portfolio optimization using cvxpy notebook

Author: chasilvester

local_optimization/SOCP/portfolio_optimization_using_cvxpy.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "9a8d9072",
+   "metadata": {},
+   "source": [
+    "# Installing the NAG Library and running this notebook\n",
+    "To run this notebook, you will need to install the NAG Library for Python (Mark 29.3 or newer) and a license key. You can find the software and have a license key (trials are available) from our website here: [Getting Started with the NAG Library](https://www.nag.com/content/getting-started-nag-library?lang=py&os=linux)\n",
+    "\n",
+    "We are solving a classic portfolio optimization problem using the NAG Library integration in CVXPY. It can be formulated in the following way:\n",
+    "\n",
+    "\\begin{equation*}\n",
+    "    \\begin{aligned}\n",
+    "        &\\min_{x \\in \\mathbb{R}^n} &&\\frac{1}{2} x^T Q_0 x + r^T_0 x\n",
+    "        \\\\\n",
+    "        &\\textrm{subject to } &&\\frac{1}{2} x^T Q_1 x + r^T_1 x \\leq 0,\n",
+    "        \\\\\n",
+    "        & &&e^Tx = 1,\n",
+    "        \\\\\n",
+    "        & && x \\geq 0,\n",
+    "    \\end{aligned}\n",
+    "\\end{equation*}\n",
+    "where $e$ refers to the vector of all ones."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "dcbfd044",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Import modules\n",
+    "from cvxpy import Minimize, Problem, Variable, quad_form, sum, atoms, OPTIMAL, NAG\n",
+    "import numpy as np\n",
+    "import naginterfaces"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "4d4bec67-2af9-4d14-932c-ac616f223be8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-0.17415932352686342"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Define number of assets\n",
+    "n = 500 \n",
+    "\n",
+    "# Generate random data\n",
+    "np.random.seed(2)\n",
+    "r0 = np.matrix(np.random.randn(n, 1))\n",
+    "r1 = np.matrix(np.random.randn(n, 1))\n",
+    "q0 = np.matrix(np.random.randn(n, n))\n",
+    "q0 = q0.T * q0\n",
+    "q1 = np.matrix(np.random.randn(n, n))\n",
+    "q1 = q1.T * q1\n",
+    "\n",
+    "# Skip psd check due to issues with ARPACK\n",
+    "q0 = atoms.affine.wraps.psd_wrap(q0)\n",
+    "q1 = atoms.affine.wraps.psd_wrap(q1)\n",
+    "\n",
+    "# Create the cvxpy problem:\n",
+    "# Define the variables\n",
+    "x = Variable(len(r1))\n",
+    "\n",
+    "# Define the constraints\n",
+    "constraints = [\n",
+    "               0 <= x, \n",
+    "               sum(x) == 1,\n",
+    "               0.5*quad_form(x, q1) + (r1.T @ x) <= 0]\n",
+    "\n",
+    "# Define the objective function\n",
+    "objective = Minimize(0.5*quad_form(x, q0) + r0.T @ x)\n",
+    "\n",
+    "# Set up dictionary for option setting\n",
+    "nag_params = {'SOCP System Formulation':'AS',\n",
+    "              'SOCP Factorization Method':'MA86'\n",
+    "              }\n",
+    "\n",
+    "# Define the problem\n",
+    "prob = Problem(objective, constraints)\n",
+    "\n",
+    "# Solve the problem using NAG\n",
+    "prob.solve(solver=NAG, nag_params=nag_params)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.10.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}