Ch03b_MV_NoShortSales.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Variance Frontier with Short Sales Constraints\n",
    "\n",
    "This notebook alculates mean variances frontiers for two cases *(1)* when there are no restrictions on the portfolio weights and *(2)* when we impose the restriction that no weights can be negative.\n",
    "\n",
    "We use the package [OSQP.jl](https://github.com/osqp/OSQP.jl) which solves problems of the type:\n",
    "\n",
    "$\\min 0.5\\theta' P \\theta + q' \\theta$ subject to $l \\leq A \\theta \\leq u$.\n",
    "\n",
    "As an alternative, consider the [EfficientFrontier.jl](https://github.com/PharosAbad/EfficientFrontier.jl) package."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Utility Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, LinearAlgebra, SparseArrays, OSQP\n",
    "\n",
    "include(\"src/printmat.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inputs to MV Calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mμ in %:\u001b[22m\u001b[39m\n",
      "A     11.50\n",
      "B      9.50\n",
      "C      6.00\n",
      "\n",
      "\u001b[34m\u001b[1mΣ in bp:\u001b[22m\u001b[39m\n",
      "          A         B         C\n",
      "A    166.00     34.00     58.00\n",
      "B     34.00     64.00      4.00\n",
      "C     58.00      4.00    100.00\n",
      "\n",
      "\u001b[34m\u001b[1mRf in %:\u001b[22m\u001b[39m\n",
      "     3.000\n"
     ]
    }
   ],
   "source": [
    "μ = [11.5, 9.5, 6]/100      #expected returns\n",
    "Σ = [166  34  58;           #covariance matrix\n",
    "      34  64   4;\n",
    "      58   4 100]/100^2\n",
    "Rf = 0.03\n",
    "\n",
    "assetNames = [\"A\",\"B\",\"C\"]\n",
    "printblue(\"μ in %:\")\n",
    "printmat(μ*100;rowNames=assetNames,prec=2)\n",
    "\n",
    "printblue(\"Σ in bp:\")\n",
    "printmat(Σ*10000;rowNames=assetNames,colNames=assetNames,prec=2)\n",
    "\n",
    "printblue(\"Rf in %:\")\n",
    "printlnPs(Rf*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Traditional MV Calculations \n",
    "\n",
    "(when there are no constraints) from the chapter on MV analysis.\n",
    "\n",
    "The file included below contains the function `MVCalc()` from the chapter on MV analysis. It calculates the (MV efficient) portfolio standard deviation for a given required return (`μˣ`), for the case of no restrictions on the portfolio except that the weights sum to one.\n",
    "\n",
    "### A Remark on the Code\n",
    "- `[MVCalc(μˣ,μ,Σ)[1] for μˣ in μˣ_range]` is the same as writing a loop over all values in `μˣ_range` and extracting the first output from `MVCalc()` for each iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"src/MvCalculations.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "μˣ_range = range(0.04,0.15,length=201)\n",
    "\n",
    "StdRₚ  = [MVCalc(μˣ,μ,Σ)[1] for μˣ in μˣ_range]         #MV calculations without portfolio restrictions\n",
    "\n",
    "p1 = plot( StdRₚ*100,μˣ_range*100,\n",
    "           linecolor = :red,\n",
    "           linewidth = 2,\n",
    "           label = \"MVF\",\n",
    "           legend = :topleft,\n",
    "           xlim = (0,15),\n",
    "           ylim = (0,15),\n",
    "           title = \"MVF (no portfolio constraints)\",\n",
    "           xlabel = \"Std(Rₚ), %\",\n",
    "           ylabel = \"ERₚ, %\" )\n",
    "scatter!(sqrt.(diag(Σ))*100,μ*100,color=:red,label=\"assets\")\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MV Frontier when Short Sales are Not Allowed\n",
    "\n",
    "The code below solves the problem \n",
    "\n",
    "$\\min \\text{Var}(R_p) \\: \\text{ s.t. } \\: \\text{E}R_p = \\mu^*$,\n",
    " \n",
    "and where we also require $w_i\\ge 0$ and $\\sum_{i=1}^{n}w_{i}=1$. \n",
    "\n",
    "It is straightforward to add other constraints, for instance, that all weights are between 0 and 0.5.\n",
    "\n",
    "### A Remark on the Code\n",
    "- The function `MeanVarNoSS(μ,Σ,μˣ)` takes a vector `μˣ_range` as input and loops over those `μˣ_range[i]` values that are feasible (must be between the lowest and highest values in $\\mu$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MeanVarNoSS"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    MeanVarNoSS(μ,Σ,μˣ_range_range)\n",
    "\n",
    "Calculate mean variance frontier when short sales are not allowed.\n",
    "\n",
    "\n",
    "# Input\n",
    "- `μ::Vector`:        n vector, mean returns\n",
    "- `Σ::Matrix`:        nxn, covariance matrix of returns, can contain riskfree assets\n",
    "- `μˣ_range::Vector`: K vector, mean returns to calculate results for\n",
    "\n",
    "# Output\n",
    "- `StdRp::Vector`:    K vector, standard deviation of mean-variance portfolio (risky only) with mean `μˣ_range[i]`\n",
    "- `w_p::Matrix`:      Kxn, portfolio weights of       \"\"\n",
    "\n",
    "# Requires\n",
    "- LinearAlgebra, SparseArrays, OSQP\n",
    "\n",
    "\"\"\"\n",
    "function MeanVarNoSS(μ,Σ,μˣ_range)   #MV with no short-sales, numerical minimization\n",
    "\n",
    "    (K,n) = (length(μˣ_range),length(μ))\n",
    "    vv    = findall( minimum(μ) .<= μˣ_range .<= maximum(μ) )  #solve only if feasible\n",
    "\n",
    "    P = sparse(2*Σ)                  #P and A must be sparse\n",
    "    q = zeros(n)\n",
    "    A = sparse([μ';ones(1,n);I])\n",
    "    l = [NaN;1;zeros(n)]\n",
    "    u = [NaN;1;ones(n)]\n",
    "\n",
    "    prob = OSQP.Model()              #initial set up of problem\n",
    "    settings = Dict(:verbose => false)\n",
    "    OSQP.setup!(prob;P=P,q=q,A=A,l=l,u=u,settings...)\n",
    "\n",
    "    (w_p,StdRp) = (fill(NaN,K,n),fill(NaN,K))\n",
    "    for i in vv         #loop over (feasible) μˣ_range elements\n",
    "        (l[1],u[1]) = (μˣ_range[i],μˣ_range[i])\n",
    "        OSQP.update!(prob;l=l,u=u)   #update problem\n",
    "        result = OSQP.solve!(prob)\n",
    "        w = result.info.status == :Solved ? result.x : NaN\n",
    "        if !any(isnan,w)\n",
    "            w_p[i,:] = w\n",
    "            StdRp[i] = sqrt(w'Σ*w)\n",
    "        end\n",
    "    end\n",
    "\n",
    "    return StdRp, w_p\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "StdRₚ_no_ss = MeanVarNoSS(μ,Σ,μˣ_range)[1];    #MV calculations with no short sales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( [StdRₚ StdRₚ_no_ss]*100,μˣ_range*100,\n",
    "           linecolor = [:red :green],\n",
    "           linestyle = [:solid :dash],\n",
    "           linewidth = 2,\n",
    "           label = [\"no constraints\" \"no short sales\"],\n",
    "           xlim = (0,15),\n",
    "           ylim = (0,15),\n",
    "           legend = :topleft,\n",
    "           title  = \"MVF (with/without constraints)\",\n",
    "           xlabel = \"Std(Rₚ), %\",\n",
    "           ylabel = \"ERₚ, %\" )\n",
    "scatter!(sqrt.(diag(Σ))*100,μ*100,color=:red,label=\"assets\")\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.11.1",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}