black_litterman.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "black_litterman.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOg2YJjka8tSaYYoxR/h7i/",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/tylee33/DLforFinance/blob/master/black_litterman.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sABuL6W1COJ_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "3c7ad41d-27dc-4751-c45c-8cf5d4e77064"
      },
      "source": [
        "%pylab\n",
        "%matplotlib inline\n",
        "pylab.rcParams['figure.figsize'] = (10, 6)\n",
        "import scipy.optimize\n",
        "from pandas import *"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using matplotlib backend: agg\n",
            "Populating the interactive namespace from numpy and matplotlib\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B0R_F0eRCuFO",
        "colab_type": "text"
      },
      "source": [
        "**Few helper functions**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-A5pieQ9Cwev",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Calculates portfolio mean return\n",
        "def port_mean(W, R):\n",
        "    return sum(R * W)\n",
        "\n",
        "# Calculates portfolio variance of returns\n",
        "def port_var(W, C):\n",
        "    return dot(dot(W, C), W)\n",
        "\n",
        "# Combination of the two functions above - mean and variance of returns calculation\n",
        "def port_mean_var(W, R, C):\n",
        "    return port_mean(W, R), port_var(W, C)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KCoWmbf_C1EW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Given risk-free rate, assets returns and covariances, this function calculates\n",
        "# mean-variance frontier and returns its [x,y] points in two arrays\n",
        "def solve_frontier(R, C, rf):\n",
        "    def fitness(W, R, C, r):\n",
        "        # For given level of return r, find weights which minimizes portfolio variance.\n",
        "        mean, var = port_mean_var(W, R, C)\n",
        "        penalty = 100 * abs(\n",
        "            mean - r)  # Big penalty for not meeting stated portfolio return effectively serves as optimization constraint\n",
        "        return var + penalty\n",
        "\n",
        "    frontier_mean, frontier_var = [], []\n",
        "    n = len(R)  # Number of assets in the portfolio\n",
        "    for r in linspace(min(R), max(R), num=20):  # Iterate through the range of returns on Y axis\n",
        "        W = ones([n]) / n  # start optimization with equal weights\n",
        "        b_ = [(0, 1) for i in range(n)]\n",
        "        c_ = ({'type': 'eq', 'fun': lambda W: sum(W) - 1.})\n",
        "        optimized = scipy.optimize.minimize(fitness, W, (R, C, r), method='SLSQP', constraints=c_, bounds=b_)\n",
        "        if not optimized.success:\n",
        "            raise BaseException(optimized.message)\n",
        "        # add point to the efficient frontier [x,y] = [optimized.x, r]\n",
        "        frontier_mean.append(r)\n",
        "        frontier_var.append(port_var(optimized.x, C))\n",
        "    return array(frontier_mean), array(frontier_var)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e1MPMJyZC4BN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Given risk-free rate, assets returns and covariances, this function calculates\n",
        "# weights of tangency portfolio with respect to sharpe ratio maximization\n",
        "def solve_weights(R, C, rf):\n",
        "    def fitness(W, R, C, rf):\n",
        "        mean, var = port_mean_var(W, R, C)  # calculate mean/variance of the portfolio\n",
        "        util = (mean - rf) / sqrt(var)  # utility = Sharpe ratio\n",
        "        return 1 / util  # maximize the utility, minimize its inverse value\n",
        "    n = len(R)\n",
        "    W = ones([n]) / n  # start optimization with equal weights\n",
        "    b_ = [(0., 1.) for i in range(n)]  # weights for boundaries between 0%..100%. No leverage, no shorting\n",
        "    c_ = ({'type': 'eq', 'fun': lambda W: sum(W) - 1.})  # Sum of weights must be 100%\n",
        "    optimized = scipy.optimize.minimize(fitness, W, (R, C, rf), method='SLSQP', constraints=c_, bounds=b_)\n",
        "    if not optimized.success: raise BaseException(optimized.message)\n",
        "    return optimized.x"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "64Zl6mv2C6y1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Result:\n",
        "    def __init__(self, W, tan_mean, tan_var, front_mean, front_var):\n",
        "        self.W=W\n",
        "        self.tan_mean=tan_mean\n",
        "        self.tan_var=tan_var\n",
        "        self.front_mean=front_mean\n",
        "        self.front_var=front_var\n",
        "        \n",
        "def optimize_frontier(R, C, rf):\n",
        "    W = solve_weights(R, C, rf)\n",
        "    tan_mean, tan_var = port_mean_var(W, R, C)  # calculate tangency portfolio\n",
        "    front_mean, front_var = solve_frontier(R, C, rf)  # calculate efficient frontier\n",
        "    # Weights, Tangency portfolio asset means and variances, Efficient frontier means and variances\n",
        "    return Result(W, tan_mean, tan_var, front_mean, front_var)\n",
        "\n",
        "def display_assets(names, R, C, color='black'):\n",
        "    scatter([C[i, i] ** .5 for i in range(n)], R, marker='x', color=color), grid(True)  # draw assets\n",
        "    for i in range(n): \n",
        "        text(C[i, i] ** .5, R[i], '  %s' % names[i], verticalalignment='center', color=color) # draw labels\n",
        "\n",
        "def display_frontier(result, label=None, color='black'):\n",
        "    text(result.tan_var ** .5, result.tan_mean, '   tangent', verticalalignment='center', color=color)\n",
        "    scatter(result.tan_var ** .5, result.tan_mean, marker='o', color=color), grid(True)\n",
        "    plot(result.front_var ** .5, result.front_mean, label=label, color=color), grid(True)  # draw efficient frontier"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-fy5SgLoC9Ud",
        "colab_type": "text"
      },
      "source": [
        "**Load historical prices**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5HtgrujXC_5G",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Function loads historical stock prices of nine major S&P companies and returns them together\n",
        "# with their market capitalizations, as of 2013-07-01\n",
        "def load_data():\n",
        "    symbols = ['XOM', 'AAPL', 'MSFT', 'JNJ', 'GE', 'GOOG', 'CVX', 'PG', 'WFC']\n",
        "    cap = {'XOM': 403.02e9, 'AAPL': 392.90e9, 'MSFT': 283.60e9, 'JNJ': 243.17e9, 'GE': 236.79e9,\n",
        "           'GOOG': 292.72e9, 'CVX': 231.03e9, 'PG': 214.99e9, 'WFC': 218.79e9}\n",
        "    n = len(symbols)\n",
        "    prices_out, caps_out = [], []\n",
        "    for s in symbols:\n",
        "        dataframe = pandas.read_csv('data/%s.csv' % s, index_col=None, parse_dates=['date'])\n",
        "        prices = list(dataframe['close'])[-500:] # trailing window 500 days\n",
        "        prices_out.append(prices)\n",
        "        caps_out.append(cap[s])\n",
        "    return symbols, prices_out, caps_out\n",
        "\n",
        "names, prices, caps = load_data()\n",
        "n = len(names)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2IZb17tyDCBu",
        "colab_type": "text"
      },
      "source": [
        "**Estimate assets historical return and covariances**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5_Mk9rYcEXHM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Function takes historical stock prices together with market capitalizations and\n",
        "# calculates weights, historical returns and historical covariances\n",
        "def assets_historical_returns_and_covariances(prices):\n",
        "    prices = matrix(prices)  # create numpy matrix from prices\n",
        "    # create matrix of historical returns\n",
        "    rows, cols = prices.shape\n",
        "    returns = empty([rows, cols - 1])\n",
        "    for r in range(rows):\n",
        "        for c in range(cols - 1):\n",
        "            p0, p1 = prices[r, c], prices[r, c + 1]\n",
        "            returns[r, c] = (p1 / p0) - 1\n",
        "    # calculate returns\n",
        "    expreturns = array([])\n",
        "    for r in range(rows):\n",
        "        expreturns = append(expreturns, numpy.mean(returns[r]))\n",
        "    # calculate covariances\n",
        "    covars = cov(returns)\n",
        "    expreturns = (1 + expreturns) ** 250 - 1  # Annualize returns\n",
        "    covars = covars * 250  # Annualize covariances\n",
        "    return expreturns, covars\n",
        "\n",
        "W = array(caps) / sum(caps) # calculate market weights from capitalizations\n",
        "R, C = assets_historical_returns_and_covariances(prices)\n",
        "rf = .015  # Risk-free rate"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XhsRlMSMEZzb",
        "colab_type": "text"
      },
      "source": [
        "**Asset returns and weights**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cvBoRCUDEcnk",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 128
        },
        "outputId": "2c82dd2d-10d5-4d26-df19-1c00ff29d2a0"
      },
      "source": [
        "display(pandas.DataFrame({'Return': R, 'Weight (based on market cap)': W}, index=names).T)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>XOM</th>\n",
              "      <th>AAPL</th>\n",
              "      <th>MSFT</th>\n",
              "      <th>JNJ</th>\n",
              "      <th>GE</th>\n",
              "      <th>GOOG</th>\n",
              "      <th>CVX</th>\n",
              "      <th>PG</th>\n",
              "      <th>WFC</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Return</th>\n",
              "      <td>0.072993</td>\n",
              "      <td>0.129536</td>\n",
              "      <td>0.172047</td>\n",
              "      <td>0.143764</td>\n",
              "      <td>0.140385</td>\n",
              "      <td>0.331958</td>\n",
              "      <td>0.092131</td>\n",
              "      <td>0.112222</td>\n",
              "      <td>0.268935</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Weight (based on market cap)</th>\n",
              "      <td>0.160119</td>\n",
              "      <td>0.156098</td>\n",
              "      <td>0.112673</td>\n",
              "      <td>0.096611</td>\n",
              "      <td>0.094076</td>\n",
              "      <td>0.116297</td>\n",
              "      <td>0.091787</td>\n",
              "      <td>0.085415</td>\n",
              "      <td>0.086925</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                                   XOM      AAPL  ...        PG       WFC\n",
              "Return                        0.072993  0.129536  ...  0.112222  0.268935\n",
              "Weight (based on market cap)  0.160119  0.156098  ...  0.085415  0.086925\n",
              "\n",
              "[2 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nsqA9X9VEgNj",
        "colab_type": "text"
      },
      "source": [
        "**Asset covariances**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gga5ujQNEiuo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 328
        },
        "outputId": "099b4294-d015-4e08-ee43-bccc946eacfb"
      },
      "source": [
        "display(pandas.DataFrame(C, columns=names, index=names))"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>XOM</th>\n",
              "      <th>AAPL</th>\n",
              "      <th>MSFT</th>\n",
              "      <th>JNJ</th>\n",
              "      <th>GE</th>\n",
              "      <th>GOOG</th>\n",
              "      <th>CVX</th>\n",
              "      <th>PG</th>\n",
              "      <th>WFC</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>XOM</th>\n",
              "      <td>0.039015</td>\n",
              "      <td>0.022296</td>\n",
              "      <td>0.027982</td>\n",
              "      <td>0.019595</td>\n",
              "      <td>0.036647</td>\n",
              "      <td>0.026728</td>\n",
              "      <td>0.038245</td>\n",
              "      <td>0.018216</td>\n",
              "      <td>0.042972</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AAPL</th>\n",
              "      <td>0.022296</td>\n",
              "      <td>0.091844</td>\n",
              "      <td>0.024599</td>\n",
              "      <td>0.011578</td>\n",
              "      <td>0.027814</td>\n",
              "      <td>0.033249</td>\n",
              "      <td>0.028240</td>\n",
              "      <td>0.011532</td>\n",
              "      <td>0.036756</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>MSFT</th>\n",
              "      <td>0.027982</td>\n",
              "      <td>0.024599</td>\n",
              "      <td>0.051014</td>\n",
              "      <td>0.016842</td>\n",
              "      <td>0.032649</td>\n",
              "      <td>0.026231</td>\n",
              "      <td>0.030815</td>\n",
              "      <td>0.013724</td>\n",
              "      <td>0.040321</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>JNJ</th>\n",
              "      <td>0.019595</td>\n",
              "      <td>0.011578</td>\n",
              "      <td>0.016842</td>\n",
              "      <td>0.019456</td>\n",
              "      <td>0.021048</td>\n",
              "      <td>0.015547</td>\n",
              "      <td>0.021005</td>\n",
              "      <td>0.013196</td>\n",
              "      <td>0.026861</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GE</th>\n",
              "      <td>0.036647</td>\n",
              "      <td>0.027814</td>\n",
              "      <td>0.032649</td>\n",
              "      <td>0.021048</td>\n",
              "      <td>0.059233</td>\n",
              "      <td>0.031083</td>\n",
              "      <td>0.040677</td>\n",
              "      <td>0.019377</td>\n",
              "      <td>0.053928</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GOOG</th>\n",
              "      <td>0.026728</td>\n",
              "      <td>0.033249</td>\n",
              "      <td>0.026231</td>\n",
              "      <td>0.015547</td>\n",
              "      <td>0.031083</td>\n",
              "      <td>0.066899</td>\n",
              "      <td>0.030258</td>\n",
              "      <td>0.015123</td>\n",
              "      <td>0.039019</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>CVX</th>\n",
              "      <td>0.038245</td>\n",
              "      <td>0.028240</td>\n",
              "      <td>0.030815</td>\n",
              "      <td>0.021005</td>\n",
              "      <td>0.040677</td>\n",
              "      <td>0.030258</td>\n",
              "      <td>0.050857</td>\n",
              "      <td>0.019587</td>\n",
              "      <td>0.048326</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>PG</th>\n",
              "      <td>0.018216</td>\n",
              "      <td>0.011532</td>\n",
              "      <td>0.013724</td>\n",
              "      <td>0.013196</td>\n",
              "      <td>0.019377</td>\n",
              "      <td>0.015123</td>\n",
              "      <td>0.019587</td>\n",
              "      <td>0.025152</td>\n",
              "      <td>0.022479</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>WFC</th>\n",
              "      <td>0.042972</td>\n",
              "      <td>0.036756</td>\n",
              "      <td>0.040321</td>\n",
              "      <td>0.026861</td>\n",
              "      <td>0.053928</td>\n",
              "      <td>0.039019</td>\n",
              "      <td>0.048326</td>\n",
              "      <td>0.022479</td>\n",
              "      <td>0.089826</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           XOM      AAPL      MSFT  ...       CVX        PG       WFC\n",
              "XOM   0.039015  0.022296  0.027982  ...  0.038245  0.018216  0.042972\n",
              "AAPL  0.022296  0.091844  0.024599  ...  0.028240  0.011532  0.036756\n",
              "MSFT  0.027982  0.024599  0.051014  ...  0.030815  0.013724  0.040321\n",
              "JNJ   0.019595  0.011578  0.016842  ...  0.021005  0.013196  0.026861\n",
              "GE    0.036647  0.027814  0.032649  ...  0.040677  0.019377  0.053928\n",
              "GOOG  0.026728  0.033249  0.026231  ...  0.030258  0.015123  0.039019\n",
              "CVX   0.038245  0.028240  0.030815  ...  0.050857  0.019587  0.048326\n",
              "PG    0.018216  0.011532  0.013724  ...  0.019587  0.025152  0.022479\n",
              "WFC   0.042972  0.036756  0.040321  ...  0.048326  0.022479  0.089826\n",
              "\n",
              "[9 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UGPzPALqElhM",
        "colab_type": "text"
      },
      "source": [
        "**Mean-Variance Optimization (based on historical returns)**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AxqG8aCxEobT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 453
        },
        "outputId": "3bb55892-ca68-4c8d-8e8d-6fb10758cc92"
      },
      "source": [
        "res1 = optimize_frontier(R, C, rf)\n",
        "\n",
        "display_assets(names, R, C, color='blue')\n",
        "#display_frontier(res1, color='blue')\n",
        "xlabel('variance $\\sigma$'), ylabel('mean $\\mu$'), show()\n",
        "display(pandas.DataFrame({'Weight': res1.W}, index=names).T)"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAF1CAYAAACzjX2vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJEmqoP8fCsmKPHNEm4kAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>XOM</th>\n",
              "      <th>AAPL</th>\n",
              "      <th>MSFT</th>\n",
              "      <th>JNJ</th>\n",
              "      <th>GE</th>\n",
              "      <th>GOOG</th>\n",
              "      <th>CVX</th>\n",
              "      <th>PG</th>\n",
              "      <th>WFC</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Weight</th>\n",
              "      <td>1.528002e-16</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.684932e-17</td>\n",
              "      <td>0.450921</td>\n",
              "      <td>5.244599e-17</td>\n",
              "      <td>0.528356</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.020723</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                 XOM  AAPL          MSFT  ...  CVX   PG       WFC\n",
              "Weight  1.528002e-16   0.0  1.684932e-17  ...  0.0  0.0  0.020723\n",
              "\n",
              "[1 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nFLr4kSAGHtf",
        "colab_type": "text"
      },
      "source": [
        "**Black-litterman reverse optimization**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2BEqHNNjGKZV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Calculate portfolio historical return and variance\n",
        "mean, var = port_mean_var(W, R, C)\n",
        "\n",
        "lmb = (mean - rf) / var  # Calculate risk aversion\n",
        "Pi = dot(dot(lmb, C), W)  # Calculate equilibrium excess returns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zhwFJdB0GO6d",
        "colab_type": "text"
      },
      "source": [
        "**Mean-variance Optimization (based on equilibrium returns)**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DzPTbo7aGN_0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 470
        },
        "outputId": "ad0f0c2e-52a8-49b1-ab0a-5b7ad8a358ac"
      },
      "source": [
        "res2 = optimize_frontier(Pi+rf, C, rf)\n",
        "\n",
        "display_assets(names, R, C, color='red')\n",
        "#display_frontier(res1, label='Historical returns', color='red')\n",
        "display_assets(names, Pi+rf, C, color='green')\n",
        "#display_frontier(res2, label='Implied returns', color='green')\n",
        "xlabel('variance $\\sigma$'), ylabel('mean $\\mu$'), legend(), show()\n",
        "display(pandas.DataFrame({'Weight': res2.W}, index=names).T)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "No handles with labels found to put in legend.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAF1CAYAAACzjX2vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>XOM</th>\n",
              "      <th>AAPL</th>\n",
              "      <th>MSFT</th>\n",
              "      <th>JNJ</th>\n",
              "      <th>GE</th>\n",
              "      <th>GOOG</th>\n",
              "      <th>CVX</th>\n",
              "      <th>PG</th>\n",
              "      <th>WFC</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Weight</th>\n",
              "      <td>0.160429</td>\n",
              "      <td>0.15617</td>\n",
              "      <td>0.112453</td>\n",
              "      <td>0.097424</td>\n",
              "      <td>0.093807</td>\n",
              "      <td>0.116209</td>\n",
              "      <td>0.091813</td>\n",
              "      <td>0.084692</td>\n",
              "      <td>0.087002</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "             XOM     AAPL      MSFT  ...       CVX        PG       WFC\n",
              "Weight  0.160429  0.15617  0.112453  ...  0.091813  0.084692  0.087002\n",
              "\n",
              "[1 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KMss8j1yGbSD",
        "colab_type": "text"
      },
      "source": [
        "**Determine views to the equilibrium returns and prepare views (Q) and link (P) matrices**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_Pr-IPP7GeXl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 239
        },
        "outputId": "11fe88dd-321c-400e-b646-911e8e9fb54e"
      },
      "source": [
        "def create_views_and_link_matrix(names, views):\n",
        "    r, c = len(views), len(names)\n",
        "    Q = [views[i][3] for i in range(r)]  # view matrix\n",
        "    P = zeros([r, c])\n",
        "    nameToIndex = dict()\n",
        "    for i, n in enumerate(names):\n",
        "        nameToIndex[n] = i\n",
        "    for i, v in enumerate(views):\n",
        "        name1, name2 = views[i][0], views[i][2]\n",
        "        P[i, nameToIndex[name1]] = +1 if views[i][1] == '>' else -1\n",
        "        P[i, nameToIndex[name2]] = -1 if views[i][1] == '>' else +1\n",
        "    return array(Q), P\n",
        "\n",
        "views = [('MSFT', '>', 'GE', 0.02),\n",
        "         ('AAPL', '<', 'JNJ', 0.02)]\n",
        "\n",
        "Q, P = create_views_and_link_matrix(names, views)\n",
        "print('Views Matrix')\n",
        "display(DataFrame({'Views':Q}))\n",
        "print('Link Matrix')\n",
        "display(DataFrame(P))"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Views Matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Views</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.02</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Views\n",
              "0   0.02\n",
              "1   0.02"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Link Matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-1.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.0</td>\n",
              "      <td>-1.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     0    1    2    3    4    5    6    7    8\n",
              "0  0.0  0.0  1.0  0.0 -1.0  0.0  0.0  0.0  0.0\n",
              "1  0.0 -1.0  0.0  1.0  0.0  0.0  0.0  0.0  0.0"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "42xwl8hWGjrC",
        "colab_type": "text"
      },
      "source": [
        "**Optimization based on Equilibrium returns with adjusted views**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v2jQppGUGlo6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 470
        },
        "outputId": "de839208-9dab-4412-952e-6ada5cb8cc17"
      },
      "source": [
        "tau = .025  # scaling factor\n",
        "\n",
        "# Calculate omega - uncertainty matrix about views\n",
        "omega = dot(dot(dot(tau, P), C), transpose(P))  # 0.025 * P * C * transpose(P)\n",
        "# Calculate equilibrium excess returns with views incorporated\n",
        "sub_a = inv(dot(tau, C))\n",
        "sub_b = dot(dot(transpose(P), inv(omega)), P)\n",
        "sub_c = dot(inv(dot(tau, C)), Pi)\n",
        "sub_d = dot(dot(transpose(P), inv(omega)), Q)\n",
        "Pi_adj = dot(inv(sub_a + sub_b), (sub_c + sub_d))\n",
        "\n",
        "res3 = optimize_frontier(Pi + rf, C, rf)\n",
        "\n",
        "display_assets(names, Pi+rf, C, color='green')\n",
        "display_frontier([res2], label='Implied returns', color='green')\n",
        "display_assets(names, Pi_adj+rf, C, color='blue')\n",
        "#display_frontier(res3, label='Implied returns (adjusted views)', color='blue')\n",
        "xlabel('variance $\\sigma$'), ylabel('mean $\\mu$'), legend(), show()\n",
        "display(pandas.DataFrame({'Weight': res2.W}, index=names).T)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "No handles with labels found to put in legend.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAF1CAYAAACzjX2vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncQb2F3oAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>XOM</th>\n",
              "      <th>AAPL</th>\n",
              "      <th>MSFT</th>\n",
              "      <th>JNJ</th>\n",
              "      <th>GE</th>\n",
              "      <th>GOOG</th>\n",
              "      <th>CVX</th>\n",
              "      <th>PG</th>\n",
              "      <th>WFC</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Weight</th>\n",
              "      <td>0.160429</td>\n",
              "      <td>0.15617</td>\n",
              "      <td>0.112453</td>\n",
              "      <td>0.097424</td>\n",
              "      <td>0.093807</td>\n",
              "      <td>0.116209</td>\n",
              "      <td>0.091813</td>\n",
              "      <td>0.084692</td>\n",
              "      <td>0.087002</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "             XOM     AAPL      MSFT  ...       CVX        PG       WFC\n",
              "Weight  0.160429  0.15617  0.112453  ...  0.091813  0.084692  0.087002\n",
              "\n",
              "[1 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}