{ "cells": [ { "cell_type": "markdown", "id": "cbbf2344", "metadata": {}, "source": [ "# The Noise That Looks Like Correlation\n", "\n", "Estimate the correlation matrix of 200 assets from 500 days of returns and it will show correlations even when there are none. Between assets that are truly independent, the sample correlations scatter around zero, and the largest of the 19,900 pairs looks like a real relationship. The eigenvalues of the matrix spread across a wide band, and random matrix theory says exactly how wide: Marchenko and Pastur derived the band in 1967. Everything inside it is indistinguishable from noise.\n", "\n", "This notebook measures the band on pure noise, plants a market with sectors to see which eigenvalues rise above it, cleans the matrix by keeping only those, and then shows why it matters: a minimum-variance portfolio built on the raw matrix promises a risk it does not deliver, by an amount the theory predicts in advance." ] }, { "cell_type": "markdown", "id": "5271dfa7", "metadata": {}, "source": [ "## Pure Noise\n", "\n", "Two hundred assets, five hundred days, every return independent with unit variance. The ratio $q = N/T = 0.4$ sets the band in which the eigenvalues of the sample correlation matrix must fall, and the density inside it:\n", "\n", "$$\\lambda_\\pm = \\left(1 \\pm \\sqrt{q}\\right)^2, \\qquad \\rho(\\lambda) = \\frac{\\sqrt{(\\lambda_+ - \\lambda)(\\lambda - \\lambda_-)}}{2\\pi q \\lambda}$$\n", "\n", "The true correlation matrix here is the identity: every true eigenvalue is exactly 1." ] }, { "cell_type": "code", "execution_count": 1, "id": "46aefc4e", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:50.897518Z", "iopub.status.busy": "2026-10-02T04:28:50.897429Z", "iopub.status.idle": "2026-10-02T04:28:50.930771Z", "shell.execute_reply": "2026-10-02T04:28:50.930280Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "q = N/T = 0.4\n", "Marchenko-Pastur band: 0.1351 to 2.6649\n", "sample eigenvalues: 0.1362 to 2.6158\n", "eigenvalues outside the band: 0 of 200\n" ] } ], "source": [ "#| label: Two Hundred Independent Assets\n", "import numpy as np\n", "\n", "N, T = 200, 500 # assets, days\n", "q = N / T\n", "rng = np.random.default_rng(1967) # the year of Marchenko and Pastur\n", "X = rng.standard_normal((T, N)) # independent returns, unit variance\n", "C = np.corrcoef(X, rowvar=False) # the sample correlation matrix\n", "lam = np.linalg.eigvalsh(C)\n", "lo, hi = (1 - np.sqrt(q)) ** 2, (1 + np.sqrt(q)) ** 2\n", "outside = np.sum((lam < lo) | (lam > hi))\n", "\n", "print(f\"q = N/T = {q}\")\n", "print(f\"Marchenko-Pastur band: {lo:.4f} to {hi:.4f}\")\n", "print(f\"sample eigenvalues: {lam.min():.4f} to {lam.max():.4f}\")\n", "print(f\"eigenvalues outside the band: {outside} of {N}\")" ] }, { "cell_type": "markdown", "id": "b13b25f8", "metadata": {}, "source": [ "Every true eigenvalue is 1, yet the sample ones run from about a seventh of that to more than two and a half times it. The same noise shows up pair by pair: a sample correlation between two independent series has a standard deviation of about $1/\\sqrt{T}$, and with 19,900 pairs some of them are bound to look large." ] }, { "cell_type": "code", "execution_count": 2, "id": "8b33cce6", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:50.931869Z", "iopub.status.busy": "2026-10-02T04:28:50.931753Z", "iopub.status.idle": "2026-10-02T04:28:50.934181Z", "shell.execute_reply": "2026-10-02T04:28:50.933825Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pairs: 19900\n", "spread of the pair correlations: 0.0447\n", "theory, 1/sqrt(T): 0.0447\n", "the largest |correlation|: 0.1853\n", "pairs beyond 0.1 either way: 513\n" ] } ], "source": [ "#| label: The Largest Correlation Between Independent Assets\n", "iu = np.triu_indices(N, k=1)\n", "r = C[iu] # every pair, once\n", "print(f\"pairs: {r.size}\")\n", "print(f\"spread of the pair correlations: {r.std():.4f}\")\n", "print(f\"theory, 1/sqrt(T): {1 / np.sqrt(T):.4f}\")\n", "print(f\"the largest |correlation|: {np.abs(r).max():.4f}\")\n", "print(f\"pairs beyond 0.1 either way: {np.sum(np.abs(r) > 0.1)}\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "78a638c9", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:50.935250Z", "iopub.status.busy": "2026-10-02T04:28:50.935175Z", "iopub.status.idle": "2026-10-02T04:28:51.280094Z", "shell.execute_reply": "2026-10-02T04:28:51.279598Z" } }, "outputs": [ { "data": { "image/png": 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I0LFjxzR9+nS1aNEi2xgmTpxoxtC3b19Jl69TBw8erPXr1+vUqVOKj4/X3r179cUXX+j666/Pdpl5UalSJb322mtauXKljh49qsTERJ09e1abN2/WBx98oGuvvdYt65WksLAwPfXUU5ozZ46io6MVGxurxMREHT16VIsXL9bQoUNVt27dbJcTGRmpl156ScuXL9exY8eUmJio06dPa/PmzRo5cqSuu+66bJfh6jq2TZs2Gj9+vHbu3Glee3/88cfmdGf3Iho2bKhPPvlE27dv19mzZ2UYhmbNmuV0vQVxbyI3mjRpopdffllz587Vvn37FBsbq6SkJJ04cUKrV6/WW2+9pcqVK2e5jCvb26FDB3Pc8uXLM3wWV+/bVyxbtsyc1r59+2zjdWfZ3nDDDRo/frx2796tS5cu6dy5c1q/fr2GDBmi0NDQbJebF/7+/urXr59mzZqlAwcOKD4+XhcvXtSuXbv01VdfqUuXLjnajuXLl5vjO3TokOlzdzyu5cSV49E333xjjuvXr5/TMr2ybD8/P8XExMgwDCUnJ6tYsWIul+9Y7ikpKQoPD3eZd9GiRWbeTp06ZRl3r169NHXqVO3du1exsbGKjY3V3r17NWXKFN111125+gxyIif3Hp3d34qKitLw4cO1detWnT9/XnFxcdq5c6dGjx6tKlWq5CqGDh06aMqUKTpw4ID5vbNy5Uo98cQTCgkJyfO2derUSZ9//rn++usvnT171jwW//rrrxo0aJCCg4OzXYazz6dp06ZmPYuLi9PZs2e1fv16vfzyywoLC8tVjP7+/nrwwQc1bdo07du3TzExMYqLi9P+/fs1depU9ezZM9tluPr+79ixo77//nvt27fP/P5fsWKFBg0aJH9//xzHGBgYqKeeekorV67M8D0+ZcqUDMfM3CqI+6Cu7sn37NlTc+bM0cGDB5WYmKiTJ09q4cKFeuCBB7Jd1oEDB8xx1apVc3rMyOm9elfccV+7adOm+u9//6s//vhD586dU0pKiuLj43Xs2DGtXbtWY8eO1d13353ld0FkZKReeOEFLVq0SEePHlVCQoKSk5N1/vx5/fXXX/rxxx/1/PPPq1q1ajmKKa910PG7wXFdBw4ccFoWzr57C+I8HfBmBolEIpFIJBIp5+nJJ580zp8/b2QlLS3N+Oqrr4yAgACny+jbt6+Zd+LEiVmur0OHDsbx48ddris1NdUYOnSoISnDeE9shyRj2LBhZv5hw4YZFStWNH7//fcsl/v1118bNpvN6fJ27Nhh5uvVq1eOyuTuu+8259m5c2em6c2bNzdiYmKyjOmK/fv3G9dff32W66tataqZPzo6Os95rk7R0dHmPFWrVs0yb69evYxjx45luz1z5swxwsPDLa83JBKJRCKRSCRSUU4DBgwwLl26lKNrklWrVjldRkFf17Rv397Mv2zZMiMkJMSYOnVqlssdNmyYOX/p0qWzvPZLS0szBg0alGUMEydONPP37dvXaNmypXHkyBGXy0xJSckQQ062K6u8NpvNePPNN434+Pgstzs5Odl46623Cny/ePzxx42zZ89mue4rbrnlFpfLefjhh7O9vk9JSTFGjRpl2O12l8u5+jo2ICDA+Pzzz50u7+OPPzbncyRdvk+QkpKSaZ5Zs2ZlWmdB3ZvI6X2W9evXZ7muK5KSkoz//Oc/LpeTG3379s0w77Jly8xp7du3z3IfcVfZSjLeeOMNIzU11eVy9+3bZ1SvXr1A9/nmzZsbe/bsyfYzW7hwoREZGZnldmQnu/qf1fEoN8tesGCBOd5VPQ0KCjISEhIyLOO2225zmjcgIMD8vkhMTDSCg4Od5qtZs6bxxx9/ZBvrxo0bC7QcHbnKc/X9rR49emS5H1+6dMm49dZbs123n5+f8dVXX2W5vX/99ZdRq1atTPcrs1pupUqVjKVLl2b7WR45csRo27Ztrj6fYcOGZVnPDh8+bLRs2TJHn3379u1zVH/WrFljVKxYMcvlXLFs2TIjICDA+OKLL7Jc5qZNm5zWyatTnTp1jJ07d2a5rLFjxxr+/v6W3Ae9+rsiPDzcmD17dpbLnD9/vtN66LisnMhrnSvo8z8/Pz9j3LhxOY57xIgRTpfTvXv3HJ/DHD582K11MDffDYaR+bu3IM7TSSRvTjlvFgwAAAB9/PHHeu6558z/T58+rbVr1+rEiRMKDg5W48aN1aBBA9ntdvXv318VK1bUbbfdlueniVq0aKFffvnFfFIxPT1dGzdu1I4dOxQYGKjmzZurVq1aevPNN3XmzBnLt6N48eL69ddf1aBBA126dEmrVq3S4cOHFRYWpo4dO5pP4jzyyCPavXu3Ro4cmWkZ3333nd555x1J0gMPPKAZM2Zkuz2OT3199913maaXKlXKfHLv5MmT2rFjh44cOaJLly4pNDRUNWvWVPPmzRUQEKDq1atrxYoVatKkifbt25ftuq3w3HPP6aOPPpLdfrnj4IsXL2rt2rU6cuSI/Pz8VK9ePTVt2lR2u1233367li9frjZt2ighIcHiyAEAAICip0ePHvryyy/N/x3P31NTU1WiRAnVqlVL9evXz7K3ZXdf13z99dfq3bu3UlJStHr1au3du1ehoaHq1KmTypcvL0l64403tHv3bs2ePVu//fabGjdurISEBK1cuVKHDh1SyZIl1blzZ0VERMhut2v06NH6448/tG7dumzXX7VqVY0aNUoRERGKjY3V0qVLdfLkSVWsWFEdO3ZUsWLF5O/vrzfeeEN2u93s6Tqv7Ha7pk2bpl69epnjjhw5og0bNuj06dMqXry4WrRooZo1ayogIECvvvqqypQpo8cffzxf673i008/1TPPPGP+n5qaqo0bN2rPnj1KTExUmTJldP3116t69eqS5LJ3jRdeeEEffvih+X9iYqJWrFihQ4cOqVSpUurYsaMiIyPl7++v559/XlWqVMmwzVn5+OOPNXDgQEnStm3b9OeffyolJUW1atVy+TrAF198UW+88YYkae/evdqwYYPi4+NVrVo1paSkZFq+J++xSDJ7NEpMTNSOHTu0d+9eXbx4UTabTRUqVFCLFi1UpkwZBQYGmvcsPvjgg0zLGTNmjCTpjjvuUFRUlCRp1qxZOnr0aKa8O3fuzFOs7izbYcOGmXVoy5Yt2r59u1JSUnT99debPbtdc801mj17tpo0aaK0tLQ8bYOjG2+8UQsWLMhwj2vDhg36+++/FRgYqJYtW6pmzZqSpJtvvlmrV69W27ZtM9zviomJMT/7qKgo3XHHHZKko0ePZurJbs+ePbmKb/HixYqLi1OdOnXM3s527typJUuWZMrruOzly5era9euki731LRw4cJM+Vu1apWpDnfs2FHz5s3LlLdFixZmzz4bNmxQYmJipjx16tTRihUrVLZsWXPctm3btHXrVhmGocaNG6thw4aSLvcmtGbNGrVr1y7Xn0lB6NKli8aNGyd/f38dPHhQa9euVUxMjKpXr64OHTooICBAoaGhmj59uurXr5+h16arffvtt7r//vvN/8+fP69ly5bp7NmzqlKlijp06KB69epp/vz5mjNnTo7iq1OnjpYsWaKKFStKurxfbt68WX///bcSEhIUFRWldu3aKTw8XFFRUVq0aJG6deuWoac7V55++mnzeLhnzx6tX79eycnJatCggZo1aybpcu9Gv/76q9q3b68///zT5bJ69eqlKVOmKDAwUJIUHx+vdevW6cCBA0pPT1etWrXUqlUrBQQEqFWrVlq7dq2aNWumU6dOZRvnl19+qX79+iktLU3r16/Xrl27ZLfb1bJlS9WpU0fS5V4Jv/322yzfIFGlSpUMn6Uk/fXXX9q8ebMMw1CTJk3UoEEDPfHEE4qPj882rivcdR/U399fM2fOVJcuXZSUlKQ1a9Zo3759Cg4O1o033mj2ktetWzeNGjVKTz75ZIb5d+7cqTFjxigsLMzsUTImJkbffvttjrctJwr6/O+DDz7IcC7jeO5jt9sVGRmpunXrmmXvzA033KAZM2aYPZs57o9JSUkKDw9XjRo11KBBgyx7YJQKpg46fjf06dPH7Mlx0qRJio2NzbROx+/qgjpPB7yd5S3XSCQSiUQikbwhPfzww+YTJRcuXDD69+9v+Pv7Z8rXoUMH4/Dhw2ZeZ0+m5uQJ2KCgIGP37t1mvn379hlNmzbNlO/uu+824uLiMj2x6IntkDL2NHYlhokTJxqlSpXKkC8kJMSYMmWKmTcmJsYIDQ3NtLwqVaoYaWlphmFcfqLy6uVcnUqVKmUkJSUZhnH56eNq1aplytO8eXPjrbfeMurVq+dyOWXKlDEmTZpkxrdo0SKXea3saaxTp07mE4qJiYnG4MGDjZCQkEz5GjVqZPz111/m8j777DPL6xCJRCKRSCQSiVQU0+bNm83z8tGjRzs9f5dkFCtWzOjVq5fx7rvvOp1e0Nc1jj2NXLmW+/333zP1SBMcHGxMmzbNzLt7927j008/NQzDMGbOnGmUKVMmQ/6SJUsay5cvN/MvWbLEZQyOPfskJiYahmEYkydPNsLCwjItc8aMGWbe1NRUo1WrVtluV1Y9Db355ptmvmPHjhl33HGH03y9evXK0EPO3Xffne994vHHHzcc/fDDD0alSpWc5q1Xr57xySefGDfddFOmaa1atcrQo9e8efOMsmXLZsgTGBhovP/++xnW9/zzzztdl+N17JXlHjx40GmvHoGBgeawo+TkZOP8+fNGjx49spynoO9N5LSnsc8++8zo1q2by96b7Ha70bdvXyM2NtYwjMs9jjm7z3Al5abXsNzM486yTUxMNNLS0ow9e/YYzZo1c7rPX7nPYhiG8dBDD+V7ny9ZsmSGcty9e7fRpEmTTPnuv//+DL29/Pzzzy6XmZteBXOTcvN2AElGixYtzPzr1693mueNN94w85w8edIwDMP4448/nOZ97bXXzLzDhw/PND05hAsxAAAoz0lEQVQgIMDYsmWLmefEiRNG586dM+W76aabjFOnTpn5Nm3a5LSO5TY5cpXH8f5WQkKCERsbazzwwAOZ8tWtWzfDfvH111+7XOaDDz6YYd2jR4/OVI/Lly9vLF682NzPr3DV01hoaGiGNx7MmzfPuOaaazLlCwsLMz777DMz39GjR132ZuUoMTHRiI+PN+6///5M+Vq3bp1h2//880+X5VO3bl2zXqSlpRkjR440SpQokSlf9erVjZUrV2bYnuzqzpXv//Xr1xu1a9fOlPeZZ57JsE033nijyzJatGiRme/8+fNOe9Pr2rWr2TuV43HGU/dBHev3lW2fN29epp7Z/Pz8jJEjR5p509LSXMaYl3vAuUkFef4XERFhJCcnG4Zx+Xu+T58+LpdZvnx546mnnjIeeeSRTNN++uknc10//vijUbJkSafLCAoKMrp162Z8/vnnHquDuenBTiq483QSycuT5QGQSCQSiUQiFfpUvHhx49y5c+YFavPmzbPMX6dOHfP1FqdPn850sZGTG1CON5Hj4uKcXjBdST179jSu5ontkDI2GjMMw5gyZYrL5QUFBRkHDx40895zzz1O8zn+wPDYY49lGaPj57Ry5cp8l/W8efPM5dWpU8dpHqsajdlstgwNCXv27Jnl8sqVK2e+2jQpKcmIioryaL0hkUgkEolEIpGKeipWrJh5/n7w4EGPrTcn1zWOPxobhmHs3LnT6YM90uVryTNnzmTIv3jxYsNmsznNX6VKFbPBS1pamlGuXDmn+a5+Hdwvv/zicpl+fn4ZXl20YsWKbLfLVUOSqlWrmvGdOXMmy+tt6XLDpSt27NiRr7IpWbKkcfHiRXN5Y8eOzfOyHK+df//99yxf3/jJJ5+YeS9cuGAUL17c6efiKC4uzrj22muzjcNRampqlo0KruxPBX1vIrcNfbJL99xzj7m89957z2U+dzUac3fZnj592qhQoYLLZTo2lpg/f36+P0/HRlNnz5512UhSynyPy9X+VFgajfn5+ZmvjktJScnU6NWxPA8cOGCMHj3arCvOGv5cafRkGIbRsWPHTNP79etnTk9KSsryVXRNmzY1G4gYRsE0AHTkKo/j/a20tLQsX6976623mnljYmIMPz+/THlsNluG+4kTJkxwubzg4GBj69atGeJ01WjMsYHezJkzXX7/XEmO31mDBw/O9vMxDNf3PqXLjcEcHwJ++OGHneZz3Ceee+65LGMMDQ3N0HjK2fH16u//3bt3G8WKFXO5zOnTp5t5XX1ndenSJUOZd+jQweXy2rZtaz4wfIWn7oNe/UrJFStWON3nriTHVxq7KnN3NxrLTcru/O+2224zp0+ePDnP6zl9+rRhGJcb3mW172SX3FEHc9NozKrzdBKpECbLAyCRSCQSiUQq9MnxqapRo0blaJ7PP//cnOfqJ5ZzcgNqw4YNZp633nor2/UtWbIkw0WvJ7ZDythoLDEx0eWPAVfSe++9Z+b/8MMPneZ59NFHzTzZNQRbtWqVmTe7BmY5SXfffbe5vKeeesppHqsajXXv3t2c/tNPP+VomS+99JI5j6snjkkkEolEIpFIJJJ7UoUKFczz8c2bN3tsvTm5rrn6R2NnPUM5JsceLAzDMBo2bJhl/hUrVph5nfU2ImX88S8tLS3bxlv169fPEEOtWrWy3C5XDUlGjRpl5nnmmWdy9JkuWLDAnKdx48Z5LpvBgwdnuFZ07H0rN6lOnToZPousGo5IlxsSOPY65Oz6+eqGRVk1lnJMjn744Yds87vj3kRBNxqz2+1mQ6BNmza5zOeORmOeKNvs7g84xnD69Ol8f57Hjh0zl5ddoxcpY8OHqVOnOs1TWBqNSTLmz59vznPrrbdmmBYcHGw2DPrmm2+MO+64w8zbvXv3DHkDAwPNHqUSEhKc9oi3du1ac/5PPvkk29gce+dZs2ZNvj8fR67yON7fyqq3OGf7R/369TNN79q1qzn90qVLRkRERJbLc2zAZBjOG435+/sbJ06cMD/rq3vNdJYqVKhgNnb6888/s/18XDVudkwffvhhluXTsGFDc7qr3umuTvfee685z6effppl3TEM58dUV5+/q+PhDz/8YOaZNm1atjF+9913GWLw1H3QqxuNZfd9PnDgQDPvjBkznOYpTI3Gsjv/6927tzk9p9+/ztKVXuLOnj2b52W4qw7mptGYVefpJFJhS5df/gsAAIAs3Xrrrebw1KlTczTP0qVLzeG2bdvman3FixdXkyZNzP+/++67bOfJSR53b8fvv/+ukydPZplny5Yt5nC1atWc5vnxxx+VmJgoSWrTpo2qVKniNF/VqlXVunVrSVJSUpKmT5+e5bolKSQkRB07dtQzzzyjESNG6JNPPtF///tfM/Xu3dvMe/3112e7PE/y9H4IAAAAIH/OnDmjhIQESVL9+vXN65f8Kujrmvj4eM2bNy/LPNu3bzeH9+zZo23btmWZ/6+//jKHq1evnm0Ma9as0f79+7Nd5ubNm83/O3bsmO1ynbHy2qpr167m8Pjx45WcnJyn5Thu+5YtW7R169Ys88fHx+v77793Or8rP/zwQ67jysk8heXatkGDBurTp4+GDh2qDz/8MEMd+vTTT2UYhpnPZrMVyDpzwhNl++OPP2Y5fdeuXYqPj5cklS5dWsWLF892ma5cd911qlChgiQpNTVV3377bbbzfPXVV+Zwhw4d8rxuT1m+fLk5fPXn36pVKwUHB0uSli1bphUrVig9Pd1p3hYtWig0NFSStGHDBvPe2BXFixdX06ZNzf8nTJiQbWyOn2WzZs3M5XtKdvuaJP3555/msLN7hY6f0/z583Xu3Lksl7d48WIdOXIkyzxNmzZVuXLlJElLlizR6dOns43z+PHj2rVrl6TL3+nh4eFZ5s/Jvj5p0iRz2Fn5OB4vHet5VnJzvExISNDcuXOzzJOTe7mOZZTb7XbF3d8V+/bty7BtzuRk2z0pv+d/hw8fNofvvPNOlSlTJk9xXFlORESE7rnnnjwtwxN1MDvuOk8HvI2/1QEAAAB4g1atWpnDjz32mPr27ZvtPJUqVTKHK1eunKv1NWzYUH5+fpKkixcvmhdDWVm/fn22edy9HY4/Irhy9uxZc9jVhd3Fixc1b9483XXXXbLb7XrggQf07rvvZsr3wAMPyG6//BzEvHnzdOHCBZfrLVWqlIYPH64+ffrk+IKydOnSOcrnKY7ld9ddd6l9+/bZzlOiRAlzOLf7IQAAAID8SUlJ0ezZs9W7d28FBARo6dKlmjZtmmbMmKGVK1fq4sWLuVqeu65r/vnnH6WmpmaZ5/z58+bwjh07sl2m44/6OYl17dq12ea5ku/KQ1aNGzfO0TyOIiIiVLt2bUmXHz4aNmxYjuarW7euOZyfa6sWLVqYw8uWLcvzchy3fc2aNTmaZ/Xq1XrmmWckKcODas4kJyfn6Br/an/88Ue2eTx9j+Vqffr00SuvvGLuB9kJDAxUiRIlsrznUJDcXbYXLlzItkGNdLnOX2nAEh4erri4uBzFcjXH7dm9e3e2DX6ky9tzRYUKFVShQgUdP348T+v3hKwajTk2elu2bJnOnTun7du3q1GjRlnmdVzmFQ0bNpS//+WfdmNjY7NtvCtJW7duVVxcnIoXLy5/f381atQox8fbglAQ9wod96Gcxr5+/foMx42rOR6HKlWqpP/+9785Wm7JkiUlSXa7XZUqVdLff//tMm9OYt2+fbtiY2MVFhYmf39/NWzYUOvWrXMaZ8eOHVW1atVsl+nYyDW74+Xu3buz/f7PrnwqVqyosmXLmv87xu/KunXrlJ6ebt7Xdcbd90EL6j62JxTU+d+6det06NAhValSRVWrVtWOHTs0ceJEzZ07V+vXr1dKSkqOlj19+nQNGTJE0uXGjPfee6+mTZumZcuW5ajxl+SZOpidgj5PB7wVjcYAAACyUaxYsQwXYwMGDMj1MkqVKpWr/I5P+eTkRl5O8nliO3JyIeV48RkQEOAy33fffae77rpLkrJsNOaY35UqVapo5cqVObqx4igsLCxX+d2tYsWK5vB9992X6/lzux8CAAAAyL/nn39eN9xwg2rVqqWgoCD16dNHffr0UVpamnbs2KFVq1Zp0aJFWrBgQZa9TrnzuiYn13KOPyrnNn9W135XHDp0KNs8V+fLSw8ZV3o8kqSgoCA99dRTuV5GXq+twsLCMvQik13Pallx3PaDBw/maJ4DBw6Yw9k1Jjx//rzS0tJyHVd2PxZbcY/F0ddff61HHnkk1/OFhYV5rNGYu8s2pz+C5/T+TXbysj2nTp1SQkKCQkJCJF3epsLcaOyPP/5QTEyMwsPDdf3116tEiRLm53ylIVh0dLR5/Fq+fLkaNWqkBg0aKCIiwmxIl12jMcfP0rHHoKwYhqHDhw/ruuuuk+T5ByQL4l6h43bn5bvCGcd7bI0aNVKjRo1ytFxH2R2LchrrkSNHzPK5+nvNMU7HnrdyqiDu5Wb3fe4Y86VLlzI0tHIlNjZWFy9ezDI+d98HLcj72O5UkOd/qampeuihh/TLL78oLCxMZcqU0eDBgzV48GAlJCRo06ZNWrlypebPn59lo+W33npLHTp0UKtWrWS323XnnXfqzjvvlHT5QYRVq1ZpyZIlmjt3rssGx56ogzlRUOfpgDfj9ZQAAADZcHxCKa+uPAWYU47d/l95HUB2snvi0xPbceXVDQVh3rx55k2GevXqZepSu3HjxuaT3ufOncvyVSpTp041L6xjYmI0atQo3XLLLapevbqKFSsmu90um80mm82W4QZdVk+7WSG/ZZjb/RAAAABA/p08eVJNmzbViBEjdOLECXO8n5+fGjZsqEGDBmn27Nk6fvy4XnrpJZfXIe68rsnttVxBXvtdkdNr30uXLpnDeXnQx4pr/CuujjevPTdJGe8bOH4mWcnNZ3fldU25dfXr9K5m5ec/YMCADA3GFixYoD59+qh+/foqWbKkAgMDzTpks9kyNMTy5P0Bd5etO+pvVvKyPVfnLWwP9V0tLS1Nv//+u6TLx/Z27dpJkoKDg83eBR17FrzSIMxut5u9JwUGBpo97yQmJjptsOGNn2VB7G95uU+a3efjiWNRQXyvufteoFXlI7m/jDx5H9udCvr8b+XKlWrUqJEmTZqUobxCQkJ044036tVXX9Xq1au1a9cu9ejRw+ky4uPj1b59e7344ouKjo7OMK1WrVrq37+/pk6dqhMnTuj99983X9HryMrzAUcFdZ4OeDP2agAAgGxcfQFbqlSpDDcRc5Ku7m4+O443jh2fQs5KsWLFCt125EdKSop+/PFH83/HXsWu/v/HH390+aRPq1at1KZNG0mXn2Jr2bKlXnjhBf322286cOCA4uPjM9wksPJGZHYXnY5l2Lhx41yXX/Xq1d29CQAAAACciI2N1dChQxUVFaUWLVroxRdf1KxZszL0yhQREaH33ntPM2fOzDS/N13X5FVern1jY2NzvR7H66qLFy/m+rrKZrPp4YcfzvV6ncXr+EN7bjneN8jufoCzfHn57AqClfcmXnzxRXN46NChuvXWWzV58mTt2LFDFy9ezPRaLqvqkbeWrSt52Z6r8xa2bXLG2SsqW7duraCgIEkZG42tWLFC6enpGfK2bNnS7Flt/fr1SkpKyrSOovJZXs3d90k//fTTPH0XrFixIst1FMT3mmOcd9xxR57idLe8lI+UuzIqqvdB3XX+Fx0drX79+qlMmTK65ZZbNGLECC1dujRDI7LatWtr9uzZev75550uIyUlRR999JGuueYaNWrUSE8//bS+//77DG9DKVasmAYPHqxly5ZlajjmiTqYU/k9Twe8HY3GAAAAsnHx4sUMT8qWL1/e7es8c+aMORwVFZWjeSpVqpTldCu2I78cXznZu3dv80aHzWZT7969zWmTJ092uYzOnTubw5MmTdLOnTuzXGduu/p2xfFmc06fesruCauTJ0+aw95QfgAAAAAySk9P14YNG/TRRx/pzjvvVLly5dS2bVv9/PPPZp6ePXvqrrvuyjCfVdc1nlSlSpUc5atcubI57HjtnFOO11UlSpQwG2l4QmxsbIYfZPPzg7bjD5k5/eyqVatmDuflsysIVt2bqFSpkmrVqiXp8qs333333Szzh4WFFchrr/LCW8vWlbxsT5kyZTLUzcK2Tc44azTm2OuPY6Ox8+fPa9u2bS7zOns1pZTxs8zuPuAVNpst38dNq+VlH3LcZmc8cY8tp7E63vu9uny84V6gY/kUK1ZMERER2c5TvHhx7oPmgLvP/+Lj4/Xbb79p6NCh6ty5syIjI9WrVy/z+CRJ7777boZXSTqzbds2jRkzRvfff78qV66sxo0ba8KECeb0li1batCgQRnmKYzlm9fzdMDb0WgMAAAgBzZs2GAOX3m6x522bdumtLQ0SVLJkiVVu3btbOdp3rx5tnk8vR35tXr1au3fv1/S5RsoV26kderUybxY3b9/v1avXu1yGY4Xtdu3b892nVdeIZBfMTEx5nBObjRXrlw525sl69evN4e9ofwAAAAAZM0wDK1evVo9e/bUb7/9Zo7v3r17hnxWXdd4UsuWLXOU78rr2yRp8+bNuV7PiRMndOjQIfP/1q1b53oZ+eF4XdepU6c8L2fLli3mcE63wTFfXj67gmLFvQnHOrRr1y6lpqZmmb9t27ZuebVrTnhz2TrjuD116tTJ0T0Sx/3i+PHjOn78uFticyavZfrHH3+Y94IaNmyoUqVKmQ3B9u7dq6NHj2bIf6URWd26dVW6dOkcNRrbtm2bue+Gh4erQYMG2cbVqFEjs1fD1NRU/fnnn7nZrELBcR/K6XfFldeCuuJ4LHbX90BOYq1fv77Cw8MlOS8fb7gXeOzYMZ06dcr8Pyfb3bJly2yPsd6w7ZJ7X3Pp6fO/xMREzZw5Ux06dDBf1RgUFKRbbrklV8vZunWr+vfvr/Hjx5vjrj63dVcdLMjyyOl5OuDtaDQGAACQA7/88os5/MQTT7h9fbGxsRluiFz9akZnHnzwwWzzeHo7CsLUqVPN4Svb6LitjtOdudLdv5R9F+kVKlRQjx498hJmJnFxcTp79qyky0/ZXXmi2ZV77rkn22U6lt8jjzxivuIAAAAAgPebO3euOVyuXLkM06y6rvGkNm3aZOgtyZm6devqhhtuMP931bAiO47XVk8++WSelpFXCxYsMIcHDBigwMDAPC1n6dKl5nCTJk2ybTwSEhKi++67z+n8nmbFvYnc1CEp53E59poWEBCQ+8Cc8OaydWbnzp1moy9/f/8c3b/q37+/OezYQ5cn5LVM09PT9fvvv0uS7Ha7unXrZj7g6Wwbrhy/7Ha7unbtaja0SUxM1Nq1a52uIy4uTps2bTL/79evX7ZxOX6WGzZsyNDbobdw/PxuvfXWbBsedurUKduexlavXq3z589Luvwg5+23357/QK+Sk329T58+5vDGjRszlY/j8fLOO+9U2bJlCy7AAuRYRg899FC2+R232xVvuQ/qju+BK6w6/zt//nyGh7SvPi/NqTlz5rhchrvqoLvKI6vzdMDb0WgMAAAgB7744gvzIuaGG27QsGHDcjxvZGRkjp5OvZpjF87PPfdcljfPb7/9dnXp0iXbZVqxHfnl+OrJO++8U//X3v0HRVG/ARx/REATxqEQKKvRLBW1tPxBijlqyjhGTebPzBJrisy0mWqmcirJyZomMs1RESIOMUtUVEpJUfG3qEiWTiKKmiX4A0WEEPGg5/uH435Z7g4OOUHi/Zp5Zjju2c9+dm8Xdj/77J6Pj4+MHDnS7vv23HhSmUj1dwG5ublJTEyMSwcgKt8xVd1A3r333ivTp0+vsb2kpCQ5duyYiFy/02zhwoVO98XLy8upgXEAAAAAruPt7e30BavKF7grP7FDpGHPa+qLm5ubfPPNN9W+P2/ePOP1jh07JDs7+6bmNXv2bONpPSNHjpSwsDCnp63rhcJvv/1WiouLReT6VwrOnTv3ptrJzs6Wbdu2Ga/nz58v7u7uDvNnzZpl9P3y5cs13oB1KzXE2MTJkyeNi+8PP/xwtV8NOnbsWKcvXt+4WUzE/BVzddGYP1tHYmJijJ9nzJhR7VedPfPMM/L0008brxctWnRL+1ZVXT7TyoUzH3zwgfG32F7R2Pbt241vGXjvvfeMr+Pcs2ePlJWVOZxHdHS08fObb75ZbVFhz5495fXXXzde1/e6dJXU1FTjCZFeXl7y5ZdfOsxt0aKFzJ49u8Y2r127Zvr7u3Dhwhq/gq8yZ4q3Bg8eXO3X2AUGBsrUqVON17GxsTY5GRkZxvbTqlUrWbJkidPHFR4eHuLj4+NUbl1V7vvYsWNlwIABDnODg4PlhRdeqLHNxjIOWlhYaOzLfn5+1f69ri1XH/8589WhNzg6LvX09BQvL686tSFy6/bB2vwNd9VxOvBfoARBEARBEETNERYWppXFx8fr/fff7zA/ODhYFyxYoCUlJerl5eWwLYvFYnf6li1b6tGjR428nJwc7dmzp03eqFGjtLi4WEtLS039q4/lEBGNiIgw2oqIiKhxPQ4cONDI37Jli1Prft++fcY0K1asMH7et29fjdN27txZKyoqjGkiIyO1ZcuWppyAgABdvXq1qqoWFxfX2L927doZOSdPnnQ47wkTJhh5V69e1ZEjR9rkPP7445qTk6MVFRV69epVI79du3Z22xwyZIharVYjb926dRoYGOiwDz169NAvvvhCCwoKtFu3bg2+HxEEQRAEQRBEU4qBAwdqbm6uRkREaJcuXezmuLm56dixY/XKlSvGcf748eNNObfivKa252bOnMdWDmfOFS0Wi+mcSfX6Oaq3t7cpz8fHRxMTE43ciooK7d+/f52Wq3L/KioqNDIyUn19fe3mNm/eXENCQjQhIUHz8vLqvF288cYbWtmyZcv03nvvtZvbtWtXnTt3roaEhNi8169fP9P5YXJysvr5+ZlyPDw89PPPPzfN7+2337Y7L2fPdatGZc5O4+qxCWe2z127dhk5mZmZ2qlTJ9P7zZo10ylTpmhZWZlarVbTPunoHP399983cn7++Wenln3Lli3GNAMHDrSbczt8tidPnqxx+Z0NHx8f/fvvv432srKytEePHjZ548aN03/++ce03I7avJnxJWciICDAaPfKlSvVbpdVo3fv3mrPPffcYzc/MzPTJremsTUPDw89cOCAkZ+Xl6eDBg2yyRsyZIieO3fOyNu/f7+6u7vXef1U5qptp/L/grCwMLs5EydONM17zpw52qJFC5vPLjU1VVXVNMbmaJ16eXnpoUOHTOty9OjR2qxZM7v5vr6++tprr2lmZqZGRkbWuH6uXr2qJSUl+vzzz9vk9e3bV0+dOmXkHjp0SD08POy22a1bNy0qKjJy09PTNSgoyOH67Nixo3700Ueam5uroaGhLtl3nPncN2/ebORcvHhRhw8fbpMTEhKiFy5cUFXVsrKyGrcTV4+D1vZYxtm/nVlZWUbe6NGj67yf3QhXH/9FRETogQMHdPLkyRoQEOBwv5g1a5bRjtVq1fvuu8+0TgoKCjQyMlJ79erlsO9Dhw7V8+fPG+1Mnz69XvbBqKgoo7358+dXu35ddZxOEP+BaPAOEARBEARBNJqYOXOm6STZarVqRkaGLlmyRKOionTJkiW6ZcsWvXTpkinvZorGRK4PipaUlBi5FRUVunv3bo2NjdWEhAQ9cuSI8d6UKVNMefWxHCL1UzT21ltvqT3Tpk1zavr4+HjTdLm5ubpmzRqNiYnR1NRUYyDp8uXLGh4eXmP/nB0waN68uWkgT/X6IF1sbKxaLBbT4OCMGTOcHlR79dVXTQMmFRUVeujQIV26dKlGRUXp4sWLNTU11TQ4qKoUjREEQRAEQRBEPUfl8x/V6xfDUlJSNC4uTmNiYjQ5OVlPnz5tytm2bZvdi2WuPq+53YrGIiIitKCgwFiG1atXa3R0tCYnJ5sugqqqzpo1y6l1XtNyVZ6/6vUL/Dt37tTFixdrVFSULl26VHft2mWaf35+vku2jQULFpjmbbVadff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"text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 461, "width": 1222 } }, "output_type": "display_data" } ], "source": [ "#| echo: false\n", "#| fig-cap: Left, the eigenvalues of the sample correlation matrix of 200 independent assets over 500 days, against the Marchenko–Pastur density for q = 0.4; the dashed lines are the band's edges, and every true eigenvalue is 1. Right, the 19,900 pair correlations against a normal curve with standard deviation 1/√T.\n", "import matplotlib.pyplot as plt\n", "TEAL, ORANGE, GREY, ROSE = \"#2a9d8f\", \"#f4a261\", \"#8a94a6\", \"#e76f51\"\n", "plt.style.use(\"dark_background\"); plt.rcParams[\"font.size\"] = 12\n", "\n", "def tidy(ax):\n", " ax.spines[\"top\"].set_visible(False); ax.spines[\"right\"].set_visible(False)\n", "\n", "def mp(x, q, s2=1.0):\n", " a, b = s2 * (1 - np.sqrt(q)) ** 2, s2 * (1 + np.sqrt(q)) ** 2\n", " y = np.zeros_like(x)\n", " m = (x > a) & (x < b)\n", " y[m] = np.sqrt((b - x[m]) * (x[m] - a)) / (2 * np.pi * q * s2 * x[m])\n", " return y\n", "\n", "fig, (a, b) = plt.subplots(1, 2, figsize=(12.4, 4.8))\n", "a.hist(lam, bins=40, density=True, color=TEAL, alpha=0.65, label=\"sample eigenvalues\")\n", "x = np.linspace(0.01, 3.0, 600)\n", "a.plot(x, mp(x, q), color=\"white\", lw=2, label=\"Marchenko–Pastur, q = 0.4\")\n", "for e in (lo, hi):\n", " a.axvline(e, color=ORANGE, lw=1.2, ls=\"--\")\n", "a.axvline(1.0, color=ROSE, lw=1.2, ls=\":\", label=\"every true eigenvalue\")\n", "a.set_xlabel(\"eigenvalue\"); a.set_ylabel(\"density\"); a.legend(fontsize=10.5, loc=\"upper center\", facecolor=\"black\", edgecolor=\"none\", framealpha=0.9); tidy(a)\n", "b.hist(r, bins=60, density=True, color=TEAL, alpha=0.65, label=\"19,900 pair correlations\")\n", "g = np.linspace(-0.2, 0.2, 400); sd = 1 / np.sqrt(T)\n", "b.plot(g, np.exp(-0.5 * (g / sd) ** 2) / (sd * np.sqrt(2 * np.pi)), color=\"white\", lw=2, label=\"normal, sd 1/√T\")\n", "b.set_xlabel(\"sample correlation of two independent assets\"); b.set_ylabel(\"density\")\n", "b.legend(frameon=False, fontsize=10.5); tidy(b)\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "8bf40bcb", "metadata": {}, "source": [ "## A Market With Sectors\n", "\n", "Now plant structure. Every asset loads 0.4 on one market factor, and each belongs to one of four sectors that adds a loading of 0.3 on its own factor; the rest is independent noise, so every asset still has unit variance. The true correlation matrix has exactly four eigenvalues above the rest: one for the market and three that tell the sectors apart. The question is whether the sample matrix shows four.\n", "\n", "The edge of the noise band must first be corrected for the market, which carries a share of the total variance (Laloux and co-authors, 1999): the variance left for the noise is $\\sigma^2 = 1 - \\lambda_{\\max}/N$, and the edge becomes $\\sigma^2 (1 + \\sqrt{q})^2$." ] }, { "cell_type": "code", "execution_count": 4, "id": "a3c7e8c6", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:51.281271Z", "iopub.status.busy": "2026-10-02T04:28:51.281131Z", "iopub.status.idle": "2026-10-02T04:28:51.294945Z", "shell.execute_reply": "2026-10-02T04:28:51.294393Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "top true eigenvalues: 37.25, 5.25, 5.25, 5.25, 0.75, 0.75\n", "top sample eigenvalues: 37.02, 6.24, 5.45, 4.97, 1.91, 1.83\n", "noise edge after the market: 2.1716\n", "sample eigenvalues above it: 4\n" ] } ], "source": [ "#| label: Planting a Market and Four Sectors\n", "beta, gamma, K = 0.4, 0.3, 4 # market loading, sector loading, sectors\n", "sector = np.arange(N) % K\n", "idio = np.sqrt(1 - beta**2 - gamma**2)\n", "m = rng.standard_normal((T, 1))\n", "s = rng.standard_normal((T, K))\n", "R = beta * m + gamma * s[:, sector] + idio * rng.standard_normal((T, N))\n", "\n", "C_true = beta**2 + gamma**2 * (sector[:, None] == sector[None, :])\n", "np.fill_diagonal(C_true, 1.0)\n", "C_s = np.corrcoef(R, rowvar=False)\n", "lam_t = np.linalg.eigvalsh(C_true)[::-1]\n", "lam_s = np.linalg.eigvalsh(C_s)[::-1]\n", "sigma2 = 1 - lam_s[0] / N # the noise variance left after the market\n", "edge = sigma2 * (1 + np.sqrt(q)) ** 2\n", "\n", "show = lambda v: \", \".join(f\"{x:.2f}\" for x in v)\n", "print(f\"top true eigenvalues: {show(lam_t[:6])}\")\n", "print(f\"top sample eigenvalues: {show(lam_s[:6])}\")\n", "print(f\"noise edge after the market: {edge:.4f}\")\n", "print(f\"sample eigenvalues above it: {np.sum(lam_s > edge)}\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "c835da27", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:51.295981Z", "iopub.status.busy": "2026-10-02T04:28:51.295887Z", "iopub.status.idle": "2026-10-02T04:28:51.494540Z", "shell.execute_reply": "2026-10-02T04:28:51.493868Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 439, "width": 1021 } }, "output_type": "display_data" } ], "source": [ "#| echo: false\n", "#| fig-cap: The 200 eigenvalues of the sample correlation matrix of the planted market, largest first, on a log scale. Four rise above the noise edge corrected for the market (dashed): the market itself and the three that tell the four sectors apart. The rest sit in the noise band, where the true eigenvalues are all 0.75.\n", "fig, a = plt.subplots(figsize=(10.4, 4.6))\n", "k = np.arange(1, N + 1)\n", "a.semilogy(k, lam_s, \"o\", ms=4, color=TEAL, label=\"sample eigenvalues\")\n", "a.semilogy(k, lam_t, \"-\", lw=1.6, color=GREY, label=\"true eigenvalues\")\n", "a.axhline(edge, color=ORANGE, lw=1.4, ls=\"--\", label=\"noise edge, corrected for the market\")\n", "for i, t in ((0, \"the market\"), (2, \"the sectors\")):\n", " a.annotate(t, (k[i], lam_s[i]), textcoords=\"offset points\", xytext=(12, 4), color=ROSE, fontsize=11)\n", "a.set_xlabel(\"rank\"); a.set_ylabel(\"eigenvalue (log scale)\"); a.set_xlim(0, N + 1)\n", "a.legend(frameon=False, fontsize=10.5, loc=\"upper right\"); tidy(a)\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "98e4b145", "metadata": {}, "source": [ "## Cleaning by Clipping\n", "\n", "The simplest cure keeps what rises above the band and treats the rest as noise: the eigenvalues above the edge stay, every eigenvalue inside the band is replaced by their average so the trace stays the same, and the matrix is rebuilt and rescaled back to a correlation matrix (Laloux, Cizeau, Bouchaud and Potters, 1999). Because the truth is known here, the cleaning can be judged directly." ] }, { "cell_type": "code", "execution_count": 6, "id": "4cd4851d", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:51.496510Z", "iopub.status.busy": "2026-10-02T04:28:51.495949Z", "iopub.status.idle": "2026-10-02T04:28:51.511078Z", "shell.execute_reply": "2026-10-02T04:28:51.510420Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "distance to the truth, sample: 0.2075\n", "distance to the truth, cleaned: 0.1159\n" ] } ], "source": [ "#| label: Eigenvalue Clipping\n", "def clip(C, edge):\n", " w, V = np.linalg.eigh(C)\n", " noise = w <= edge\n", " w = w.copy()\n", " w[noise] = w[noise].mean() # the bulk flattened, the trace kept\n", " Cc = (V * w) @ V.T\n", " d = np.sqrt(np.diag(Cc))\n", " return Cc / np.outer(d, d) # back to a correlation matrix\n", "\n", "C_c = clip(C_s, edge)\n", "err = lambda A: np.linalg.norm(A - C_true) / np.linalg.norm(C_true)\n", "print(f\"distance to the truth, sample: {err(C_s):.4f}\")\n", "print(f\"distance to the truth, cleaned: {err(C_c):.4f}\")" ] }, { "cell_type": "markdown", "id": "14aef821", "metadata": {}, "source": [ "## The Risk It Promises, and the Risk It Delivers\n", "\n", "A minimum-variance portfolio weights the assets by $w \\propto C^{-1}\\mathbf{1}$, and the inverse amplifies the smallest eigenvalues, which are the noisiest. Its **predicted** variance is computed with the matrix it was built from; its **real** variance with the truth. For Gaussian returns the theory is exact in the limit: built on the raw sample covariance, the predicted variance is $(1-q)$ times the true minimum and the real one is $1/(1-q)$ times it (Pafka and Kondor, 2003). The portfolio believes it is safer than the best possible portfolio, and is in fact riskier.\n", "\n", "Two hundred fresh samples are drawn from the planted market. Each builds a raw portfolio and a cleaned one, and each is scored both ways." ] }, { "cell_type": "code", "execution_count": 7, "id": "c155c262", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:51.512216Z", "iopub.status.busy": "2026-10-02T04:28:51.512122Z", "iopub.status.idle": "2026-10-02T04:28:56.122464Z", "shell.execute_reply": "2026-10-02T04:28:56.121892Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "raw predicted 0.604 x the minimum, real 1.656 x\n", "cleaned predicted 0.765 x the minimum, real 1.183 x\n", "theory predicted 0.600 x the minimum, real 1.667 x\n" ] } ], "source": [ "#| label: Two Hundred Portfolios, Raw and Cleaned\n", "Lc = np.linalg.cholesky(C_true)\n", "one = np.ones(N)\n", "best = 1 / (one @ np.linalg.solve(C_true, one)) # the true minimum\n", "\n", "def minvar(S):\n", " w = np.linalg.solve(S, one)\n", " return w / w.sum()\n", "\n", "score = {\"raw\": [], \"cleaned\": []}\n", "for _ in range(200):\n", " Z = rng.standard_normal((T, N)) @ Lc.T # a fresh sample from the truth\n", " S = Z.T @ Z / T # its covariance (mean known: 0)\n", " d = np.sqrt(np.diag(S))\n", " Cz = S / np.outer(d, d)\n", " e = (1 - np.linalg.eigvalsh(Cz)[-1] / N) * (1 + np.sqrt(q)) ** 2\n", " S_c = clip(Cz, e) * np.outer(d, d) # cleaned; sample vols kept\n", " for name, M in ((\"raw\", S), (\"cleaned\", S_c)):\n", " w = minvar(M)\n", " score[name].append((w @ M @ w / best, w @ C_true @ w / best))\n", "\n", "for name, v in score.items():\n", " p, r = np.mean(v, axis=0)\n", " print(f\"{name:8s} predicted {p:.3f} x the minimum, real {r:.3f} x\")\n", "print(f\"theory predicted {1 - q:.3f} x the minimum, real {1 / (1 - q):.3f} x\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "1fcce404", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T04:28:56.123700Z", "iopub.status.busy": "2026-10-02T04:28:56.123617Z", "iopub.status.idle": "2026-10-02T04:28:57.873499Z", "shell.execute_reply": "2026-10-02T04:28:57.872685Z" } }, "outputs": [ { "data": { "image/png": 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2bVJ6erq5DMGhswh4Wo4gJyfH4+AE+NfGfXZd8vgSvXPbmbJFhrf7/LLqOl1KogRwK8XW/qVovIsbFZC4QHd38qBUzbt1fLsHsg1Itemzu8/VJY8v0ddbCwPUOgAAAACARNIfAIDDimPdBtUWFsmamtLhWLWFRXKs2+iHVgVGfX29ioqKVFRU5PU5P/zwg8LDwxUXF+d2sEBr28XFxW5jJiYm+tR+T4MIpP8NJEhISFBCQoLXMf/4xz/qH//4R4v9J5xwgm688Ua3AwWavi4rK2N2gXZYa8To2roBeiyiQFkh7mercCfHsOq2+r5aa3wTwNYB3VecDwNpvGGLCkxcoDvLzkz0KeHfKD7aqnm3jteZMxcxkA0AAAAAAoikPwAAhxNXg3KeeVn9Z0yXJdr3JxpdVdXKeeYlqYcmgB0OhxwOh/bu7fha6q+99prWrVvXbICAu8EDFoul2Xl2u91tvMjISEVG+vaUq6eBBEOGDNHVV1/d5vkNDQ0qKytrNhhg4sSJbpdfyM7ONq9ZUlKimpoan9rcXUVkpClr+rXaHRmlS+rjdWpIuSaFFuuE0AqP53zfEKt3G5L1pWGTKzLk4PkPzVJNbkEnthzo+hzOuoDELa8OTFyguwqzhOjNm8/o0FI10sHE/9xbxum4GQtU72LJGsBbg9LjNWFkX6XYIhUXGS6Hs05F5U4tXrtXW/OYvQsAAADNkfQHAOAwU5Obr5ynZitr+rU+Jf5dVdXKeWo2iUgvLV++XMuXL2+1TkhIiGw2W7OBAJ6WNYiJidH69evNutHR0V63xdclCBqFhoaaSyYMGDBAdXV1bhP+kvTvf/9bo0ePNl9XVVW1ugxB4+tNmzZpw4YNXr+nLskSqqxpU83+5VKIVhjxWuGKVz+XU6eFlitR9YoJaVClESq7wvRFg0171HwwhyU6SlnTrtH2ux+SXD1zgA3gi6JyZ4DiVgckLtBdnTuyrwak2vwSa0CqTRNG9tXC1Xv8Eg/oqcIsITp3ZF9dN26wTs9Od1tn5qWjtGJjnl5cukWL1u5lMA0AAAAkkfQHAOCwVLVtp3Y/NEtZ065p11T/tYVFynnmJRL+fmYYhsrKylRWVqbdu3e3Wre4uFjDhw83X0dERLQ5i0DjtqeZCwK5BEGj6OhoRUdHKyMjo9WYs2bN0s0339xi/5AhQ/Tyyy+7HTDgbttut3sckBBocSOGeexXexSp1xu8n6nBmpqiuGOz5Viz3l/NA7q9xWv3aualowIQN8fvMYHu7Lpxg/0ej6Q/4Fl2ZqLevPkMrwbbnJ6drtOz07WjsFyXP7GU5TMAAABA0h8AgMNVTW6Btt/9kOKOzVbi2FMUO3Sgx7oVm7bJvvwrOX7cyBPHXUxNTY0KCgpUUOD7QIx///vf+vLLL90OFHD3unF5gfYk/b3lKWZaWlqzmQO8UVFRIbvdrtNPP107d+5scfzUU09Vampqi4EDDofDp7Y3Shp7cofOP1Ti2FNI+gNNbM0r04qNeR6fgPTF8o152pbPVMlAo0Hp8X7tY5I0NjtdA9Pi6WuAGycPStW8W8e3ezmNAak2fXb3ubrk8SX6emthgFoHAACA7oCkPwAAhzNXgxxr1suxZr2sfXorbsQwhdliFRoZqQanU/XlFXKs26Dagv3BbikCaM+ePdqzx/sn7yIjI5WUlKSIiAiPdT755BP16tWr2WCBhISENmPb7Xa3+30ZRBAbG6vY2FiPSyXcdNNNmjRpUov99fX1zWYMOHQJgvXr12v+/PluY1rTeitmiOcBNL6IHTpQ1j696YdAEy8u3eLXhOSLS7f4LRbQE0wY2TdAcbNI+gOHyM5M9Cnh3yg+2qp5t47XmTMX8cQ/AADAYYykPwAAkCTVFuxX8cfLgt0MdANOp1N5eXmt1pk8eXKLfaGhoUpISGh1RoHVq1e7jefrzAFS+wcShIWFKSUlRSkp7qfof++999wm/ZOTk3XfB/P17Hr376Ej4kYMo38CTSxau1c7Csv9st74jsJyLVrjfvkT4HCVYvN+KZr2xY0KSFyguwqzhOjNm8/wOeHfKD7aqrm3jNNxMxao3mX4qXUAAADoTkj6AwAAoFM0NDSYT8y316uvvqrFixe7HTDQ2nIEoaGhqq2tdRszMTHRp/fR2iCCyobALH8x6rRTlZzUp9mMAyUlJSotLZXL5QrINYGurN5l6Ionl+nTv0zoUKKktLJGlz+xVK4GEiRAU3GR4QGJa4sKTFyguzp3ZF+/DGCTDk71P2FkXy1c7f0MXgAAAOg5SPoDAACgy6upqdG+ffu0b9++dp1nsVg8HnvllVf0xRdfeBw8EBbm/p/KngYtJCUlqbLO/QCDjhp96im678573R4rKytrMRhg69at+utf/+q2flpamkpLS1VdXR2QtgKdZeM+uy55fInPUyKXVtbo0ieWMhUy4IbDWReQuOXVgYkLdFfXjRvs93gk/YH2GZQerwkj+yrFFqm4yHA5nHUqKndq8dq92prHkjQAgO6DpD8AAAB6rNaegp81a1ar58bGxrqdQWDDhg1u60dHR6tjE7O20har58jx8fGKj4/XEUccYe5bvXq1x6T/zp07FRkZqZqaGnOwQNMBA5727dixw+MsB0CwfL21UGfOXKS5t4xr15OSOwrLdTkJf8CjonJngOIy4AxoNCg9Xqdnp/s15tjsdA1Mi9e2fBKVQGvCLCE6d2RfXTdusMd+OPPSUVqxMU8vLt2iRWv3snQG0AEMrgE6B0l/AAAAwI2KigpVVFRo717v1vpevny5/vv3EKVOmuj3tiRFRrervqfkfGRkpCIjD67THBERobS0NKWlpXkV87e//a1eeumlFvvHjx+va665ptkAAU/bNTU17XofgDc25ZbquBkLNOHnP9yObSWBsvznP9wu5g+3QKsWr92rmZeOCkDcHL/HBLqrCSP7BihuFkl/oBXZmYl68+YzvBowenp2uk7PTmfAKOADBtcAnY+kPwAAAOAnjnUbApL0X/vu+3r0k+VulyJITExUTExMs/qtLUHgK08xjznmGF1++eVexaiqqjIHARQWFurMM890W++EE06Qy+UyBwuUl5fLMPiff3hW7zK0cPUeLVy9RwPT4jVhZJZSbFGyRYWrvLpOReXVWrw2hyQI4KWteWVasTHPr08hL9+YRx8EmkixRQYoblRA4gI9wcmDUn1aGmpAqk2f3X2uLnl8ib7eWhig1gE9B4NrgOAg6Q8AAAD4SW3+flVu3qaYIQP9FrNi0zY989hzrdaJiIhQYmKiORigvLzcbb3w8HB9//335mCBxMREhYaGetUOT7MHJCYmenW+dHAJhOjoaGVkZKh3794e682ZM0dHH320+drlcqm0tNTtMgRNX69Zs8bj8gs4fGzLLyOxCPjBi0u3+DXp/+LSLX6LBfQEcZHhAYlriwpMXKC7y85M9Cnh3yg+2qp5t47XmTMXkZQEWsHgGiB4SPoDAAAAflSy/Gu/Jv3ty79qs05NTY0KCgpUUFDQar09e/Zo9OjR5uuQkBDFx8e3mD3A3YwC+/btcxvT19kDPM0cILUcSGCxWJScnKzk5ORWY957771uk/4nnXSSnnvuOY+DBdztczgcPr0vBJ81rbfiRgxTWFysQiMj1eB0qt5RIce6DarN3x/s5gHdxqK1e7WjsNyrJ7TasqOwXIvWeLdcDnC4cDjrAhK3vDowcYHuLMwSojdvPsPnhH+j+Gir5t4yTsfNWMA05IAbDK4BgoukPwAAAOBHjnUbVFtYJGtqSodj1RYWybFuox9a5Z5hGCotLVVpaanPMR555BHNmzevxZID7raTkpKUkJAgyXPSPyQkpF2zBzTlaTaC9PR0DR8+vF2x6uvrZbfbNXToUB04cKDF8XPOOUfJycktBgzY7XbV19f71H50gCVUcSOGKWnsyR4H3aROmqjKzdtUsvxrOdZtkFwNndxIoHupdxm64sll+vQvEzqUJCmtrNHlTyyVq4HkCNBUUbkzQHGrAxIX6M7OHdnXL4PYpINPI08Y2VcLV+/xSzygp2BwDRB8JP0BAAAAf3I1KOeZl9V/xnRZon1fU9VVVa2cZ16SGrp2YnLv3r3au9f7pzdDQ0OVkJCgiIgIt8etVqvmzJnTYuBAcnKyrNbW/3jgaSCBL7MRhIWFKSUlxeNSCbfddpvGjRvn9pjD4XA7e4Ddbtd3332n9957r93tgWcRGWnKmjbVq4E2MUMGKmbIQNUWFinnmZdUk9v67BjA4W7jPrsueXyJz09slVbW6FLWZgXcWrx2r2ZeOioAcXP8HhPo7q4bN9jv8Uj6A80xuAYIPpL+AAAAgJ/V5OYr56nZypp+rU+Jf1dVtXKemt0jE5INDQ2tTu1fU1Ojq6++2u2x6OjoVmcS+PHHH92e5+sSBBUVFaqtrW13zLi4OMXFxalfv34tjr300ktuk/5HH320Nm7c6HGwgKdlCRpfN3TxwSGBEj3wSJ/6mTU1Rf1n3KScp2aratvOALUO6Bm+3lqoM2cu0txbxrXrD7k7Cst1OQl/wKOteWVasTFPp2en+y3m8o152pZf5rd4QE8wKD3er/1MksZmp2tgWjz9DWiCwTVA8JH0BwAAAAKgattO7X5olrKmXdOuqf55AtmzqqoqVVVVad++fe0679FHH9WLL77YbJkBd0sPHPq6oqLCY0xfBxK0NhtBeHi4UlNTlZqa2q6Yxx9/vFavXt1i/6RJk/SLX/yi1QEDVVVVPr2PriAiI83ngTWSZImOUtb0a7X7oVn0N6ANm3JLddyMBZowsq+uGzdYY1tJnizfmKcXl27R4rV7mZIVaMOLS7f4NRn54tItfosF9BQTRvYNUNwskv7AzxhcA3QNJP0BAACAAKnJLdD2ux9S3LHZShx7imKHul9rXJIqNm2TfflXcvy4kbXG/czlcqm4uFjFxcV+i/n4448rLS3N7YCBxMRExcXFuT3PU9I/MTHR57Z4innuued6nDWhUU1NTYtBAT/88IPuv/9+t/UHDBigkpISlZWVBXd2AUuosqZN7dASGtLPif9p12j73Q/R74A21LsMLVy9RwtX79HAtHhNGJmlFFuUbFHhKq+uU1F5tRavzeEPs0A7LFq7VzsKy/0yHfKOwnItWuP9kkvA4SLFFhmguB37dyjQkzC4BugaSPoDAAAAgeRqkGPNejnWrJe1T2/FjRimMFusQiMj1eB0qr68Qo51G1RbsD/YLUU7PPnkk60eDw8PV2JiYovBAJ6WILBarSoqKlJSUpIsFku72tLa7AFtiYiIUFpamtLS0sx9kZHu/zAaFRWl7du3Szq4TENZWVmrSw403d6wYYPsdnu73ldr4kYMa9cMGq2xpqYo7thsOdas90s84HCwLb+MP8ACflDvMnTFk8v06V8mKD7a6nOc0soaXf7EUrkamF0DOFRcZHhA4tqiAhMX6I4YXAN0DST9AQAAgE5SW7BfxR8vC3Yz0Anq6uq0f/9+7d/v3WCOhQsXqnfv3goJCVFcXJxXyw80vi4rc59483UJAk/J+aazEYSGhpqDGrxx0UUX6b333mux/9e//rWuuOKKNgcPlJSUqLy8XIZxMJmRNPZkH96ZZ4ljTyHpDwAIio377Lrk8SWad+t4nxL/pZU1uvSJpdqUW+r/xgE9gMNZF5C45dWBiQt0RwyuAboGkv4AAAAA0EUYhqHy8nKVl5dr9+7dHYp19913q1+/fm6XH2g6eCAhIUGhoaHmeR2ZOcATTzGHDx+uCy+80KsYLpdLpaWl+nHfHk3/4Quf2+JO7NCBsvbpzYwbAICg+Hproc6cuUhzbxnXrqn+dxSW63IS/kCrisqdAYpbHZC4QHfE4BqgayDpDwAAAAA90IoVK7yqFxISovj4eHNAgKeZAxoaGvTFF1+Y9ZKTkz0uBXAofwwksFgsSk5O1s7cnV6f0x5HnTVOm16dG5DYAAC0ZVNuqY6bsUATRvbVdeMGa2x2use6yzfm6cWlW7R47V7Vu5jSH2jN4rV7NfPSUQGIm+P3mEB3xeAaoGsg6Q8AAAAAhzHDMFRaWqrS0tJW623atEljxoxpti8yMrLVmQQatwsKCtzG9HZ5gKZKqgPzh5++gwdpk5v95513nv7xj380W26grW273a66Op5KAQC0T73L0MLVe7Rw9R4NTIvXhJFZSrFFyRYVrvLqOhWVV2vx2hxty3c/QA9AS1vzyrRiY55Ob2UgTXst35hHPwSaYHAN0DWQ9AcAAAAA+MTpdCovL095eXk+nX/77bfr8ccfd7vswKGvG0tlXa2f38VBlfXu46anp2vQoEHtjudwOJScnOw2+X/ZZZcpLi7OHCzQdMBARUVFu68FAOh5tuWXkVQE/OTFpVv8mvR/cekWv8UCegIG1wBdA0l/AAAAAEBQ+DJgIGPyxYo/4xS/t6WuotLtfl9mI5Ck0NBQj0/733HHHRo5cqT7dtTVuZ1FoKSkRMuWLdOHH37o9lohISFyuVw+tRUAAKAnW7R2r3YUlmtAqq3DsXYUlmvRmr1+aBXQszC4Bgg+kv4AAAAAgG7DWWJXfADiFufsc7vf16R/SUmJx2NJSUkej4WHhys1NVWpqaktjtXX17tN+o8aNUrfffedysrK3A4WaG05gvz8fAYLAACAHq3eZeiKJ5fp079MUHy01ec4pZU1uvyJpXI1GH5sHdAzMLgGCD6S/gAAAACAbsOxboNSJ030e9w9y750u3/GjBn629/+5tXyA0335ebmerxWa0n/1ngaSNAYLz4+XvHx8TriiCO8jjlgwADt3Lmzxf5rr71WQ4cObXXgQGlpqRoaGnx6L+jerGm9FTdimMLiYhUaGakGp1P1jgo51m1Qbf7+YDcPAIAWNu6z65LHl2jereN9SvyXVtbo0ieWalNuqf8bB/QADK4Bgo+kPwAAAACg26jN36/KzdsUM2Sg32JWbNqm2gLPicqKigpVVFQoJyfHL9f7y1/+0uoAgsTERFkslhbn2e12t/F8HUQgeR5IcP7552vixLYHV5SWljYbDLBixQr9/e9/b1HPYrFoyJAhZl2n0+lzmxEkllDFjRimpLEne+x/qZMmqnLzNpUs/1qOdRskF4NCAABdx9dbC3XmzEWae8u4dj2NvKOwXJeT8AfaxOAaILhI+gMAAAAAupWS5V/7NelvX/6V32J5Y9asWa0eDwkJUVxcXIsBAWvWrHFb3zAM5eTkKCkpSTExMV63o6GhQWVlZW6PebusQUJCghISEnTkkUdKkoqLi93WS01N1fr1683X1dXVrS5D0PT16tWrPQ54QOeIyEhT1rSpsqamtFk3ZshAxQwZqNrCIuU885Jqcgs6oYUAAHhnU26pjpuxQBNG9tV14wZrbCtrkC/fmKcXl27R4rV7Ve/iqWPAGwyuAYKHpD8AAAAAoFtxrNug2sIirxKQbaktLJJj3UY/tMp/DMNQeXm5ysvLtXv37jbrz507V3PnzpUkWa3WVpciaLodHh4uw3D/B2xfZw/wdjaCqKgoRUVFKT3d8x/aG51++un6/PPPW+z/3e9+p//7v//zuPzAodu1tbU+vafDXfTAI5U1/VpZoqPadZ41NUX9Z9yknKdmq2pbyyUkAAAIlnqXoYWr92jh6j0amBavCSOzlGKLki0qXOXVdSoqr9bitTnalu9+cCSA1jG4BggOkv4AAAAAgO7F1aCcZ15W/xnT252IbBamqlo5z7wk9aB16Wtra1VYWKjCwsIOxbnhhhuUlpbW5jIEycnJioyMNM/ztFyAtzMHuOMp5vDhw3X22Wd7HaeyslJ2u10//PCDLrzwQrd1LrzwQjkcjmYDBsrLy31pdo8QkZHmU8K/kSU6SlnTr9Xuh2bxxD8AoEvall9Gch8IAAbXAJ2PpD8AAAAAoNupyc1XzlOzfU5IuqqqlfPUbBKRHnz55Zde142MjDQHAZSWlrqtU11drU8//bTZgAFvBwJ4Svq3dzaCmJgYxcTEaO/evW6Ph4SE6N1335XFYmm2v76+Xna7vdXlCD799FNt2bKlXe3p8iyhypo2tUMDa6SfE//TrtH2ux+SXD1ngA0AAAC8w+AaoHOQ9AcAAAAAdEtV23Zq90OzlDXtmnZN9c9a4/7ldDqVl5envLw8j3VWr16ts846q9m+0NBQJSQkeFx+oPF1cXGx25i+LkHgaRCBzWZrkfCXpLCwMKWkpCglxfPv2G9+8xu3Sf+rrrpK999/v8clBzwtR1BRUeHTe/OnuBHD/LKEhnRwqv+4Y7PlWLPeL/EAAAAAAM2R9AcAAAAAdFs1uQXafvdDijs2W4ljT1Hs0IEe61Zs2ib78q/k+HEjTxx3AQ0NDWaye8eOHe0+f8qUKerdu3eLwQLuBg40bsfHx/tt5oCmPMVMS0tTv3791K9fv3bFKy0t9TgTwvXXXy+r1ep24IDdbpfL5Wp3+91JGnuyX+I0Shx7Ckl/AAAAAAgQkv4AAAAAgO7N1SDHmvVyrFkva5/eihsxTGG2WIVGRqrB6VR9eYUc6zaotmB/sFsKPyosLFRhYWG7zrFYLLJarW6PVVdX64knnvA4eCA8PNxjXLvd7na/rwMJHA6Hx2N33nlnq4MIysvL3c4i8MEHH+ijjz5qUT88PFzh4eGqqqoy91nTeitmiOcBNL6IHTpQ1j696YcAAAAAEAAk/QEAAAAAPUZtwX4Vf7ws2M1AF+VyuVRdXe32WEFBgW699VaP58bExHicQcDTTAWxsbE+tdPTzAGSPM4A0Mhms8lms6l///7N9u/Zs8dt0n/cuHH66KOPVFtbaw4QeHP7Rr13INentrcmbsQw+icAAAAABABJfwAAAAAAgDZUVlaqsrJSOTk5Xp8zbdo03XLLLUpISPA4YMDd9s6dO93GCwsLk81m86n9bS1rYLVa1adPH/Xp00c2xwEpAEn/fkMGKW3ffnNwgdPp9Ps1AAAAAOBwRNIfAAAAAAAgQOrq6lRUVKSioqIOxwoJCdH111/vdvmBpq9jYmJanNueJQgq62o73FZ3zrvoIt33z2fN19XV1c2WIFi4cKEee+yxFudFRkZq2LBhZr2ysjIZhhGQNgIAAABAd0TSHwAAAAAAoBuoq6vTCy+80GY9q9XaYlDADz/84Lau0+nU9u3blZiYqMTERIWGhiom3OrvpkuSYq3N40ZFRSkqKkrp6emSpI0bN7o976ijjtKqVavM1w0NDSotLTUHATQdOHDo9ueff66ysrKAvB8AAAAA6CpI+gMAAAAAAPQgtbW1KiwsVGFhYZt1Z8+erdmzZ0s6OJNAfHy8UiaMV/i4k/3erqTI6FaPt7UEQaPQ0FBzMENbhg8frvXr17fYf+edd+qss85yO1jA3b7y8vI2rwUAAAAAwULSHwAAAAAAADIMQ6Wlpapa/oWOCkDSv3rDFn1aUNJsFoL4+HiFhoZK8pz0T0xM9PmanmIec8wxGjNmjNdx6uvrVVpaqqVLl+qyyy5rcTwkJERXXnlliwEDdrtddXV1PrcfAAAAALxB0h8AAAAAAACm2vz9qty8TTFDBvotZsWmbZr+2K0t9oeGhio+Pl5JSUkqLS11e25xcbE++OCDZssVJCUlKSIios3r2u12t/u9mSWgqbCwMPXq1UsxMTFuj9tsNr322mtuj1VUVLS6FMGCBQv0008/tas96Pmsab0VN2KYwuJiFRoZqQanU/WOCjnWbVBt/v5gNw8AAABdDEl/AAAAAAAANFOy/Gu/Jv3ty79yu7+hoUF2u91jcl6SvvrqK331Vcvzo6Kimg0CaDqDQOMsAlVVVW5jtjfp38iX2QhiY2MVGxurvn37uj2+fv16t0n/2267TXfccYfHJQg8vbbb7XK5XD69PwSZJVRxI4YpaezJHvtf6qSJqty8TSXLv5Zj3QbJ1dDJjQQAAEBXRNIfAAAAAAAAzTjWbVBtYZGsqSkdjlVbWCTHuo1+aFVz1dXVys3NVW5ubrvPPfvss5WcnOx2wICn7aSkJI9Jf18HEUieZyPo3bu3Wdo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" ] }, "metadata": { "image/png": { "height": 461, "width": 1022 } }, "output_type": "display_data" } ], "source": [ "#| echo: false\n", "#| fig-cap: The variance a minimum-variance portfolio predicts for itself (circles) and the variance it really has (squares), as multiples of the true minimum, for 100 assets and a growing ratio q = N/T. The curves are the theory for the raw sample covariance, 1 − q and 1/(1 − q); teal is the raw matrix, amber the cleaned one. Built on noise, the portfolio promises less than the minimum and delivers more.\n", "Nq, qs = 100, np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])\n", "sec = np.arange(Nq) % K\n", "Ct = beta**2 + gamma**2 * (sec[:, None] == sec[None, :]); np.fill_diagonal(Ct, 1.0)\n", "Lq, oq = np.linalg.cholesky(Ct), np.ones(Nq)\n", "bq = 1 / (oq @ np.linalg.solve(Ct, oq))\n", "res = {\"raw\": [], \"cleaned\": []}\n", "for qq in qs:\n", " Tq = int(round(Nq / qq)); acc = {\"raw\": [], \"cleaned\": []}\n", " for _ in range(60):\n", " Z = rng.standard_normal((Tq, Nq)) @ Lq.T\n", " S = Z.T @ Z / Tq; d = np.sqrt(np.diag(S)); Cz = S / np.outer(d, d)\n", " e = (1 - np.linalg.eigvalsh(Cz)[-1] / Nq) * (1 + np.sqrt(qq)) ** 2\n", " for name, M in ((\"raw\", S), (\"cleaned\", clip(Cz, e) * np.outer(d, d))):\n", " w = np.linalg.solve(M, oq); w = w / w.sum()\n", " acc[name].append((w @ M @ w / bq, w @ Ct @ w / bq))\n", " for name in acc:\n", " res[name].append(np.mean(acc[name], axis=0))\n", "fig, a = plt.subplots(figsize=(10.4, 4.8))\n", "xx = np.linspace(0.05, 0.85, 200)\n", "a.plot(xx, 1 - xx, color=\"white\", lw=1.4, ls=\"--\", label=\"theory, predicted: 1 − q\")\n", "a.plot(xx, 1 / (1 - xx), color=\"white\", lw=1.4, label=\"theory, real: 1/(1 − q)\")\n", "for name, col in ((\"raw\", TEAL), (\"cleaned\", ORANGE)):\n", " v = np.array(res[name])\n", " a.plot(qs, v[:, 0], \"o\", color=col, ms=7, label=f\"{name}, predicted\")\n", " a.plot(qs, v[:, 1], \"s\", color=col, ms=7, label=f\"{name}, real\")\n", "a.axhline(1.0, color=GREY, lw=1, ls=\":\")\n", "a.set_xlabel(\"q = N/T (assets per day of data)\"); a.set_ylabel(\"variance ÷ the true minimum\")\n", "a.set_ylim(0, 5.2); a.legend(frameon=False, fontsize=10, ncol=2, loc=\"upper left\"); tidy(a)\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "767dc23e", "metadata": {}, "source": [ "## What the Noise Costs\n", "\n", "With 200 assets and 500 days, all but four of the 200 eigenvalues of the planted market's sample matrix sit in the band that pure noise would fill. A portfolio built on the raw matrix promises a variance 40% below the true minimum and delivers one 66% above it: 0.604 and 1.656 times the minimum, against 0.600 and 1.667 from the theory, written down before a single number is drawn. Clipping the band costs a few lines of code and brings the real variance down to 18% above the minimum. It does not create information, though: it only stops the optimiser from trading on noise.\n", "\n", "## Sources\n", "\n", "1. V. A. Marčenko and L. A. Pastur, \"Distribution of eigenvalues for some sets of random matrices\", *Mathematics of the USSR-Sbornik* 1 (1967) 457–483.\n", "2. L. Laloux, P. Cizeau, J.-P. Bouchaud and M. Potters, \"Noise dressing of financial correlation matrices\", *Physical Review Letters* 83 (1999) 1467–1470.\n", "3. V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. N. Amaral and H. E. Stanley, \"Universal and nonuniversal properties of cross correlations in financial time series\", *Physical Review Letters* 83 (1999) 1471–1474.\n", "4. S. Pafka and I. Kondor, \"Noisy covariance matrices and portfolio optimization II\", *Physica A* 319 (2003) 487–494.\n", "5. J. Bun, J.-P. Bouchaud and M. Potters, \"Cleaning large correlation matrices: tools from random matrix theory\", *Physics Reports* 666 (2017) 1–109." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }