{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Robust Mean - Variance Portfolio\n", "\n", "Consider the problem of allocating to allocate a capital over multiple assets to maximize portfolio's expected return, while ensuring a very low probability that the actual return falls below the computed value. This approach addresses the inherent uncertainty in portfolio returns, making it a robust optimization problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the example taken from [1, Section 3.4], we have $n = 200$ assets. Let $r_i$ denote the return, and $\\sigma_i$ denote the standard deviation associated with the $i$-th asset. The last asset represents cash, so we set its return to $r_{n}=1.05$ and standard deviation to $\\sigma_n = 0$. The returns of the remaining assets $r_i$, for $i=1,\\dots, n-1$, are random variables taking values in the intervals $[\\mu_i - \\sigma_i ,\\mu_i + \\sigma_i ]$. The vectors $\\mu$ and $\\sigma$ are defined as\n", "\n", "$$ \\mu_i = 1.05 + \\frac{0.3\\left(n - i\\right)}{n - 1} , \\quad \\sigma_i = 0.05 + \\frac{0.6\\left(n - i\\right)}{n - 1}, \\quad i=1,\\dots,n-1. $$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve this problem, we first import the required packages and generate the data. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import lropt\n", "import cvxpy as cp\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "n = 200\n", "cash_return = 1.05\n", "\n", "#Define mu\n", "mu = np.zeros(n)\n", "mu[-1] = cash_return\n", "for i in range(n - 1):\n", " mu[i] = cash_return + 0.3 * (n - i) / (n- 1) \n", "\n", "#Define sigma\n", "sigma = np.zeros(n)\n", "for i in range(n - 1):\n", " sigma[i] = 0.05 + 0.6 * (n - i) / (n - 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem we want to solve is the uncertain linear optimization problem of the form\n", "$$\\begin{array}{ll}\n", "\\text{maximize} & t \\\\\n", "\\text{subject to} & r^Tx \\geq t \\quad \\forall r \\in \\mathcal{U} \\\\\n", " & 1^T x= 1 \\\\\n", " & x \\geq 0,\n", "\\end{array}$$\n", "where $x_i$ is the normalized capital to be invested in asset $i$, and $r$ is the uncertain vector of returns. We model the uncertain returns as $r_i = \\mu_i + \\sigma_i z_i$ for $i=1,\\dots,n$, where $z = (z_1,\\dots,z_n)$ is a vector of uncertain parameters. In the following snippet, we solve this problem using Ellipsoidal and Budget uncertainty sets of the form:\n", "$$\\begin{array}{ll}\n", "&\\mathcal{U}_{\\rm ellip} = \\{ r = \\mu + {\\bf diag}(\\sigma) z \\mid \\|z\\|_2 \\le \\rho \\}\\\\\n", "&\\mathcal{U}_{\\rm budg} = \\{ r = \\mu + {\\bf diag}(\\sigma) z \\mid \\|z\\|_{\\infty} \\le \\rho,\\; \\|z\\|_{1} \\le \\rho \\},\\\\\n", "\\end{array}\n", "$$\n", "for different values of the set radius $\\rho$.\n" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "names = ['Ellipsoidal', 'Budget']\n", "rho_values = np.linspace(0.1, 2.0, 10) # Range of rho values\n", "\n", "uncertainty_sets = {\n", " 'ellipsoidal': lambda rho: lropt.Ellipsoidal(rho=rho, b=mu, a=np.diag(sigma)),\n", " 'budget': lambda rho: lropt.Budget(rho1=rho, rho2=rho, b=mu, a=np.diag(sigma))\n", "}\n", "\n", "results = {}\n", "for uc_name, uc in uncertainty_sets.items():\n", " \n", " results_uc = []\n", " for rho in rho_values:\n", " t = cp.Variable()\n", " x = cp.Variable(n)\n", " r = lropt.UncertainParameter(n, uncertainty_set=uc(rho))\n", "\n", " constraints = [\n", " r @ x >= t,\n", " cp.sum(x) == 1,\n", " x >= 0\n", " ]\n", "\n", " objective = cp.Maximize(t)\n", " prob = lropt.RobustProblem(objective, constraints)\n", " prob.solve()\n", "\n", " optimal_allocation = x.value\n", " optimal_return = t.value\n", "\n", " # Estimates of covariance and risk based on simplified model\n", " cov_matrix = np.diag(sigma ** 2)\n", " variance = np.dot(optimal_allocation.T, np.dot(cov_matrix, optimal_allocation))\n", " risk = np.sqrt(variance)\n", "\n", " results_uc.append({\n", " 'rho': rho,\n", " 'return': optimal_return,\n", " 'risk': risk\n", " })\n", "\n", " results[uc_name] = pd.DataFrame(results_uc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following code creates a graph of the tradeoff curve of risk and return over a range of values of $\\rho$." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14, 8))\n", "plt.rcParams.update({\"font.size\": 18})\n", "colors = ['tab:red', 'tab:blue']\n", "\n", "for idx, uc in enumerate(uncertainty_sets.keys()):\n", " plt.plot(results[uc]['risk'], results[uc]['return'], color=colors[idx], marker='o', label=uc)\n", "\n", "plt.xlabel('Risk')\n", "plt.ylabel('Return')\n", "plt.legend(title='Uncertainty Set')\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# References\n", "\n", "1. Bertsimas, Dimitris, and Dick Den Hertog. Robust and Adaptive Optimization. [Dynamic Ideas LLC], 2022." ] } ], "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": "3.12.1" } }, "nbformat": 4, "nbformat_minor": 4 }