jupyter/Mehra Prescott Yield Curve.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aa29ec91",
   "metadata": {},
   "source": [
    "# Yield curve in the Mehra&ndash;Prescott economy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bacc39a",
   "metadata": {},
   "source": [
    "For this problem, we extend the codes from the main analysis of the Mehra&ndash;Prescott model.\n",
    "\n",
    "To quickly review, Mehra and Prescott (1985) proposed an economy with underlying uncertainty\n",
    "described by a two-state Markov chain $x_{t}$ with transition matrix\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{P}=\\left[\n",
    "\\begin{array}{cc}\n",
    "\\phi  & 1-\\phi  \\\\\n",
    "1-\\phi  & \\phi\n",
    "\\end{array}%\n",
    "\\right] .\n",
    "\\end{equation*}\n",
    "\n",
    "Consumption growth is modeled as a stationary process\n",
    "\n",
    "\\begin{equation*}\n",
    "\\frac{C_{t+1}}{C_{t}}=\\exp \\left( g_{C}\\left( x_{t},x_{t+1}\\right) \\right)\n",
    "\\end{equation*}\n",
    "\n",
    "represented by the matrix $\\Gamma _{C}$ with elements\n",
    "\n",
    "\\begin{equation*}\n",
    "\\left[ \\Gamma _{C}\\right] _{ij}=\\exp \\left( g_{C}\\left(\n",
    "x_{t}=e_{i},x_{t+1}=e_{j}\\right) \\right) .\n",
    "\\end{equation*}\n",
    "\n",
    "Preferences are of the CRRA\\ form with time preference $\\beta $ and relative\n",
    "risk aversion $\\gamma $, implying the SDF of the form\n",
    "\n",
    "\\begin{equation*}\n",
    "\\frac{S_{t+1}}{S_{t}}=\\beta \\left( \\frac{C_{t+1}}{C_{t}}\\right) ^{-\\gamma\n",
    "}=\\beta \\exp \\left( -\\gamma g_{C}\\left( x_{t},x_{t+1}\\right) \\right)\n",
    "\\end{equation*}\n",
    "\n",
    "represented by the matrix $\\Gamma _{S}$ with elements\n",
    "\n",
    "\\begin{equation*}\n",
    "\\left[ \\Gamma _{S}\\right] _{ij}=\\beta \\exp \\left( -\\gamma g_{C}\\left(\n",
    "x_{t}=e_{i},x_{t+1}=e_{j}\\right) \\right) =\\beta \\left[ \\Gamma _{C}\\right]\n",
    "_{ij}^{-\\gamma }\n",
    "\\end{equation*}\n",
    "\n",
    "where the $-\\gamma $ power applies elementwise.\n",
    "\n",
    "Mehra and Precott (1985) assume that the consumption growth matrix is given by\n",
    "\n",
    "\\begin{equation*}\n",
    "\\Gamma _{C}=\\left[\n",
    "\\begin{array}{cc}\n",
    "1+\\mu +\\delta  & 1+\\mu -\\delta  \\\\\n",
    "1+\\mu +\\delta  & 1+\\mu -\\delta\n",
    "\\end{array}%\n",
    "\\right]\n",
    "\\end{equation*}\n",
    "\n",
    "so that state $e_{1}$ is the high-growth state, state $e_{2}$ is the\n",
    "low-growth state."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94e06ec4",
   "metadata": {},
   "source": [
    "## Bond prices and the yield curve\n",
    "\n",
    "A zero-coupon risk-free bond is an asset that pays one unit of the numeraire (consumption, dollars) at a pre-specified date. We can therefore denote the price of a bond that is just about to mature in the current period $t$ as\n",
    "\n",
    "$$Q^{[0]}_t = 1.$$\n",
    "\n",
    "The superindex $[0]$ denotes time to maturity. Then we can apply the recursive valuation formula: if we have the time $t+1$ price of a bond that has $T-1$ remaining period until maturity, denoted $Q^{[T-1]}_{t+1}$, then we can compute the time-$t$ price as\n",
    "\n",
    "$$Q_t^{[T]} = E_t \\left[ \\frac{S_{t+1}}{S_t} Q_{t+1}^{[T-1]} \\right].$$\n",
    "\n",
    "Notice the notation $Q_t^{[T]}$, since in period $t$, the bond has $T$ periods until maturity.\n",
    "\n",
    "The <b>yield</b> (or yield to maturity) on this bond is the average (per period) return investor earns between today and the maturity of the bond. This yield is safe because the terminal payoff at maturity is fixed. From this definition, the yield is\n",
    "\n",
    "$$y_t^{[T]} = \\frac{1}{T} \\log \\frac{1}{Q_t^{[T]}} = -\\frac{1}{T} \\log Q_t^{[T]}.$$\n",
    "\n",
    "The yield on the one-period bond (bond with maturity equal to one period) is the risk-free rate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e74b6161",
   "metadata": {},
   "source": [
    "## Matrix implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a370657d",
   "metadata": {},
   "source": [
    "Since the state follows an $n$-state Markov chain, stationary functions of the state $x_t$ can be represented as vectors of length $n$. We can therefore encode the price of a bond with maturity $T$ using a state-dependent price vector $\\mathbf{q}^{[T]}$ with entries\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{q}^{[T]}_{i}=Q^{[T]}\\left( x_{t}=e_{i}\\right) .\n",
    "\\end{equation*}\n",
    "\n",
    "Using the matrix structure, the recursive valuation equation can be expressed as\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{q}^{[T]}_{i}=q\\left( x_{t}=e_{i}\\right) =\\sum_{j=1}^{n}%\n",
    "\\left[ \\mathbf{P}\\right] _{ij}\\left[ \\Gamma _{S}\\right] _{ij} \\mathbf{q}^{[T-1]}_{j}.\n",
    "\\end{equation*}\n",
    "\n",
    "This can be written in compact form as\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{q}^{[T]}=\\left( \\mathbf{P}\\ast \\Gamma _{S}\\right)\n",
    " \\mathbf{q}^{[T-1]}\n",
    "\\end{equation*}\n",
    "\n",
    "where $\\ast$ is the symbol for elementwise multiplication and $\\mathbf{1}$ is a vector of ones.\n",
    "\n",
    "Consequently, the yield for the bond with maturity $T$ is given by\n",
    "\n",
    "$$\\mathbf{y}^{[T]} = -\\frac{1}{T}\\log \\mathbf{q}^{[T]}.$$\n",
    "\n",
    "Plotting the yield curve in a particular state $x_t = e_i$ corresponds to plotting $\\mathbf{y}^{[T]}_i$ as a function of $T$ for the selected range of horizons."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38f8e39e",
   "metadata": {},
   "source": [
    "## Numerical implementation\n",
    "\n",
    "The numerical implementation extends the function <b>solve_Mehra_Prescott</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "42e25a9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root package econutil imported.\n"
     ]
    }
   ],
   "source": [
    "# import some useful predefined functions from the course package\n",
    "from econutil import *\n",
    "from econutil.plot import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "affa39f6",
   "metadata": {},
   "source": [
    "Function that solves for asset pricing moments in the Mehra-Prescott economy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ac465c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_Mehra_Prescott(model):\n",
    "\n",
    "    S = model[\"SDF\"]\n",
    "    P = model[\"P\"]\n",
    "    GAMMAG = model[\"GAMMAG\"]\n",
    "\n",
    "    N = P.shape[0]\n",
    "    I = np.asmatrix(np.identity(N))\n",
    "    one = np.asmatrix(np.ones([N, 1]))\n",
    "\n",
    "    # first compute the unconditional stationary distribution PII (assuming it is unique)\n",
    "    # unconditional stationary distribution is the eigenvector of P' associated\n",
    "    # with eigenvalue equal to 1 (the largest eigenvalue)\n",
    "    eigval, eigvec = np.linalg.eig(P.transpose())\n",
    "    idx = np.abs(eigval).argsort()\n",
    "    eigval = eigval[idx]\n",
    "    eigvec = eigvec[:, idx]\n",
    "    PII = eigvec[:, -1] / sum(eigvec[:, -1])\n",
    "\n",
    "    # conditional gross risk-free rate (Nx1 vector)\n",
    "    Rf = 1 / (np.multiply(P, S) * one)\n",
    "    # unconditional gross risk-free rate\n",
    "    ERf = Rf.transpose() * PII\n",
    "\n",
    "    # recursive formula for the price-dividend ratio: q =  P.*S.*G * (q + 1)\n",
    "    # solution given by\n",
    "    # q = inv(I - P.*S.*G) * (P.*S.*G)*1 = (I - P.*S.*G) \\ (P.*S.*G)*1\n",
    "    # the .* operator is the elementwise multiplication, 1 is an Nx1 vector of ones\n",
    "\n",
    "    # solution for the infinite-horizon asset only valid\n",
    "    # if P.*S.*G has eigenvalues inside the unit circle\n",
    "    M = np.multiply(np.multiply(P, S), GAMMAG)\n",
    "    eigval, eigvec = np.linalg.eig(M)\n",
    "    maxeig = max(eigval)\n",
    "\n",
    "    if maxeig < 1:\n",
    "        # asset price (Nx1 vector)\n",
    "        q = np.linalg.inv(I - M) * (M * one)\n",
    "        # returns (NxN matrix of returns R(i,j)\n",
    "        R = np.multiply(\n",
    "            np.multiply(np.tile(q.transpose(), [N, 1]) + 1, 1 / np.tile(q, [1, N])),\n",
    "            GAMMAG,\n",
    "        )\n",
    "        # conditional expected returns (Nx1 vector)\n",
    "        EtR = np.asmatrix(np.diag(R * P.transpose())).transpose()\n",
    "        # unconditional expected return\n",
    "        ER = EtR.transpose() * PII\n",
    "        # excess returns, realized and expected\n",
    "        Re = R - np.tile(Rf, [1, N])\n",
    "        EtRe = EtR - Rf\n",
    "        ERe = ER - ERf\n",
    "    else:\n",
    "        q = np.asmatrix(np.empty([N, 1])) * np.nan\n",
    "        R = np.asmatrix(np.empty([N, N])) * np.nan\n",
    "        EtR = np.asmatrix(np.empty([N, 1])) * np.nan\n",
    "        ER = np.nan\n",
    "        Re = np.asmatrix(np.empty([N, N])) * np.nan\n",
    "        EtRe = np.asmatrix(np.empty([N, 1])) * np.nan\n",
    "        ERe = np.nan\n",
    "\n",
    "    # compute the yield curve\n",
    "    capT = 100\n",
    "    \n",
    "    y = np.asmatrix(np.zeros([N, capT]))\n",
    "    q = np.asmatrix(np.ones([N, 1]))\n",
    "    print(np.multiply(P,S))\n",
    "    print(q)\n",
    "    print(q.shape)\n",
    "    for T in range(capT):\n",
    "        q = np.multiply(P, S) * q\n",
    "        y[:, T] = -1 / (T + 1) * np.log(q)\n",
    "        print(y)\n",
    "\n",
    "    sol = {\n",
    "        \"PII\": PII,\n",
    "        \"Rf\": Rf,\n",
    "        \"ERf\": ERf,\n",
    "        \"q\": q,\n",
    "        \"R\": R,\n",
    "        \"EtR\": EtR,\n",
    "        \"ER\": ER,\n",
    "        \"Re\": Re,\n",
    "        \"EtRe\": EtRe,\n",
    "        \"ERe\": ERe,\n",
    "        \"y\": y,\n",
    "    }\n",
    "    return sol"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a83ec840",
   "metadata": {},
   "source": [
    "Solve a list of economies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "69cebf3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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      "[[0.0719435 ]\n",
      " [0.07070537]]\n",
      "[[0.06685449]\n",
      " [0.06570394]]\n",
      "[[0.06212546]\n",
      " [0.06105629]]\n",
      "[[0.05773094]\n",
      " [0.0567374 ]]\n",
      "[[0.05364727]\n",
      " [0.05272401]]\n",
      "[[0.04985247]\n",
      " [0.04899452]]\n",
      "[[0.04632609]\n",
      " [0.04552883]]\n",
      "[[0.04304916]\n",
      " [0.04230829]]\n",
      "[[0.04000403]\n",
      " [0.03931557]]\n",
      "[[0.03717429]\n",
      " [0.03653453]]\n",
      "[[0.03454473]\n",
      " [0.03395022]]\n",
      "[[0.03210116]\n",
      " [0.03154871]]\n",
      "[[0.02983045]\n",
      " [0.02931707]]\n",
      "[[0.02772036]\n",
      " [0.02724329]]\n",
      "[[0.02575952]\n",
      " [0.02531621]]\n",
      "[[0.02393739]\n",
      " [0.02352543]]\n",
      "[[0.02224415]\n",
      " [0.02186133]]\n",
      "[[0.02067068]\n",
      " [0.02031495]]\n",
      "[[0.01920852]\n",
      " [0.01887794]]\n",
      "[[0.01784978]\n",
      " [0.01754259]]\n",
      "[[0.01658716]\n",
      " [0.01630169]]\n",
      "[[0.01541384]\n",
      " [0.01514857]]\n",
      "[[0.01432353]\n",
      " [0.01407702]]\n",
      "[[0.01331033]\n",
      " [0.01308127]]\n",
      "[[0.01236881]\n",
      " [0.01215595]]\n",
      "[[0.01149389]\n",
      " [0.01129608]]\n",
      "[[0.01068085]\n",
      " [0.01049704]]\n",
      "[[0.00992533]\n",
      " [0.00975452]]\n",
      "[[0.00922325]\n",
      " [0.00906452]]\n",
      "[[0.00857083]\n",
      " [0.00842333]]\n",
      "[[0.00796457]\n",
      " [0.0078275 ]]\n",
      "[[0.00740118]\n",
      " [0.00727381]]\n",
      "[[0.00687765]\n",
      " [0.00675929]]\n",
      "[[0.00639115]\n",
      " [0.00628116]]\n",
      "[[0.00593907]\n",
      " [0.00583686]]\n",
      "[[0.00551896]\n",
      " [0.00542398]]\n",
      "[[0.00512857]\n",
      " [0.00504031]]\n",
      "[[0.00476579]\n",
      " [0.00468377]]\n",
      "[[0.00442868]\n",
      " [0.00435246]]\n",
      "[[0.00411541]\n",
      " [0.00404459]]\n",
      "[[0.0038243 ]\n",
      " [0.00375849]]\n",
      "[[0.00355379]\n",
      " [0.00349263]]\n",
      "[[0.0033024 ]\n",
      " [0.00324557]]\n",
      "[[0.0030688 ]\n",
      " [0.00301599]]\n",
      "[[0.00285173]\n",
      " [0.00280265]]\n",
      "[[0.00265001]\n",
      " [0.0026044 ]]\n",
      "[[0.00246256]\n",
      " [0.00242018]]\n",
      "[[0.00228837]\n",
      " [0.00224898]]\n",
      "[[0.0021265]\n",
      " [0.0020899]]\n",
      "[[0.00197607]\n",
      " [0.00194207]]\n",
      "[[0.00183629]\n",
      " [0.00180469]]\n",
      "[[0.0017064 ]\n",
      " [0.00167704]]\n",
      "[[0.0015857 ]\n",
      " [0.00155841]]\n",
      "[[0.00147353]\n",
      " [0.00144817]]\n",
      "[[0.0013693 ]\n",
      " [0.00134573]]\n",
      "[[0.00127244]\n",
      " [0.00125054]]\n",
      "[[0.00118243]\n",
      " [0.00116208]]\n",
      "[[0.00109879]\n",
      " [0.00107988]]\n",
      "[[0.00102107]\n",
      " [0.0010035 ]]\n",
      "[[0.00094884]\n",
      " [0.00093251]]\n",
      "[[0.00088172]\n",
      " [0.00086655]]\n",
      "[[0.00081935]\n",
      " [0.00080525]]\n",
      "[[0.0007614 ]\n",
      " [0.00074829]]\n",
      "[[0.00070754]\n",
      " [0.00069536]]\n",
      "[[0.00065749]\n",
      " [0.00064617]]\n",
      "[[0.34493813 0.60682589]\n",
      " [0.45724357 0.45778093]]\n",
      "[[1.]\n",
      " [1.]]\n",
      "(2, 1)\n",
      "[[0.95176402]\n",
      " [0.9150245 ]]\n",
      "[[0.88356026]\n",
      " [0.85406875]]\n",
      "[[0.82304465]\n",
      " [0.79497863]]\n",
      "[[0.7663131 ]\n",
      " [0.74025793]]\n",
      "[[0.71353828]\n",
      " [0.6892677 ]]\n",
      "[[0.66439205]\n",
      " [0.6417944 ]]\n",
      "[[0.61863161]\n",
      " [0.59759023]]\n",
      "[[0.57602285]\n",
      " [0.55643074]]\n",
      "[[0.53634882]\n",
      " [0.51810613]]\n",
      "[[0.49940737]\n",
      " [0.48242116]]\n",
      "[[0.46501029]\n",
      " [0.44919402]]\n",
      "[[0.43298234]\n",
      " [0.41825542]]\n",
      "[[0.40316034]\n",
      " [0.38944775]]\n",
      "[[0.37539235]\n",
      " [0.36262422]]\n",
      "[[0.3495369 ]\n",
      " [0.33764819]]\n",
      "[[0.32546227]\n",
      " [0.3143924 ]]\n",
      "[[0.3030458 ]\n",
      " [0.29273838]]\n",
      "[[0.28217328]\n",
      " [0.27257579]]\n",
      "[[0.26273837]\n",
      " [0.25380192]]\n",
      "[[0.24464205]\n",
      " [0.23632111]]\n",
      "[[0.22779214]\n",
      " [0.2200443 ]]\n",
      "[[0.21210277]\n",
      " [0.20488858]]\n",
      "[[0.19749403]\n",
      " [0.19077671]]\n",
      "[[0.18389147]\n",
      " [0.17763681]]\n",
      "[[0.1712258 ]\n",
      " [0.16540194]]\n",
      "[[0.15943248]\n",
      " [0.15400975]]\n",
      "[[0.14845145]\n",
      " [0.1434022 ]]\n",
      "[[0.13822673]\n",
      " [0.13352526]]\n",
      "[[0.12870626]\n",
      " [0.1243286 ]]\n",
      "[[0.11984151]\n",
      " [0.11576537]]\n",
      "[[0.11158733]\n",
      " [0.10779194]]\n",
      "[[0.10390167]\n",
      " [0.10036769]]\n",
      "[[0.09674536]\n",
      " [0.09345478]]\n",
      "[[0.09008194]\n",
      " [0.08701801]]\n",
      "[[0.08387748]\n",
      " [0.08102457]]\n",
      "[[0.07810035]\n",
      " [0.07544394]]\n",
      "[[0.07272113]\n",
      " [0.07024768]]\n",
      "[[0.0677124 ]\n",
      " [0.06540932]]\n",
      "[[0.06304866]\n",
      " [0.0609042 ]]\n",
      "[[0.05870613]\n",
      " [0.05670937]]\n",
      "[[0.0546627 ]\n",
      " [0.05280347]]\n",
      "[[0.05089776]\n",
      " [0.04916659]]\n",
      "[[0.04739214]\n",
      " [0.0457802 ]]\n",
      "[[0.04412797]\n",
      " [0.04262705]]\n",
      "[[0.04108862]\n",
      " [0.03969108]]\n",
      "[[0.03825861]\n",
      " [0.03695733]]\n",
      "[[0.03562351]\n",
      " [0.03441186]]\n",
      "[[0.03316992]\n",
      " [0.03204172]]\n",
      "[[0.03088531]\n",
      " [0.02983482]]\n",
      "[[0.02875806]\n",
      " [0.02777992]]\n",
      "[[0.02677733]\n",
      " [0.02586656]]\n",
      "[[0.02493302]\n",
      " [0.02408498]]\n",
      "[[0.02321574]\n",
      " [0.02242611]]\n",
      "[[0.02161673]\n",
      " [0.02088149]]\n",
      "[[0.02012786]\n",
      " [0.01944326]]\n",
      "[[0.01874154]\n",
      " [0.01810409]]\n",
      "[[0.0174507 ]\n",
      " [0.01685716]]\n",
      "[[0.01624877]\n",
      " [0.01569611]]\n",
      "[[0.01512962]\n",
      " [0.01461502]]\n",
      "[[0.01408756]\n",
      " [0.0136084 ]]\n",
      "[[0.01311727]\n",
      " [0.01267111]]\n",
      "[[0.01221381]\n",
      " [0.01179838]]\n",
      "[[0.01137257]\n",
      " [0.01098576]]\n",
      "[[0.01058928]\n",
      " [0.01022911]]\n",
      "[[0.00985993]\n",
      " [0.00952457]]\n",
      "[[0.00918082]\n",
      " [0.00886856]]\n",
      "[[0.00854848]\n",
      " [0.00825773]]\n",
      "[[0.0079597 ]\n",
      " [0.00768897]]\n",
      "[[0.00741147]\n",
      " [0.00715939]]\n",
      "[[0.006901  ]\n",
      " [0.00666628]]\n",
      "[[0.00642569]\n",
      " [0.00620713]]\n",
      "[[0.00598311]\n",
      " [0.00577961]]\n",
      "[[0.00557102]\n",
      " [0.00538154]]\n",
      "[[0.00518731]\n",
      " [0.00501088]]\n",
      "[[0.00483003]\n",
      " [0.00466575]]\n",
      "[[0.00449736]\n",
      " [0.00434439]]\n",
      "[[0.0041876 ]\n",
      " [0.00404517]]\n",
      "[[0.00389918]\n",
      " [0.00376655]]\n",
      "[[0.00363062]\n",
      " [0.00350713]]\n",
      "[[0.00338056]\n",
      " [0.00326557]]\n",
      "[[0.00314772]\n",
      " [0.00304065]]\n",
      "[[0.00293092]\n",
      " [0.00283123]]\n",
      "[[0.00272905]\n",
      " [0.00263622]]\n",
      "[[0.00254108]\n",
      " [0.00245465]]\n",
      "[[0.00236606]\n",
      " [0.00228559]]\n",
      "[[0.0022031 ]\n",
      " [0.00212816]]\n",
      "[[0.00205136]\n",
      " [0.00198159]]\n",
      "[[0.00191007]\n",
      " [0.0018451 ]]\n",
      "[[0.00177851]\n",
      " [0.00171802]]\n",
      "[[0.00165602]\n",
      " [0.00159969]]\n",
      "[[0.00154196]\n",
      " [0.00148951]]\n",
      "[[0.00143575]\n",
      " [0.00138692]]\n",
      "[[0.00133686]\n",
      " [0.00129139]]\n",
      "[[0.00124479]\n",
      " [0.00120245]]\n",
      "[[0.00115905]\n",
      " [0.00111963]]\n",
      "[[0.00107922]\n",
      " [0.00104251]]\n",
      "[[0.00100489]\n",
      " [0.00097071]]\n",
      "[[0.00093568]\n",
      " [0.00090385]]\n",
      "[[0.00087123]\n",
      " [0.0008416 ]]\n",
      "[[0.00081122]\n",
      " [0.00078363]]\n"
     ]
    }
   ],
   "source": [
    "# model specification\n",
    "model = {\"PHI\": 0.43, \"MU\": 0.018, \"DELTA\": 0.036}\n",
    "\n",
    "model[\"P\"] = np.asmatrix(\n",
    "    [[model[\"PHI\"], 1 - model[\"PHI\"]], [1 - model[\"PHI\"], model[\"PHI\"]]]\n",
    ")\n",
    "model[\"GAMMAC\"] = np.asmatrix(\n",
    "    [\n",
    "        [1 + model[\"MU\"] + model[\"DELTA\"], 1 + model[\"MU\"] - model[\"DELTA\"]],\n",
    "        [1 + model[\"MU\"] + model[\"DELTA\"], 1 + model[\"MU\"] - model[\"DELTA\"]],\n",
    "    ]\n",
    ")\n",
    "model[\"GAMMAG\"] = model[\"GAMMAC\"].copy()\n",
    "\n",
    "# define a list of economies via combinations of parameters [BETA, GAMMA]\n",
    "model_vec = [[0.99, 2], [0.96, 2], [0.99, 4]]\n",
    "yield_curves = [0] * 3\n",
    "\n",
    "for i, m in enumerate(model_vec):\n",
    "    model[\"BETA\"] = m[0]\n",
    "    model[\"GAMMA\"] = m[1]\n",
    "    model[\"SDF\"] = model[\"BETA\"] * np.power(model[\"GAMMAC\"], -model[\"GAMMA\"])\n",
    "    sol = solve_Mehra_Prescott(model)\n",
    "    yield_curves[i] = sol[\"y\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e6d21cbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display yield curve results\n",
    "capT = yield_curves[0].shape[1]\n",
    "\n",
    "param = {\n",
    "    \"figsize\": [15, 6],\n",
    "    \"fontsize\": 16,\n",
    "    \"subplots\": [1, 2],\n",
    "    \"title\": \"\",\n",
    "    \"xlim\": [0, capT],\n",
    "    \"ylim\": [0, 9],\n",
    "    \"xlabel\": \"maturity $T$\",\n",
    "    \"ylabel\": \"yield $y^{[T]}_1$\",\n",
    "    \"ylogscale\": False,\n",
    "    \"showgrid\": True,\n",
    "    \"highlightzero\": False,\n",
    "    \"showNBERrecessions\": False,\n",
    "    \"showNBERrecessions_y\": [0, 7],\n",
    "}\n",
    "\n",
    "fig, ax = GenerateTSPlot(param)\n",
    "\n",
    "ax[0, 0].plot(\n",
    "    np.linspace(1, capT, capT),\n",
    "    np.squeeze(np.asarray(yield_curves[0][0, :])) * 100,\n",
    "    linewidth=1,\n",
    "    marker=\"*\",\n",
    "    color=tolColor[\"tolVibrantBlue\"],\n",
    "    linestyle=\"solid\",\n",
    "    label=\"$\\\\beta = \"\n",
    "    + str(model_vec[0][0])\n",
    "    + \"$, $\\\\gamma = \"\n",
    "    + str(model_vec[0][1])\n",
    "    + \" $\",\n",
    ")\n",
    "ax[0, 0].plot(\n",
    "    np.linspace(1, capT, capT),\n",
    "    np.squeeze(np.asarray(yield_curves[1][0, :])) * 100,\n",
    "    linewidth=1,\n",
    "    marker=\"*\",\n",
    "    color=tolColor[\"tolVibrantOrange\"],\n",
    "    linestyle=\"solid\",\n",
    "    label=\"$\\\\beta = \"\n",
    "    + str(model_vec[1][0])\n",
    "    + \"$, $\\\\gamma = \"\n",
    "    + str(model_vec[1][1])\n",
    "    + \" $\",\n",
    ")\n",
    "ax[0, 0].plot(\n",
    "    np.linspace(1, capT, capT),\n",
    "    np.squeeze(np.asarray(yield_curves[2][0, :])) * 100,\n",
    "    linewidth=1,\n",
    "    marker=\"*\",\n",
    "    color=tolColor[\"tolVibrantTeal\"],\n",
    "    linestyle=\"solid\",\n",
    "    label=\"$\\\\beta = \"\n",
    "    + str(model_vec[2][0])\n",
    "    + \"$, $\\\\gamma = \"\n",
    "    + str(model_vec[2][1])\n",
    "    + \" $\",\n",
    ")\n",
    "\n",
    "ax[0, 0].set_title(\"Yield curve for state $e_1$\")\n",
    "x = ax[0, 0].legend(loc=\"lower right\")\n",
    "\n",
    "ax[0, 1].plot(\n",
    "    np.linspace(1, capT, capT),\n",
    "    np.squeeze(np.asarray(yield_curves[0][1, :])) * 100,\n",
    "    linewidth=1,\n",
    "    marker=\"*\",\n",
    "    color=tolColor[\"tolVibrantBlue\"],\n",
    "    linestyle=\"solid\",\n",
    "    label=\"$\\\\beta = \"\n",
    "    + str(model_vec[0][0])\n",
    "    + \"$, $\\\\gamma = \"\n",
    "    + str(model_vec[0][1])\n",
    "    + \" $\",\n",
    ")\n",
    "ax[0, 1].plot(\n",
    "    np.linspace(1, capT, capT),\n",
    "    np.squeeze(np.asarray(yield_curves[1][1, :])) * 100,\n",
    "    linewidth=1,\n",
    "    marker=\"*\",\n",
    "    color=tolColor[\"tolVibrantOrange\"],\n",
    "    linestyle=\"solid\",\n",
    "    label=\"$\\\\beta = \"\n",
    "    + str(model_vec[1][0])\n",
    "    + \"$, $\\\\gamma = \"\n",
    "    + str(model_vec[1][1])\n",
    "    + \" $\",\n",
    ")\n",
    "ax[0, 1].plot(\n",
    "    np.linspace(1, capT, capT),\n",
    "    np.squeeze(np.asarray(yield_curves[2][1, :])) * 100,\n",
    "    linewidth=1,\n",
    "    marker=\"*\",\n",
    "    color=tolColor[\"tolVibrantTeal\"],\n",
    "    linestyle=\"solid\",\n",
    "    label=\"$\\\\beta = \"\n",
    "    + str(model_vec[2][0])\n",
    "    + \"$, $\\\\gamma = \"\n",
    "    + str(model_vec[2][1])\n",
    "    + \" $\",\n",
    ")\n",
    "\n",
    "ax[0, 1].set_title(\"Yield curve for state $e_2$\")\n",
    "ax[0, 1].set_ylabel(\"yield $y^{[T]}_2$\")\n",
    "x = ax[0, 1].legend(loc=\"lower right\")\n",
    "\n",
    "fig.set_facecolor(\"#FFFFFF\")\n",
    "fig.savefig(\"graphs/asset_pricing_mehra_prescott_yield_curves.pdf\", bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc79ce44",
   "metadata": {},
   "source": [
    "The left panel depicts the yield curves in alternative economies for state $x_t = e_1$ (state that predicts that low growth is more likely going into the next period, because $\\phi<0.5$, while the right panel shows yield curves for state $x_t = e_2$. Same colors depict the yield curves in the same economy.\n",
    "\n",
    "To understand the shapes of the curves, we have to understand that interest rates are determined by three forces:\n",
    "\n",
    "* <b>Time preference</b>: The higher the impatience, the higher must be the interest rates to compensate investors for saving\n",
    "\n",
    "* <b>Elasticity of substitution over time</b>: Investors dislike imbalanced consumption over time and want to smooth it out. When the economy is growing more (or agents have lower elasticity of substitution), agents want to borrow more to be able to consume more today, paying off the debt by sacrificing consumption in the future. To disincentivize this, interest rates must be higher.\n",
    "\n",
    "* <b>Risk aversion</b>: Risk-free bonds are a safe asset, so when the economy is riskier or agents more risk averse, these safe assets are more attractive, and interest rates must decrease in equilibrium to disincentivize this saving.\n",
    "\n",
    "First, focus on the baseline economy ($\\beta=0.99$, $\\gamma =2$, blue lines). When growth is expected to be low (left panel), shorter-maturity interest rates are lower than when growth is expected to be high (right panel). This is in line with the elasticity of substitution effect. When growth is expected to be high, agents want to borrow more, and to disincentivize this (in order to clear the market for the risk-free asset), interest rates must be higher to make borrowing more costly.\n",
    "\n",
    "Also notice, that while short-maturity yields fluctuate across states, long-maturity yields do not. This is a reflection of the stationarity of the economy. Over longer horizons, expected growth rate is independent on the current state.\n",
    "\n",
    "Second, the orange lines depict the effect of increasing the impatience (a decrease in $\\beta$ relative to the benchmark economy). More impatient agents would like to borrow more, so to disincentivize this in equilibrium, interest rates must increase.\n",
    "\n",
    "Third, the green lines (relative to blue lines) represent the effect of increasing the risk aversion parameter $\\gamma$. However, one has to understand that an increase in $\\gamma$ has two effects: it increases risk aversion but also decreases willingness to substitute intertemporally.\n",
    "\n",
    "The increase in risk aversion makes safe assets more attractive, which will decrease interest rates in equilibrium. The decrease in intertemporal elasticity of substitution makes agents want to borrow more, which increases interest rates in equilibrium. The latter effect dominates, so interest rates increase.\n",
    "\n",
    "There is one more notable observation to make. The Mehra and Prescott (1985) economy suffers from risk premia that are too low relatively to empirically observed values. These risk premia can increase by increasing $\\gamma$ substantially, however, we observed that this increases the risk-free rate way too much. The graph above shows another undesirable efffect of increasing risk aversion: the volatility of short-run rates (the difference in the short run rate between state $e_1$ and state $e_2$ increases substantially. However, we know that empirically, interest rates are rather smooth. So increasing risk aversion creates another puzzle: some of the models that attempt to fit risk premia generate volatility of risk-free rates that are at odds with data."
   ]
  }
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