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etf-leverage-demostration.ipynb
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "view-in-github", | |
"colab_type": "text" | |
}, | |
"source": [ | |
"<a href=\"https://colab.research.google.com/gist/CY0xZ/c79d4dbd0a82b89f71ff08a9f6d67f92/leverage-demostration.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "K1gv8fo6MN1W" | |
}, | |
"outputs": [], | |
"source": [ | |
"pip install yfinance" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "-5R4OtJyPBDT" | |
}, | |
"outputs": [], | |
"source": [ | |
"import pandas as pd\n", | |
"import numpy as np\n", | |
"from functools import reduce\n", | |
"import pandas_datareader.data as web\n", | |
"import datetime\n", | |
"import random\n", | |
"import matplotlib.pyplot as plt\n", | |
"import matplotlib as mpl\n", | |
"import seaborn as sns\n", | |
"from datetime import datetime\n", | |
"\n", | |
"\n", | |
"mpl.style.use('ggplot')\n", | |
"figsize = (25, 25)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "W79qH25fM_Db", | |
"outputId": "7e5a8e36-5c40-451c-db74-f0b68f6cfaf2" | |
}, | |
"outputs": [ | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"\r[*********************100%%**********************] 1 of 1 completed" | |
] | |
}, | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Date\n", | |
"2017-01-04 1.005722\n", | |
"2017-01-05 1.004947\n", | |
"2017-01-06 1.008482\n", | |
"2017-01-09 1.004903\n", | |
"2017-01-10 1.004903\n", | |
" ... \n", | |
"2024-04-24 2.246241\n", | |
"2024-04-25 2.235961\n", | |
"2024-04-26 2.258788\n", | |
"2024-04-29 2.265968\n", | |
"2024-04-30 2.230323\n", | |
"Length: 1842, dtype: float64\n" | |
] | |
}, | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"\n" | |
] | |
} | |
], | |
"source": [ | |
"import yfinance as yf\n", | |
"import pandas as pd\n", | |
"from datetime import datetime\n", | |
"\n", | |
"equity = ['^GSPC']\n", | |
"Fecha_Start = '01-01-2017'\n", | |
"Fecha_End = '01-05-2024'\n", | |
"\n", | |
"start = datetime.strptime(Fecha_Start, '%d-%m-%Y')\n", | |
"end = datetime.strptime(Fecha_End, '%d-%m-%Y')\n", | |
"\n", | |
"tickers = equity\n", | |
"asset_universe = pd.DataFrame([yf.download(ticker, start=start, end=end)['Close'] for ticker in tickers],\n", | |
" index=tickers).T.fillna(method='ffill')\n", | |
"\n", | |
"portfolio_returns = asset_universe.pct_change().dropna().mean(axis=1)\n", | |
"portfolio = (asset_universe.pct_change().dropna().mean(axis=1) + 1).cumprod()\n", | |
"\n", | |
"asset_universe_returns = asset_universe.pct_change()\n", | |
"\n", | |
"print(portfolio)\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "DZvqC5S0SWyk" | |
}, | |
"outputs": [], | |
"source": [ | |
"# R = k*mu - 0.5*k^2*sigma^2/(1+k*mu)\n", | |
"# R = compound daily growth\n", | |
"# k = ETF leverage (-1,-2,-3,1,2,3...)\n", | |
"# mu = mean daily return of the benchmark\n", | |
"# sigma = is the daily volatility (i.e. standard deviation) of the daily return of the benchmark." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"colab": { | |
"background_save": true | |
}, | |
"id": "amPVGTGehMUo", | |
"outputId": "14cfea73-bc5b-488d-bbdc-87d0c842f519" | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[0.0,\n", | |
" 10.985571951931934,\n", | |
" 18.35580990238281,\n", | |
" 22.11621243628962,\n", | |
" 22.272266993794737,\n", | |
" 18.82944989846765]" | |
] | |
}, | |
"execution_count": 17, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"R=[]\n", | |
"mu = portfolio_returns.mean()\n", | |
"sigma = portfolio_returns.std()\n", | |
"for i in range(0,6):\n", | |
" k = i\n", | |
" X = (k*mu)-(0.5*k**2*sigma**2)/(1+k*mu)\n", | |
" R.append(X*252*100)\n", | |
"R" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/", | |
"height": 477 | |
}, | |
"id": "dby6k11bkDQh", | |
"outputId": "889436f8-e5f1-4fc0-b57c-05d4095751da" | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.plot(R)\n", | |
"plt.xlabel(\"Leverage\")\n", | |
"plt.ylabel(\"CAGR\")\n", | |
"plt.title(\"SPY Data\")\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "QKugCnhiY4ub" | |
}, | |
"outputs": [], | |
"source": [ | |
"# k = mu*sigma^2\n", | |
"# k = ETF leverage (-1,-2,-3,1,2,3...)\n", | |
"# mu = mean daily return of the benchmark\n", | |
"# sigma = is the daily volatility (i.e. standard deviation) of the daily return of the benchmark." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "wGfHmHULlRzA" | |
}, | |
"outputs": [], | |
"source": [ | |
"'''\n", | |
"µ = average returns of SPY\n", | |
"r = risk free rate\n", | |
"σ² = variance of SPY\n", | |
"'''" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "Pt3EQxnpgt8t" | |
}, | |
"source": [ | |
"\\begin{align}\n", | |
"f(x)= (µ-r)/σ² \\tag{1}\n", | |
"\\end{align}" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "wzAcRwOmaQO4" | |
}, | |
"outputs": [], | |
"source": [ | |
"mu = portfolio_returns.mean() * 252 #Calculates the annualized return.\n", | |
"sigma = portfolio_returns.std() * 252 ** 0.5 #Calculates the annualized volatility.\n", | |
"r = 0.011 #1 year treasury rate" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"colab": { | |
"base_uri": "https://localhost:8080/" | |
}, | |
"id": "RSSAHwiHca-v", | |
"outputId": "cc2fdab9-f0b9-4cbc-c958-8b1887d499ae" | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"3.273124512408495" | |
] | |
}, | |
"execution_count": 152, | |
"metadata": { | |
"tags": [] | |
}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"f = (mu - r) / sigma ** 2\n", | |
"f" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "egEbXVIHnpiI" | |
}, | |
"source": [ | |
"" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "0h1zwkjEeDW4" | |
}, | |
"outputs": [], | |
"source": [] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"id": "vqSk4hyW2ElV" | |
}, | |
"source": [ | |
"" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"id": "F-eQs5Zm2INu" | |
}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"accelerator": "TPU", | |
"colab": { | |
"machine_shape": "hm", | |
"provenance": [], | |
"name": "etf-leverage-demostration.ipynb", | |
"authorship_tag": "ABX9TyNjScwBBaPc58JxuMbjfC8C", | |
"include_colab_link": true | |
}, | |
"kernelspec": { | |
"display_name": "Python 3", | |
"name": "python3" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 0 | |
} |
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