Practice_task_Portfolio_VaR.ipynb

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        "<a href=\"https://colab.research.google.com/github/olesyamba/Risk_analysis/blob/main/Practice_task_Portfolio_VaR.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "metadata": {
        "id": "l9mMsyvwhvHA"
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      "source": [
        "Задача 1.\n",
        "\n",
        "Зависимость цены актива $P$ от двух риск-факторов $X,\\,Y$  моделируется функцией\n",
        "$$\n",
        "P(x,\\,y) = \\frac{x-y}{(1+y)^2}.\n",
        "$$\n",
        "   Факторы $X, Y$ нестационарны, но не обязательно положительны, так что имеет смысл переходить к разностям. Текущие значения риск-факторов: $X=0.05,\\,y=0.07$. Найдите текущие чувствительности доходности актива к приращениям этих двух факторов."
      ]
    },
    {
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        "id": "YSJZLV5NHzXS",
        "outputId": "73d9ff95-073c-4c58-8fb5-ae5f01bf4432"
      },
      "source": [
        "from autograd import grad\n",
        "\n",
        "# Функция цены актива P\n",
        "def price_asset(x, y):\n",
        "  return (x - y) / (1 + y) ** 2\n",
        "\n",
        "# Текущие значения факторов\n",
        "x0, y0 = 0.05, 0.07\n",
        "\n",
        "# Речь идет о ПРИРАЩЕНИЯХ, т.е. x1 = x0 + dx и y1 = y0 + dy\n",
        "\n",
        "# Требуется определить чувствительность ДОХОДНОСТИ актика к ПРИРАЩЕНИЯМ; запишем функцию\n",
        "def f(dx, dy):\n",
        "  return price_asset(x0 + dx, y0 + dy) / price_asset(x0, y0) - 1\n",
        "\n",
        "# Теперь определим чувствительности\n",
        "print('Верный ответ:', grad(f, [0, 1])(0.0, 0.0),'\\n')\n",
        "\n",
        "print(f(0.001, 0.0)/0.001, f(0, 0.001)/0.001)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Верный ответ: (array(-50.), array(48.13084112)) \n",
            "\n",
            "-50.00000000000004 48.040131085113735\n"
          ]
        }
      ]
    },
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      "source": [
        "Задача 2\n",
        "\n",
        "Приведённый код генерирует наблюдения за ценой актива и двумя риск-факторами. По этим данным оцените чувствительности доходностей актива к доходностям обоих риск-факторов.\n"
      ]
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        "id": "diHkgJQ6OqRe",
        "outputId": "15336b9d-fc1d-4609-a918-7359948fb7e1"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "np.random.seed(42)\n",
        "y_data = np.cumprod(1+np.random.randn(100)/10).round(4)*100\n",
        "x_data = (np.hstack([1, np.cumprod(1 + np.random.normal(0.1, 0.2, size=len(y_data) - 1) / 10 + 0.01 * np.diff(y_data))]) * 100).round(2)\n",
        "p_data = (x_data * 100 / (x_data + y_data ** 2)).round(2) + np.random.normal(0, 0.1, size=len(x_data)).round(4)\n",
        "df = pd.DataFrame({\"P\": p_data,\"X\": x_data,\"Y\": y_data},index=pd.period_range(end=\"2021-09-01\",periods=len(p_data),freq=\"D\"))\n",
        "assert df.iloc[-1, 0] == 16.7613, \"Something's wrong. Please contact the teacher.\"\n",
        "df"
      ],
      "execution_count": null,
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              "                  P       X       Y\n",
              "2021-05-25   0.7857  100.00  104.97\n",
              "2021-05-26   0.9258   96.72  103.52\n",
              "2021-05-27   0.8961  103.35  110.22\n",
              "2021-05-28   0.8483  121.03  127.01\n",
              "2021-05-29   0.8554  116.69  124.03\n",
              "...             ...     ...     ...\n",
              "2021-08-28  17.0357  101.47   22.26\n",
              "2021-08-29  16.4507  103.93   22.92\n",
              "2021-08-30  15.8800  103.76   23.52\n",
              "2021-08-31  15.9907  105.13   23.53\n",
              "2021-09-01  16.7613  105.72   22.98\n",
              "\n",
              "[100 rows x 3 columns]"
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              "      <th>2021-05-25</th>\n",
              "      <td>0.7857</td>\n",
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              "      <td>104.97</td>\n",
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              "      <td>0.9258</td>\n",
              "      <td>96.72</td>\n",
              "      <td>103.52</td>\n",
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              "      <th>2021-08-28</th>\n",
              "      <td>17.0357</td>\n",
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              "      <td>22.26</td>\n",
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              "      <th>2021-08-29</th>\n",
              "      <td>16.4507</td>\n",
              "      <td>103.93</td>\n",
              "      <td>22.92</td>\n",
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              "      <th>2021-08-30</th>\n",
              "      <td>15.8800</td>\n",
              "      <td>103.76</td>\n",
              "      <td>23.52</td>\n",
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              "      <th>2021-08-31</th>\n",
              "      <td>15.9907</td>\n",
              "      <td>105.13</td>\n",
              "      <td>23.53</td>\n",
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              "      <th>2021-09-01</th>\n",
              "      <td>16.7613</td>\n",
              "      <td>105.72</td>\n",
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      "source": [
        "from statsmodels.formula.api import ols\n",
        "\n",
        "# Вычисляем доходности цен и факторов\n",
        "returns = df.pct_change().dropna()\n",
        "display(returns)\n",
        "\n",
        "# Строим множественную линейную регрессию\n",
        "reg = ols(\"P ~ X + Y\", returns).fit()\n",
        "print(reg.summary())\n"
      ],
      "execution_count": null,
      "outputs": [
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              "                   P         X         Y\n",
              "2021-05-26  0.178312 -0.032800 -0.013813\n",
              "2021-05-27 -0.032080  0.068548  0.064722\n",
              "2021-05-28 -0.053342  0.171069  0.152332\n",
              "2021-05-29  0.008370 -0.035859 -0.023463\n",
              "2021-05-30 -0.260931 -0.022196 -0.023381\n",
              "...              ...       ...       ...\n",
              "2021-08-28  0.275605 -0.024702 -0.146472\n",
              "2021-08-29 -0.034340  0.024244  0.029650\n",
              "2021-08-30 -0.034692 -0.001636  0.026178\n",
              "2021-08-31  0.006971  0.013204  0.000425\n",
              "2021-09-01  0.048191  0.005612 -0.023374\n",
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          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                      P   R-squared:                       0.736\n",
            "Model:                            OLS   Adj. R-squared:                  0.731\n",
            "Method:                 Least Squares   F-statistic:                     133.9\n",
            "Date:                Thu, 03 Nov 2022   Prob (F-statistic):           1.69e-28\n",
            "Time:                        12:19:09   Log-Likelihood:                 99.499\n",
            "No. Observations:                  99   AIC:                            -193.0\n",
            "Df Residuals:                      96   BIC:                            -185.2\n",
            "Df Model:                           2                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "Intercept      0.0176      0.009      1.888      0.062      -0.001       0.036\n",
            "X              1.3251      0.237      5.587      0.000       0.854       1.796\n",
            "Y             -2.2116      0.157    -14.088      0.000      -2.523      -1.900\n",
            "==============================================================================\n",
            "Omnibus:                       29.032   Durbin-Watson:                   2.833\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              203.698\n",
            "Skew:                           0.566   Prob(JB):                     5.86e-45\n",
            "Kurtosis:                       9.936   Cond. No.                         29.9\n",
            "==============================================================================\n",
            "\n",
            "Notes:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        }
      ]
    },
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              "          P         X         Y\n",
              "P  1.000000 -0.436500 -0.806402\n",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ju2F8bMiPLuN"
      },
      "source": [
        "Задача 3\n",
        "\n",
        "История котировок акции дана ниже (исполните код). Других факторов риска нет. Опцион A на эту акцию имеет дельту, равную 0.7, а опцион Б имеет дельту -0.2. Используя исторический метод, оцените VaR на горизонте 1 день и на уровне 99% по портфелю, состоящему из 100 млн. в акциях, короткой позиции в 20 млн в опционах А и длинной позиции в 10 млн в опционах Б.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ImW7D65zRB07",
        "outputId": "c94f1684-3fa7-4a82-aaa0-7be6f75c9ea6"
      },
      "source": [
        "!pip install yfinance\n",
        "import yfinance as yf\n",
        "quotes = yf.download(\"V\", \"2019-01-02\", \"2019-12-23\")[\"Adj Close\"]\n",
        "quotes"
      ],
      "execution_count": null,
      "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/python3.7/dist-packages (0.1.84)\n",
            "Requirement already satisfied: pandas>=0.24.0 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.3.5)\n",
            "Requirement already satisfied: requests>=2.26 in /usr/local/lib/python3.7/dist-packages (from yfinance) (2.28.1)\n",
            "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.21.6)\n",
            "Requirement already satisfied: multitasking>=0.0.7 in /usr/local/lib/python3.7/dist-packages (from yfinance) (0.0.11)\n",
            "Requirement already satisfied: lxml>=4.5.1 in /usr/local/lib/python3.7/dist-packages (from yfinance) (4.9.1)\n",
            "Requirement already satisfied: appdirs>=1.4.4 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.4.4)\n",
            "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.24.0->yfinance) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.24.0->yfinance) (2022.5)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7.3->pandas>=0.24.0->yfinance) (1.15.0)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests>=2.26->yfinance) (2.10)\n",
            "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests>=2.26->yfinance) (1.24.3)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests>=2.26->yfinance) (2022.9.24)\n",
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            "[*********************100%***********************]  1 of 1 completed\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Date\n",
              "2019-01-02    129.773071\n",
              "2019-01-03    125.096519\n",
              "2019-01-04    130.485809\n",
              "2019-01-07    132.838760\n",
              "2019-01-08    133.561264\n",
              "                 ...    \n",
              "2019-12-16    182.997513\n",
              "2019-12-17    182.290054\n",
              "2019-12-18    181.680801\n",
              "2019-12-19    183.292282\n",
              "2019-12-20    184.726852\n",
              "Name: Adj Close, Length: 246, dtype: float64"
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          "metadata": {},
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    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K9UCfBe0RCgU",
        "outputId": "501738ad-54a2-42eb-d638-d644022ba645"
      },
      "source": [
        "# Дельта - чувствительность доходности одного актива к доходности другого актива или риск-фактора\n",
        "\n",
        "# Построим таблицу исторических сценариев доходностей акции (риск-фактора)\n",
        "returns = quotes.pct_change().dropna()\n",
        "\n",
        "# Вычисляем совокупную чувствительность портфеля\n",
        "prt_delta = (100*1 + (- 20) * 0.7 + 10 * (-0.2) ) # обращаем внимание на короткую позицию, которая в стоимости портфеля учитывается с отрицательным знаком\n",
        "print(prt_delta)\n",
        "\n",
        "# Вычисляет исторический VaR по данным\n",
        "print('VaR для акции:', - returns.quantile(1- .99, interpolation='higher'), '\\n')\n",
        "print('Верный ответ', - returns.quantile(1 -.99, interpolation='lower') * prt_delta,'\\n')\n",
        "# print('Верный ответ', - returns.quantile(.99, interpolation='lower') * (-prt_delta),'\\n') #если портфельная дельта отрицательная"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "84.0\n",
            "VaR для акции: 0.02864224169876306 \n",
            "\n",
            "Верный ответ 2.651934794723885 \n",
            "\n",
            "Верный ответ 2.1943976562139715 \n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Eo3u5dPsRwVD"
      },
      "source": [
        "Задача 4\n",
        "\n",
        "Портфель состоит на 20% из акций А, на 50% -- из акций Б и на 30% -- из акций В. Для моделирования используется 3 риск-фактора: индекс S&P 500, цена нефти и курс евро к доллару. Чувствительности доходностей акций к доходностям риск-факторов даны в таблице.\n",
        "\n",
        "|Акция|S&P|Нефть| Курс|\n",
        "|:--|--:|--:|--:|\n",
        "|А| 0.4 | -0.3 | 0 |\n",
        "|Б| 0.3 | 0.5 | 0.3|\n",
        "|В| 0.2 | 0 | -0.4|\n",
        "\n",
        "Найдите VaR на уровне 99% по этому портфелю на горизонте 1 день, используя дельта-нормальный подход.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
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        },
        "id": "jSTGmfryVowJ",
        "outputId": "25fd4278-ea71-454a-b042-3769c97e6dcb"
      },
      "source": [
        "quotes_SnP = yf.download(\"^GSPC\", \"2019-01-02\", \"2019-12-23\")[\"Adj Close\"]\n",
        "quotes_Oil = yf.download(\"BZ=F\", \"2019-01-02\", \"2019-12-23\")[\"Adj Close\"]\n",
        "quotes_FX = yf.download(\"EUR=X\", \"2019-01-02\", \"2019-12-23\")[\"Adj Close\"]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  1 of 1 completed\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "[*********************100%***********************]  1 of 1 completed\n"
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    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 946
        },
        "id": "7NsEchWnVpNb",
        "outputId": "5d31055b-d171-425e-a148-4304867bb1e6"
      },
      "source": [
        "import pandas as pd\n",
        "import scipy.stats as ss\n",
        "\n",
        "# Составим таблицы (матрицы) весов портфеля и его чувствительностей\n",
        "weights = pd.Series({'A': 0.2, 'B': 0.5, 'C': 0.3})\n",
        "display(weights)\n",
        "sensitivities = pd.DataFrame({'A': [0.4, -0.3, 0], 'B': [0.3, 0.5, 0.3], 'C': [0.2, 0, -0.4]}, index=['S&P', 'Oil', 'FX']).T\n",
        "display(sensitivities)\n",
        "\n",
        "factor_data = pd.concat([quotes_SnP, quotes_Oil, quotes_FX], axis=1)\n",
        "factor_data.columns = ['S&P', 'Oil', 'FX']\n",
        "factor_returns = factor_data.pct_change().dropna()#\n",
        "display(factor_returns,'\\n')\n",
        "\n",
        "# Определим риск-параметры (кавариационная матрица факторов и вектор средних)\n",
        "factor_covariance = factor_returns.cov()\n",
        "factor_means = factor_returns.mean()\n",
        "print('Ковариационная матрица факторов\\n',factor_covariance, '\\nВектор средних доходностней факторов \\n', factor_means)\n",
        "\n",
        "# Определяем волатильность доходности портфеля\n",
        "delta = weights @ sensitivities\n",
        "print('Deltas:\\n',delta)\n",
        "\n",
        "portfolio_sigma = np.sqrt(\n",
        "    (weights @ sensitivities) @ factor_covariance @ (sensitivities.T @ weights)\n",
        ")\n",
        "portfolio_mu = (weights @ sensitivities) @ factor_means\n",
        "\n",
        "VaR = -100*ss.norm(portfolio_mu, portfolio_sigma).ppf(0.01) # 0.99\n",
        "print('Дельта-нормальный VaR 99%:', VaR)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "A    0.2\n",
              "B    0.5\n",
              "C    0.3\n",
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        },
        {
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            "text/plain": [
              "   S&P  Oil   FX\n",
              "A  0.4 -0.3  0.0\n",
              "B  0.3  0.5  0.3\n",
              "C  0.2  0.0 -0.4"
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              "      <th>A</th>\n",
              "      <td>0.4</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>B</th>\n",
              "      <td>0.3</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C</th>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.4</td>\n",
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              "                 S&P       Oil        FX\n",
              "Date                                    \n",
              "2019-01-03 -0.024757  0.018940  0.012688\n",
              "2019-01-04  0.034336  0.019839 -0.006406\n",
              "2019-01-07  0.007010  0.004732 -0.001697\n",
              "2019-01-08  0.009695  0.024246 -0.006036\n",
              "2019-01-09  0.004098  0.046321  0.002066\n",
              "...              ...       ...       ...\n",
              "2019-12-16  0.007148  0.001840  0.005537\n",
              "2019-12-17  0.000335  0.011631 -0.001124\n",
              "2019-12-18 -0.000432  0.001059 -0.001292\n",
              "2019-12-19  0.004459  0.005592  0.003189\n",
              "2019-12-20  0.004945 -0.006011 -0.000900\n",
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              "      <th>Oil</th>\n",
              "      <th>FX</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
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              "      <th>2019-01-03</th>\n",
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              "      <th>2019-12-18</th>\n",
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          "text": [
            "Ковариационная матрица факторов\n",
            "           S&P       Oil        FX\n",
            "S&P  0.000061  0.000043 -0.000005\n",
            "Oil  0.000043  0.000386 -0.000004\n",
            "FX  -0.000005 -0.000004  0.000010 \n",
            "Вектор средних доходностней факторов \n",
            " S&P    0.001021\n",
            "Oil    0.000929\n",
            "FX     0.000123\n",
            "dtype: float64\n",
            "Deltas:\n",
            " S&P    0.29\n",
            "Oil    0.19\n",
            "FX     0.03\n",
            "dtype: float64\n",
            "Дельта-нормальный VaR 99%: 1.086021278235305\n"
          ]
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      "source": [
        "Задача 5\n",
        "\n",
        "Стоимость бескупонной облигации, обещающей выплату 1 денежной единицы через s лет от текущего момента t, зависит от ставки дисконтирования rt соответствующей срочности следующим образом:\n",
        "\n",
        "$B_t = e^{-r_t(s)s}$\n",
        "\n",
        "Дана ежедневная история ставок дисконтирования за последний год (первое значение соответствует самому старому наблюдению, последнее -- самому новому; единицы измерения %/годовых):\n",
        "\n",
        "6.37,6.36,6.35,6.34,6.34,6.35,6.36,6.36,6.37,6.33,6.32,6.32,6.33,6.15,6.16,6.09,6.1,6.06,5.94,5.91,5.92,5.87,5.8,5.73,5.71,5.64,5.6,5.58,5.58,5.56,5.52,5.46,5.43,5.39,5.36,5.36,5.37,5.38,5.37,5.36,5.36,5.35,5.38,5.38,5.33,5.29,5.26,5.22,5.13,5.11,5.08,5.05,5,4.98,4.96,4.95,4.95,4.95,4.92,4.89,4.88,4.86,4.86,4.83,4.83,4.84,4.85,4.86,4.87,4.9,4.93,4.94,4.95,4.96,4.95,4.81,4.8,4.79,4.78,4.73,4.72,4.74,4.66,4.64,4.62,4.62,4.63,4.61,4.58,4.59,4.57,4.58,4.58,4.55,4.54,4.51,4.51,4.51,4.52,4.51,4.43,4.35,4.36,4.32,4.27,4.21,4.19,4.18,4.19,4.2,4.2,4.21,4.21,4.21,4.22,4.2,4.2,4.2,4.2,4.21,4.23,4.21,4.22,4.21,4.21,4.21,4.21,4.21,4.21,4.21,4.21,4.22,4.23,4.23,4.23,4.23,4.23,4.22,4.21,4.21,4.2,4.19,4.2,4.21,4.21,4.21,4.2,4.2,4.2,4.18,4.16,4.16,4.16,4.17,4.17,4.17,4.15,4.13,4.13,4.13,4.12,4.11,4.11,4.11,4.12,4.13,4.13,4.14,4.15,4.15,4.15,4.16,4.16,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.16,4.16,4.17,4.18,4.16,4.17,4.17,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.17,4.17,4.18,4.18,4.18,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.16,4.16,4.16,4.15,4.15,4.14,4.14,4.13,4.14,4.15,4.15,4.14,4.14,4.14,4.14,4.14,4.14,4.14,4.14,4.14,4.15,4.15,4.14,4.15,4.15,4.15,4.14,4.14,4.14,4.13,4.13,4.13,4.13,4.13,4.14,4.14,4.15,4.15,4.13,4.15,4.16,4.15,4.16,4.17,4.17,4.17,4.18,4.18,4.18,4.19,4.21,4.21,4.23,4.26,4.27,4.28,4.29,4.3,4.33,4.37,4.37,4.37,4.38,4.39,4.44,4.47,4.39,4.45,4.67,4.83,4.88,4.94,5.01,5.07,5.06,5.18,5.23,5.24,5.24,5.26,5.28,5.29,5.29,5.3,5.32,5.3,5.31,5.32,5.36,5.36,5.38,5.39,5.42,5.48,5.48,5.51,5.53,5.53,5.53,5.52,5.51,5.49,5.54,5.67,5.69,5.72,5.7,5.7,5.77,5.81,5.82,5.83,5.83,5.84,5.85,5.83,5.83,5.86,5.87,5.84,5.88,5.96,5.97,6.08,6.21,6.11,6.23,6.39,6.35,6.36,6.02,5.99,5.85,5.83,5.84,5.86,5.85,5.85,5.84,5.84,5.84,5.85,5.85,5.86,5.88,5.87,5.87,5.88,5.89,5.89,5.93,6.02,6.03,6.04,6.04,6.05,6.04,6.04,6.04,6.04,6.04,6.05,6.05,6.06,6.07,6.07,6.08,6.09,6.1,6.09,6.09,6.1,6.09\n",
        "\n",
        "Известно, что портфель таких облигаций имеет текущую стоимость 300 млн и срок до погашения 1.7 лет.\n",
        "\n",
        "Используя исторический метод, найдите VaR по этому портфелю на уровне 99% на горизонте 1 день."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "id": "aSijxDj6c6MX",
        "outputId": "001e7146-42dd-4396-c21b-6e0bf84148d9"
      },
      "source": [
        "# Дюрация - чувствительность рыночной доходности облигации к приращению процентной ставки: dP/P = - D*dr\n",
        "# По заданию нужно посчитать quantile(dP) = quantile(-D*P*dr)\n",
        "\n",
        "# Подготавливаем данные\n",
        "rates_data = [6.37,6.36,6.35,6.34,6.34,6.35,6.36,6.36,6.37,6.33,6.32,6.32,6.33,6.15,6.16,6.09,6.1,6.06,5.94,5.91,5.92,5.87,5.8,5.73,5.71,5.64,5.6,5.58,5.58,5.56,5.52,5.46,5.43,5.39,5.36,5.36,5.37,5.38,5.37,5.36,5.36,5.35,5.38,5.38,5.33,5.29,5.26,5.22,5.13,5.11,5.08,5.05,5,4.98,4.96,4.95,4.95,4.95,4.92,4.89,4.88,4.86,4.86,4.83,4.83,4.84,4.85,4.86,4.87,4.9,4.93,4.94,4.95,4.96,4.95,4.81,4.8,4.79,4.78,4.73,4.72,4.74,4.66,4.64,4.62,4.62,4.63,4.61,4.58,4.59,4.57,4.58,4.58,4.55,4.54,4.51,4.51,4.51,4.52,4.51,4.43,4.35,4.36,4.32,4.27,4.21,4.19,4.18,4.19,4.2,4.2,4.21,4.21,4.21,4.22,4.2,4.2,4.2,4.2,4.21,4.23,4.21,4.22,4.21,4.21,4.21,4.21,4.21,4.21,4.21,4.21,4.22,4.23,4.23,4.23,4.23,4.23,4.22,4.21,4.21,4.2,4.19,4.2,4.21,4.21,4.21,4.2,4.2,4.2,4.18,4.16,4.16,4.16,4.17,4.17,4.17,4.15,4.13,4.13,4.13,4.12,4.11,4.11,4.11,4.12,4.13,4.13,4.14,4.15,4.15,4.15,4.16,4.16,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.16,4.16,4.17,4.18,4.16,4.17,4.17,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.18,4.17,4.17,4.18,4.18,4.18,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.17,4.16,4.16,4.16,4.15,4.15,4.14,4.14,4.13,4.14,4.15,4.15,4.14,4.14,4.14,4.14,4.14,4.14,4.14,4.14,4.14,4.15,4.15,4.14,4.15,4.15,4.15,4.14,4.14,4.14,4.13,4.13,4.13,4.13,4.13,4.14,4.14,4.15,4.15,4.13,4.15,4.16,4.15,4.16,4.17,4.17,4.17,4.18,4.18,4.18,4.19,4.21,4.21,4.23,4.26,4.27,4.28,4.29,4.3,4.33,4.37,4.37,4.37,4.38,4.39,4.44,4.47,4.39,4.45,4.67,4.83,4.88,4.94,5.01,5.07,5.06,5.18,5.23,5.24,5.24,5.26,5.28,5.29,5.29,5.3,5.32,5.3,5.31,5.32,5.36,5.36,5.38,5.39,5.42,5.48,5.48,5.51,5.53,5.53,5.53,5.52,5.51,5.49,5.54,5.67,5.69,5.72,5.7,5.7,5.77,5.81,5.82,5.83,5.83,5.84,5.85,5.83,5.83,5.86,5.87,5.84,5.88,5.96,5.97,6.08,6.21,6.11,6.23,6.39,6.35,6.36,6.02,5.99,5.85,5.83,5.84,5.86,5.85,5.85,5.84,5.84,5.84,5.85,5.85,5.86,5.88,5.87,5.87,5.88,5.89,5.89,5.93,6.02,6.03,6.04,6.04,6.05,6.04,6.04,6.04,6.04,6.04,6.05,6.05,6.06,6.07,6.07,6.08,6.09,6.1,6.09,6.09,6.1,6.09]\n",
        "rates_index = pd.period_range(end=\"2021-09-01\", periods=len(rates_data), freq=\"D\")\n",
        "rates = pd.Series((rates_data), index=rates_index)\n",
        "display(rates.diff())\n",
        "\n",
        "dur = 1.7\n",
        "q = .99\n",
        "P = 300\n",
        "\n",
        "display(-dur * P * rates.diff().dropna()/100)\n",
        "print('VaR 99% =', (-dur * P * rates.diff().dropna()/100).quantile(1-q, interpolation='higher'))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "2020-08-09     NaN\n",
              "2020-08-10   -0.01\n",
              "2020-08-11   -0.01\n",
              "2020-08-12   -0.01\n",
              "2020-08-13    0.00\n",
              "              ... \n",
              "2021-08-28    0.01\n",
              "2021-08-29   -0.01\n",
              "2021-08-30    0.00\n",
              "2021-08-31    0.01\n",
              "2021-09-01   -0.01\n",
              "Freq: D, Length: 389, dtype: float64"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "2020-08-10    0.051\n",
              "2020-08-11    0.051\n",
              "2020-08-12    0.051\n",
              "2020-08-13   -0.000\n",
              "2020-08-14   -0.051\n",
              "              ...  \n",
              "2021-08-28   -0.051\n",
              "2021-08-29    0.051\n",
              "2021-08-30   -0.000\n",
              "2021-08-31   -0.051\n",
              "2021-09-01    0.051\n",
              "Freq: D, Length: 388, dtype: float64"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "VaR 99% = -0.6629999999999994\n"
          ]
        }
      ]
    }
  ]
}