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Fronteira Eficiente - Carteira de Markovitz
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Efficient_Frontier.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fronteira Eficiente - Carteira de Markovitz"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Resolveremos numericamente o problema para traçar a fronteira média-variância através da solução do problema de minimização da variância esperada da carteira, para um nível mínimo de retorno esperado como restrição."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Importação dos pacotes utilizados"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Importamos os pacotes necessários e fazemos a inicialização da ferramenta que apresentará os gráficos."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
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"outputs": [
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"source": [
"import pandas_datareader.data as web\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import datetime as dt\n",
"import numpy as np\n",
"from scipy.optimize import minimize\n",
"\n",
"from bokeh.io import show, output_notebook\n",
"from bokeh.plotting import figure\n",
"import bokeh.palettes as palettes\n",
"from bokeh.models import NumeralTickFormatter\n",
"\n",
"output_notebook()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Captura dos preços do ativos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Selecionamos 5 ativos negociados na bolsa brasileira para o problema. Capturamos os preços a partir do início do ano de 2016."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"From 04/Jan/16 to 07/Dec/16 \n",
"\n"
]
}
],
"source": [
"first_price_date = dt.datetime(2016, 1, 1)\n",
"last_price_date = dt.datetime(2016, 12, 7)\n",
"symbols = ['VALE5', 'PETR4', 'BVMF3', 'ITUB4', 'BBAS3']\n",
"\n",
"data = pd.DataFrame()\n",
"for sym in symbols:\n",
" data[sym] = web.DataReader(sym, 'google', first_price_date, last_price_date)['Close']\n",
"data = data.dropna()\n",
"\n",
"days = data.index\n",
"print(\"From %s to %s \\n\" % (days[0].strftime(\"%d/%b/%y\"), days[-1].strftime(\"%d/%b/%y\")))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cálculo dos retornos diários"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note que o importante não é o preço dos ativos, e sim seus retornos."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"daily_returns = np.log(data / data.shift(1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cálculo da matriz de covariância e dos retornos anualizados"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Devemos sempre anualizar os retornos e a matriz de covariância. Para isso utilizamos a convenção de 252 dias úteis."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"_252_DAYS = 252\n",
"covariance_matrix = np.asarray(_252_DAYS * daily_returns.cov())\n",
"annualized_returns = np.asarray(_252_DAYS * daily_returns.mean())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Matriz de covariância anualizada"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" VALE5 PETR4 BVMF3 ITUB4 BBAS3\n",
"VALE5 0.423061 0.237970 0.086874 0.100836 0.138764\n",
"PETR4 0.237970 0.425339 0.144189 0.162488 0.266100\n",
"BVMF3 0.086874 0.144189 0.132996 0.083185 0.128917\n",
"ITUB4 0.100836 0.162488 0.083185 0.132272 0.160479\n",
"BBAS3 0.138764 0.266100 0.128917 0.160479 0.337085\n"
]
}
],
"source": [
"print(pd.DataFrame(covariance_matrix, index=symbols, columns=symbols))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Retorno anualizado"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Return\n",
"VALE5 1.112155\n",
"PETR4 0.908760\n",
"BVMF3 0.478882\n",
"ITUB4 0.431669\n",
"BBAS3 0.694936\n"
]
}
],
"source": [
"print(pd.DataFrame(annualized_returns, index=symbols, columns=['Return']))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Definição dos métodos de cálculo de variância (risco) e retorno da carteira"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Definimos as equações de variância e retorno da carteira. Lembramos que o risco é medido pelo desvio padrão, que é a raiz quadrada da variância."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def portfolio_variance(w):\n",
" _w = np.asarray(w)\n",
" return _w.dot(covariance_matrix).dot(_w)\n",
"\n",
"def portfolio_return(w):\n",
" _w = np.asarray(w)\n",
" return _w.dot(annualized_returns)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Definição do gradiente da variância para facilitar a convergência na minimização"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def portfolio_variance_gradient(w):\n",
" _w = np.asarray(w)\n",
" return 2 * _w.dot(covariance_matrix)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Definição do método de minimização da variância com restrição de retorno mínimo para a carteira"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Aqui definimos o método que, dado um retorno mínimo, minimiza a variância da carteira e retorna o vetor com a proporção de cada ativo. Devemos chamar atenção para as restrições:\n",
"\n",
"$\\bullet$ Se não há venda a descoberto, w deve ser não negativo.\n",
"\n",
"$\\bullet$ A soma dos elementos de w é sempre igual a 1.\n",
"\n",
"$\\bullet$ O retorno da carteira é sempre maior ou igual ao retorno mínimo passado como parâmetro."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def minimize_portfolio_variance(min_return, short_sale_allowed=True):\n",
" assets_number = len(symbols)\n",
"\n",
" bnds = None if short_sale_allowed \\\n",
" else [(0, None) for i in range(assets_number)] # If short sale not allowed, lower bound = 0\n",
"\n",
" initial_guess = [1 / assets_number for i in range(assets_number)]\n",
" cons = ({'type': 'eq', 'fun': lambda w: w.sum() - 1},\n",
" {'type': 'ineq', 'fun': lambda w: portfolio_return(w) - min_return})\n",
" return minimize(portfolio_variance, initial_guess,\n",
" constraints=cons,\n",
" bounds=bnds,\n",
" options={'disp': False},\n",
" method='SLSQP',\n",
" jac=portfolio_variance_gradient)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Definição do método que calcula a fronteira eficiente"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"O método que calcula a fronteira eficiente executa o método definido anteriormente para diversos valores de retorno mínimo. Assim, para cada iteração, temos um ponto da fronteira desejada."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def calculate_mv_frontier(short_sale_allowed=True):\n",
" frontier = pd.Series()\n",
" weights = pd.DataFrame()\n",
" for min_return in np.linspace(0, 1.2, num=2000):\n",
" result = minimize_portfolio_variance(min_return, short_sale_allowed=short_sale_allowed)\n",
" if not result.success:\n",
" continue\n",
" w_frontier = result.x\n",
" port_sigma = np.sqrt(portfolio_variance(w_frontier))\n",
" port_return = portfolio_return(w_frontier)\n",
" frontier.set_value(port_sigma, port_return)\n",
"\n",
" for i, symbol in enumerate(symbols):\n",
" weights.set_value(port_sigma, symbol, w_frontier[i])\n",
"\n",
" return frontier, weights"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cálculo das fronteiras e das respectivas proporções dos ativos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Agora podemos calcular as fronteiras desejadas: Uma será calculada sem vendas a descoberto e a outra com vendas a descoberto. Medimos o tempo de execução para avaliar a eficiência do algoritmo de otimização."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 7.18 s, sys: 84.1 ms, total: 7.27 s\n",
"Wall time: 7.7 s\n",
"CPU times: user 8.57 s, sys: 87.8 ms, total: 8.66 s\n",
"Wall time: 9.32 s\n"
]
}
],
"source": [
"%time frontier_ss_false, weights_ss_false = calculate_mv_frontier(short_sale_allowed=False)\n",
"%time frontier_ss_true, weights_ss_true = calculate_mv_frontier(short_sale_allowed=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Apresentação dos gráficos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fronteiras com e sem vendas a descoberto\n",
"É interessante notar que a fronteira que permite vendas a descoberto é maior, por possibilitar mais combinações de ativos. Porém, como esperado, na região em que a carteira ótima possui apenas proporções positivas, as duas fronteiras se confundem.\n",
"\n",
"Outra característica importante que deve ser notada é que o retorno máximo da carteira quando não é permitido venda a descoberto é o maior retorno dentre os ativos, alcançado quando a carteira está totalmente alocada neste ativo (proporção de 100%). Quando a venda a descoberto é permitida, alcançamos esse mesmo retorno com um risco inferior e com outros ativos na carteira.\n",
"\n",
"Dica: Ao clicar no gráfico, selecione a opção de Zoom para verificar os níveis de risco."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
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" console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
" document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
" }\n",
" };var element = document.getElementById(\"70cef20b-b5f5-43be-bfab-f5057d6bc256\");\n",
" if (element == null) {\n",
" console.log(\"Bokeh: ERROR: autoload.js configured with elementid '70cef20b-b5f5-43be-bfab-f5057d6bc256' but no matching script tag was found. \")\n",
" return false;\n",
" }\n",
" \n",
" var js_urls = [];\n",
" \n",
" var inline_js = [\n",
" function(Bokeh) {\n",
" Bokeh.$(function() {\n",
" var docs_json = {\"cd55fd21-724a-481c-ad85-2d7297ed5b30\":{\"roots\":{\"references\":[{\"attributes\":{\"label\":{\"value\":\"Short Sale 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Application\",\"version\":\"0.12.3\"}};\n",
" var render_items = [{\"docid\":\"cd55fd21-724a-481c-ad85-2d7297ed5b30\",\"elementid\":\"70cef20b-b5f5-43be-bfab-f5057d6bc256\",\"modelid\":\"5e5ea79b-c0b9-44bd-a5fe-bb9aecef90f1\"}];\n",
" \n",
" Bokeh.embed.embed_items(docs_json, render_items);\n",
" });\n",
" },\n",
" function(Bokeh) {\n",
" }\n",
" ];\n",
" \n",
" function run_inline_js() {\n",
" \n",
" if ((window.Bokeh !== undefined) || (force === \"1\")) {\n",
" for (var i = 0; i < inline_js.length; i++) {\n",
" inline_js[i](window.Bokeh);\n",
" }if (force === \"1\") {\n",
" display_loaded();\n",
" }} else if (Date.now() < window._bokeh_timeout) {\n",
" setTimeout(run_inline_js, 100);\n",
" } else if (!window._bokeh_failed_load) {\n",
" console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
" window._bokeh_failed_load = true;\n",
" } else if (!force) {\n",
" var cell = $(\"#70cef20b-b5f5-43be-bfab-f5057d6bc256\").parents('.cell').data().cell;\n",
" cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
" }\n",
" \n",
" }\n",
" \n",
" if (window._bokeh_is_loading === 0) {\n",
" console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
" run_inline_js();\n",
" } else {\n",
" load_libs(js_urls, function() {\n",
" console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
" run_inline_js();\n",
" });\n",
" }\n",
" }(this));\n",
"</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p1 = figure(width=900, height=600, title=\"Efficient Frontier\", toolbar_location=\"above\")\n",
"p1.line(frontier_ss_true.index, frontier_ss_true.values, legend=\"Short Sale Allowed\", color=\"green\", line_width=2)\n",
"p1.line(frontier_ss_false.index, frontier_ss_false.values, legend=\"No Short Sale Allowed\", color=\"blue\", line_width=2)\n",
"\n",
"p1.legend.location = \"top_left\"\n",
"p1.xaxis.axis_label = 'Risk'\n",
"p1.xaxis.formatter = NumeralTickFormatter(format=\"0.%\")\n",
"p1.yaxis.axis_label = 'Return'\n",
"p1.yaxis.formatter = NumeralTickFormatter(format=\"0.%\")\n",
"\n",
"show(p1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Proporção de cada ativo, com vendas a descoberto\n",
"Por não haver restrição nas proporções, notamos nas curvas abaixo uma aparente continuidade."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
" <div class=\"bk-root\">\n",
" <div class=\"plotdiv\" id=\"712fc52c-c738-4c54-ad7e-6286842513c0\"></div>\n",
" </div>\n",
"<script type=\"text/javascript\">\n",
" \n",
" (function(global) {\n",
" function now() {\n",
" return new Date();\n",
" }\n",
" \n",
" var force = \"\";\n",
" \n",
" if (typeof (window._bokeh_onload_callbacks) === \"undefined\" || force !== \"\") {\n",
" window._bokeh_onload_callbacks = [];\n",
" window._bokeh_is_loading = undefined;\n",
" }\n",
" \n",
" \n",
" \n",
" if (typeof (window._bokeh_timeout) === \"undefined\" || force !== \"\") {\n",
" window._bokeh_timeout = Date.now() + 0;\n",
" window._bokeh_failed_load = false;\n",
" }\n",
" \n",
" var NB_LOAD_WARNING = {'data': {'text/html':\n",
" \"<div style='background-color: #fdd'>\\n\"+\n",
" \"<p>\\n\"+\n",
" \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
" \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
" \"</p>\\n\"+\n",
" \"<ul>\\n\"+\n",
" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
" \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
" \"</ul>\\n\"+\n",
" \"<code>\\n\"+\n",
" \"from bokeh.resources import INLINE\\n\"+\n",
" \"output_notebook(resources=INLINE)\\n\"+\n",
" \"</code>\\n\"+\n",
" \"</div>\"}};\n",
" \n",
" function display_loaded() {\n",
" if (window.Bokeh !== undefined) {\n",
" Bokeh.$(\"#712fc52c-c738-4c54-ad7e-6286842513c0\").text(\"BokehJS successfully loaded.\");\n",
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" }\n",
" }\n",
" \n",
" function run_callbacks() {\n",
" window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
" delete window._bokeh_onload_callbacks\n",
" console.info(\"Bokeh: all callbacks have finished\");\n",
" }\n",
" \n",
" function load_libs(js_urls, callback) {\n",
" window._bokeh_onload_callbacks.push(callback);\n",
" if (window._bokeh_is_loading > 0) {\n",
" console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
" return null;\n",
" }\n",
" if (js_urls == null || js_urls.length === 0) {\n",
" run_callbacks();\n",
" return null;\n",
" }\n",
" console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
" window._bokeh_is_loading = js_urls.length;\n",
" for (var i = 0; i < js_urls.length; i++) {\n",
" var url = js_urls[i];\n",
" var s = document.createElement('script');\n",
" s.src = url;\n",
" s.async = false;\n",
" s.onreadystatechange = s.onload = function() {\n",
" window._bokeh_is_loading--;\n",
" if (window._bokeh_is_loading === 0) {\n",
" console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
" run_callbacks()\n",
" }\n",
" };\n",
" s.onerror = function() {\n",
" console.warn(\"failed to load library \" + url);\n",
" };\n",
" console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
" document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
" }\n",
" };var element = document.getElementById(\"712fc52c-c738-4c54-ad7e-6286842513c0\");\n",
" if (element == null) {\n",
" console.log(\"Bokeh: ERROR: autoload.js configured with elementid '712fc52c-c738-4c54-ad7e-6286842513c0' but no matching script tag was found. \")\n",
" return false;\n",
" }\n",
" \n",
" var js_urls = [];\n",
" \n",
" var inline_js = [\n",
" function(Bokeh) {\n",
" Bokeh.$(function() {\n",
" var docs_json = 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" var render_items = [{\"docid\":\"ea84622a-a3c3-4843-a4c7-77b7ad118327\",\"elementid\":\"712fc52c-c738-4c54-ad7e-6286842513c0\",\"modelid\":\"9ad12f60-7c08-4216-815d-6c9a0dc5c47c\"}];\n",
" \n",
" Bokeh.embed.embed_items(docs_json, render_items);\n",
" });\n",
" },\n",
" function(Bokeh) {\n",
" }\n",
" ];\n",
" \n",
" function run_inline_js() {\n",
" \n",
" if ((window.Bokeh !== undefined) || (force === \"1\")) {\n",
" for (var i = 0; i < inline_js.length; i++) {\n",
" inline_js[i](window.Bokeh);\n",
" }if (force === \"1\") {\n",
" display_loaded();\n",
" }} else if (Date.now() < window._bokeh_timeout) {\n",
" setTimeout(run_inline_js, 100);\n",
" } else if (!window._bokeh_failed_load) {\n",
" console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
" window._bokeh_failed_load = true;\n",
" } else if (!force) {\n",
" var cell = $(\"#712fc52c-c738-4c54-ad7e-6286842513c0\").parents('.cell').data().cell;\n",
" cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
" }\n",
" \n",
" }\n",
" \n",
" if (window._bokeh_is_loading === 0) {\n",
" console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
" run_inline_js();\n",
" } else {\n",
" load_libs(js_urls, function() {\n",
" console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
" run_inline_js();\n",
" });\n",
" }\n",
" }(this));\n",
"</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mypalette = palettes.Spectral5[0:len(symbols)]\n",
"\n",
"p2 = figure(width=900, height=600, title=\"Efficient Frontier Weights (Short Sale Allowed)\", toolbar_location=\"above\")\n",
"for i, symbol in enumerate(symbols):\n",
" p2.line(weights_ss_true[symbol].index, weights_ss_true[symbol].values, legend=symbol, color=mypalette[i], line_width=2)\n",
"\n",
"p2.legend.location = \"bottom_left\"\n",
"p2.xaxis.axis_label = 'Risk'\n",
"p2.xaxis.formatter = NumeralTickFormatter(format=\"0.%\")\n",
"p2.yaxis.axis_label = 'Weight'\n",
"p2.yaxis.formatter = NumeralTickFormatter(format=\"0.%\")\n",
"\n",
"show(p2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Proporção de cada ativo, sem vendas a descoberto\n",
"A continuidade observada no gráfico anterior não pode mais ser observada quando colocamos a restrição das vendas a descoberto."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
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" \n",
" (function(global) {\n",
" function now() {\n",
" return new Date();\n",
" }\n",
" \n",
" var force = \"\";\n",
" \n",
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" \n",
" var NB_LOAD_WARNING = {'data': {'text/html':\n",
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" \"<p>\\n\"+\n",
" \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
" \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
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" \"<ul>\\n\"+\n",
" \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
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" \"<code>\\n\"+\n",
" \"from bokeh.resources import INLINE\\n\"+\n",
" \"output_notebook(resources=INLINE)\\n\"+\n",
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" };var element = document.getElementById(\"22835ff4-3f15-4157-a807-96c7ad14d50e\");\n",
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" console.log(\"Bokeh: ERROR: autoload.js configured with elementid '22835ff4-3f15-4157-a807-96c7ad14d50e' but no matching script tag was found. \")\n",
" return false;\n",
" }\n",
" \n",
" var js_urls = [];\n",
" \n",
" var inline_js = [\n",
" function(Bokeh) {\n",
" Bokeh.$(function() {\n",
" var docs_json = 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" var render_items = [{\"docid\":\"c2263dc0-c17b-4258-bc49-bb17a17e806a\",\"elementid\":\"22835ff4-3f15-4157-a807-96c7ad14d50e\",\"modelid\":\"567b421f-b917-48cd-b652-5aab83e65991\"}];\n",
" \n",
" Bokeh.embed.embed_items(docs_json, render_items);\n",
" });\n",
" },\n",
" function(Bokeh) {\n",
" }\n",
" ];\n",
" \n",
" function run_inline_js() {\n",
" \n",
" if ((window.Bokeh !== undefined) || (force === \"1\")) {\n",
" for (var i = 0; i < inline_js.length; i++) {\n",
" inline_js[i](window.Bokeh);\n",
" }if (force === \"1\") {\n",
" display_loaded();\n",
" }} else if (Date.now() < window._bokeh_timeout) {\n",
" setTimeout(run_inline_js, 100);\n",
" } else if (!window._bokeh_failed_load) {\n",
" console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
" window._bokeh_failed_load = true;\n",
" } else if (!force) {\n",
" var cell = $(\"#22835ff4-3f15-4157-a807-96c7ad14d50e\").parents('.cell').data().cell;\n",
" cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
" }\n",
" \n",
" }\n",
" \n",
" if (window._bokeh_is_loading === 0) {\n",
" console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
" run_inline_js();\n",
" } else {\n",
" load_libs(js_urls, function() {\n",
" console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
" run_inline_js();\n",
" });\n",
" }\n",
" }(this));\n",
"</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p3 = figure(width=900, height=600, title=\"Efficient Frontier Weights (No Short Sale Allowed)\", toolbar_location=\"above\")\n",
"for i, symbol in enumerate(symbols):\n",
" p3.line(weights_ss_false[symbol].index, weights_ss_false[symbol].values, legend=symbol, color=mypalette[i], line_width=2)\n",
"\n",
"p3.legend.location = \"top_left\"\n",
"p3.xaxis.axis_label = 'Risk'\n",
"p3.xaxis.formatter = NumeralTickFormatter(format=\"0.%\")\n",
"p3.yaxis.axis_label = 'Weight'\n",
"p3.yaxis.formatter = NumeralTickFormatter(format=\"0.%\")\n",
"\n",
"show(p3)"
]
}
],
"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": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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