZp09e/bY15kwYYKtcOHCiT5HPjbvc+jQIaflderUsY0cOdL8zv1+9913bcHBwbaLFy/ajhw5Yu7DfaI+ffrYnnrqKaf7r1ixwubv72+7cuWK7eDBg+Z1PHr0qNM6zZs3tw0ePNi+77lz57bt2LHDVrJkSVv//v1tsbGx9nU7dOhg6927ty0pAwcOtN1zzz1JriMiWYsysiKSpd17773m1LrjhTWljpghbNy4sdMyXme20To9T45Zz6QwE/rYY49h/Pjx9u3yMVhLy1Pylvz58+O2224zt1lYclC+fHn79aJFi+LUqVOJPtaVK1fMz9DQUKflTZs2NRlYZn2Z5ezcubMpV2CmldlYnsbn6X36+++/TfaZpQzWpXXr1oiNjcX+/ftNlpqvQ6VKlZzW4XaYzXXcF2Zi+VjMTrOcwfLMM8+YbG7t2rXx8ssvY/Xq1QmeC0sOmJEWEbF4dgSCiIiHsZ6zQoUKTstS2+aJ23Kng0DHjh1NDWqfPn1S/BhBQUFO1xkMMhhNjHV6njWorD+1sGxgypQpJkjlNlnewGUMbrkuA13LpUuX8J///MfUxcZXqlQpU0rAgW0sweBPRwxoLSwhaNGihanRHTRokKmntbAe+ODBg5g/fz4WL16M5s2b49lnnzVlFI5lEo7PQUREGVkRkWQwU7lq1SqnZbzODGT8wC0pV69exf3332+CxtGjRyd4jOjoaPz555/2ZWfPnsXOnTtRtWrVVO87s7ccfMb6U0dWnexHH31kD1qtQJYXqz6W6tSpY+7PgD/+JTg4GLfffrvJyDIzHP92dm2w+Pv7m9reunXrmkz4sWPHnPaJQWqvXr3wzTffYMyYMZg8ebLT7Vu3bjWPJSJiUSArIpKMF198EUuWLDFdCXbt2oUvv/zSlAUkNcjKFWY1OdDp448/NqP2mZ3lha26eBqfQW7fvn3N6X1mStk1gFlLLk8tBo/MgnKbjtgZoWbNmqallRW0NmnSBJs2bTLP0TEj+8orr5hT/RzQxdILllTMmzfPPtiLAT07DrDjwg8//GDKDdatW4cRI0bgl19+cXpcBv58TA6Ka9asmXn+9Oabb5pt7tmzB9u2bTNZWwb3FpYUMOPbqlWrVL8WIuJ7FMiKiCSDGcmZM2eaGk6OtGfQ9fbbb5suAynBmlF2K2CGlbWt1sWqB2W7KWYr27dvj4YNG5qSAZ5qj19OkFIsY+C+s6bVEYNVZlKtQDZfvnxm35hFZW2uhQEv950BLjO5zIryNWAdrYX7zkCWQT/vy4km1q9fb0oP4mMt8HfffWdaajGYZSaXmd3Bgwebx2JAzYCX+2xhkMtt8fFFRCx+HPFlvyYiIj6H/81zENnAgQPRvXt3eKM777zT1Oj26NHD07siIpmIMrIiIj6OA8JYb8oaXG905swZ0+nAW4NwEUk/ysiKiIiIiFdSRlZEREREvJICWRERERHxSgpkRURERMQrKZAVEREREa+kQFZEREREvJICWRERERHxSgpkRURERMQrKZAVEREREa+kQFZERERE4I3+HzEEQihAhwF7AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 700x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Line chart: VaR / CVaR scaling with horizon ---\n",
    "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
    "horizons_weeks = [4, 13, 26, 52]\n",
    "ax.plot(horizons_weeks, hr_nominal[\"VaR95\"].values,\n",
    "        \"o-\", label=\"VaR 95%\")\n",
    "ax.plot(horizons_weeks, hr_nominal[\"CVaR95\"].values,\n",
    "        \"s-\", label=\"CVaR 95%\")\n",
    "ax.set_xlabel(\"Horizon (weeks)\")\n",
    "ax.set_ylabel(\"Risk (loss convention)\")\n",
    "ax.set_title(\"VaR / CVaR scaling with projection horizon\")\n",
    "ax.legend()\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "sec1-fan",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.593335Z",
     "iopub.status.busy": "2026-03-30T19:38:50.593272Z",
     "iopub.status.idle": "2026-03-30T19:38:50.645884Z",
     "shell.execute_reply": "2026-03-30T19:38:50.645644Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Fan chart: percentile wealth bands over 52 weeks ---\n",
    "paths = simulate_paths(\n",
    "    log_returns.values, horizon=52, n_paths=2000, seed=42,\n",
    ")\n",
    "port_cum = np.exp((paths @ w_arr))  # cumulative wealth\n",
    "pcts = np.percentile(port_cum, [5, 25, 50, 75, 95], axis=0)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "weeks = np.arange(1, 53)\n",
    "ax.fill_between(weeks, pcts[0], pcts[4], alpha=0.15, label=\"5-95%\")\n",
    "ax.fill_between(weeks, pcts[1], pcts[3], alpha=0.30, label=\"25-75%\")\n",
    "ax.plot(weeks, pcts[2], \"k-\", lw=1.5, label=\"Median\")\n",
    "ax.axhline(1, ls=\"--\", color=\"grey\", lw=0.8)\n",
    "ax.set(xlabel=\"Week\", ylabel=\"Wealth ($1 invested)\",\n",
    "       title=\"52-week fan chart -- Tangency portfolio\")\n",
    "ax.legend(); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec2-title",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 2 -- Historical Scenario Replay (COVID-Style Crisis)\n",
    "\n",
    "We locate the worst 13-week drawdown window for SPY in the dataset and\n",
    "replay those returns through the portfolio using `kernel_focus_stress`\n",
    "targeting the highest-volatility regime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "sec2-crisis",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.646966Z",
     "iopub.status.busy": "2026-03-30T19:38:50.646905Z",
     "iopub.status.idle": "2026-03-30T19:38:50.649469Z",
     "shell.execute_reply": "2026-03-30T19:38:50.649277Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Worst 13-week window: 2008-08-22 to 2008-11-21\n",
      "SPY cumulative log-return: -0.4871\n"
     ]
    }
   ],
   "source": [
    "# --- Identify worst 13-week window for SPY ---\n",
    "spy_cum = log_returns[\"SPY\"].cumsum()\n",
    "rolling_13w = spy_cum - spy_cum.shift(13)\n",
    "worst_end = rolling_13w.idxmin()\n",
    "worst_start = spy_cum.index[\n",
    "    spy_cum.index.get_loc(worst_end) - 13\n",
    "]\n",
    "crisis_returns = log_returns.loc[worst_start:worst_end]\n",
    "print(f\"Worst 13-week window: {worst_start.date()} to \"\n",
    "      f\"{worst_end.date()}\")\n",
    "print(f\"SPY cumulative log-return: \"\n",
    "      f\"{crisis_returns['SPY'].sum():.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "sec2-kernel",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.650387Z",
     "iopub.status.busy": "2026-03-30T19:38:50.650325Z",
     "iopub.status.idle": "2026-03-30T19:38:50.655024Z",
     "shell.execute_reply": "2026-03-30T19:38:50.654826Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kernel-focus stress (high SPY vol):\n"
     ]
    },
    {
     "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>return_nom</th>\n",
       "      <th>stdev_nom</th>\n",
       "      <th>VaR95_nom</th>\n",
       "      <th>CVaR95_nom</th>\n",
       "      <th>ENS_nom</th>\n",
       "      <th>return_stress</th>\n",
       "      <th>stdev_stress</th>\n",
       "      <th>VaR95_stress</th>\n",
       "      <th>CVaR95_stress</th>\n",
       "      <th>ENS_stress</th>\n",
       "      <th>KL_q_p</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>portfolio_0</th>\n",
       "      <td>0.0015</td>\n",
       "      <td>0.0138</td>\n",
       "      <td>0.0202</td>\n",
       "      <td>0.0313</td>\n",
       "      <td>1006.0</td>\n",
       "      <td>0.0216</td>\n",
       "      <td>0.0265</td>\n",
       "      <td>0.0223</td>\n",
       "      <td>0.0223</td>\n",
       "      <td>6.0834</td>\n",
       "      <td>5.1082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             return_nom  stdev_nom  VaR95_nom  CVaR95_nom  ENS_nom  \\\n",
       "portfolio_0      0.0015     0.0138     0.0202      0.0313   1006.0   \n",
       "\n",
       "             return_stress  stdev_stress  VaR95_stress  CVaR95_stress  \\\n",
       "portfolio_0         0.0216        0.0265        0.0223         0.0223   \n",
       "\n",
       "             ENS_stress  KL_q_p  \n",
       "portfolio_0      6.0834  5.1082  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Kernel-focus stress targeting high-vol regime ---\n",
    "spy_vol = log_returns[\"SPY\"].rolling(13).std().bfill()\n",
    "df_kernel = kernel_focus_stress(\n",
    "    w_arr, log_returns.values,\n",
    "    focus_series=spy_vol.values,\n",
    "    target=spy_vol.values.max(),\n",
    "    confidence=0.95,\n",
    ")\n",
    "print(\"Kernel-focus stress (high SPY vol):\")\n",
    "df_kernel.round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "sec2-compare",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.655989Z",
     "iopub.status.busy": "2026-03-30T19:38:50.655932Z",
     "iopub.status.idle": "2026-03-30T19:38:50.659541Z",
     "shell.execute_reply": "2026-03-30T19:38:50.659354Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nominal vs crisis-window performance:\n"
     ]
    },
    {
     "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>Nominal</th>\n",
       "      <th>Crisis window</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.0015</td>\n",
       "      <td>-0.0116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stdev</th>\n",
       "      <td>0.0138</td>\n",
       "      <td>0.0313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VaR95</th>\n",
       "      <td>0.0202</td>\n",
       "      <td>0.0903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CVaR95</th>\n",
       "      <td>0.0313</td>\n",
       "      <td>0.0903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ENS</th>\n",
       "      <td>1006.0000</td>\n",
       "      <td>14.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Nominal  Crisis window\n",
       "mean       0.0015        -0.0116\n",
       "stdev      0.0138         0.0313\n",
       "VaR95      0.0202         0.0903\n",
       "CVaR95     0.0313         0.0903\n",
       "ENS     1006.0000        14.0000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Compare nominal vs crisis-replay single-period ---\n",
    "nom_report = performance_report(\n",
    "    w_arr, log_returns.values, confidence=0.95\n",
    ")\n",
    "crisis_report = performance_report(\n",
    "    w_arr, crisis_returns.values, confidence=0.95\n",
    ")\n",
    "compare = pd.DataFrame(\n",
    "    {\"Nominal\": nom_report, \"Crisis window\": crisis_report}\n",
    ")\n",
    "print(\"Nominal vs crisis-window performance:\")\n",
    "compare.round(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec3-title",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 3 -- What-If Scenarios via Flexible Views\n",
    "\n",
    "We use entropy pooling to tilt the probability distribution and answer:\n",
    "\n",
    "1. **Bearish equity**: SPY expected return <= -0.5% per week, vol doubles.\n",
    "2. **Rising rates / TLT drop**: TLT expected return <= -0.3% per week.\n",
    "3. **Correlation breakdown**: SPY-TLT correlation >= +0.3 (hedge fails)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "sec3-bearish",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.660523Z",
     "iopub.status.busy": "2026-03-30T19:38:50.660456Z",
     "iopub.status.idle": "2026-03-30T19:38:50.664387Z",
     "shell.execute_reply": "2026-03-30T19:38:50.664187Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bearish equity: ENS = 758.2\n"
     ]
    }
   ],
   "source": [
    "# --- Bearish equity view ---\n",
    "fv_bear = FlexibleViewsProcessor(\n",
    "    prior_risk_drivers=log_returns,\n",
    "    mean_views={\"SPY\": (\"<=\", -0.005)},\n",
    "    vol_views={\"SPY\": (\">=\", 0.04)},\n",
    "    sequential=True,\n",
    ")\n",
    "q_bear = fv_bear.get_posterior_probabilities().ravel()\n",
    "q_bear = q_bear / q_bear.sum()\n",
    "print(f\"Bearish equity: ENS = \"\n",
    "      f\"{1.0 / (q_bear ** 2).sum():.1f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "sec3-rates",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.665429Z",
     "iopub.status.busy": "2026-03-30T19:38:50.665362Z",
     "iopub.status.idle": "2026-03-30T19:38:50.668467Z",
     "shell.execute_reply": "2026-03-30T19:38:50.668285Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rising rates: ENS = 974.0\n"
     ]
    }
   ],
   "source": [
    "# --- Rising rates / TLT drop view ---\n",
    "fv_rates = FlexibleViewsProcessor(\n",
    "    prior_risk_drivers=log_returns,\n",
    "    mean_views={\"TLT\": (\"<=\", -0.003)},\n",
    "    sequential=True,\n",
    ")\n",
    "q_rates = fv_rates.get_posterior_probabilities().ravel()\n",
    "q_rates = q_rates / q_rates.sum()\n",
    "print(f\"Rising rates: ENS = \"\n",
    "      f\"{1.0 / (q_rates ** 2).sum():.1f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "sec3-corr",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.669334Z",
     "iopub.status.busy": "2026-03-30T19:38:50.669280Z",
     "iopub.status.idle": "2026-03-30T19:38:50.672395Z",
     "shell.execute_reply": "2026-03-30T19:38:50.672204Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation breakdown: ENS = 760.0\n"
     ]
    }
   ],
   "source": [
    "# --- Correlation breakdown: SPY-TLT hedge fails ---\n",
    "fv_corr = FlexibleViewsProcessor(\n",
    "    prior_risk_drivers=log_returns,\n",
    "    corr_views={(\"SPY\", \"TLT\"): (\">=\", 0.3)},\n",
    "    sequential=True,\n",
    ")\n",
    "q_corr = fv_corr.get_posterior_probabilities().ravel()\n",
    "q_corr = q_corr / q_corr.sum()\n",
    "print(f\"Correlation breakdown: ENS = \"\n",
    "      f\"{1.0 / (q_corr ** 2).sum():.1f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "sec3-table",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.673315Z",
     "iopub.status.busy": "2026-03-30T19:38:50.673259Z",
     "iopub.status.idle": "2026-03-30T19:38:50.762167Z",
     "shell.execute_reply": "2026-03-30T19:38:50.761905Z"
    }
   },
   "outputs": [],
   "source": [
    "# --- Build scenario dict for reuse ---\n",
    "scenarios = {\n",
    "    \"Nominal\": None, \"Bearish equity\": q_bear,\n",
    "    \"Rising rates\": q_rates, \"Corr breakdown\": q_corr,\n",
    "}\n",
    "rows = []\n",
    "for name, q in scenarios.items():\n",
    "    hr = horizon_report(\n",
    "        w_arr, log_returns.values,\n",
    "        horizons=[13, 52], n_simulations=5000,\n",
    "        p=q, confidence=0.95, seed=42)\n",
    "    for h_label in hr.index:\n",
    "        row = hr.loc[h_label].to_dict()\n",
    "        row.update({\"scenario\": name, \"horizon\": h_label})\n",
    "        rows.append(row)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d5rka6lsvia",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.763270Z",
     "iopub.status.busy": "2026-03-30T19:38:50.763209Z",
     "iopub.status.idle": "2026-03-30T19:38:50.768196Z",
     "shell.execute_reply": "2026-03-30T19:38:50.767975Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stress comparison (3m & 1y horizons):\n"
     ]
    },
    {
     "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></th>\n",
       "      <th>mean</th>\n",
       "      <th>CVaR95</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scenario</th>\n",
       "      <th>horizon</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Nominal</th>\n",
       "      <th>3m</th>\n",
       "      <td>0.0232</td>\n",
       "      <td>0.0830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1y</th>\n",
       "      <td>0.0960</td>\n",
       "      <td>0.1183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Bearish equity</th>\n",
       "      <th>3m</th>\n",
       "      <td>-0.0214</td>\n",
       "      <td>0.1559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1y</th>\n",
       "      <td>-0.0700</td>\n",
       "      <td>0.2776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Rising rates</th>\n",
       "      <th>3m</th>\n",
       "      <td>0.0131</td>\n",
       "      <td>0.0979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1y</th>\n",
       "      <td>0.0633</td>\n",
       "      <td>0.1505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">Corr breakdown</th>\n",
       "      <th>3m</th>\n",
       "      <td>0.0122</td>\n",
       "      <td>0.1459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1y</th>\n",
       "      <td>0.0528</td>\n",
       "      <td>0.2404</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          mean  CVaR95\n",
       "scenario       horizon                \n",
       "Nominal        3m       0.0232  0.0830\n",
       "               1y       0.0960  0.1183\n",
       "Bearish equity 3m      -0.0214  0.1559\n",
       "               1y      -0.0700  0.2776\n",
       "Rising rates   3m       0.0131  0.0979\n",
       "               1y       0.0633  0.1505\n",
       "Corr breakdown 3m       0.0122  0.1459\n",
       "               1y       0.0528  0.2404"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Display stress comparison table ---\n",
    "stress_table = pd.DataFrame(rows).set_index(\n",
    "    [\"scenario\", \"horizon\"]\n",
    ")\n",
    "print(\"Stress comparison (3m & 1y horizons):\")\n",
    "stress_table[[\"mean\", \"CVaR95\"]].round(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec4-title",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 4 -- Combined Stress + Mean Reversion\n",
    "\n",
    "**Question**: *What if SPY drops ~15% then mean reverts over 6 months?*\n",
    "\n",
    "We model this as a two-phase simulation:\n",
    "1. **Shock phase** (13 weeks): amplified returns with a negative shift.\n",
    "2. **Recovery phase** (13 weeks): nominal returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "sec4-shock",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.769193Z",
     "iopub.status.busy": "2026-03-30T19:38:50.769126Z",
     "iopub.status.idle": "2026-03-30T19:38:50.774480Z",
     "shell.execute_reply": "2026-03-30T19:38:50.774294Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shock paths shape:    (2000, 13, 4)\n",
      "Recovery paths shape: (2000, 13, 4)\n"
     ]
    }
   ],
   "source": [
    "# --- Shock phase: 13 weeks of stressed returns ---\n",
    "# Column order: DBC, GLD, SPY, TLT -> shift SPY (index 2)\n",
    "shock_transform = linear_map(\n",
    "    scale=2.0,\n",
    "    mean_shift=np.array([0.0, 0.0, -0.005, 0.0]),\n",
    ")\n",
    "shocked_returns = shock_transform(log_returns.values)\n",
    "paths_shock = simulate_paths(\n",
    "    shocked_returns, horizon=13, n_paths=2000, seed=42,\n",
    ")\n",
    "paths_recov = simulate_paths(\n",
    "    log_returns.values, horizon=13, n_paths=2000, seed=43,\n",
    ")\n",
    "print(f\"Shock paths shape:    {paths_shock.shape}\")\n",
    "print(f\"Recovery paths shape: {paths_recov.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "sec4-combine",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.775427Z",
     "iopub.status.busy": "2026-03-30T19:38:50.775367Z",
     "iopub.status.idle": "2026-03-30T19:38:50.777813Z",
     "shell.execute_reply": "2026-03-30T19:38:50.777636Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Combined paths shape: (2000, 26, 4)\n",
      "Median terminal wealth: 1.0383\n"
     ]
    }
   ],
   "source": [
    "# --- Stitch shock + recovery into 26-week paths ---\n",
    "# Cumulative returns: recovery starts from shock endpoint\n",
    "offset = paths_shock[:, -1:, :]  # (2000, 1, 4)\n",
    "paths_recov_shifted = paths_recov + offset\n",
    "paths_full = np.concatenate(\n",
    "    [paths_shock, paths_recov_shifted], axis=1\n",
    ")\n",
    "port_wealth = np.exp(paths_full @ w_arr)\n",
    "print(f\"Combined paths shape: {paths_full.shape}\")\n",
    "print(f\"Median terminal wealth: \"\n",
    "      f\"{np.median(port_wealth[:, -1]):.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "sec4-plot",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.778760Z",
     "iopub.status.busy": "2026-03-30T19:38:50.778703Z",
     "iopub.status.idle": "2026-03-30T19:38:50.823377Z",
     "shell.execute_reply": "2026-03-30T19:38:50.823189Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Two-phase fan chart ---\n",
    "pcts = np.percentile(port_wealth, [5, 25, 50, 75, 95], axis=0)\n",
    "weeks = np.arange(1, 27)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.fill_between(weeks, pcts[0], pcts[4], alpha=0.15, label=\"5-95%\")\n",
    "ax.fill_between(weeks, pcts[1], pcts[3], alpha=0.30, label=\"25-75%\")\n",
    "ax.plot(weeks, pcts[2], \"k-\", lw=1.5, label=\"Median\")\n",
    "ax.axhline(1, ls=\"--\", color=\"grey\", lw=0.8)\n",
    "ax.axvline(13, ls=\":\", color=\"red\", lw=1, label=\"Shock / recovery\")\n",
    "ax.set(xlabel=\"Week\", ylabel=\"Wealth ($1 invested)\",\n",
    "       title=\"Shock + mean reversion: 26-week paths\")\n",
    "ax.legend(loc=\"lower right\"); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec5-title",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 5 -- Multi-Horizon Drawdown Analysis\n",
    "\n",
    "We compute the maximum-drawdown distribution at multiple horizons under\n",
    "both nominal and bearish-equity stress, answering:\n",
    "*What is the 95th-percentile max drawdown at 3 months vs 1 year?*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "sec5-dd-nominal",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.824426Z",
     "iopub.status.busy": "2026-03-30T19:38:50.824361Z",
     "iopub.status.idle": "2026-03-30T19:38:50.846815Z",
     "shell.execute_reply": "2026-03-30T19:38:50.846607Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nominal max-drawdown distribution:\n"
     ]
    },
    {
     "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>max_dd_mean</th>\n",
       "      <th>max_dd_median</th>\n",
       "      <th>max_dd_95</th>\n",
       "      <th>max_dd_worst</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horizon_weeks</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0125</td>\n",
       "      <td>0.0087</td>\n",
       "      <td>0.0385</td>\n",
       "      <td>0.1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.0340</td>\n",
       "      <td>0.0286</td>\n",
       "      <td>0.0809</td>\n",
       "      <td>0.1538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.0522</td>\n",
       "      <td>0.0447</td>\n",
       "      <td>0.1100</td>\n",
       "      <td>0.2618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>0.0747</td>\n",
       "      <td>0.0659</td>\n",
       "      <td>0.1475</td>\n",
       "      <td>0.2794</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               max_dd_mean  max_dd_median  max_dd_95  max_dd_worst\n",
       "horizon_weeks                                                     \n",
       "4                   0.0125         0.0087     0.0385        0.1185\n",
       "13                  0.0340         0.0286     0.0809        0.1538\n",
       "26                  0.0522         0.0447     0.1100        0.2618\n",
       "52                  0.0747         0.0659     0.1475        0.2794"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Nominal drawdown quantiles ---\n",
    "dd_horizons = [4, 13, 26, 52]\n",
    "dd_nom = {}\n",
    "for h in dd_horizons:\n",
    "    dd_nom[h] = drawdown_quantile(\n",
    "        w_arr, log_returns.values,\n",
    "        horizon=h, confidence=0.95,\n",
    "        n_paths=2000, seed=42,\n",
    "    )\n",
    "dd_nom_df = pd.DataFrame(dd_nom).T\n",
    "dd_nom_df.index.name = \"horizon_weeks\"\n",
    "print(\"Nominal max-drawdown distribution:\")\n",
    "dd_nom_df.round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "sec5-dd-stress",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.847857Z",
     "iopub.status.busy": "2026-03-30T19:38:50.847773Z",
     "iopub.status.idle": "2026-03-30T19:38:50.868552Z",
     "shell.execute_reply": "2026-03-30T19:38:50.868345Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bearish-equity max-drawdown distribution:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\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>max_dd_mean</th>\n",
       "      <th>max_dd_median</th>\n",
       "      <th>max_dd_95</th>\n",
       "      <th>max_dd_worst</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horizon_weeks</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0198</td>\n",
       "      <td>0.0132</td>\n",
       "      <td>0.0797</td>\n",
       "      <td>0.1396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.0605</td>\n",
       "      <td>0.0505</td>\n",
       "      <td>0.1379</td>\n",
       "      <td>0.2525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.0984</td>\n",
       "      <td>0.0916</td>\n",
       "      <td>0.1941</td>\n",
       "      <td>0.2989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>0.1472</td>\n",
       "      <td>0.1380</td>\n",
       "      <td>0.2646</td>\n",
       "      <td>0.4274</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               max_dd_mean  max_dd_median  max_dd_95  max_dd_worst\n",
       "horizon_weeks                                                     \n",
       "4                   0.0198         0.0132     0.0797        0.1396\n",
       "13                  0.0605         0.0505     0.1379        0.2525\n",
       "26                  0.0984         0.0916     0.1941        0.2989\n",
       "52                  0.1472         0.1380     0.2646        0.4274"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Stressed drawdown quantiles (bearish equity) ---\n",
    "dd_stress = {}\n",
    "for h in dd_horizons:\n",
    "    dd_stress[h] = drawdown_quantile(\n",
    "        w_arr, log_returns.values,\n",
    "        horizon=h, confidence=0.95,\n",
    "        n_paths=2000, p=q_bear, seed=42,\n",
    "    )\n",
    "dd_stress_df = pd.DataFrame(dd_stress).T\n",
    "dd_stress_df.index.name = \"horizon_weeks\"\n",
    "print(\"Bearish-equity max-drawdown distribution:\")\n",
    "dd_stress_df.round(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "sec5-bar",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.869542Z",
     "iopub.status.busy": "2026-03-30T19:38:50.869470Z",
     "iopub.status.idle": "2026-03-30T19:38:50.904167Z",
     "shell.execute_reply": "2026-03-30T19:38:50.903932Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Bar chart: 95th percentile max DD across horizons ---\n",
    "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
    "x = np.arange(len(dd_horizons))\n",
    "w_bar = 0.35\n",
    "ax.bar(x - w_bar/2, dd_nom_df[\"max_dd_95\"].values,\n",
    "       w_bar, label=\"Nominal\")\n",
    "ax.bar(x + w_bar/2, dd_stress_df[\"max_dd_95\"].values,\n",
    "       w_bar, label=\"Bearish equity\")\n",
    "ax.set_xticks(x)\n",
    "ax.set_xticklabels([f\"{h}w\" for h in dd_horizons])\n",
    "ax.set_ylabel(\"95th pctl Max Drawdown\")\n",
    "ax.set_title(\"Max drawdown by horizon: Nominal vs Stressed\")\n",
    "ax.legend(); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "sec5-hist",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.905339Z",
     "iopub.status.busy": "2026-03-30T19:38:50.905265Z",
     "iopub.status.idle": "2026-03-30T19:38:50.920949Z",
     "shell.execute_reply": "2026-03-30T19:38:50.920693Z"
    }
   },
   "outputs": [],
   "source": [
    "# --- Simulate 1-year paths for drawdown histograms ---\n",
    "paths_nom_1y = simulate_paths(\n",
    "    log_returns.values, horizon=52, n_paths=2000, seed=42,\n",
    ")\n",
    "paths_str_1y = simulate_paths(\n",
    "    log_returns.values, horizon=52, n_paths=2000,\n",
    "    p=q_bear, seed=42,\n",
    ")\n",
    "def _max_dd(paths, w):\n",
    "    wealth = np.exp(paths @ w)\n",
    "    peak = np.maximum.accumulate(wealth, axis=1)\n",
    "    dd = (peak - wealth) / np.where(peak > 0, peak, 1)\n",
    "    return dd.max(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "1srp5ap40po",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.922150Z",
     "iopub.status.busy": "2026-03-30T19:38:50.922073Z",
     "iopub.status.idle": "2026-03-30T19:38:50.992976Z",
     "shell.execute_reply": "2026-03-30T19:38:50.992744Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Histogram: 1-year max drawdown distribution ---\n",
    "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
    "ax.hist(_max_dd(paths_nom_1y, w_arr), bins=50,\n",
    "        alpha=0.5, label=\"Nominal\", density=True)\n",
    "ax.hist(_max_dd(paths_str_1y, w_arr), bins=50,\n",
    "        alpha=0.5, label=\"Bearish equity\", density=True)\n",
    "ax.set(xlabel=\"Max Drawdown\", ylabel=\"Density\",\n",
    "       title=\"1-Year max drawdown distribution\")\n",
    "ax.legend(); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec6-title",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 6 -- Multi-Portfolio Comparison\n",
    "\n",
    "We compare the tangency portfolio against the minimum-risk portfolio and\n",
    "an equal-weight (1/N) allocation across scenarios and horizons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "sec6-portfolios",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.994082Z",
     "iopub.status.busy": "2026-03-30T19:38:50.994011Z",
     "iopub.status.idle": "2026-03-30T19:38:50.997478Z",
     "shell.execute_reply": "2026-03-30T19:38:50.997268Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Portfolio weights:\n"
     ]
    },
    {
     "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>Tangency</th>\n",
       "      <th>Min-Risk</th>\n",
       "      <th>Equal-Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>DBC</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.168</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GLD</th>\n",
       "      <td>0.334</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SPY</th>\n",
       "      <td>0.403</td>\n",
       "      <td>0.237</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TLT</th>\n",
       "      <td>0.263</td>\n",
       "      <td>0.490</td>\n",
       "      <td>0.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Tangency  Min-Risk  Equal-Weight\n",
       "DBC     0.000     0.168          0.25\n",
       "GLD     0.334     0.105          0.25\n",
       "SPY     0.403     0.237          0.25\n",
       "TLT     0.263     0.490          0.25"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Build alternative portfolios ---\n",
    "w_minrisk, _, _ = frontier.min_risk()\n",
    "w_equal = pd.Series(\n",
    "    1.0 / len(ASSETS), index=ASSETS, name=\"Equal Weight\",\n",
    ")\n",
    "portfolios = {\n",
    "    \"Tangency\": w_tangency.values,\n",
    "    \"Min-Risk\": w_minrisk.values,\n",
    "    \"Equal-Weight\": w_equal.values,\n",
    "}\n",
    "print(\"Portfolio weights:\")\n",
    "pd.DataFrame(portfolios, index=ASSETS).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "sec6-horizon",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:50.998540Z",
     "iopub.status.busy": "2026-03-30T19:38:50.998428Z",
     "iopub.status.idle": "2026-03-30T19:38:51.221969Z",
     "shell.execute_reply": "2026-03-30T19:38:51.221647Z"
    }
   },
   "outputs": [],
   "source": [
    "# --- Horizon + drawdown for each portfolio x scenario ---\n",
    "combo_rows = []\n",
    "for pname, w in portfolios.items():\n",
    "    for sname, q in scenarios.items():\n",
    "        hr = horizon_report(w, log_returns.values, horizons=[13, 52],\n",
    "                            n_simulations=3000, p=q, confidence=0.95, seed=42)\n",
    "        dd = drawdown_quantile(w, log_returns.values, horizon=52,\n",
    "                               confidence=0.95, n_paths=1000, p=q, seed=42)\n",
    "        for hl in hr.index:\n",
    "            row = {\"portfolio\": pname, \"scenario\": sname,\n",
    "                   \"horizon\": hl, \"max_dd_95\": dd[\"max_dd_95\"]}\n",
    "            row.update(hr.loc[hl].to_dict())\n",
    "            combo_rows.append(row)\n",
    "combo_df = pd.DataFrame(combo_rows)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "sec6-summary",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:51.223163Z",
     "iopub.status.busy": "2026-03-30T19:38:51.223092Z",
     "iopub.status.idle": "2026-03-30T19:38:51.229717Z",
     "shell.execute_reply": "2026-03-30T19:38:51.229527Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multi-portfolio stress summary (CVaR95 + DD95):\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">CVaR95</th>\n",
       "      <th colspan=\"2\" halign=\"left\">max_dd_95</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>horizon</th>\n",
       "      <th>1y</th>\n",
       "      <th>3m</th>\n",
       "      <th>1y</th>\n",
       "      <th>3m</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>portfolio</th>\n",
       "      <th>scenario</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">Equal-Weight</th>\n",
       "      <th>Bearish equity</th>\n",
       "      <td>0.2866</td>\n",
       "      <td>0.1597</td>\n",
       "      <td>0.2759</td>\n",
       "      <td>0.2759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Corr breakdown</th>\n",
       "      <td>0.2488</td>\n",
       "      <td>0.1432</td>\n",
       "      <td>0.2546</td>\n",
       "      <td>0.2546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nominal</th>\n",
       "      <td>0.1375</td>\n",
       "      <td>0.0864</td>\n",
       "      <td>0.1512</td>\n",
       "      <td>0.1512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rising rates</th>\n",
       "      <td>0.1562</td>\n",
       "      <td>0.0959</td>\n",
       "      <td>0.1756</td>\n",
       "      <td>0.1756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">Min-Risk</th>\n",
       "      <th>Bearish equity</th>\n",
       "      <td>0.2504</td>\n",
       "      <td>0.1405</td>\n",
       "      <td>0.2307</td>\n",
       "      <td>0.2307</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Corr breakdown</th>\n",
       "      <td>0.2459</td>\n",
       "      <td>0.1455</td>\n",
       "      <td>0.2415</td>\n",
       "      <td>0.2415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nominal</th>\n",
       "      <td>0.1182</td>\n",
       "      <td>0.0778</td>\n",
       "      <td>0.1310</td>\n",
       "      <td>0.1310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rising rates</th>\n",
       "      <td>0.1818</td>\n",
       "      <td>0.0992</td>\n",
       "      <td>0.1798</td>\n",
       "      <td>0.1798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"4\" valign=\"top\">Tangency</th>\n",
       "      <th>Bearish equity</th>\n",
       "      <td>0.2862</td>\n",
       "      <td>0.1595</td>\n",
       "      <td>0.2667</td>\n",
       "      <td>0.2667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Corr breakdown</th>\n",
       "      <td>0.2372</td>\n",
       "      <td>0.1437</td>\n",
       "      <td>0.2452</td>\n",
       "      <td>0.2452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nominal</th>\n",
       "      <td>0.1168</td>\n",
       "      <td>0.0846</td>\n",
       "      <td>0.1429</td>\n",
       "      <td>0.1429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rising rates</th>\n",
       "      <td>0.1485</td>\n",
       "      <td>0.0927</td>\n",
       "      <td>0.1694</td>\n",
       "      <td>0.1694</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             CVaR95         max_dd_95        \n",
       "horizon                          1y      3m        1y      3m\n",
       "portfolio    scenario                                        \n",
       "Equal-Weight Bearish equity  0.2866  0.1597    0.2759  0.2759\n",
       "             Corr breakdown  0.2488  0.1432    0.2546  0.2546\n",
       "             Nominal         0.1375  0.0864    0.1512  0.1512\n",
       "             Rising rates    0.1562  0.0959    0.1756  0.1756\n",
       "Min-Risk     Bearish equity  0.2504  0.1405    0.2307  0.2307\n",
       "             Corr breakdown  0.2459  0.1455    0.2415  0.2415\n",
       "             Nominal         0.1182  0.0778    0.1310  0.1310\n",
       "             Rising rates    0.1818  0.0992    0.1798  0.1798\n",
       "Tangency     Bearish equity  0.2862  0.1595    0.2667  0.2667\n",
       "             Corr breakdown  0.2372  0.1437    0.2452  0.2452\n",
       "             Nominal         0.1168  0.0846    0.1429  0.1429\n",
       "             Rising rates    0.1485  0.0927    0.1694  0.1694"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Summary table: portfolio x scenario x horizon ---\n",
    "summary = combo_df.pivot_table(\n",
    "    index=[\"portfolio\", \"scenario\"],\n",
    "    columns=\"horizon\",\n",
    "    values=[\"CVaR95\", \"max_dd_95\"],\n",
    ")\n",
    "print(\"Multi-portfolio stress summary (CVaR95 + DD95):\")\n",
    "summary.round(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec7-title",
   "metadata": {},
   "source": [
    "---\n",
    "## Section 7 -- Summary Dashboard\n",
    "\n",
    "A single table bringing together the key findings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "sec7-dashboard",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-30T19:38:51.230744Z",
     "iopub.status.busy": "2026-03-30T19:38:51.230616Z",
     "iopub.status.idle": "2026-03-30T19:38:51.237000Z",
     "shell.execute_reply": "2026-03-30T19:38:51.236824Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== 1-Year Dashboard ===\n"
     ]
    },
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"4\" halign=\"left\">CVaR95</th>\n",
       "      <th colspan=\"4\" halign=\"left\">max_dd_95</th>\n",
       "      <th colspan=\"4\" halign=\"left\">mean</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scenario</th>\n",
       "      <th>Bearish equity</th>\n",
       "      <th>Corr breakdown</th>\n",
       "      <th>Nominal</th>\n",
       "      <th>Rising rates</th>\n",
       "      <th>Bearish equity</th>\n",
       "      <th>Corr breakdown</th>\n",
       "      <th>Nominal</th>\n",
       "      <th>Rising rates</th>\n",
       "      <th>Bearish equity</th>\n",
       "      <th>Corr breakdown</th>\n",
       "      <th>Nominal</th>\n",
       "      <th>Rising rates</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>portfolio</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Equal-Weight</th>\n",
       "      <td>0.2866</td>\n",
       "      <td>0.2488</td>\n",
       "      <td>0.1375</td>\n",
       "      <td>0.1562</td>\n",
       "      <td>0.2759</td>\n",
       "      <td>0.2546</td>\n",
       "      <td>0.1512</td>\n",
       "      <td>0.1756</td>\n",
       "      <td>-0.0807</td>\n",
       "      <td>0.0245</td>\n",
       "      <td>0.0753</td>\n",
       "      <td>0.0539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Min-Risk</th>\n",
       "      <td>0.2504</td>\n",
       "      <td>0.2459</td>\n",
       "      <td>0.1182</td>\n",
       "      <td>0.1818</td>\n",
       "      <td>0.2307</td>\n",
       "      <td>0.2415</td>\n",
       "      <td>0.1310</td>\n",
       "      <td>0.1798</td>\n",
       "      <td>-0.0472</td>\n",
       "      <td>0.0113</td>\n",
       "      <td>0.0609</td>\n",
       "      <td>-0.0015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tangency</th>\n",
       "      <td>0.2862</td>\n",
       "      <td>0.2372</td>\n",
       "      <td>0.1168</td>\n",
       "      <td>0.1485</td>\n",
       "      <td>0.2667</td>\n",
       "      <td>0.2452</td>\n",
       "      <td>0.1429</td>\n",
       "      <td>0.1694</td>\n",
       "      <td>-0.0740</td>\n",
       "      <td>0.0495</td>\n",
       "      <td>0.0974</td>\n",
       "      <td>0.0648</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     CVaR95                                      \\\n",
       "scenario     Bearish equity Corr breakdown Nominal Rising rates   \n",
       "portfolio                                                         \n",
       "Equal-Weight         0.2866         0.2488  0.1375       0.1562   \n",
       "Min-Risk             0.2504         0.2459  0.1182       0.1818   \n",
       "Tangency             0.2862         0.2372  0.1168       0.1485   \n",
       "\n",
       "                  max_dd_95                                      \\\n",
       "scenario     Bearish equity Corr breakdown Nominal Rising rates   \n",
       "portfolio                                                         \n",
       "Equal-Weight         0.2759         0.2546  0.1512       0.1756   \n",
       "Min-Risk             0.2307         0.2415  0.1310       0.1798   \n",
       "Tangency             0.2667         0.2452  0.1429       0.1694   \n",
       "\n",
       "                       mean                                      \n",
       "scenario     Bearish equity Corr breakdown Nominal Rising rates  \n",
       "portfolio                                                        \n",
       "Equal-Weight        -0.0807         0.0245  0.0753       0.0539  \n",
       "Min-Risk            -0.0472         0.0113  0.0609      -0.0015  \n",
       "Tangency            -0.0740         0.0495  0.0974       0.0648  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Final dashboard DataFrame ---\n",
    "dash = combo_df[\n",
    "    combo_df[\"horizon\"] == \"1y\"\n",
    "].pivot_table(\n",
    "    index=\"portfolio\",\n",
    "    columns=\"scenario\",\n",
    "    values=[\"mean\", \"CVaR95\", \"max_dd_95\"],\n",
    ")\n",
    "print(\"=== 1-Year Dashboard ===\")\n",
    "dash.round(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sec7-takeaways",
   "metadata": {},
   "source": [
    "### Key Takeaways\n",
    "\n",
    "1. **Risk scales non-linearly**: CVaR at 1-year is substantially larger\n",
    "   than 4x the 3-month figure due to compounding and fat tails.\n",
    "\n",
    "2. **Bearish equity stress** significantly increases CVaR and drawdowns\n",
    "   for equity-heavy portfolios, while the min-risk allocation is more\n",
    "   resilient.\n",
    "\n",
    "3. **Correlation breakdown** (positive SPY-TLT) undermines the\n",
    "   diversification benefit of bonds, widening the drawdown distribution.\n",
    "\n",
    "4. **Shock + mean reversion** shows that even with a recovery phase,\n",
    "   the median terminal wealth may remain below the starting level for\n",
    "   concentrated equity portfolios.\n",
    "\n",
    "5. **Equal-weight** provides a simple but effective hedge across\n",
    "   scenarios, sitting between tangency and min-risk on most metrics.\n",
    "\n",
    "6. **Rising rates** stress primarily hits bond-heavy allocations;\n",
    "   a pure equity portfolio is indirectly affected through correlation\n",
    "   channels.\n",
    "\n",
    "These results illustrate why multi-scenario, multi-horizon stress\n",
    "testing is essential for robust portfolio construction."
   ]
  }
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