YieldCurve_PCA.ipynb

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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "\n",
    "import plotly\n",
    "import plotly.express as px\n",
    "\n",
    "pd.options.mode.chained_assignment = None  # default='warn'\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "\n",
    "pd. options. plotting. backend = \"plotly\"\n",
    "\n",
    "import plotly.io as pio\n",
    "pio.renderers.default = 'jupyterlab'\n",
    "\n",
    "pd.set_option('precision',4)\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Yield curve historical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Obtained from \n",
    "# https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield\n",
    "\n",
    "USTYC = pd.read_csv(\"USTreasury_YieldCurve.csv\")\n",
    "\n",
    "KeepCols = ['Date','3 Mo','6 Mo','1 Yr','2 Yr','5 Yr','10 Yr','20 Yr','30 Yr']\n",
    "USTYC = USTYC.loc[:,KeepCols]\n",
    "USTYC.columns = USTYC.columns.str.replace(' ','')\n",
    "\n",
    "USTYC[\"Date\"] = pd.to_datetime(USTYC[\"Date\"],format=\"%m/%d/%y\")\n",
    "YCols = USTYC.columns.difference([\"Date\"])\n",
    "USTYC[YCols] = USTYC[YCols]/100\n",
    "USTYC = USTYC.rename(columns=dict(zip(YCols,['T'+x for x in YCols])))"
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "YCDates = ['20200131','20200229','20200331','20200430','20200531','20200630']\n",
    "\n",
    "plotDF = pd.melt(USTYC,id_vars=\"Date\",var_name=\"Maturity\",value_name=\"Yield\")\n",
    "plotDF = plotDF.loc[plotDF[\"Date\"].isin(YCDates),:].reset_index(drop=True)\n",
    "plotDF[\"Maturity\"] = plotDF[\"Maturity\"].str.slice(start=1)\n",
    "plotDF[\"Date\"] = plotDF[\"Date\"].dt.date.astype(str)\n",
    "\n",
    "px.line(plotDF,x=\"Maturity\",y=\"Yield\",color=\"Date\",title=\"US Treasury Yield Curves\")\\\n",
    ".update_layout(yaxis=dict(tickformat=\".2%\")).update_traces(mode='lines+markers')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "## Background"
   ]
  },
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   "source": [
    "Let $\\mathbf{X}$ be an $n\\times k$ matrix whose columns are centered - i.e., the mean of each column is zero. Then the $k\\times k$ covariance matrix $\\mathbf{\\Sigma}$ is\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{\\Sigma} = \\frac{1}{n}\\mathbf{X'X}\n",
    "\\end{equation}\n",
    "\n",
    "We can diagonalize the covariance matrix by the similarity transformation\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{\\Sigma} = \\mathbf{U\\Lambda U'}\n",
    "\\end{equation}\n",
    "where\n",
    "* $\\mathbf{U}$ is a $k\\times k$ matrix whose columns are eigenvectors of $\\mathbf{\\Sigma}$\n",
    "* $\\mathbf{U}$ is an orthogonal matrix, $\\mathbf{UU'= U'U = I}$\n",
    "* $\\mathbf{\\Lambda}$ is a diagonal matrix consisting of the eigenvalues of $\\mathbf{\\Sigma}$\n",
    "\n",
    "In addition:\n",
    "\n",
    "* If $\\mathbf{\\Sigma}$ is real and symmetric, its eigenvalues are real\n",
    "* If the eigenvalues $\\lambda_i > 0 \\; \\forall\\, i$, then $\\mathbf{\\Sigma}$ is positive definite\n",
    "* If some $\\lambda_i = 0$, then $\\mathbf{\\Sigma}$ is positive semi-definite if the *non-zero* $\\lambda_i$ are greater than zero\n",
    "\n",
    "**Variation and reduction in dimensionality**\n",
    "\n",
    "$$\n",
    "\\text{Total variation} = \\sum_i \\sigma_i^2 = tr(\\mathbf{\\Sigma}) = tr(\\mathbf{\\Lambda}) = \\sum_i \\lambda_i\n",
    "$$\n",
    "where $tr(.)$ is the trace of a matrix and we have used the fact that $tr(\\mathbf{\\Sigma})=tr(\\mathbf{U\\Lambda U'})=tr(\\mathbf{U'U\\Lambda})=tr(\\mathbf{\\Lambda})$.\n",
    "\n",
    "The vectors in $\\mathbf{X}$ can be transformed to a new basis by post-multiplying them with the matrix $\\mathbf{U}$:\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{P} = \\mathbf{X U}\n",
    "\\end{equation}\n",
    "\n",
    "The columns of $\\mathbf{P}$ are known as principal components. These components are orthogonal to each other. The $j$th principal component is \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{P}_j = \\mathbf{X}\\mathbf{U}_j\n",
    "\\end{equation}\n",
    "where $\\mathbf{U}_j$ is the $j$th column of $\\mathbf{U}$.\n",
    "\n",
    "The proportion of total variation explained by the $j$th principal component is $\\frac{\\lambda_i}{\\sum_i \\lambda_i}$. Often, a few principal components can account for a large fraction of the variation. Thus we may choose to ignore the eigenvectors corresponding to the smaller eigenvalues. This is what leads to **dimensionality reduction**.\n",
    "\n",
    "The matrix $\\mathbf{X}$ can be recovered by noting that $\\mathbf{X}=\\mathbf{PU'}$.\n",
    "\n",
    "**Relationship to Singular Value Decomposition (SVD)**\n",
    "\n",
    "Singular value decomposition is a non-unique decomposition of the matrix $\\mathbf{X}$ such that\n",
    "\n",
    "$$\n",
    "\\mathbf{X}_{n\\times k} = \\mathbf{V}_{n\\times n} \\mathbf{S}_{n\\times k} \\mathbf{U'}_{k\\times n}\n",
    "$$\n",
    "\n",
    "and \n",
    "* $\\mathbf{V, U}$ are unitary (orthogonal if $\\mathbf{X}$ is real)\n",
    "* $\\mathbf{S}$ is diagonal\n",
    "\n",
    "From this, we see that\n",
    "\n",
    "$$\n",
    "\\mathbf{\\Sigma} = \\frac{1}{n}\\mathbf{X'X} = \\frac{1}{n} \\mathbf{U\\,S\\,V'\\,V\\,S\\,U'} = \\frac{1}{n} \\mathbf{U\\, S^2\\, U'}\n",
    "$$\n",
    "\n",
    "which means that $\\frac{1}{n} \\mathbf{S^2} = \\mathbf{\\Lambda}$. Since $\\mathbf{S}$ is diagonal, it follows that\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} s_i^2 = \\lambda_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "np.set_printoptions(precision=3, suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA factors for US Treasury yield curve changes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "YCdf = USTYC.set_index(\"Date\").diff().dropna()       # daily changes\n",
    "YCX = YCdf.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 71.314  89.542  95.239  97.401  98.51   99.316  99.729 100.   ]\n"
     ]
    }
   ],
   "source": [
    "# Running PCA on the entire panel\n",
    "\n",
    "dvec = YCdf.index\n",
    "\n",
    "pca = PCA()          # Creating an object\n",
    "fit = pca.fit(YCX)\n",
    "\n",
    "evr = np.cumsum(fit.explained_variance_ratio_)\n",
    "PC = pd.DataFrame(pca.fit_transform(YCX), columns=['PC'+str(x) for x in range(pca.n_components_)])\n",
    "PC = pd.concat([pd.Series(dvec),PC],axis=1)\n",
    "\n",
    "print(100*evr)\n",
    "#PC"
   ]
  }
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