markowitz_model.ipynb

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    {
      "cell_type": "markdown",
      "source": [
        "## Imports"
      ],
      "metadata": {
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      }
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          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1179fb2a-9c8b-48a9-a3d7-0c8ff8313a20"
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      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: yfinance in /usr/local/lib/python3.9/dist-packages (0.2.12)\n",
            "Requirement already satisfied: numpy>=1.16.5 in /usr/local/lib/python3.9/dist-packages (from yfinance) (1.22.4)\n",
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            "Requirement already satisfied: cryptography>=3.3.2 in /usr/local/lib/python3.9/dist-packages (from yfinance) (39.0.2)\n",
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            "Requirement already satisfied: pandas>=1.3.0 in /usr/local/lib/python3.9/dist-packages (from yfinance) (1.3.5)\n",
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          ]
        }
      ],
      "source": [
        "!pip install yfinance\n",
        "import random\n",
        "import yfinance as yf\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "np.set_printoptions(precision=30)\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Problem\n",
        "\n",
        "Having chosen the portfolio optimization problem, the objective is to optimize the distribution of capital for investment in a given number of stocks.\n",
        "\n",
        "We've used the classic Markowitz model, also called mean-variance model, as a basis. From the average stock return, covariance matrix of stocks, risk aversion coefficient and expected return values, we can calculate the optimal division of allocated capital.\n",
        "\n",
        "## Objective function\n",
        "\n",
        "The function to be optimized comes directly from the markowitz model:\n",
        "\n",
        "![](https://drive.google.com/uc?id=1brKvjGx5DJir20RrixoUIS8JzJ--GoE-)\n",
        "\n",
        "Note that we can solve this maximization problem by minimizing the negative objective function:\n",
        "\n",
        "$$\\text{Minimize } \\frac{1}{2}⋅γ⋅x^TSx - r^Tx$$\n",
        "\n",
        "subject to:\n",
        "\n",
        "$$∑ x_i = 1 $$\n",
        "\n",
        "since the sum of the capital distribution must not exceed 1, which would be equivalent to 100% of the capital value.\n",
        "\n",
        "## Data used\n",
        "\n",
        "Through the Yahoo Finance library, we obtained the historical stock exchange data for the input data."
      ],
      "metadata": {
        "id": "CJ0pC9WV-usR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# stocks to be analyzed\n",
        "#stocks = ['AAPL','AMZN','NFLX','GOOG', 'NYT', 'META', 'MSFT', 'TSLA', 'KO', 'BAC']\n",
        "stocks = ['AMZN','BAC','TSLA']\n",
        "#stocks = ['AMZN','GOOG','TSLA', 'META']\n",
        "\n",
        "# time frame for analysis\n",
        "start_date = '2017-01-01'\n",
        "end_date = '2022-01-01'\n",
        "\n",
        "# average number of days per year that operations can be carried out\n",
        "NUM_TRADING_DAYS = 252\n",
        "\n",
        "# method to get stock price history\n",
        "def download_data():\n",
        "  stock_data = {}\n",
        "  for stock in stocks:\n",
        "    ticker = yf.Ticker(stock)\n",
        "    stock_data[stock] = ticker.history(start=start_date, end=end_date)['Close'] # price at closing of stocks\n",
        "  return pd.DataFrame(stock_data)\n",
        "\n",
        "# calculate daily return from history\n",
        "def calculate_return(data):\n",
        "  log_return = np.log(data/data.shift(1)) # daily return\n",
        "  return log_return[1:] # removing first row with NaN values\n",
        "\n",
        "# call to get history\n",
        "dataset = download_data()\n",
        "print('Price History\\n', dataset)\n",
        "\n",
        "# plot of stock prices over time\n",
        "dataset.plot(figsize=(10,5))\n",
        "plt.title(\"Price comparison at closing\")\n",
        "plt.show()\n",
        "\n",
        "# daily fractional return plot\n",
        "frac_return = {}\n",
        "for stock in stocks:\n",
        "    frac_return[stock] = [(price - dataset[stock][max(i_p-1, 0)])/dataset[stock][max(i_p-1, 0)] for i_p, price in enumerate(dataset[stock])]\n",
        "    plt.plot(frac_return[stock], label=stock)\n",
        "plt.xlabel('Date')\n",
        "plt.legend()\n",
        "plt.title('Daily fractional return ') # price fluctuation\n",
        "plt.show()\n",
        "\n",
        "# getting daily returns\n",
        "daily_returns = calculate_return(dataset)\n",
        "anual_returns = daily_returns.mean() * NUM_TRADING_DAYS # average annual return\n",
        "cov_matrix = daily_returns.cov() * NUM_TRADING_DAYS # annual return covariance matrix\n",
        "\n",
        "print('\\naverage annual return\\n\\n', anual_returns)\n",
        "print('\\ncovariance matrix\\n\\n', cov_matrix)"
      ],
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          "height": 1000
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      "execution_count": 92,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Price History\n",
            "                                  AMZN        BAC        TSLA\n",
            "Date                                                        \n",
            "2017-01-03 00:00:00-05:00   37.683498  19.755684   14.466000\n",
            "2017-01-04 00:00:00-05:00   37.859001  20.123968   15.132667\n",
            "2017-01-05 00:00:00-05:00   39.022499  19.887217   15.116667\n",
            "2017-01-06 00:00:00-05:00   39.799500  19.887217   15.267333\n",
            "2017-01-09 00:00:00-05:00   39.846001  19.773220   15.418667\n",
            "...                               ...        ...         ...\n",
            "2021-12-27 00:00:00-05:00  169.669495  43.343128  364.646667\n",
            "2021-12-28 00:00:00-05:00  170.660995  43.401386  362.823334\n",
            "2021-12-29 00:00:00-05:00  169.201004  43.333424  362.063324\n",
            "2021-12-30 00:00:00-05:00  168.644501  43.236324  356.779999\n",
            "2021-12-31 00:00:00-05:00  166.716995  43.197491  352.260010\n",
            "\n",
            "[1259 rows x 3 columns]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "average annual return\n",
            "\n",
            " AMZN    0.297888\n",
            "BAC     0.156717\n",
            "TSLA    0.639529\n",
            "dtype: float64\n",
            "\n",
            "covariance matrix\n",
            "\n",
            "           AMZN       BAC      TSLA\n",
            "AMZN  0.086204  0.027627  0.065491\n",
            "BAC   0.027627  0.113689  0.050563\n",
            "TSLA  0.065491  0.050563  0.361932\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Definitions"
      ],
      "metadata": {
        "id": "GsfcozS_-slp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# covariance matrix\n",
        "S = cov_matrix.to_numpy()\n",
        "\n",
        "# symmetric matrix form\n",
        "S_ = np.divide(S + S.transpose(), 2)\n",
        "\n",
        "# vector r with returns\n",
        "r = anual_returns.to_numpy()\n",
        "\n",
        "# objective function\n",
        "def f(x, gamma = 1):\n",
        "  return (0.5*gamma)*np.dot(np.dot(x.T,S),x) - np.dot(r.T,x)\n",
        "\n",
        "# function gradient\n",
        "def df(x, gamma = 1):\n",
        "    return gamma*np.dot(S_,x.T) - r\n",
        "\n",
        "# function hessian\n",
        "def hessian(gamma = 1):\n",
        "  return gamma * S_\n",
        "\n",
        "# normalization of weights for restriction\n",
        "def normaliza_pesos(pesos):\n",
        "  return pesos / sum(pesos)\n",
        "\n",
        "# creation of random weights\n",
        "def peso_aleatorio(dimension = len(stocks)):\n",
        "  p = np.random.rand(dimension)\n",
        "  return normaliza_pesos(p)\n",
        "\n",
        "# expected return for a given vector of weights\n",
        "def retorno_esperado(pesos):\n",
        "  return np.sum(pesos @ anual_returns.to_numpy())\n",
        "\n",
        "# level of risk or volatility\n",
        "def volatilidade(pesos):\n",
        "    return np.sqrt(np.dot(pesos,np.dot(pesos,S)))\n",
        "\n",
        "# ratio between return and risk\n",
        "def proporcao(ret, vol):\n",
        "  return ret/vol"
      ],
      "metadata": {
        "id": "yxeytgXr-q6e"
      },
      "execution_count": 93,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Efficient Frontier Curve\n",
        "\n",
        "The efficient frontier curve values ​​investment portfolios on a fractional return scale versus a risk scale.\n",
        "\n",
        "The efficient frontier graphically represents the possible portfolios that maximize returns for the risk assumed.\n",
        "\n",
        "The shape of the curve is positively inclined, as the greater the risk, the greater the return to compensate for your investment.\n",
        "\n",
        "![](https://drive.google.com/uc?id=1O2C8vSPwKTm7cfW3UOyTytOaWreGJE48)"
      ],
      "metadata": {
        "id": "SMljW5MQFdxP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# efficient frontier curve plot\n",
        "def portfolio_aleatorio(returns):\n",
        "    p = np.asmatrix(np.mean(returns, axis=1))\n",
        "    w = np.asmatrix(peso_aleatorio(returns.shape[0]))\n",
        "    C = np.asmatrix(np.cov(returns))\n",
        "    \n",
        "    mu = w * p.T\n",
        "    sigma = np.sqrt(w * C * w.T)\n",
        "    \n",
        "    # recursion to reduce outliers\n",
        "    if sigma > 2: return portfolio_aleatorio(returns)\n",
        "    return mu, sigma\n",
        "\n",
        "n_portfolios = 2000\n",
        "n_obs = 1000\n",
        "dados_teste = np.random.randn(len(stocks), n_obs)\n",
        "\n",
        "means, stds = np.column_stack([\n",
        "    portfolio_aleatorio(dados_teste)\n",
        "    for _ in range(n_portfolios)\n",
        "])\n",
        "\n",
        "# plotting the efficient frontier curve for several different portfolios of our model\n",
        "fig = plt.figure()\n",
        "plt.plot(stds, means, 'o', markersize=5)\n",
        "plt.xlabel('risk')\n",
        "plt.ylabel('return average')\n",
        "plt.title('Average and volatility from the generated portfolios')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "YmB0Fp8W-rAx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "2f2a256d-093a-4c73-dc66-30c53c5eca9f"
      },
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Gradient Descent Algorithm"
      ],
      "metadata": {
        "id": "2bTwu3LxFb7h"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# lists to store iteration results\n",
        "lista_iter = []\n",
        "lista_x= []\n",
        "lista_x_norm= []\n",
        "lista_fx= []\n",
        "lista_dfx= []\n",
        "lista_dfx_norm = []\n",
        "lista_retorno= []\n",
        "lista_prop = []\n",
        "lista_dk = []\n",
        "lista_dk_norm = []\n",
        "\n",
        "# starting with random weight\n",
        "peso_inicial = peso_aleatorio()\n",
        "print(\"Initial weight\\n\", peso_inicial, \"\\n\")\n",
        "\n",
        "# initial values\n",
        "k = 0\n",
        "proximo_x = peso_inicial\n",
        "error = 1e-5\n",
        "alpha = 1e-5\n",
        "limite_iteracoes = 250\n",
        "risk_free = 0.5\n",
        "passo_fixo = 0.5\n",
        "\n",
        "# main loop\n",
        "while k <= limite_iteracoes:\n",
        "\n",
        "  grad = df(proximo_x, risk_free)\n",
        "  #print('gradient with k =', k, ': ', grad)\n",
        "  \n",
        "  # testing convergence to stop\n",
        "  if np.linalg.norm(grad) < error: break\n",
        "  \n",
        "  dk = -1 * grad # descent direction\n",
        "  #print('dk with k =', k, ': ', dk)\n",
        "\n",
        "  # starting linear search (backtracking)\n",
        "  lamb_bt = 1 # initial lambda\n",
        "  while( f(proximo_x + lamb_bt*dk, risk_free) >= f(proximo_x, risk_free) + alpha*lamb_bt*(np.dot(grad.T,dk)) ):\n",
        "    lamb_bt = 0.5 * lamb_bt\n",
        "\n",
        "  # starting exact linear search\n",
        "  #lamb_exata = np.dot(grad.T,grad) / np.dot((grad.T @ hessian(risk_free)), grad)\n",
        "\n",
        "  # saving data\n",
        "  lista_x.append(proximo_x)\n",
        "  lista_x_norm.append(normaliza_pesos(proximo_x))\n",
        "  lista_fx.append(-f(proximo_x, risk_free))\n",
        "  lista_dfx.append(grad)\n",
        "  lista_dfx_norm.append(normaliza_pesos(grad))\n",
        "  lista_retorno.append(retorno_esperado(normaliza_pesos(proximo_x)))\n",
        "  lista_iter.append(k)\n",
        "  lista_prop.append(proporcao(retorno_esperado(normaliza_pesos(proximo_x)), volatilidade(normaliza_pesos(proximo_x))))\n",
        "  lista_dk.append(dk)\n",
        "  lista_dk_norm.append(normaliza_pesos(dk))\n",
        "\n",
        "  # calculating next x\n",
        "  proximo_x = proximo_x + lamb_bt*dk\n",
        "  #print('x with k =', k, ': ', proximo_x)\n",
        "\n",
        "  # checking negative values ​​in the next x (boundary conditions)\n",
        "  def correct_negative_values():\n",
        "    for i, elem in enumerate(proximo_x):\n",
        "      if(elem < 0):\n",
        "        #print('proximo_x with negative value ', elem,'at k = ', k, 'index ', i)\n",
        "        proximo_x[i] *= -1\n",
        "      \n",
        "  # checking massive capital for a single stock\n",
        "  def corrects_massive_investment():\n",
        "    pn = normaliza_pesos(proximo_x)\n",
        "    for i, elem in enumerate(pn):\n",
        "      if(elem > 0.2): # capital limit of 20% for single stock\n",
        "        proximo_x[i] *= 0.9 # reduce 10% of investment\n",
        "\n",
        "  correct_negative_values() # check for boundary conditions\n",
        "\n",
        "  corrects_massive_investment() # check for capital limit, it can affect convergence\n",
        "\n",
        "  # iteration increment\n",
        "  k = k + 1\n",
        "\n",
        "print(\"Result Dataframe\")\n",
        "dataframe = pd.DataFrame(list(zip(lista_iter, lista_fx, lista_retorno, lista_prop)), columns=['iteration','f(x)','return','return/risk ratio'])\n",
        "#print(dataframe.to_string())\n",
        "print(dataframe)\n",
        "\n",
        "#dataframe.plot(x='iteration', y='f(x)')\n",
        "dataframe.plot(x='iteration', y='return')\n",
        "#dataframe.plot(x='iteration', y='return/risk ratio')\n",
        "\n",
        "print('Maximum return with following capital division:', normaliza_pesos(proximo_x))"
      ],
      "metadata": {
        "id": "Z96MMSHESwEA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 608
        },
        "outputId": "bdc3e47d-9945-49e2-fb2b-66fa38f5cde9"
      },
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Initial weight\n",
            " [0.45027008327274204 0.3281125067971629  0.22161740993009496] \n",
            "\n",
            "Result Dataframe\n",
            "     iteration      f(x)    return  return/risk ratio\n",
            "0            0  0.308262  0.327282           1.186553\n",
            "1            1  0.628969  0.403756           1.215573\n",
            "2            2  0.832933  0.421378           1.207043\n",
            "3            3  0.963362  0.427613           1.202803\n",
            "4            4  1.049058  0.429559           1.200708\n",
            "..         ...       ...       ...                ...\n",
            "246        246  1.252338  0.421360           1.206541\n",
            "247        247  1.249739  0.425234           1.208081\n",
            "248        248  1.251319  0.422896           1.207173\n",
            "249        249  1.248988  0.426598           1.208563\n",
            "250        250  1.250788  0.424174           1.207662\n",
            "\n",
            "[251 rows x 4 columns]\n",
            "Maximum return with following capital division: [0.3328877199167706  0.21521719188685884 0.4518950881963706 ]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Plot"
      ],
      "metadata": {
        "id": "55nxCM2lQKjq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import plotly.graph_objs as go\n",
        "\n",
        "def vector_plot(tvects,is_vect=True,orig=[0,0,0]):\n",
        "\n",
        "    if is_vect:\n",
        "        if not hasattr(orig[0],\"__iter__\"):\n",
        "            coords = [[orig,np.sum([orig,v],axis=0)] for v in tvects]\n",
        "        else:\n",
        "            coords = [[o,np.sum([o,v],axis=0)] for o,v in zip(orig,tvects)]\n",
        "    else:\n",
        "        coords = tvects\n",
        "\n",
        "    data = []\n",
        "    for i,c in enumerate(coords):\n",
        "        X1, Y1, Z1 = zip(c[0])\n",
        "        X2, Y2, Z2 = zip(c[1])\n",
        "        vector = go.Scatter3d(x = [X1[0],X2[0]],\n",
        "                              y = [Y1[0],Y2[0]],\n",
        "                              z = [Z1[0],Z2[0]],\n",
        "                              marker = dict(size = [0,5],\n",
        "                                            color = ['blue'],\n",
        "                                            line=dict(width=5,\n",
        "                                                      color='DarkSlateGrey')),\n",
        "                              name = 'Vector'+str(i+1))\n",
        "        data.append(vector)\n",
        "\n",
        "    layout = go.Layout(\n",
        "             margin = dict(l = 4,\n",
        "                           r = 4,\n",
        "                           b = 4,\n",
        "                           t = 4)\n",
        "                  )\n",
        "    fig = go.Figure(data=data,layout=layout)\n",
        "    fig.show()"
      ],
      "metadata": {
        "id": "PdbYe1Zf-q-H"
      },
      "execution_count": 96,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# plot of descent directions\n",
        "try: vector_plot(lista_dk_norm)\n",
        "except: print('not a 3d vector')"
      ],
      "metadata": {
        "id": "AlDBZamuUtQU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "b6188cd7-4a87-4aba-b9f8-fb1010e83324"
      },
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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          "metadata": {}
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    },
    {
      "cell_type": "code",
      "source": [
        "# x vector plot\n",
        "try: vector_plot(lista_x_norm)\n",
        "except: print('not a 3d vector')"
      ],
      "metadata": {
        "id": "PdtisEqhUuvI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "0cd50a99-2313-4ae4-f7e2-e4328f7835ad"
      },
      "execution_count": 98,
      "outputs": [
        {
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