main.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FHnPh2eLH0RX"
      },
      "source": [
        "# SP500 Simulation with a Normal Distribution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0124IYiEuPbH"
      },
      "source": [
        "## Getting the Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gn5pe1MDCBPH"
      },
      "source": [
        "Now let's get the the price data from Yahoo Finance."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "c-sXgq3IGNoI"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "from datetime import datetime"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "sUP-zij8sfRs"
      },
      "outputs": [],
      "source": [
        "DATA_URL =\"https://query1.finance.yahoo.com/v7/finance/download/%5EGSPC?period1=-1325635200&period2=1614211200&interval=1d&events=history&includeAdjustedClose=true\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Processing the Dataframe"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "eyfbfLdiGfK8",
        "outputId": "abb1f249-739e-4af8-9d51-e51364ff358d"
      },
      "outputs": [
        {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Date</th>\n",
              "      <th>Open</th>\n",
              "      <th>High</th>\n",
              "      <th>Low</th>\n",
              "      <th>Close</th>\n",
              "      <th>Adj Close</th>\n",
              "      <th>Volume</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1927-12-30</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1928-01-03</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1928-01-04</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1928-01-05</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1928-01-06</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23393</th>\n",
              "      <td>2021-02-18</td>\n",
              "      <td>3915.860107</td>\n",
              "      <td>3921.979980</td>\n",
              "      <td>3885.030029</td>\n",
              "      <td>3913.969971</td>\n",
              "      <td>3913.969971</td>\n",
              "      <td>4773430000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23394</th>\n",
              "      <td>2021-02-19</td>\n",
              "      <td>3921.159912</td>\n",
              "      <td>3930.409912</td>\n",
              "      <td>3903.070068</td>\n",
              "      <td>3906.709961</td>\n",
              "      <td>3906.709961</td>\n",
              "      <td>4823940000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23395</th>\n",
              "      <td>2021-02-22</td>\n",
              "      <td>3885.550049</td>\n",
              "      <td>3902.919922</td>\n",
              "      <td>3874.709961</td>\n",
              "      <td>3876.500000</td>\n",
              "      <td>3876.500000</td>\n",
              "      <td>5870190000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23396</th>\n",
              "      <td>2021-02-23</td>\n",
              "      <td>3857.070068</td>\n",
              "      <td>3895.979980</td>\n",
              "      <td>3805.590088</td>\n",
              "      <td>3881.370117</td>\n",
              "      <td>3881.370117</td>\n",
              "      <td>6280650000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23397</th>\n",
              "      <td>2021-02-24</td>\n",
              "      <td>3873.709961</td>\n",
              "      <td>3928.649902</td>\n",
              "      <td>3859.600098</td>\n",
              "      <td>3925.429932</td>\n",
              "      <td>3925.429932</td>\n",
              "      <td>5942350000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>23398 rows × 7 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "             Date         Open         High          Low        Close  \\\n",
              "0      1927-12-30    17.660000    17.660000    17.660000    17.660000   \n",
              "1      1928-01-03    17.760000    17.760000    17.760000    17.760000   \n",
              "2      1928-01-04    17.719999    17.719999    17.719999    17.719999   \n",
              "3      1928-01-05    17.549999    17.549999    17.549999    17.549999   \n",
              "4      1928-01-06    17.660000    17.660000    17.660000    17.660000   \n",
              "...           ...          ...          ...          ...          ...   \n",
              "23393  2021-02-18  3915.860107  3921.979980  3885.030029  3913.969971   \n",
              "23394  2021-02-19  3921.159912  3930.409912  3903.070068  3906.709961   \n",
              "23395  2021-02-22  3885.550049  3902.919922  3874.709961  3876.500000   \n",
              "23396  2021-02-23  3857.070068  3895.979980  3805.590088  3881.370117   \n",
              "23397  2021-02-24  3873.709961  3928.649902  3859.600098  3925.429932   \n",
              "\n",
              "         Adj Close      Volume  \n",
              "0        17.660000           0  \n",
              "1        17.760000           0  \n",
              "2        17.719999           0  \n",
              "3        17.549999           0  \n",
              "4        17.660000           0  \n",
              "...            ...         ...  \n",
              "23393  3913.969971  4773430000  \n",
              "23394  3906.709961  4823940000  \n",
              "23395  3876.500000  5870190000  \n",
              "23396  3881.370117  6280650000  \n",
              "23397  3925.429932  5942350000  \n",
              "\n",
              "[23398 rows x 7 columns]"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_origin = pd.read_csv(DATA_URL)\n",
        "df_origin"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Date</th>\n",
              "      <th>Open</th>\n",
              "      <th>High</th>\n",
              "      <th>Low</th>\n",
              "      <th>Close</th>\n",
              "      <th>Adj Close</th>\n",
              "      <th>Volume</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1927-12-30</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1928-01-03</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>17.760000</td>\n",
              "      <td>0</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1928-01-04</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>17.719999</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1928-01-05</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>17.549999</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1928-01-06</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>17.660000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "      <td>...</td>\n",
              "      <td>...</td>\n",
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              "    <tr>\n",
              "      <th>23393</th>\n",
              "      <td>2021-02-18</td>\n",
              "      <td>3915.860107</td>\n",
              "      <td>3921.979980</td>\n",
              "      <td>3885.030029</td>\n",
              "      <td>3913.969971</td>\n",
              "      <td>3913.969971</td>\n",
              "      <td>4773430000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23394</th>\n",
              "      <td>2021-02-19</td>\n",
              "      <td>3921.159912</td>\n",
              "      <td>3930.409912</td>\n",
              "      <td>3903.070068</td>\n",
              "      <td>3906.709961</td>\n",
              "      <td>3906.709961</td>\n",
              "      <td>4823940000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23395</th>\n",
              "      <td>2021-02-22</td>\n",
              "      <td>3885.550049</td>\n",
              "      <td>3902.919922</td>\n",
              "      <td>3874.709961</td>\n",
              "      <td>3876.500000</td>\n",
              "      <td>3876.500000</td>\n",
              "      <td>5870190000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23396</th>\n",
              "      <td>2021-02-23</td>\n",
              "      <td>3857.070068</td>\n",
              "      <td>3895.979980</td>\n",
              "      <td>3805.590088</td>\n",
              "      <td>3881.370117</td>\n",
              "      <td>3881.370117</td>\n",
              "      <td>6280650000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23397</th>\n",
              "      <td>2021-02-24</td>\n",
              "      <td>3873.709961</td>\n",
              "      <td>3928.649902</td>\n",
              "      <td>3859.600098</td>\n",
              "      <td>3925.429932</td>\n",
              "      <td>3925.429932</td>\n",
              "      <td>5942350000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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              "<p>23398 rows × 7 columns</p>\n",
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            ],
            "text/plain": [
              "            Date         Open         High          Low        Close  \\\n",
              "0     1927-12-30    17.660000    17.660000    17.660000    17.660000   \n",
              "1     1928-01-03    17.760000    17.760000    17.760000    17.760000   \n",
              "2     1928-01-04    17.719999    17.719999    17.719999    17.719999   \n",
              "3     1928-01-05    17.549999    17.549999    17.549999    17.549999   \n",
              "4     1928-01-06    17.660000    17.660000    17.660000    17.660000   \n",
              "...          ...          ...          ...          ...          ...   \n",
              "23393 2021-02-18  3915.860107  3921.979980  3885.030029  3913.969971   \n",
              "23394 2021-02-19  3921.159912  3930.409912  3903.070068  3906.709961   \n",
              "23395 2021-02-22  3885.550049  3902.919922  3874.709961  3876.500000   \n",
              "23396 2021-02-23  3857.070068  3895.979980  3805.590088  3881.370117   \n",
              "23397 2021-02-24  3873.709961  3928.649902  3859.600098  3925.429932   \n",
              "\n",
              "         Adj Close      Volume  \n",
              "0        17.660000           0  \n",
              "1        17.760000           0  \n",
              "2        17.719999           0  \n",
              "3        17.549999           0  \n",
              "4        17.660000           0  \n",
              "...            ...         ...  \n",
              "23393  3913.969971  4773430000  \n",
              "23394  3906.709961  4823940000  \n",
              "23395  3876.500000  5870190000  \n",
              "23396  3881.370117  6280650000  \n",
              "23397  3925.429932  5942350000  \n",
              "\n",
              "[23398 rows x 7 columns]"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df = df_origin.copy()\n",
        "df[\"Date\"] = pd.to_datetime(df[\"Date\"], infer_datetime_format=True) # Parse the datetime\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7m-Dvy8ACIcu"
      },
      "source": [
        "## Visualizing the data\n",
        "\n",
        "What does the data look like?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "mK1_h851uH2_"
      },
      "outputs": [],
      "source": [
        "import seaborn as sns\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "sns.set_theme()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "id": "Of8nf8GSHRrp",
        "outputId": "a7c101b0-c5ca-4da0-b40e-70db451686b9"
      },
      "outputs": [
        {
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            "text/plain": [
              "<Figure size 1500x750 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(10,5), dpi=150)\n",
        "plt.title(\"S&P 500 Historical Price\")\n",
        "plt.plot(df[\"Date\"], df[\"Adj Close\"])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZiGLIi7RGP7B"
      },
      "source": [
        "Now, let's look at the distribution of daily price changes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "NOL903vjGn5C",
        "outputId": "428191ce-150a-4678-8023-731a1fa9884d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1500x750 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "price = df[\"Adj Close\"].to_numpy()\n",
        "log_price = np.log(price)\n",
        "log_price_delta = np.ediff1d(log_price)\n",
        "plt.figure(figsize=(10,5), dpi=150)\n",
        "plt.hist(log_price_delta, range=(-0.1, 0.1), bins=200)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ylAUWajaqR-3"
      },
      "source": [
        "Let's see how a Normal curve fits the observed data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [],
      "source": [
        "from scipy.stats import norm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 291
        },
        "id": "Sf0dM6ieI6Cl",
        "outputId": "0fe2ba77-6f84-407d-9ccd-aac982e1718e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1050x450 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "mean, std = log_price_delta.mean(), log_price_delta.std()\n",
        "xx = np.linspace(-0.1, 0.1, num=100)\n",
        "yy = norm.pdf(xx, mean, std)\n",
        "plt.figure(figsize=(7,3), dpi=150)\n",
        "plt.title(\"Distribution of Daily Changes\")\n",
        "plt.plot(xx, yy, c='r')\n",
        "plt.hist(log_price_delta, range=(-0.1, 0.1), bins=200, density=True)\n",
        "plt.savefig(\"readme/distribution.png\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5MTu8ATuGj7b"
      },
      "source": [
        "Now let's simulate future prices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 310
        },
        "id": "e2blwMhTGkgJ",
        "outputId": "0b091b1b-36ca-4c46-b141-82489228e423"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1050x450 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "YEARS = 40\n",
        "num = norm.rvs(loc=mean, scale=std, size=(365 * YEARS, ))\n",
        "num = np.exp(log_price[0] + np.cumsum(np.concatenate([log_price_delta, num])))\n",
        "xx = np.arange(num.shape[0])\n",
        "plt.figure(figsize=(7,3), dpi=150)\n",
        "plt.title(\"S&P 500 Simulated\")\n",
        "plt.plot(xx[:log_price_delta.shape[0]], num[:log_price_delta.shape[0]])\n",
        "plt.plot(xx[log_price_delta.shape[0]:], num[log_price_delta.shape[0]:], 'r-')\n",
        "plt.yscale('log')\n",
        "plt.xlabel(\"Days since 1927\")\n",
        "plt.ylabel(\"Log SP500\")\n",
        "plt.savefig(\"readme/simulated.png\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "SP500 Projection.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.7"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}