financial market behavior during covid k means clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# When did the pandemic start and stop for financial markets?  K-means analysis of daily financial data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.cluster import KMeans\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load and normalize data between 2018 and 2021"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "base_path = 'C:/Users/jacke/Documents/Data Projects/'\n",
    "\n",
    "filenames = [\"MutualFund prices - A-E.csv\", \"MutualFund prices - F-K.csv\", \"MutualFund prices - L-P.csv\", \"MutualFund prices - Q-Z.csv\", \"MutualFunds.csv\", \"ETF prices.csv\", \"ETFs.csv\"]\n",
    "\n",
    "price_data = pd.read_csv(base_path + filenames[5])\n",
    "price_data['price_date'] = pd.to_datetime(price_data['price_date'])\n",
    "data = price_data.pivot(index='price_date', columns='fund_symbol', values='adj_close')\n",
    "\n",
    "# Drop data before 2018\n",
    "data = data[data.index >= '2018-01-01']\n",
    "\n",
    "# Drop columns with all NaN values\n",
    "data.dropna(axis=1, how='any', inplace=True)\n",
    "\n",
    "# Normalize the data\n",
    "scaler = StandardScaler()\n",
    "normalized_data = scaler.fit_transform(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot an elbow curve to determine how many clusters would be appropriate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\jacke\\anaconda3\\lib\\site-packages\\sklearn\\cluster\\_kmeans.py:881: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=4.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Determine the optimal number of clusters using the elbow method\n",
    "OMP_NUM_THREADS=4\n",
    "inertia = []\n",
    "K = range(1, 11)\n",
    "for k in K:\n",
    "    kmeans = KMeans(n_clusters=k, random_state=0)\n",
    "    kmeans.fit(normalized_data)\n",
    "    inertia.append(kmeans.inertia_)\n",
    "\n",
    "# Plot the elbow curve\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(K, inertia, 'bo-')\n",
    "plt.xlabel('Number of clusters (k)')\n",
    "plt.ylabel('Inertia')\n",
    "plt.title('Elbow Method For Optimal k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Selecting k=3 as our number of clusters, proceed with the k-means clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2    541\n",
      "1    255\n",
      "0    190\n",
      "Name: Cluster, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# Fit K-means with the optimal number of clusters (In this case, k=3)\n",
    "optimal_k = 3 \n",
    "kmeans = KMeans(n_clusters=optimal_k, random_state=0)\n",
    "kmeans.fit(normalized_data)\n",
    "labels = kmeans.labels_\n",
    "\n",
    "# Add the cluster labels to the original data\n",
    "data['Cluster'] = labels\n",
    "\n",
    "print(data['Cluster'].value_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform PCA to reduce the data to 2-d to visualize the clusters and plot it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the clusters using PCA (to reduce to 2D for visualization)\n",
    "pca = PCA(n_components=2)\n",
    "principal_components = pca.fit_transform(normalized_data)\n",
    "pc_df = pd.DataFrame(data=principal_components, columns=['PC1', 'PC2'])\n",
    "pc_df['Cluster'] = labels\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "for cluster in range(optimal_k):\n",
    "    clustered_data = pc_df[pc_df['Cluster'] == cluster]\n",
    "    plt.scatter(clustered_data['PC1'], clustered_data['PC2'], label=f'Cluster {cluster}')\n",
    "plt.xlabel('Principal Component 1')\n",
    "plt.ylabel('Principal Component 2')\n",
    "plt.title('K-means Clusters (PCA-reduced Data)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3 distinct categories can be seen, indicating a significant change in behavior of the markets between the three periods identified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the clusters over time\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.plot(data.index, data['Cluster'], marker='o', linestyle='', alpha=0.7)\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Cluster')\n",
    "plt.title('Clusters Over Time')\n",
    "plt.yticks(range(optimal_k))  # Ensure y-axis only has the cluster labels\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the clusters by time, we can see a distinct period around when the pandemic began, and when the markets entered post-pandemic behavior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first date observed in cluster 0 is 2018-01-02 00:00:00\n",
      "The first date observed in cluster 1 is 2020-11-24 00:00:00\n",
      "The first date observed in cluster 2 is 2020-02-27 00:00:00\n"
     ]
    }
   ],
   "source": [
    "# Group by 'Cluster' and find the first date observed in each cluster\n",
    "first_dates = data.groupby('Cluster').apply(lambda df: df.index.min())\n",
    "\n",
    "# Print the first date observed within each cluster\n",
    "for cluster, date in first_dates.items():\n",
    "    print(f\"The first date observed in cluster {cluster} is {data.iloc[date][0]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the k-means clustering, the behavior of the markets first changed in Feburary 27 of 2020, and then again in November 24 of the same year; albeit not to a pre-pandemic norm but rather to a new post-pandemic regime.  While the start of the pandemic lines up with the beginning of the official recession in the United States, we can see that the markets retained their pandemic variance levels until several months after the recession officially ended."
   ]
  }
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