{ "cells": [ { "cell_type": "markdown", "id": "272b1163", "metadata": {}, "source": [ "# 63% of Stocks Lost to the Average Stock\n", "\n", "Put a dollar into each of 459 S&P 500 stocks in February 2013 and hold every one of them for five years. The average stock, which is what all 459 dollars together returned, turned \\$1 into \\$2.00. The median stock turned it into \\$1.73, and 288 of the 459, 62.7%, finished below the average.\n", "\n", "Nothing was wrong with those 288 stocks in particular. Compounding puts most stocks below their own average, by an amount a one-line formula predicts: 60.6% here, against the 62.7% that happened. This notebook measures the gap, shows why it widens the longer a stock is held, splits it stock by stock into volatility drag, and finds where the five years' gains went." ] }, { "cell_type": "markdown", "id": "1c65b67f", "metadata": {}, "source": [ "## Five Years of 459 Stocks\n", "\n", "The returns are daily closing prices of the S&P 500 members from 8 February 2013 to 7 February 2018, from a public-domain Kaggle dataset: 470 stocks have a price on every one of the 1,259 days. The prices are not adjusted for splits and spin-offs, so a stock is dropped if it has a one-day move by a factor of more than 1.75, or a move of more than 20% that reverses by more than 20% the next day, which is a bad print; that removes 11 and leaves 459. These are price returns, without dividends, and the 459 are survivors: every stock here was still trading in February 2018." ] }, { "cell_type": "code", "execution_count": 1, "id": "53bd463f", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:48.529002Z", "iopub.status.busy": "2026-10-06T03:00:48.528905Z", "iopub.status.idle": "2026-10-06T03:00:48.714931Z", "shell.execute_reply": "2026-10-06T03:00:48.714476Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "459 stocks, 1258 trading days, 11 Feb 2013 to 07 Feb 2018\n", "$1 in the average stock: $2.00\n", "$1 in the median stock: $1.73\n", "stocks below the average: 288 of 459 (62.7%)\n" ] } ], "source": [ "#| label: Five Years of 459 Stocks\n", "import numpy as np\n", "import pandas as pd\n", "\n", "rets = pd.read_csv(\"data/sp500_returns.csv\", index_col=\"date\", parse_dates=True)\n", "X = rets.sum() # each stock's five-year log return\n", "W = np.exp(X) # $1 in each stock, bought and held\n", "print(f\"{rets.shape[1]} stocks, {rets.shape[0]} trading days, \"\n", " f\"{rets.index[0]:%d %b %Y} to {rets.index[-1]:%d %b %Y}\")\n", "print(f\"$1 in the average stock: ${W.mean():.2f}\")\n", "print(f\"$1 in the median stock: ${W.median():.2f}\")\n", "print(f\"stocks below the average: {np.sum(W < W.mean())} of {W.size} \"\n", " f\"({np.mean(W < W.mean()):.1%})\")" ] }, { "cell_type": "markdown", "id": "f2f6ed07", "metadata": {}, "source": [ "## Why the Average Beats the Median\n", "\n", "Write a stock's final wealth as $W = e^{X}$, where $X$ is its log return over the five years. If $X$ is normal across the stocks, with mean $m$ and spread $s$, the average stock ends with $e^{m + s^2/2}$ and the median stock with $e^{m}$. A stock beats the average only if its log return clears $m + s^2/2$, which is half a standard deviation above the middle:\n", "\n", "$$\\Pr\\big(W < \\mathbb{E}[W]\\big) = \\Pr\\Big(X < m + \\tfrac{1}{2}s^2\\Big) = \\Phi\\big(\\tfrac{1}{2}s\\big) > \\tfrac{1}{2} \\quad \\text{for every } s > 0.$$\n", "\n", "Normality is not what makes it true. For any spread of $X$ that is symmetric about its median, Jensen's inequality puts the average of $e^{X}$ above $e$ raised to that median, which is the median stock's wealth, so at least half the stocks sit below the average whenever they differ at all. The normal case only says how far below." ] }, { "cell_type": "code", "execution_count": 2, "id": "3044023d", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:48.716183Z", "iopub.status.busy": "2026-10-06T03:00:48.716084Z", "iopub.status.idle": "2026-10-06T03:00:49.037000Z", "shell.execute_reply": "2026-10-06T03:00:49.036687Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "spread of the five-year log returns, s: 0.536\n", "predicted share below the average, Phi(s/2): 60.6%\n", "skew of the log returns: -0.12, excess kurtosis: 2.34\n", "skew of the wealth itself: 5.11\n" ] } ], "source": [ "#| label: The Lognormal Prediction\n", "from scipy.stats import norm, skew, kurtosis\n", "\n", "s = X.std(ddof=1)\n", "print(f\"spread of the five-year log returns, s: {s:.3f}\")\n", "print(f\"predicted share below the average, Phi(s/2): {norm.cdf(s / 2):.1%}\")\n", "print(f\"skew of the log returns: {skew(X):.2f}, \"\n", " f\"excess kurtosis: {kurtosis(X):.2f}\")\n", "print(f\"skew of the wealth itself: {skew(W):.2f}\")" ] }, { "cell_type": "markdown", "id": "d929c9e0", "metadata": {}, "source": [ "The spread of the five-year log returns is 0.536, so the formula predicts 60.6% below the average; 62.7% were. The log returns are close to symmetric, with a skew of −0.12, but fatter-tailed than a normal curve, with an excess kurtosis of 2.34. The wealth they compound into is not symmetric at all: its skew is 5.11, a long tail of stocks that multiplied several times over." ] }, { "cell_type": "code", "execution_count": 3, "id": "f599d921", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:49.038179Z", "iopub.status.busy": "2026-10-06T03:00:49.038032Z", "iopub.status.idle": "2026-10-06T03:00:49.400638Z", "shell.execute_reply": "2026-10-06T03:00:49.400259Z" } }, "outputs": [ { "data": { "image/png": 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kTp06vYrw9O6772rFihW6ceOGnj17pkePHun06dOaPn26ChcuHK86smbNqq+//lpnzpzRkydP5O/vryNHjmj06NFGf1Zcz/3x4e3tHa1/zc3NTVOmTNHp06f18OFDmUwmDR8+PMZ5xYoV07Rp03TixIlofQrr1q1T165dzfYpjB8/XiaTSb169TLee7kPw2Qyafz48cZxc/1LsYms32QymZ3JeN68ecZxKeJ7NGLECO3fv193795VWFiYVq9eLSliJuSX4ylZsqR+//13XblyRc+ePdODBw+0fft2vffee3Hc5Yj7+vXXX+vQoUPy9/dXaGio/P399e+//2rnzp0aO3asKlSoEGc9AJDSWJ4SAAAAwH9G5cqVtWbNGrm6ukZ7v2LFiqpYsaI6dOig+vXrx5ogIUnDhg3T1KlT5eDgEO39XLlyqVGjRmrUqJE+/PBDtWrVKtoyWwl1+fJlZcmSJcb7zs7OcnZ2VtWqVTVs2DC9//77WrZsWbQyL1680OLFizV8+HCVKVNGFSpU0PHjx2Nty87OzugoPXHihE6ePBmjTJ06dbRkyRIjkSSSvb29smXLpipVqmj48OHq0aOH1q5dG+f1zZgxQx988IHFMkm5B1Fly5ZNnp6eqlq1arT3ixUrpmLFiqlXr15q165dnDFLEZ16q1atilGXFJHkVbx4cfXr109ff/21xo0bF686zenfv79+/fVX2draRns/e/bsyp49u4oWLaomTZqobNmy0ZYNTKzu3btr1qxZypAhQ7T38+TJozx58qhFixYaOXKkWrZsqRs3bsRaT7169bRo0aIY3xNJKliwoAoWLKh3331XLi4umjBhQoJi7Nevn2bMmCEbGxudO3dO77zzjsVYkiLynt6/f1/u7u7y8/MzjoWHh+vRo0c6ePCgDh48qClTpihjxoxJai9qomlYWFii66lTp44kKSgoSF5eXrGWu3Hjhq5cuaJChQqpVq1aMWZSi6xHijsJZ8eOHapXr55xnoeHR6LjB54+fart27erefPmkqRevXrp0KFDsZZ/9913lSlTJknSgwcPtGfPnlcSJwAAAP5P3rx59d1330mSPv74Y/n6+iapPicnJ+XKlcsYOGVuxrCXZc2a1diPq/3Q0FA9fPhQuXLlUvHixeXi4iIfH58kxRybbNmy6e+//472jCVFJCdlzpxZpUuX1qBBg/TZZ5/p+++/j7WeihUrytPTM9pgPUdHR1WqVEmVKlVSjx491KRJk2SPv3Hjxlq2bJnZvplI6dKl0zfffKOPPvpINjbRUwsi+xRatmypoUOHqm3btil2r5MqX7582rRpk0qUKBGv8r1799aMGTOi9Q86ODiofv36ql+/vho2bKg+ffqYPbdFixZaunSpHB0do72fNWtWZc2aVYULF1bdunXVuHFj1a5dO/EXBQDJgKQxAAAAIJEyOtjGXeg/LDD4ebLWd/jwYZUuXVqtW7fW119/LSmig+bw4cPRyj19+tTs+S4uLtqwYYPs7Ow0ceJE7dixQwEBASpSpIg++eQTVahQQRUrVtR3332n/v37m63jiy++0MSJEyVJV69e1YwZM3T+/Hn5+PgoZ86cat68uQYMGKCiRYtq27ZtqlSpku7du5eo67W2ttbBgwfl6empkydPytfXV+Hh4cqXL5/c3d3Vt29fOTo6auHChbp27VqMP6rPnz/fGPnZs2dPi0ljrVq1UrZs2YzzXlavXj1t2rRJdnZ2CggI0KxZs/TPP//o+vXrypAhg95++20NHz5cuXLl0ooVK9SoUSNj9iFzhg8frgoVKujYsWP69ddfdebMGdna2qp69erGaN/kuAdSROflunXrjCSvkydP6scff9TZs2eVPn16NWrUSCNGjNCKFSt0//792D8QRSQGHjx4UG5ubnrx4oWWLl0qT09PeXt7KywsTOXKldPgwYNVrlw5jR07ViEhIcZ3NSFKlSql3377TTY2Nnrw4IFmz56t3bt3y8/PT9bW1sqTJ48qVaqkZs2aGaNhJWnNmjVGh3PkyO7GjRvrzp070ep/+PBhtNcdOnTQX3/9JSmi83zWrFlat26dHj58qCJFimjQoEFyd3dX2bJltXv3blWoUEGPHj2KEXfTpk21fv16o5N4zZo1WrFihS5fvqywsDDlzZtXtWrVineCXlRfffWVxo4dKyliOcdWrVqZjSG5FCxYUJK0b9++aAljsQkMDExSe5FJV5J09uzZRNWRPn16vfXWW5IiEi6fP7f8O/jcuXMqVKiQ7O3tVbhwYV26dMk4VqpUqWjl4qonUsmSJRMTOhDNjBkzoiWN/fLLL2a/h+nTp9dXX31lvJ49e3aSki4BAACQOHPmzFGmTJm0fft2zZ07N0l1LV68WLlz5zZmpXrx4oVOnDghDw8PzZkzR0FBQWbPi7oSjqUEJyminyDqwJ/SpUunSCKTnZ2dtm7daiynfvLkSU2fPl1nzpyJ1h/h5OSk7777Ti9evND06dNj1OPi4qItW7YYs1+vXbtW8+bN040bN5QrVy516tRJPXr00PLly5M1/rx58xp1RvajPX78WIUKFYr2nDx79mxjadCTJ09q9uzZunz5svz8/OTm5qb27durW7duqlatmjw9PVWjRg09e/ZMUsT//VeuXKlJkyapTZs2kiI+j5cltm8tIdasWaOiRYtq3rx5WrVqle7cuaOcOXOanVW/UaNGql69uq5evaqffvpJR48e1YsXL1SjRg198cUXypkzp95//31t375dixcvjnZujhw5tGjRIjk6OiooKEh//PGHtmzZort378pkMilXrlwqX758iiQBAkBikDQGAAAAJEJGB1v5zO6W2mGkKpf+HsmaOBYUFKSzZ89GW6rK29s73gkWxYoV0+3bt1WzZk1dvXrVeP/48ePasGGDjh8/rqJFi6pHjx4aM2ZMjMSaGjVqGMv+/fTTTxo1alSMP05v3rxZS5cu1bZt2+Tm5qZJkybFmoAWl0qVKunff/+N8f6RI0f0999/a9q0aTpw4ICxVGajRo2ilTtx4oROnTqlsmXLqkuXLvroo4/04sULs21FTucfGhqqRYsWRTuWMWNGLVmyRHZ2dtq3b59atmwZI1ln7969+vPPP7Vnzx4VLVpUs2bNUsmSJaMlNEVVoUIFrVq1Sp06dYp2Dw8cOJCs90CKmJ2qVq1akiKWoGjevHm0ZJq9e/dq5cqV2rt3r4oVK2Y23kjz58+Xm5ubfH191ahRI505cyba8X/++Ufz5s3T0qVL1a5dO40bN04LFy5M8GxYHTt2NBKvGjRoYHbmt7Vr12rcuHFGsp8kBQQEKCAgIFpn6qVLl3T9+vVY28qUKZN+//13SVJISIiaNm2qXbt2GcePHTumZcuWafbs2erXr58KFCigb7/9Nsb3OmvWrFq0aJFsbGwUGhqqzp07G0s4RDp69KjWrFmjMWPGKHfu3PG6FzY2NpozZ46xVMWKFSvUvXt3hYSExOv8xHr27JkcHBwsLrmaXNzc3Izre/LkSYz7Fl958+Y1/rASn+/czZs3jf38+fNHSxqLumxHXHW9XA9gTv78+XXt2jXjda9evbRgwQKzZTdu3Kg9e/bI3d1dDg4O2rBhg1q3bq3Tp08bZbJly6YlS5aoSJEikiJmGZs6dWqKXgMAAABi6tOnj5o0aaKnT58muv8jqjx58kR7bWNjo8qVK6ty5coaOnSo2rVrZ/YZOTAwUDdv3lTevHlVokQJ5cqVS3fv3jXbRvXq1aPNsp1SzzFjxowxEsY2bNigtm3bRuuX2bt3r5YvX649e/Yoa9asmjJlitasWRPt/82S9MMPPxgJYxMmTDD6piJt2rRJe/bs0Z9//pms8Ucmh9WqVSta38yxY8eM/U6dOhkJYx999JF++OGHaHUcP35c69ev17p167R8+XKVK1dOI0aM0DfffCNJ8vPzk5+fX7R+psQOpEqqcuXKqX379vF6Jq9Vq5Z27NihFi1aGAlwUkR/1Y4dO3T06FHZ29trxIgRMZLGWrRoYcyW3KVLF7Oz9W/cuFHffPNNtD4fAEgtMRcXBgAAAIA31LBhw6IljEUKCgrSzz//LCliucWaNWvGKPP555/L2tpap0+f1siRI2OdzeTAgQOaMWOGpIgl7uzt7RMVq7lkqahu3Lihb7/9VpJUv359Zc6cOUaZyFnDcuTIoWbNmpmtJ2fOnMboRU9PzxizbQ0YMMBYFqJz586xzu509+5djRo1SlLEMo0vL70QVWBgoPr27RvnjDDJcQ8GDx4sKSIhrnfv3mZnXzp16pQmTZpksa3KlSuradOmkiJmSns5YSzSixcv1L9/f4WEhMjOzk7vv/++xXrNiUyoevjwodnO8Kj8/f0TXH9UvXv3Npbx+P7776MljEU1dOhQo+O6R48eyp49e7TjQ4YMMTozJ02aZLGTNTw8PMbsZ+Y4OTlpw4YNRkLV9OnT1alTpxRPGJNk3IeaNWtq2LBhSpcuXYq0Y21trfnz5xuj3KdOnRrnjHexiTpSPuoo+9hEnR3t5eU1E1KXpXrwZvvf//6n48ePR9sGDhxoHK9cuXKM48ePHze7PG1CdenSxfg98dZbb+nEiRPasWOH5syZozVr1ujGjRtq3LixJOn58+fq2LGjxaWlAQAAkPxcXV2NJKFx48aZ7W+Jj/DwcG3evFn9+/dXmTJl5OTkJFtbW+XNm1fdu3fXqVOnJEUkMW3dutWYGfplkc+h1tbWsQ4osLGx0eTJk6O9lxLPMTY2NhoyZIikiAFevXr1MjuQ78yZM/rss88kRfRHDR06NNrxnDlzqn379kbZCRMmmG1v3rx52rhxY3JegiTp008/tdg3EzkjuKenZ4yEsahWrVplfD79+vVL3iCTyeLFi+M9iCs4OFjdunWLljAW6ezZs1q/fr2kiGVFX/5+RR1Et3PnTovtJLXPBwCSAzONAWmQa7+Ez4pye45HCkQCAACQfAICArRmzZpYj0dd2rBQoULRjjk6Ohp/nF6+fLnCw8MttrVz506NGjVKDg4Oqly5svbv35/4wP+/7NmzK3PmzLK3tzcSWCKXZbCyslKFChViJPwsWrRIU6dOla2trXr27Kl169bFqLdLly6ytY1YStXc0pSRSwnu3btXt2/fthhj1M6uWrVqxZqAtG7dukQtLZjQe5ArVy6VLVtWkrRt2zaL8c+bN09TpkwxZmp6WeR9CA4O1t9//20xTn9/f50+fVqVK1c2ZjlLiFu3bkmKmL2rffv2WrlyZYLriK/I77UkzZo1K9ZyISEhmjdvniZMmCB7e3vVqVNHq1atMo5HLiMRHBysn376Kclx5c6dWxs3blSFChUUHh6ujz/+WNOmTUtyvfE1btw4NWzYUBkzZtRPP/2k4cOHa/v27ZIivlcZMmSIdVmUhJg+fboaNGggKeJnLHK0dWKkT5/e2I+6zGtsoibfRT03oXVZqgdvtpIlS6pAgQKxHndyclL58uVjvG9nZ5fktm/fvq369etryZIlqlChgqysrFSvXr1oS7lKEcvU9O7dWzt27EhymwAAAK9a+sJvpUi9rv26vZK/2cyZM0eZM2fWP//8Y3ZZxfhauHChFi5cGOP9W7duycPDQ8uWLZOHh4c6duyoHDly6Oeff1aLFi1ilJ8yZYq6du0qZ2dn9ezZU5kyZdLkyZN16tQpWVtbq3r16powYYLefvtthYSEGIP8os46llwqVKhgzFy9cuVKPXjwINayCxYs0Pfffx+t7ylSvXr1jD6bv/76K9YZ3SXpzz//jHXAYGKEhobGmCUrqmLFiqlUqVKSZLFcpJ07d6pdu3YqUKCAXF1d4+xjetVimwnZnG3btllc0vTQoUNq3769rKys9NZbbxmJj9L/9flIEQl0lpLtAOB1wExjAMwqmCu3Zg0YamzLly9X0aJFUzssAACAWF26dMlislfUDrzIaeIjVaxY0eikmzhxokwmk8Vtw4YNxrlJmXGlRYsWWrt2rfz9/eXn56fLly/r7NmzOnPmjM6cOaM5c+YYZV+e+UmK+GP6pk2bJEnNmzc3O6195NKUfn5+0eKWIhKxKlWqJClimcS4rjvqjESWrvvEiROv5B5EJoxJEUtHWnL//v0YS0BEVbVqVUmSg4ODnj9/Hue9iFxGNTGfv4eHh5GQtGLFCu3du1ejR49WrVq1kr0zO/Ie3bx5M1rHpTlRlw8tV66csW9tbW28Pn78uB4/fpykmIoXL66DBw+qQoUKCgkJ0XvvvfdKE8akiBHc7u7uOnLkiCSpYMGCxmjoDz74QI8fP5aXl5dGjBiR6FHp48aNM0aeX758WR06dIgzIdWSqCOc45O0E3UWxJdHRyekLkv1AElx8eJFVatWTT169JCnp6du3LihkJAQ3b17VwcPHtTHH3+skiVLpsiMCgAAALCsd+/eeueddxQaGqo+ffok6VkmLs+fP1evXr2MJJ3mzZsrb968Mcr5+PioVatW8vPzkyS1bdtW//zzj4KDg/X06VNt375db7/9tg4cOKA//vjDOC/q7MnJJWp/RNRnaXOePXtm9JOULFlSNjb/N6dLQvo14jqeUP/++6/FZ7zIfhIpIvEvrn6SX3/91SifHLMTJ7eE9FWdP3/e4nFLfYxr1641lk79/vvvdfz4cY0bN0716tUzO4M+AKQ2ksYAmJXF0UktKlU1tg4dOrC2NgAAeK09ffrU4vGoHZzW1tbRjkWODk2MxCT52NjYaOnSpVq/fr1atWplLB+YmHYiR0ra29vrvffei3asbNmyxiwxixcvjrFUQtasWY1kuYSydN3xmV4/Oe5B1P+f3rt3L87zIzvtzEnsdyAxn7+3t7datmypmzdvSpLefvttTZ06Vfv27dOjR4904MABjRo1Klk6E52dnSVJvr6+cZaNOoo28jwp4j5H/swkx0jhzp07G7MbjR8/XsuXL09ynYlx4sQJValSRTVq1NDkyZOjzWRkbW2tatWqadq0abp48aJq166doLrHjBljLCty7do11a9f3+L3Lz6i/qHDyckpzvJRy7z8R5KE1GWpHrzZ3nrrLaVLly7B2/Xr12PUdf369Whl4juK//nz51q4cKGaNWum/Pnzy8HBQblz51bNmjX1/fffW5yxAQAAACkjT548xsCeqVOn6syZMyne5rNnz7Rs2TLjdZ06dcyWO3DggMqWLavp06fHGBh17do1ffrpp6pTp060fp+UWAIw6jNzQp63raysovV/JKRfI6nPlC+L67686r6ylJaQ70FS+hgfP36sJk2a6Ny5c5Kk8uXLa8KECdqxY4f8/f11/PhxjR8/PtoylgCQmlieEgAAAECaF3WU56RJk7R06dJ4nxvX7E3mjBkzRp06dZIUMePRTz/9JC8vL928eVNPnz41krvq1atnJLJELtf4snXr1unBgwfG8gy//fabcSxyljHJ/DT8Ua978+bNGjVqVLyv4eHDh7EeCwsLi/P85LwHySHyXvj7+8vd3T3e58VnmUBzduzYocKFC6tVq1Z655139Pbbb6to0aKytbVVjRo1VKNGDX366afq0qWLtmzZkqg2Xleenp6qWbOmMmfOrPHjx+vEiRPavHlzqsXj5eUlLy8vSZLJZNKMGTO0b98+de/eXe+8845cXFz0v//9T6VKlTIS/Sz56KOPNGXKFEnSjRs3VK9evXidF5dbt24pPDxcVlZWypcvX5zlo5a5ceNGtGM3btxQjRo1jHKWEnMs1QMAAADgv2fYsGHKkiWLnj59qsuXLxvP7rFxdHQ0yjx9+jTGLOfxdfHiRWPf0kxVvr6+GjFihEaMGKHs2bMra9asevjwoe7fv2+UibpyzqtIensTxdV3E7XPaNCgQdqzZ0+86/b29k50XCklJWfLe9nJkydVpkwZNWnSRC1bttTbb7+tkiVLytraWuXLl1f58uU1evRoDRw40OzSrQDwKpE0BgAAACRCYPBzufT3SO0wUlVg8PPUDiHZRC5tIEV0mp09ezZF2/vggw8kSVevXlW1atWMpQpfFp+ZXp8/f66lS5dq8ODBqlKlikqUKKHz58/L2tpaXbp0kSSdOnVKx48fj3HugwcPjCQUBweHFL/uqJLjHkQdJRqfEbC5cuWK9Zifn5+KFy+ujBkz6uLFizFmZUsJoaGhWrlypVauXCkpYvnN+vXrq0ePHmrevLmcnZ21atUqFS5cONEjih88eCA3N7d4jWCNWiZqEpG/v7/CwsJkbW2tPHnyJCqOqA4dOqTx48dr06ZNypYtm9auXauOHTtq3bp1Sa47Ody7d09LlizRkiVL9Pnnn2vSpEnKmDGjBg4cqM8//9ziuaNGjdJ3330nKWJJ0Hr16llcFjUhgoKCdO3aNRUsWFCFCxeWjY2Nxe9pyZIlJUkhISG6fPlytGNRf9ZLlixp9vfDy/W8fB4AAACA/6bIJeodHR3jNYNsjhw5jMF3165dS3TSWNQZm+L7TH7//v1oyWJSRLJT5KzrT5480enTpxMVjyVRn5kT8rwdHh4ebRDey/0alpZFtNSnkRKi9pU9e/bslT0PRk1ms7KyvGiao6NjSoeTaOHh4fL09JSnp6ekiGUs69Spo86dO6tTp07KkCGD5s2bp1OnTunkyZOpHC2AtIzlKQEAAIBECgx+nqa3lGIymVKs7tgcP37c6JRKyCxTiZEtWza5urpKktasWRNrspQkVa1aNV51zp8/39iPnF2sSZMmRqdk1ONRvXjxQqdOnZIkVa5cWQ4ODvFqL6mS6x5Exi5JVapUsdims7OzsSSiOUePHpUk2draqmbNmhbrSin379/X8uXL1aJFC2PGOCcnJ7Vu3TpauYT8jETeo7x588rNzc1i2ajXHbXDMiwsTCdOnJAkVaxYUZkyZYp3+7E5fPiw6tevLz8/P9nb22vlypVq3759kutNblOnTlVwcLAkqVy5chbLjhw5Ut9//72kiFnB6tWrp6tXryZrPLt375YUsdRH9erVYy2XL18+FSpUSJK0f//+GCPII+uRImbzsyTq8YSMLAcAAACAhIj6zJWYWd0jNWnSxBiAtmLFinjNhp5QUfsj4upDcHBwMJLYzp07Fy0hLiH9GnEdT26R/SRS0vvKEtKPERgYaOzHNZgy6iCn193jx4+1fv16de3aVZ988omkiETJuGbyA4CURtIYAAAAgNfKs2fPjP3I0a0p7eHDh9q1a5ckqU6dOqpcuXKKtRV1en9LIyIzZswYbXlJS44cOWKM+OzWrZusrKyMc58/fy4Pj9hnxVu1apURy+DBg+PVXlIl1z24e/eu0cHasGFDi7Ng9erVy+II1cj7IEUsL5jaoi7XmCNHjmjHEvIzsmnTJmM/cnY3c+zs7NS7d29JUnBwsPHzEGn16tWSIjq7hw0bZjn4eDp58qTq1q0rHx8f2draasmSJeratWuy1J1cwsPDjQ59S39oGDFihH744QdJ0u3bt1WvXj1duXIl2eOJnJVOkvr37x9rub59+5o9J9LevXvl6+srSerQoUOsiYCFCxdW3bp1JUn//PMPy1MCAAAAacCIESOULl26OLdI165dM9576623EtVmjhw5jOSZsLAw7dy5M1H1WFtba9KkSZIinud++eWXRNUTl2PHjhkzgrdv317Ozs6xlu3Ro4ecnJwkRX9Gl6SdO3fq+fOIgZndu3ePdl9fFvnM/qqcPHnSmLW6U6dOcQ5EsyRqP4adnZ3Fst7e3sZSkpYS5VxcXNSwYcNEx5SaLPX5AMCrRtIYAAAAgNfKnTt3jP1ixYq9sna//PJLY6nGFStWxNm2m5ub3n///QS34+fnZyxj0LJlS2XPnj1GGXt7ey1atChBSw9ELhnh6uqqDh06qFWrVpIiOiSjLinwsp9//tk4/vXXXxvnxcbR0dHoQE6s5LwHkTNy2dvba+7cudES0iKVLl1aY8eOtVjPvn37tHXrViOmr7/+2mL5dOnSqV27dipRooTFcua0bdvWYoeyJL3zzjvG/svJRwn5GZk/f76x9MWoUaNUp04ds+V++ukno3P/r7/+irbUhhRxnyPfGzt2rNq0aRNrm+nSpYv3Mpbnzp2Tu7u7bt68KRsbGy1YsEB9+vSJtfz48eNlMplkMpk0fvz4eLVhzpgxY5Q+ffo4y/Xu3dvo3I9tuYjhw4dr2rRpkv4vYezl5SDjo06dOsa1xfYHEk9PT2Mpya5du6px48YxypQrV85IfLxz547ZmQZNJpO+/fZbSRFLZET+HEVlZ2en2bNnG8mWkydPTvA1AQAAAEjbChQoEOcs6s7OzlqzZo0xmMXDwyPGkpORImctN8fe3l4LFy40ZvX6+eefjeen5BYWFqZff/1VkpQ5c2bNnz/fbH9EyZIljWepkJAQ45xI9+7dMwb6lC1bVl988YXZ9rp3764WLVok5yXES+Rzd4YMGbR27Vq5uLhYLF+8eHGzM2clpB/j8ePHOnbsmCSpdevWKl68eIwy6dOnl4eHxysbbJoQTZs2Vd68eS2WadasmbGfEgPOACAhYv7rBQAAAACp6NixYwoMDFTGjBk1ZswY3b9/X2fOnFFoaKgkKSgoSDdv3kz2dvft26fPPvtMU6ZMUYECBXT8+HEtXLhQmzZtMmbXyZ49u8qVK6fGjRurTp068vLy0p9//pmgdkwmkxYsWKCRI0cqT5488vLy0nfffadTp04pPDxcFStW1LBhw1S8eHHt3r071iSfl3l4eOibb76RjY2NZs6caSw1GdvSlJEeP36s9u3ba8uWLbK3t9fatWu1YcMGrVy5UhcvXlRwcLCyZMmiEiVKyN3dXS1atJCTk5N+/vnnRC/xkJz3YM6cOerRo4dq1aqlpk2b6vDhw/rxxx919uxZpU+fXg0bNtTIkSMVGhqqixcvqlixYrEui9C9e3d5eXmpQIEC+uyzz9S8eXPNmzdPx44d0+PHj+Xk5KSCBQuqWrVqatu2rfLkyaOGDRvq/PnzCbr+YcOGafHixdq2bZu2b9+us2fP6v79+7K3t1f+/Pn13nvvGUtSXrt2TevWrYt2/r59+4wEx8mTJ8vKykqXL182ZsQKCAgwZpEKDAxU//79tWLFCtnb22vz5s2aOXOm1q9fr4cPH6pw4cIaNGiQMZvUtWvXNHr06BgxP3r0SF27dtWGDRtkZ2en1atXa82aNVq+fLkuX76ssLAwubm5qUaNGurYsaP++usvTZgwIV734/Lly3J3d9f27dtVsGBBzZ49W/b29poxY0aC7mtCTJkyRR999JEWL16sjRs36tixY8YfJdKnT6/atWurW7duRmJoUFCQ/vjjjxj1DBw4UNOnT5ckPX36VEOHDpWdnZ1KlSoVa9tPnz7VtWvXEhW3yWTSoEGDtHPnTjk4OGjdunWaNm2aNm7cqBcvXqhu3br65JNPlD59eoWHh2vIkCHRRnRH9euvv6pz586qWrWqunXrply5cunXX3/VrVu3VKRIEY0aNcoY1b1mzRqtWbMmUTEDAAAASLvy58+vXbt26dixY1q/fr2OHz8uHx8fhYSEKFeuXKpTp4769etnzLZ06dIli7N/L1myRDY2NlqzZo2OHj2q+/fvK0uWLKpWrZr69++vQoUKSZK2bNliLAGYUr799lu1bdtWFStWVIsWLXT48GFNnz5dZ86cUfr06dWoUSONGDFCGTNmlCR98sknun79eox6Ro0apcaNG8vZ2VlfffWVKlSooPnz5+vGjRvKlSuXOnbsqF69eunAgQPGUpgJWe4xKRYvXqzatWtr4MCBqlixos6dO6c///xTO3bs0J07d2RjY6NcuXKpfPnyat68uapXry4PDw8tW7YsWj179uwx9n/77Td9/fXXunnzptGvdP/+/WiD16ZPny4PDw85ODho586dmjRpkry8vGRjY6NKlSpp+PDhKlSokPbv369atWq9knsRX506dVK3bt20d+9ebd68WadOndK9e/dkZWUlV1dXtWnTRt27d5cU0dcSOQgUAFILSWMAAAAAXivPnj3Tt99+q4kTJ8rV1VWLFy+OdnzXrl2qV69eirQ9depU3b17Vz/99JMyZcqk/v37W1wCLiAgIFHtjB07VlWrVtXbb7+tQoUKadasWTHKzJkzR0uWLNGOHTviVaePj4+2bt2qd955R1mzZpUU0em2fv36OM/ds2ePateurcWLF6tw4cJq0aKFxRGsjx8/TnIHZXLdA5PJpFatWsnT01NVq1ZV+fLlY3S4PXz4UB06dNCXX36pYsWKKTg42Gxdd+/eVfXq1bVw4UI1atRI5cqVMxKCzHnx4oWePn0avwt+iYODQ5z3+d9//1Xr1q0VFBQU7f3r169r3rx56tOnj0qVKhUjmWf+/PnRlq1YuXKlevTooVmzZilDhgz68MMP9eGHH8Zo79SpU2rZsmWs3+vNmzfrnXfe0aJFi5QzZ061adPG4oxjCXHt2jW5u7trx44dKlq0qH777Tc5ODgYM3hFypAhg7Ef28jz+PDx8ZGLi4uGDRtmLLcZufzFmDFjNGbMGKNsYGCgunTpYnZpxqgjqB0dHfX333/H2XZSf4d5eXkZiXlZsmTRp59+qk8//TRamWfPnmn48OHGsqLmPH/+XC1atNC6detUvXp1NWrUSI0aNYpRbv369erSpUui4wUAAACAihUrqmLFihbLbN26VT179rT4rJcuXTrVqFFDNWrUMHs8LCxMs2fP1ocffmgMPkwpoaGhatSokf7++2/VqVNH5cuXNztw7/nz5/r8889j7V/w8fFR48aN5enpqZw5c6pt27Zq27ZttDLnzp1T586djefS2Po1UsIHH3yg69eva/z48cqSJYtGjhypkSNHxlreXJ/C3r17tW3bNjVs2FC1a9eOsUznl19+GW3g2aJFi1S/fn29//77yp07d4wZ2kJCQtS/f3/lzZv3tUsakyQbGxvVq1fP4rO/r6+v2rdvLx8fn1cYGQDERNIYAAAAgNfOpEmTdPHiRfXu3VvlypWTs7PzK5tyfv78+Vq9erX69OmjJk2aqHTp0sqWLZskyd/fX5cvX5aXl5c8PT21e/fuRLURFBSkevXq6YMPPlCXLl1UsmRJ2dnZ6d69ezp06JDmzp2rzZs3x3uWsUgLFiyItqzhkiVL9Pz583ide/jwYWMZgdatW6tKlSrKkSOH7O3t9fjxY3l7e+vYsWPatm2bNmzYYCTYJFZy3gN/f3/VrFlTAwYMUNeuXVWyZEnZ2trq9u3b2rhxo3788UfduHHD6KC1lOx39+5dNW7cWO7u7uratatq1aolV1dXOTk5KSgoSLdu3dKZM2e0Y8cOrV69Wvfu3UvwtXfu3FlNmzaVu7u7Spcurdy5cytHjhxKly6d/Pz8dPLkSa1Zs0YLFy6MtZO7X79+OnTokDp37qzSpUsra9assrW1jbXNhQsXavv27RoyZIiaNGmit956S46Ojnrw4IGOHTumlStXauHChXHOHrdt2za99dZb6tu3r1q0aKHSpUvL2dlZYWFhun37tk6cOKGNGzdq+fLlCb4vt2/flru7u7Zt26bSpUvrhx9+kIODg7755hujzNtvvy0pYgmPuGbRs8TNzU0NGzZUkyZNVLVqVRUuXFhZs2aVvb29wsPDFRgYqCtXrmjr1q367bffUmR2w6RYv369SpUqpSFDhqhFixbKnz+/rKysdPv2bW3evFm//fabLl26FGc9fn5+qlWrlnr27KkuXboY36X79+/r6NGjWrBgQbwS4QAAAADAnKNHj+q9995T1apVVblyZeXJk0fOzs5ydHRUYGCgbty4IS8vLy1evFh79+6Ns76xY8eqZcuWqlWrlvLmzStnZ2c9ffpUt27d0tatW/XXX3/p1KlTr+DKIvj7+6tu3bp699131aVLF1WtWlU5cuRQaGiobty4oe3bt+vXX3/V5cuXLdZz7NgxFS9eXB999JFat26tt956S6Ghobpy5YqWL1+uX375xZhRXkr8IMbEmjJliubPn69+/fqpQYMGKlasmLJly6awsDDdv39fFy9e1IEDB7RhwwYdPnzYbB3NmzfXsGHD1LZtWxUvXlyZMmUyu6RnpD59+mjLli3q37+/ypcvL0dHR/n4+GjHjh2aPn26Tp8+bSyf+ToZMWKEPD09VbduXZUrV04uLi7KmTOnbGxs5O/vr7Nnz2rDhg36888/FRgYmNrhAoDSSXo181fiteDq6qpbt25Jiugkv337dipHhNTg2q9bnGUqFiysdZ9E/89WjRo15OXlFes5GR1s5TPbfN0u/T0UGBy/P1gCAAAAyc3Ozk4BAQFycHDQggUL1KtXr9QOCQnk6Oiohw8fytbWVqNGjYoxC1lyMJlMMUY4A/hvo68MAACklPj8LSaxbs/xSLG68Xpyd3c3Bi/27t07SQOpAACIxExjwBsuJR86AAAAgP+Kjh07GqNy9+/fn8rRIDHc3d1la2srHx8fzZgxI7XDAQAAAADglenRo4exT78GACC5WKV2AAAAAAAAJIWbm1u0ZRpeVrx4cf3www+SpCdPnmjZsmWvKjQko3r16kmSvvnmGwUHB6dyNAAAAAAAJI9ChQpZPN6+fXv17t1bkrR37179+++/ryIsAEAawExjAAAAAIA3WvPmzTVx4kQtX75ce/bskbe3t168eCFXV1c1atRI77//vpycnCRJn3zyiR4/fpzKESMxRo8erdGjR6d2GAAAAAAAJKtJkyapfPnyWr58uQ4dOiQfHx/Z2NioUKFCateund59911ZWVkpNDRUw4cPT+1wAQD/ISSNAQAAAADeeDly5NDgwYM1ePBgs8fDwsL01Vdf6bfffnvFkeFNki5dutQOAQAAAACQBhUvXlzjxo2L9XhAQIC6dOmi48ePv8KoAAD/dSSNAQAAAADeaH///bdMJpMaNWqkUqVKKXv27MqSJYuePHmiGzduaPfu3Zo5c6YuXLiQ2qECAAAAAABEM2HCBJ08eVINGjRQgQIFlD17djk6OurRo0e6cOGCNm/erJkzZ8rf3z+1QwUA/MeQNAbArKCQYB298n9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", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 461, "width": 1222 } }, "output_type": "display_data" } ], "source": [ "#| echo: false\n", "#| fig-cap: Left, what $1 became in each of the 459 stocks after five years, with the average stock (orange) and the median stock (white, dashed); the long right tail lifts the average above most of the stocks. Right, the same five years as log returns, against a normal curve with the same mean and spread.\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", "fig, (a, b) = plt.subplots(1, 2, figsize=(12.4, 4.8))\n", "a.hist(W, bins=np.arange(0, W.max() + 0.25, 0.25), color=TEAL, alpha=0.65)\n", "a.axvline(W.mean(), color=ORANGE, lw=2.2,\n", " label=f\"the average stock, ${W.mean():.2f}\")\n", "a.axvline(W.median(), color=\"white\", lw=1.6, ls=\"--\",\n", " label=f\"the median stock, ${W.median():.2f}\")\n", "a.set_xlabel(\"what $1 became, Feb 2013 to Feb 2018\"); a.set_ylabel(\"stocks\")\n", "a.legend(frameon=False, fontsize=10.5); tidy(a)\n", "b.hist(X, bins=40, density=True, color=TEAL, alpha=0.65, label=\"459 log returns\")\n", "x = np.linspace(X.min() - 0.2, X.max() + 0.2, 500)\n", "b.plot(x, norm.pdf(x, X.mean(), s), color=\"white\", lw=2,\n", " label=\"normal, same mean and spread\")\n", "b.set_xlabel(\"five-year log return\"); b.set_ylabel(\"density\")\n", "b.legend(frameon=False, fontsize=10.5); tidy(b)\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "4fa25d78", "metadata": {}, "source": [ "## The Longer You Hold\n", "\n", "The spread $s$ of the log returns grows with the time a stock is held, roughly as its square root, so $\\Phi(s/2)$ grows too. Year by year the share below the average stays just above half, as low as 50.3% in 2015, 231 of the 459 stocks:" ] }, { "cell_type": "code", "execution_count": 4, "id": "119a83ad", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:49.402105Z", "iopub.status.busy": "2026-10-06T03:00:49.401934Z", "iopub.status.idle": "2026-10-06T03:00:49.408654Z", "shell.execute_reply": "2026-10-06T03:00:49.408174Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "year days below the average Phi(s/2)\n", "2013 225 55.3% 54.0%\n", "2014 252 51.0% 53.7%\n", "2015 252 50.3% 55.1%\n", "2016 252 52.1% 54.1%\n", "2017 251 54.7% 54.5%\n" ] } ], "source": [ "#| label: Year by Year\n", "print(\"year days below the average Phi(s/2)\")\n", "for year, g in rets.groupby(rets.index.year):\n", " if len(g) < 200: # 2018 holds only five weeks\n", " continue\n", " w = np.exp(g.sum())\n", " pred = norm.cdf(np.log(w).std() / 2)\n", " print(f\"{year} {len(g):4d} {np.mean(w < w.mean()):17.1%} {pred:8.1%}\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "8de99826", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:49.409553Z", "iopub.status.busy": "2026-10-06T03:00:49.409461Z", "iopub.status.idle": "2026-10-06T03:00:49.423456Z", "shell.execute_reply": "2026-10-06T03:00:49.423134Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "held 0.5 years: 53.4% below the average (Phi(s/2): 52.8%)\n", "held 1.0 years: 59.0% below the average (Phi(s/2): 54.3%)\n", "held 2.0 years: 62.5% below the average (Phi(s/2): 55.8%)\n", "held 3.0 years: 57.1% below the average (Phi(s/2): 58.5%)\n", "held 4.0 years: 62.7% below the average (Phi(s/2): 58.3%)\n", "held 5.0 years: 62.7% below the average (Phi(s/2): 60.6%)\n" ] } ], "source": [ "#| label: The Longer You Hold\n", "cum = rets.cumsum()\n", "ends = np.append(np.arange(21, len(rets), 21), len(rets)) # a month at a time\n", "H = ends / 252 # years held\n", "wealth = [np.exp(cum.iloc[k - 1]) for k in ends] # a dollar, by horizon\n", "share = np.array([np.mean(w < w.mean()) for w in wealth])\n", "pred = np.array([norm.cdf(cum.iloc[k - 1].std() / 2) for k in ends])\n", "for yrs in (0.5, 1, 2, 3, 4, 5):\n", " i = np.argmin(np.abs(H - yrs))\n", " print(f\"held {H[i]:3.1f} years: {share[i]:.1%} below the average \"\n", " f\"(Phi(s/2): {pred[i]:.1%})\")" ] }, { "cell_type": "markdown", "id": "e935444f", "metadata": {}, "source": [ "Held from February 2013, the share rises from 53.4% at six months to 59.0% at one year and 62.7% at five, though not smoothly: at three years it was back to 57.1%. The prediction rises more smoothly, from 52.8% to 60.6%. Over one year, \"most\" is barely true; over five, it is almost two in three." ] }, { "cell_type": "code", "execution_count": 6, "id": "20cec58c", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:49.424512Z", "iopub.status.busy": "2026-10-06T03:00:49.424422Z", "iopub.status.idle": "2026-10-06T03:00:49.522606Z", "shell.execute_reply": "2026-10-06T03:00:49.522120Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 440, "width": 1222 } }, "output_type": "display_data" } ], "source": [ "#| echo: false\n", "#| fig-cap: The share of the 459 stocks below the average stock, for every holding period from one month to five years, all starting in February 2013 (teal), against the lognormal prediction Φ(s/2) with s measured at each horizon (white). The dotted line is one half.\n", "fig, ax = plt.subplots(figsize=(12.4, 4.6))\n", "ax.plot(H, 100 * share, color=TEAL, lw=2.2, label=\"the 459 stocks\")\n", "ax.plot(H, 100 * pred, color=\"white\", lw=1.8, ls=\"--\",\n", " label=\"lognormal prediction, Φ(s/2)\")\n", "ax.axhline(50, color=GREY, lw=1, ls=\":\")\n", "ax.set_xlabel(\"years held\"); ax.set_ylabel(\"stocks below the average stock (%)\")\n", "ax.set_ylim(45, 70); ax.legend(frameon=False, fontsize=10.5); tidy(ax)\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "7aa88b65", "metadata": {}, "source": [ "## Volatility Drag, Stock by Stock\n", "\n", "The same inequality works inside each stock. A stock's growth rate is its average daily return less about half its daily variance, $g \\approx \\mu - \\tfrac{1}{2}\\sigma^2$, so of two stocks with the same average return, the more volatile one ends with less." ] }, { "cell_type": "code", "execution_count": 7, "id": "92889a47", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:49.523613Z", "iopub.status.busy": "2026-10-06T03:00:49.523528Z", "iopub.status.idle": "2026-10-06T03:00:49.528985Z", "shell.execute_reply": "2026-10-06T03:00:49.528735Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "median yearly arithmetic return: 13.6%\n", "median yearly growth rate: 11.0%\n", "median yearly drag, mean minus growth: 2.56%\n", "half the variance predicts: 2.56%\n", "correlation of the two, stock by stock: 0.9992\n" ] } ], "source": [ "#| label: Volatility Drag, Stock by Stock\n", "simple = np.expm1(rets) # daily simple returns\n", "mu, var = simple.mean(), simple.var()\n", "g = rets.mean() # the growth rate actually achieved\n", "drag = 252 * (mu - g) # the yearly gap between the two\n", "print(f\"median yearly arithmetic return: {252 * mu.median():.1%}\")\n", "print(f\"median yearly growth rate: {252 * g.median():.1%}\")\n", "print(f\"median yearly drag, mean minus growth: {drag.median():.2%}\")\n", "print(f\"half the variance predicts: {(252 * var / 2).median():.2%}\")\n", "r = np.corrcoef(drag, var)[0, 1]\n", "print(f\"correlation of the two, stock by stock: {r:.4f}\")" ] }, { "cell_type": "markdown", "id": "f994891f", "metadata": {}, "source": [ "For the median stock, an average return of 13.6% a year compounded at 11.0%. The drag between them, 2.56% a year, matches half the variance to the hundredth of a percent, and across the 459 stocks the two agree with a correlation of 0.9992." ] }, { "cell_type": "markdown", "id": "fea55ef3", "metadata": {}, "source": [ "## Where the Gains Came From\n", "\n", "A long right tail means a few stocks carried the average." ] }, { "cell_type": "code", "execution_count": 8, "id": "34d5acf7", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:49.529880Z", "iopub.status.busy": "2026-10-06T03:00:49.529800Z", "iopub.status.idle": "2026-10-06T03:00:49.532338Z", "shell.execute_reply": "2026-10-06T03:00:49.532032Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "$1 in each of 459 stocks gained $460 in all\n", "the top 46 stocks made 39% of it\n", "the top half made 89%\n", "stocks that lost money: 58\n" ] } ], "source": [ "#| label: Where the Gains Came From\n", "gain = (W - 1).sort_values(ascending=False)\n", "top = int(round(0.1 * gain.size))\n", "print(f\"$1 in each of {gain.size} stocks gained ${gain.sum():.0f} in all\")\n", "print(f\"the top {top} stocks made {gain.iloc[:top].sum() / gain.sum():.0%} \"\n", " f\"of it\")\n", "print(f\"the top half made {gain.iloc[:gain.size // 2].sum() / gain.sum():.0%}\")\n", "print(f\"stocks that lost money: {np.sum(W < 1)}\")" ] }, { "cell_type": "markdown", "id": "bfd2ff25", "metadata": {}, "source": [ "Together the 459 dollars gained \\$460. The best 46 stocks, a tenth of them, made 39% of that gain, and the best half made 89% of it. Fifty-eight stocks lost money outright." ] }, { "cell_type": "markdown", "id": "40b8cdf0", "metadata": {}, "source": [ "## Compounding Alone\n", "\n", "Keep each stock's own drift and volatility, but let the stocks move independently of each other, and simulate the five years 200 times." ] }, { "cell_type": "code", "execution_count": 9, "id": "55e8d8b5", "metadata": { "execution": { "iopub.execute_input": "2026-10-06T03:00:49.533172Z", "iopub.status.busy": "2026-10-06T03:00:49.533091Z", "iopub.status.idle": "2026-10-06T03:00:49.539598Z", "shell.execute_reply": "2026-10-06T03:00:49.539217Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "independent stocks, same drifts and vols: 67.9% below (middle 90%: 64.0% to 72.6%)\n", "their spread s: 0.780, against the market's 0.536\n", "the real market: 62.7% below\n" ] } ], "source": [ "#| label: Compounding Alone\n", "rng = np.random.default_rng(20261005)\n", "m, sd, T = rets.mean().to_numpy(), rets.std().to_numpy(), len(rets)\n", "X_sim = rng.normal(m * T, sd * np.sqrt(T), size=(200, m.size)) # 200 markets\n", "sims = np.array([np.mean(np.exp(x) < np.exp(x).mean()) for x in X_sim])\n", "print(f\"independent stocks, same drifts and vols: {sims.mean():.1%} below \"\n", " f\"(middle 90%: {np.quantile(sims, 0.05):.1%} \"\n", " f\"to {np.quantile(sims, 0.95):.1%})\")\n", "x_sim = rng.normal(m * T, sd * np.sqrt(T))\n", "print(f\"their spread s: {x_sim.std():.3f}, against the market's {s:.3f}\")\n", "print(f\"the real market: {np.mean(W < W.mean()):.1%} below\")" ] }, { "cell_type": "markdown", "id": "67efacd0", "metadata": {}, "source": [ "Independent stocks would leave 67.9% below the average, more than the real 62.7%. The reason is the market itself. It moves every stock together, so it is part of each stock's volatility but spreads no stock away from the others: independent stocks with the same volatilities would spread out to 0.780, against the 0.536 the real 459 reached." ] }, { "cell_type": "markdown", "id": "7b6076f6", "metadata": {}, "source": [ "## What It Means\n", "\n", "The average stock is not a stock. It is a portfolio of all 459, and it collects the mean of their outcomes, while one stock picked at random most likely ends up near the median. The gap between the two is volatility, compounded: small over a year, and almost two stocks in three over five.\n", "\n", "These 459 are survivors. Stocks that left the index or stopped trading during the five years, often after large losses, are not in the data, so the true share below the average is likely higher. Over the whole US market since 1926, Bessembinder (2018) found that most common stocks did worse over their lifetimes than one-month Treasury bills, and that a small fraction of companies accounts for all of the market's net wealth creation.\n", "\n", "## Sources\n", "\n", "1. H. Bessembinder, \"Do stocks outperform Treasury bills?\", *Journal of Financial Economics* 129 (2018) 440–457.\n", "2. C. Nugent, \"S&P 500 stock data\", Kaggle dataset camnugent/sandp500 (CC0: Public Domain)." ] } ], "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 }