{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " Loading BokehJS ...\n", "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", "(function(root) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " var force = true;\n", "\n", " if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n", " root._bokeh_onload_callbacks = [];\n", " root._bokeh_is_loading = undefined;\n", " }\n", "\n", " var JS_MIME_TYPE = 'application/javascript';\n", " var HTML_MIME_TYPE = 'text/html';\n", " var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n", " var CLASS_NAME = 'output_bokeh rendered_html';\n", "\n", " /**\n", " * Render data to the DOM node\n", " */\n", " function render(props, node) {\n", " var script = document.createElement(\"script\");\n", " node.appendChild(script);\n", " }\n", "\n", " /**\n", " * Handle when an output is cleared or removed\n", " */\n", " function handleClearOutput(event, handle) {\n", " var cell = handle.cell;\n", "\n", " var id = cell.output_area._bokeh_element_id;\n", " var server_id = cell.output_area._bokeh_server_id;\n", " // Clean up Bokeh references\n", " if (id !== undefined) {\n", " Bokeh.index[id].model.document.clear();\n", " delete Bokeh.index[id];\n", " }\n", "\n", " if (server_id !== undefined) {\n", " // Clean up Bokeh references\n", " var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n", " cell.notebook.kernel.execute(cmd, {\n", " iopub: {\n", " output: function(msg) {\n", " var element_id = msg.content.text.trim();\n", " Bokeh.index[element_id].model.document.clear();\n", " delete Bokeh.index[element_id];\n", " }\n", " }\n", " });\n", " // Destroy server and session\n", " var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n", " cell.notebook.kernel.execute(cmd);\n", " }\n", " }\n", "\n", " /**\n", " * Handle when a new output is added\n", " */\n", " function handleAddOutput(event, handle) {\n", " var output_area = handle.output_area;\n", " var output = handle.output;\n", "\n", " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n", " if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n", " return\n", " }\n", "\n", " var toinsert = output_area.element.find(`.${CLASS_NAME.split(' ')[0]}`);\n", "\n", " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n", " toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n", " // store reference to embed id on output_area\n", " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n", " }\n", " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n", " var bk_div = document.createElement(\"div\");\n", " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n", " var script_attrs = bk_div.children[0].attributes;\n", " for (var i = 0; i < script_attrs.length; i++) {\n", " toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n", " }\n", " // store reference to server id on output_area\n", " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n", " }\n", " }\n", "\n", " function register_renderer(events, OutputArea) {\n", "\n", " function append_mime(data, metadata, element) {\n", " // create a DOM node to render to\n", " var toinsert = this.create_output_subarea(\n", " metadata,\n", " CLASS_NAME,\n", " EXEC_MIME_TYPE\n", " );\n", " this.keyboard_manager.register_events(toinsert);\n", " // Render to node\n", " var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n", " render(props, toinsert[0]);\n", " element.append(toinsert);\n", " return toinsert\n", " }\n", "\n", " /* Handle when an output is cleared or removed */\n", " events.on('clear_output.CodeCell', handleClearOutput);\n", " events.on('delete.Cell', handleClearOutput);\n", "\n", " /* Handle when a new output is added */\n", " events.on('output_added.OutputArea', handleAddOutput);\n", "\n", " /**\n", " * Register the mime type and append_mime function with output_area\n", " */\n", " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n", " /* Is output safe? */\n", " safe: true,\n", " /* Index of renderer in `output_area.display_order` */\n", " index: 0\n", " });\n", " }\n", "\n", " // register the mime type if in Jupyter Notebook environment and previously unregistered\n", " if (root.Jupyter !== undefined) {\n", " var events = require('base/js/events');\n", " var OutputArea = require('notebook/js/outputarea').OutputArea;\n", "\n", " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n", " register_renderer(events, OutputArea);\n", " }\n", " }\n", "\n", " \n", " if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n", " root._bokeh_timeout = Date.now() + 5000;\n", " root._bokeh_failed_load = false;\n", " }\n", "\n", " var NB_LOAD_WARNING = {'data': {'text/html':\n", " \"
\\n\"+\n", " \"

\\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", " \"

\\n\"+\n", " \"\\n\"+\n", " \"\\n\"+\n", " \"from bokeh.resources import INLINE\\n\"+\n", " \"output_notebook(resources=INLINE)\\n\"+\n", " \"\\n\"+\n", " \"
\"}};\n", "\n", " function display_loaded() {\n", " var el = document.getElementById(\"7caf8012-e1db-4332-be5e-7e8b3eb8e9ed\");\n", " if (el != null) {\n", " el.textContent = \"BokehJS is loading...\";\n", " }\n", " if (root.Bokeh !== undefined) {\n", " if (el != null) {\n", " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n", " }\n", " } else if (Date.now() < root._bokeh_timeout) {\n", " setTimeout(display_loaded, 100)\n", " }\n", " }\n", "\n", "\n", " function run_callbacks() {\n", " try {\n", " root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n", " }\n", " finally {\n", " delete root._bokeh_onload_callbacks\n", " }\n", " console.info(\"Bokeh: all callbacks have finished\");\n", " }\n", "\n", " function load_libs(js_urls, callback) {\n", " root._bokeh_onload_callbacks.push(callback);\n", " if (root._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", " root._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", " root._bokeh_is_loading--;\n", " if (root._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(\"7caf8012-e1db-4332-be5e-7e8b3eb8e9ed\");\n", " if (element == null) {\n", " console.log(\"Bokeh: ERROR: autoload.js configured with elementid '7caf8012-e1db-4332-be5e-7e8b3eb8e9ed' but no matching script tag was found. \")\n", " return false;\n", " }\n", "\n", " var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.10.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.10.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.10.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.10.min.js\"];\n", "\n", " var inline_js = [\n", " function(Bokeh) {\n", " Bokeh.set_log_level(\"info\");\n", " },\n", " \n", " function(Bokeh) {\n", " \n", " },\n", " function(Bokeh) {\n", " console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.10.min.css\");\n", " Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.10.min.css\");\n", " console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.10.min.css\");\n", " Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.10.min.css\");\n", " console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.10.min.css\");\n", " Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.10.min.css\");\n", " }\n", " ];\n", "\n", " function run_inline_js() {\n", " \n", " if ((root.Bokeh !== undefined) || (force === true)) {\n", " for (var i = 0; i < inline_js.length; i++) {\n", " inline_js[i].call(root, root.Bokeh);\n", " }if (force === true) {\n", " display_loaded();\n", " }} else if (Date.now() < root._bokeh_timeout) {\n", " setTimeout(run_inline_js, 100);\n", " } else if (!root._bokeh_failed_load) {\n", " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n", " root._bokeh_failed_load = true;\n", " } else if (force !== true) {\n", " var cell = $(document.getElementById(\"7caf8012-e1db-4332-be5e-7e8b3eb8e9ed\")).parents('.cell').data().cell;\n", " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n", " }\n", "\n", " }\n", "\n", " if (root._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", "}(window));" ], "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n var force = true;\n\n if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n var NB_LOAD_WARNING = {'data': {'text/html':\n \"
\\n\"+\n \"

\\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 \"

\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\n\n function display_loaded() {\n var el = document.getElementById(\"7caf8012-e1db-4332-be5e-7e8b3eb8e9ed\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n }\n finally {\n delete root._bokeh_onload_callbacks\n }\n console.info(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(js_urls, callback) {\n root._bokeh_onload_callbacks.push(callback);\n if (root._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 root._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 root._bokeh_is_loading--;\n if (root._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(\"7caf8012-e1db-4332-be5e-7e8b3eb8e9ed\");\n if (element == null) {\n console.log(\"Bokeh: ERROR: autoload.js configured with elementid '7caf8012-e1db-4332-be5e-7e8b3eb8e9ed' but no matching script tag was found. \")\n return false;\n }\n\n var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.10.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.10.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.10.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.10.min.js\"];\n\n var inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n \n function(Bokeh) {\n \n },\n function(Bokeh) {\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.10.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.10.min.css\");\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.10.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.10.min.css\");\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.10.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.10.min.css\");\n }\n ];\n\n function run_inline_js() {\n \n if ((root.Bokeh !== undefined) || (force === true)) {\n for (var i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n var cell = $(document.getElementById(\"7caf8012-e1db-4332-be5e-7e8b3eb8e9ed\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._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}(window));" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "from bokeh.io import output_notebook\n", "from bokeh.plotting import figure, show\n", "import scipy.optimize as sco\n", "output_notebook()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 基本分散投資はマーコビッツの平均分散モデルが使われます。\n", "* 各資産の収益率、リスク、相関、共分散を使い、各資産にどのように投資したらどのようなリスクリターンの運用になるかを作ります。 \n", "* 1952年に発表された古い理論です。まぁ単純で簡単に作れるから使われているのだろう。\n", "* 難点 リターンの予想が難しいが、そのリターン予想にポートフォリオの決定が大きく影響される。\n", "* Scipyで2次計画問題を解く \n", "https://qiita.com/ryoshi81/items/b323a363e5442a15db6d \n", "* 最近の理論になるとブラック・リッターマンとかリスクパリティとかあります。 \n", " \n", "### ブラックリッターマン\n", "* qiitaの記事 https://qiita.com/nokomitch/items/0d1812763114e6266bf3 \n", "* サイト　　http://www.blacklitterman.org/ \n", "* なんかすげーみたいな評価がされていますが、色々パラメーター決めるの難しそう。\n", " \n", "### リスクパリティ \n", "* 今までのやり方は結局リスクが大きい商品のポートフォリオへの影響が大きい。\n", "* 資産のリスクはあまり変化しない。\n", "* 各資産のリスクを同一にする。\n", "* そうすると基本債券のウェイトが高くなり、リターンが下がるがその分、レバレッジを掛ける。\n", "* 世界最大のヘッジファンド:ブリッジウォーターが提唱したやり方で、徐々に取り入れられ始めているのではないか？\n", "* しかし、現在債券バブルと言われる環境下にあるので、それほどおすすめでない。\n", "* Bridgewater /Research_Library/Risk_parity: https://www.bridgewater.com/research-library/risk-parity/ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## さて進めましょう！\n", "* 今回はロボアドバイザー大手のウェルスナビのモデルを使います。 \n", "https://www.wealthnavi.com/image/WealthNavi_WhitePaper.pdf \n", "* リターンの推測にはブラック・リターマンが使われている。 \n", "* 上記のPDFにウェルスナビの考えるリスクリターンと相関が掲載されています。\n", "* 資産クラスは米国株、欧日株、新興株、米国債券、物価連動債、金、不動産の7資産となっています。" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rtns = np.array([0.065, 0.075, 0.085, 0.019, 0.023, 0.039, 0.058]) # 収益率（年率）\n", "rsks = np.array([0.124, 0.148, 0.184, 0.028, 0.048, 0.179, 0.149]) # リスク（年率）\n", "corrs = np.array([\n", " [1.0, 0.9, 0.8, -0.1, 0, 0, 0.7],\n", " [0.9, 1.0, 0.8, -0.1, 0.1, 0.1, 0.6],\n", " [0.8, 0.8, 1.0, 0.1, 0.2, 0.3, 0.6],\n", " [-0.1, -0.1, 0.1, 1.0, 0.8, 0.4, 0.4],\n", " [0, 0.1, 0.2, 0.8, 1.0, 0.5, 0.4],\n", " [0, 0.1, 0.3, 0.4, 0.4, 1.0, 0.1],\n", " [0.7, 0.6, 0.6, 0.4, 0.4, 0.1, 1.0]\n", "]) # 相関" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", "
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figure(width= 800, height = 500, title='各資産のリスクリターン')\n", "p.cross(rsks, rtns, size=20)\n", "p.xaxis.axis_label='リスク'\n", "p.yaxis.axis_label='リターン'\n", "show(p)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# 相関行列と標準偏差から共分散行列を作成\n", "# 相関係数(x, y) = 共分散 / (標準偏差(x) * 標準偏差(y) )\n", "# 共分散 = 相関係数(x, y) * (標準偏差(x) * 標準偏差(y))\n", "# これを作る部分が難しい。なんか簡単な方法ないのかなぁ。\n", "\n", "a1 = []\n", "a2 = []\n", "a3 = []\n", "a4 = []\n", "a5 = []\n", "a6 = []\n", "a7 = []\n", "\n", "def testi(r = 0.065, box = a1, volls = rsks):\n", " for i in range(len(rsks)):\n", " box.append(np.dot(r ,rsks[i]))\n", " return np.array(box)\n", "\n", "b1 = testi()\n", "b2 = testi(r = rsks[1], box = a2)\n", "b3 = testi(r = rsks[2], box = a3)\n", "b4 = testi(r = rsks[3], box = a4)\n", "b5 = testi(r = rsks[4], box = a5)\n", "b6 = testi(r = rsks[5], box = a6)\n", "b7 = testi(r = rsks[6], box = a7)\n", "\n", "SIgma = [b1 * np.array(corrs[0]), b2 * np.array(corrs[1]), b3 * np.array(corrs[2]), \\\n", " b4 * np.array(corrs[3]), b5 * np.array(corrs[4]), b6 * np.array(corrs[5]), b7 * np.array(corrs[6])]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 以上で各資産のリスクリターン共分散を作成しました。\n", "## 以下ではscipy.optimize.minimize()を解くための引数などを作ります。\n", "* 目的関数、初期解、ソルバー、資産配分の上下制約、制約条件が必要です。" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# 目的関数\n", "def min_func_var(weights):\n", " return np.dot(weights.T, np.dot(SIgma, weights))\n", "\n", "# 初期解\n", "x0 = [1.0 / len(rtns)] * len(rtns)\n", "\n", "# 目標リターン（各資産の最高、最低で作る。レバレッジを掛けない限り採用資産のリターンの最高がポートフォリオのリターンの上限となる）\n", "\n", "max_ret = rtns.max()\n", "min_ret = rtns.min()\n", "trets = np.linspace(min_ret, max_ret, 100)\n", "\n", "# 投資比率制限（空売りを出来なくする）\n", "bnds = [(0, None)] * len(rtns)\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "tvols = []\n", "\n", "for tret in trets:\n", " cons = [{'type': 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figure(width = 800, height=500, title='ポートフォリオのリスクリターン')\n", "p.line(tvols, trets, line_color='blue', line_width=3)\n", "p.cross(rsks, rtns, size = 20)\n", "p.xaxis.axis_label='ポートフォリオのリスク'\n", "p.yaxis.axis_label = 'ポートフォリオのリターン' \n", "show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 資産にちょっと変更を加えてみる\n", "* 投資の基本として資産間の相関の低いものを入れるとポートフォリオのリターンが向上すると言うものがあります。\n", "* 分散投資とよく言われますが、よく似た動きの商品を沢山購入しても実は意味がありません。\n", "* ここではもしもの話として米株、欧日株、新興株の相関が低下したとしてのポートフォリオの見てみます。" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "corrs2 = np.array([\n", " [1.0, 0.2, 0.1, -0.1, 0, 0, 0.7],\n", " [0.2, 1.0, 0.1, -0.1, 0.1, 0.1, 0.6],\n", " [0.1, 0.1, 1.0, 0.1, 0.2, 0.3, 0.6],\n", " [-0.1, -0.1, 0.1, 1.0, 0.8, 0.4, 0.4],\n", " [0, 0.1, 0.2, 0.8, 1.0, 0.5, 0.4],\n", " [0, 0.1, 0.3, 0.4, 0.4, 1.0, 0.1],\n", " [0.7, 0.6, 0.6, 0.4, 0.4, 0.1, 1.0]\n", "])\n", "\n", "# 最初の\n", "corrs = np.array([\n", " [1.0, 0.9, 0.8, -0.1, 0, 0, 0.7],\n", " [0.9, 1.0, 0.8, -0.1, 0.1, 0.1, 0.6],\n", " [0.8, 0.8, 1.0, 0.1, 0.2, 0.3, 0.6],\n", " [-0.1, -0.1, 0.1, 1.0, 0.8, 0.4, 0.4],\n", " [0, 0.1, 0.2, 0.8, 1.0, 0.5, 0.4],\n", " [0, 0.1, 0.3, 0.4, 0.4, 1.0, 0.1],\n", " [0.7, 0.6, 0.6, 0.4, 0.4, 0.1, 1.0]\n", "]) # 相関" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "c1 = []\n", "c2 = []\n", "c3 = []\n", "c4 = []\n", "c5 = []\n", "c6 = []\n", "c7 = []\n", "\n", "d1 = testi(r = rsks[0], box = c1)\n", "d2 = testi(r = rsks[1], box = c2)\n", "d3 = testi(r = rsks[2], box = c3)\n", "d4 = testi(r = rsks[3], box = c4)\n", "d5 = testi(r = rsks[4], box = c5)\n", "d6 = testi(r = rsks[5], box = c6)\n", "d7 = testi(r = rsks[6], box = c7)\n", "\n", "SIgma2 = [d1*np.array(corrs2[0]), d2*np.array(corrs2[1]), d3*np.array(corrs2[2]), d4*np.array(corrs2[3]), \\\n", " d5*np.array(corrs2[4]), d6*np.array(corrs2[5]), d7*np.array(corrs2[6])]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[array([ 0.015376 , 0.0036704, 0.0022816, -0.0003472, 0. ,\n", " 0. , 0.0129332]),\n", " array([ 0.0036704, 0.021904 , 0.0027232, -0.0004144, 0.0007104,\n", " 0.0026492, 0.0132312]),\n", " array([ 0.0022816, 0.0027232, 0.033856 , 0.0005152, 0.0017664,\n", " 0.0098808, 0.0164496]),\n", " array([-0.0003472, -0.0004144, 0.0005152, 0.000784 , 0.0010752,\n", " 0.0020048, 0.0016688]),\n", " array([ 0. , 0.0007104, 0.0017664, 0.0010752, 0.002304 ,\n", " 0.004296 , 0.0028608]),\n", " array([ 0. , 0.0026492, 0.0098808, 0.0020048, 0.0034368,\n", " 0.032041 , 0.0026671]),\n", " array([ 0.0129332, 0.0132312, 0.0164496, 0.0016688, 0.0028608,\n", " 0.0026671, 0.022201 ])]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "SIgma2" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def min_func_var2(weights):\n", " return np.dot(weights.T, np.dot(SIgma2, weights))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "tvols2 = []\n", "\n", "for tret in trets:\n", " cons = [{'type': 'eq', 'fun': lambda x: np.sum(x) - 1},\n", " {'type': 'ineq', 'fun': lambda x: np.sum(rtns * x) - tret}]\n", " res = sco.minimize(fun=min_func_var2, x0 = x0, method = 'SLSQP', bounds = bnds, constraints = cons)\n", " tvols2.append((np.sqrt(res['fun'])))\n", "\n", "tvols2 = np.array(tvols2) " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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figure(width=800, height = 500, title='ポートフォリオのリスクリターン')\n", "p.line(tvols, trets, line_color='blue', line_width=3, legend='高相関')\n", "p.line(tvols2, trets, line_color='red', line_width=3, legend='低相関')\n", "p.cross(rsks, rtns, size=20)\n", "\n", "p.xaxis.axis_label ='ポートフォリオのリスク'\n", "p.yaxis.axis_label = 'ポートフォリオのリターン'\n", "p.legend.location = 'top_left'\n", "show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }