tutorial/318_portfolio_en.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "tutorial019_portfolio_optimization_en",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "vUO0DrZ2gpJR",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#Portfolio Optimization\n",
        "Portfolio optimization is a simple optimization problem using the existing financial data. We find out the best combination of assets by calculating the return and risk.\n"
      ]
    },
    {
      "metadata": {
        "id": "AFLU6xz-hItB",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "##Cost Function\n",
        "To solve portfolio optimization we have the cost function like below.\n",
        "\n",
        "<img src=\"https://render.githubusercontent.com/render/math?math=E%20%3D%20-%5Csum%5Cmu_ix_i%20%2B%20%5Cgamma%5Csum%5Cdelta_%7Bij%7Dx_ix_j%2BB%5Cleft(%5Csum%20x_i-K%5Cright)%5E2\">\n",
        "\n",
        "The 1st term shows the return of the assets and the 2nd as risk we estimate. The 3rd term is the constaint for the number of assets how many assets we select.\n",
        "\n",
        "##Example\n",
        "Now we have an example. Choose 2 assets from 6 possibility.\n",
        "Here we use dummy data on return and risk.\n",
        "\n",
        "As a return data we use,\n",
        "\n",
        "<img src=\"https://github.com/mdrft/Wildqat/blob/master/examples_ja/img/019_0.png?raw=1\">\n",
        "\n",
        "As a risk data we use,\n",
        "\n",
        "<img src=\"https://github.com/mdrft/Wildqat/blob/master/examples_ja/img/019_1.png?raw=1\">\n",
        "\n",
        "First we prepare blueqat and numpy"
      ]
    },
    {
      "metadata": {
        "id": "bM_eRNMFOkm_",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "!pip install -U blueqat"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "WPbJZpMui8Pw",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import blueqat.opt as wq\n",
        "import numpy as np\n",
        "a = wq.opt()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "meI9n8WJjAyS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "First let's think about return. Put return data into the diagonal of the matrix."
      ]
    },
    {
      "metadata": {
        "id": "9XOZ4TFhjHpM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "c5548de4-d1fd-48e6-b50d-ccf86be81e39"
      },
      "cell_type": "code",
      "source": [
        "ret = wq.diag([-0.026,-0.031,-0.007,-0.022,-0.010,-0.055])\n",
        "print(ret)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.026  0.     0.     0.     0.     0.   ]\n",
            " [ 0.    -0.031  0.     0.     0.     0.   ]\n",
            " [ 0.     0.    -0.007  0.     0.     0.   ]\n",
            " [ 0.     0.     0.    -0.022  0.     0.   ]\n",
            " [ 0.     0.     0.     0.    -0.01   0.   ]\n",
            " [ 0.     0.     0.     0.     0.    -0.055]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "uGC6JKYEjb-s",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Next we think about risk."
      ]
    },
    {
      "metadata": {
        "id": "If-m1F_CjHdy",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "ris = [[0,0.0015,0.0012,0.0018,0.0022,0.0012],[0,0,0.0017,0.0022,0.0005,0.0019],[0,0,0,0.0040,0.0032,0.0024],[0,0,0,0,0.0012,0.0076],[0,0,0,0,0,0.0021],[0,0,0,0,0,0]]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "l5OIEJTyleV6",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "By adding these 2 matrix, we get the final QUBO to calculate."
      ]
    },
    {
      "metadata": {
        "id": "lUudk7iclRyf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "92bd4ae1-27d5-462e-e6c1-15042dd92a1c"
      },
      "cell_type": "code",
      "source": [
        "a.qubo = ret + np.asarray(ris)*0.5\n",
        "print(a.qubo)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.026    0.00075  0.0006   0.0009   0.0011   0.0006 ]\n",
            " [ 0.      -0.031    0.00085  0.0011   0.00025  0.00095]\n",
            " [ 0.       0.      -0.007    0.002    0.0016   0.0012 ]\n",
            " [ 0.       0.       0.      -0.022    0.0006   0.0038 ]\n",
            " [ 0.       0.       0.       0.      -0.01     0.00105]\n",
            " [ 0.       0.       0.       0.       0.      -0.055  ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "I5bMskkhl3Pg",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#Constraint for K assets.\n",
        "Finally we need one more term to make a constraint on the number of assets we choose.\n",
        "Here we try a simple function which blueqat provide, sel() function to choose 2 from 6."
      ]
    },
    {
      "metadata": {
        "id": "Sz1vh59SlStJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "67bd87e3-6e98-462f-a491-b85e602653f0"
      },
      "cell_type": "code",
      "source": [
        "a.qubo += wq.sel(6,2)\n",
        "print(a.qubo)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-3.026    2.00075  2.0006   2.0009   2.0011   2.0006 ]\n",
            " [ 0.      -3.031    2.00085  2.0011   2.00025  2.00095]\n",
            " [ 0.       0.      -3.007    2.002    2.0016   2.0012 ]\n",
            " [ 0.       0.       0.      -3.022    2.0006   2.0038 ]\n",
            " [ 0.       0.       0.       0.      -3.01     2.00105]\n",
            " [ 0.       0.       0.       0.       0.      -3.055  ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "CdPmcVcVmShE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "44aaa1ce-c947-4d11-b4b1-863afa858c75"
      },
      "cell_type": "code",
      "source": [
        "print(a.sa())\n",
        "print(a.E[-1])"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.5345256328582764\n",
            "[0, 0, 1, 0, 0, 1]\n",
            "-4.060799999999999\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "KEij7FQFmhzY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Finally we get result just 2 assets have value 1 and others has 0.\n",
        "The assets which has value 1 were selected.\n",
        "\n",
        "We can also check the time evolution of cost function."
      ]
    },
    {
      "metadata": {
        "id": "4cxwz5UCmZkc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "outputId": "397d64c2-7603-494e-8b25-eb8a8c751607"
      },
      "cell_type": "code",
      "source": [
        "a.plot()"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAFKCAYAAAAnj5dkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmRBCCAkZ/z8j/IAOOmVVOAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "EIfyRtAeP8Ck",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}