{ "metadata": { "language": "Julia", "name": "", "signature": "sha256:ce095980840a107dc498d7d24e5e775b7fe8e8fc47b967a14c04e608f5bd19f4" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Portfolio Optimization\n", "\n", "In this problem, we will find the portfolio allocation that minimizes risk while achieving a given expected return $R_\\mbox{target}$.\n", "\n", "Suppose that we know the mean returns $R \\in \\mathbf{R}^n$ and the covariance $Q \\in \\mathbf{R}^{n \\times n}$ of the $n$ assets. We would like to find a portfolio allocation $x \\in \\mathbf{R}^n$, $\\sum_i x_i = 1$, minimizing the *risk* of the portfolio, which we measure as the variance $x^T Q x$ of the portfolio. The requirement that the portfolio allocation achieve the target expected return can be expressed as $x^T R >= R_\\mbox{target}$. We suppose further that our portfolio allocation must comply with some lower and upper bounds on the allocation, $x_\\mbox{lower} \\leq x \\leq x_\\mbox{upper}$.\n", "\n", "This problem can be written as\n", "\n", "\\begin{array}{ll}\n", " \\mbox{minimize} & x^T Q x \\\\\n", " \\mbox{subject to} & x^T R >= R_\\mbox{target} \\\\\n", " & \\sum_i x_i = 1 \\\\\n", " & x_\\mbox{lower} \\leq x \\leq x_\\mbox{upper}\n", "\\end{array}\n", "\n", "where $x \\in \\mathbf{R}^n$ is our optimization variable.\n", "\n", "We can solve this problem as follows." ] }, { "cell_type": "code", "collapsed": false, "input": [ "using Convex, ECOS\n", "\n", "# generate problem data\n", "srand(0)\n", "n = 50\n", "R = 5*randn(n)\n", "A = randn(n, 5)\n", "Q = A * A' + diagm(rand(n))\n", "R_target = 5\n", "x_lower = 0\n", "x_upper = 1\n", "\n", "x = Variable(length(R))\n", "p = minimize(quadform(x, Q), \n", " x' * R >= R_target, \n", " sum(x) == 1, \n", " x_lower <= x, \n", " x <= x_upper )\n", "\n", "solve!(p, ECOSSolver(verbose = false)) \n", "\n", "# the minimal risk\n", "p.optval" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "0.025263946889697284" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that we can achieve an extremely low risk portfolio (with variance .025) with the desired expected return. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal portfolio invests in only about half of the assets." ] }, { "cell_type": "code", "collapsed": false, "input": [ "sum(x.value.>1e-4)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "27" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at the optimal portfolio we chose:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(x=1:n,y=x.value,Geom.bar,Guide.xlabel(\"Asset Index\"),Guide.ylabel(\"Fraction of Portfolio\"))" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n" ], "metadata": {}, "output_type": "pyout", "png": 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", 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