Update ch9 Markovitz portfolio notebook

notebooks/09/02-markowitz-portfolio-with-chance-constraint.ipynb

@@ -108,7 +108,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "id": "0e194e8d",
    "metadata": {
     "tags": []
@@ -118,49 +118,33 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Solver status: ok, optimal\n",
-      "Solution:"
-     ]
-    },
-    {
-     "data": {
-      "text/markdown": [
-       "$\\tilde x = -0.000$, $x_1 = 0.667$,  $x_2 = 0.255$,  $x_3 = 0.078$"
-      ],
-      "text/plain": [
-       "<IPython.core.display.Markdown object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
+      "Solver status: ok, Termination condition: optimal\n",
+      "Solution: xtilde = 0.070, x_1 = 0.620, x_2 = 0.239, x_3 = 0.071\n",
       "Maximum objective value: 1.23\n"
      ]
     }
    ],
    "source": [
-    "# set our risk threshold and risk levels (sometimes you may get an infeasible problem if the chance\n",
-    "# constraint becomes too tight!)\n",
+    "# set our risk threshold and risk levels (sometimes you may get an infeasible\n",
+    "# problem if the chance constraint becomes too tight!)\n",
     "alpha = 0.6\n",
     "beta = 0.3\n",
     "\n",
-    "# specify the initial capital, the risk-free return the number of risky assets, their expected returns, and their covariance matrix.\n",
+    "# specify the initial capital, the risk-free return the number of risky assets,\n",
+    "# their expected returns, and their covariance matrix.\n",
     "C = 1\n",
-    "R = 1.05\n",
+    "R = 1.25\n",
     "n = 3\n",
     "mu = np.array([1.25, 1.15, 1.35])\n",
     "Sigma = np.array([[1.5, 0.5, 2], [0.5, 2, 0], [2, 0, 5]])\n",
     "\n",
-    "# Check how dramatically the optimal solution changes if we assume i.i.d. deviations for the returns.\n",
-    "# Sigma = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n",
+    "# Check how dramatically the optimal solution changes if we assume i.i.d.\n",
+    "# deviations for the returns. # Sigma = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n",
     "\n",
     "# To change covariance matrix, make sure you input a semi-definite positive one.\n",
-    "# The easiest way to generate a random covariance matrix is first generating a random m x m matrix A\n",
-    "# and then taking the matrix A^T A (which is always semi-definite positive)\n",
+    "# The easiest way to generate a random covariance matrix is first generating\n",
+    "# a random m x m matrix A and then taking the matrix A^T A (which is always\n",
+    "# semi-definite positive)\n",
     "# m = 3\n",
     "# A = np.random.rand(m, m)\n",
     "# Sigma = A.T @ A\n",
@@ -174,7 +158,7 @@
     "\n",
     "    @model.Objective(sense=pyo.maximize)\n",
     "    def objective(m):\n",
-    "        return mu @ m.x\n",
+    "        return mu @ m.x + R * m.xtilde\n",
     "\n",
     "    @model.Constraint()\n",
     "    def chance_constraint(m):\n",
@@ -191,12 +175,12 @@
     "model = markowitz_chanceconstraints(alpha, beta, mu, Sigma)\n",
     "result = SOLVER.solve(model)\n",
     "\n",
-    "print(f\"Solver status: {result.solver.status}, {result.solver.termination_condition}\")\n",
-    "print(f\"Solution:\", end=\"\")\n",
-    "display(\n",
-    "    Markdown(\n",
-    "        f\"$\\\\tilde x = {model.xtilde.value:.3f}$, $x_1 = {model.x[0].value:.3f}$,  $x_2 = {model.x[1].value:.3f}$,  $x_3 = {model.x[2].value:.3f}$\"\n",
-    "    )\n",
+    "print(\n",
+    "    f\"Solver status: {result.solver.status}, Termination condition: {result.solver.termination_condition}\"\n",
+    ")\n",
+    "print(f\"Solution: \", end=\"\")\n",
+    "print(\n",
+    "    f\"xtilde = {model.xtilde.value:.3f}, x_1 = {model.x[0].value:.3f}, x_2 = {model.x[1].value:.3f}, x_3 = {model.x[2].value:.3f}\"\n",
     ")\n",
     "print(f\"Maximum objective value: {model.objective():.2f}\")"
    ]