2 - Zero-Coupon Bonds.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from bond_pricing import equiv_rate, annuity_pv, annuity_fv, annuity_rate, annuity_instalment\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import PercentFormatter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Yields to Maturity on Zero-Coupon Bonds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$PV=\\frac{FV}{(1+\\frac{APR_{PER}}{PER})^{Years \\times PER}}$$\n",
    "$$APR_{PER}=\\left[\\left(\\frac{FV}{PV}\\right)^{\\frac{1}{Years\\times PER}} - 1\\right]\\times PER$$\n",
    "\n",
    "- PV = present value, or price, of the bond, \n",
    "- FV = future value, which usually is 100 (percent of par value) at maturity, \n",
    "- Years = number of years to maturity, \n",
    "- PER = periodicity—the number of evenly-spaced periods in the year; and \n",
    "- $APR_{PER}$ = yield to maturity, stated as an annual percentage rate corresponding to PER.\n",
    "\n",
    "The “s.a.” tag, commonly used in bond markets, means that the yield is stated on a semiannual bond basis and is an annual percentage rate that has a periodicity of 2. The assumption of two periods in the year, while totally arbitrary, is common in financial markets because the yield on the zero then can be compared directly to yields to maturity on traditional semiannual payment fi xedincome bonds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm =  0.10239 (s.a)\n"
     ]
    }
   ],
   "source": [
    "pv = 50\n",
    "fv = 1000\n",
    "years = 30\n",
    "per = 2\n",
    "\n",
    "ytm = ((fv/pv)**(1/(years*per)) - 1) * per\n",
    "print(f'{ytm = : 0.5f} (s.a)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm =  0.10239 (s.a)\n"
     ]
    }
   ],
   "source": [
    "pv = 50\n",
    "fv = 1000\n",
    "years = 30\n",
    "per = 2\n",
    "\n",
    "ytm = annuity_rate(n_periods=years, instalment=0, pv=pv, terminal_payment=fv, immediate_start=False, cf_freq=1, comp_freq=2)\n",
    "print(f'{ytm = : 0.5f} (s.a)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm =  0.10151 (s.a)\n"
     ]
    }
   ],
   "source": [
    "pv = 250\n",
    "fv = 1000\n",
    "years = 14\n",
    "per = 2\n",
    "\n",
    "ytm = ((fv/pv)**(1/(years)) - 1)\n",
    "ytm = equiv_rate(rate=ytm, from_freq=1, to_freq=2)\n",
    "print(f'{ytm = : 0.5f} (s.a)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm =  0.05174 (s.a)\n"
     ]
    }
   ],
   "source": [
    "pv = 60\n",
    "fv = 100\n",
    "years = 10\n",
    "per = 2\n",
    "\n",
    "ytm = ((fv/pv)**(1/(years*per)) - 1) * per\n",
    "print(f'{ytm = : 0.5f} (s.a)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Continuous Compounding "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are times in bond math when it is convenient to assume continuous compounding. That is, there are assumed to be an infinite number of compounding periods in the year. Continuous-time finance is particularly useful in **interest rate term structure** and **option valuation models**. The formula for the APR given PER = ∞ and the two cash flows PV and FV involves the natural logarithm (LN):\n",
    "\n",
    "$$APR_{∞}=\\frac{1}{Years}\\times\\ln\\left(\\frac{FV}{PV}\\right)$$\n",
    "$$APR_{∞}=PER\\times\\ln\\left(1+\\frac{APR_{PER}}{PER}\\right)$$\n",
    "$$APR_{PER}=PER\\times\\left[EXP\\left(\\frac{APR_{∞}}{PER}\\right)-1\\right]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm_1 = 0.05108\n",
      "ytm_2 = 0.05108\n",
      "ytm_3 = 0.05108\n"
     ]
    }
   ],
   "source": [
    "pv = 60\n",
    "fv = 100\n",
    "years = 10\n",
    "\n",
    "ytm_1 = np.log(fv/pv) * 1/years\n",
    "ytm_2 = np.log(1 + 0.05174/2) * 2\n",
    "ytm_3 = equiv_rate(rate=0.05174, from_freq=2, to_freq=np.inf)\n",
    "print(f'{ytm_1 = :0.5f}\\n{ytm_2 = :0.5f}\\n{ytm_3 = :0.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm_1 = 0.05174\n",
      "ytm_2 = 0.05174\n"
     ]
    }
   ],
   "source": [
    "pv = 60\n",
    "fv = 100\n",
    "years = 10\n",
    "\n",
    "ytm_1 = 2 * (np.exp(0.05108/2) - 1)\n",
    "ytm_2 = equiv_rate(rate=0.05108, from_freq=np.inf, to_freq=2)\n",
    "print(f'{ytm_1 = :0.5f}\\n{ytm_2 = :0.5f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constant-Yield Price Trajectory / Carrying Value & Horizon Yield"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A useful yardstick for assessing a **horizon yield** (holding-period rate of return) when the bond is sold prior to maturity is the **constant-yield price trajectory**. This is the path the bond price will take over the time to maturity assuming no default.\n",
    "\n",
    "The movement along the constant-yield price trajectory represents **interest earned** and is also called the **carrying values** for the bond."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rate = 0.05174\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Year 0 PV = 60.0\n",
      "Year 1 PV = 63.145\n",
      "Year 2 PV = 66.454\n",
      "Year 3 PV = 69.937\n",
      "Year 4 PV = 73.602\n",
      "Year 5 PV = 77.46\n",
      "Year 6 PV = 81.519\n",
      "Year 7 PV = 85.792\n",
      "Year 8 PV = 90.288\n",
      "Year 9 PV = 95.02\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pv = 60\n",
    "fv = 100\n",
    "per = 2\n",
    "years = 10\n",
    "rate = ((fv/pv)**(1/(years*per)) - 1) * per\n",
    "print(f'{rate = :0.5f}')\n",
    "\n",
    "years_x = np.arange(0, 11)\n",
    "\n",
    "def pv(fv, rate, years, per):\n",
    "  return fv / ((1 + rate/per)**(years*per))\n",
    "\n",
    "pv_y = pv(fv, rate, years_x, per)\n",
    "\n",
    "plt.figure(num=0, dpi=150)\n",
    "plt.plot(10-years_x, pv_y)\n",
    "plt.ylim(ymin=0)\n",
    "plt.title('Constant-Yield Price Trajectory, 10-Year, \\n Zero-Coupon Corporate Bond Priced to Yield 5.174% (s.a.)')\n",
    "plt.xlabel('Years')\n",
    "plt.ylabel('Price')\n",
    "\n",
    "for i in range(10):\n",
    "  print(f\"Year {i} PV =\", round(fv/(1 + rate/per)**((10-i)*per), 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the investor is able to sell the corporate zero in 2 years at a yield less than 5.174% (s.a.), the sale price will be above the trajectory and there will be a capital gain. For example, suppose that the investor sells the zero at year 2 for a price of 68 (percent of par value). At that time, the now 8-year corporate zero is trading at 4.879% (s.a.)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm = 4.87935%\n"
     ]
    }
   ],
   "source": [
    "fv = 100\n",
    "pv = 68\n",
    "years = 8\n",
    "per = 2\n",
    "\n",
    "ytm = ((fv/pv)**(1/(years*per)) - 1) * per * 100\n",
    "print(f'{ytm = :.5f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The investor’s realized 2-year holding-period rate of return turns out to be 6.357% (s.a.), which is greater than the original yield of 5.174% because the **price is above the constant-yield trajectory**.\n",
    "\n",
    "Notice that we set FV equal to 68—the redemption value of 100 is irrelevant here because the bond is sold for 68."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm = 6.35710%\n"
     ]
    }
   ],
   "source": [
    "fv = 68\n",
    "pv = 60\n",
    "years = 2\n",
    "per = 2\n",
    "\n",
    "ytm = ((fv/pv)**(1/(years*per)) - 1) * per * 100\n",
    "print(f'{ytm = :.5f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much is the capital gain if the bond that is purchased at 60 is sold in year 2 at 68? Unlike equity, it should not be 8, the difference between the sale and purchase price. The movement along the constant-yield price trajectory shown in plot above represents interest earned. So, interest income is 3.145 for the first year (= 63.145 – 60) and 3.309 for the second year (= 66.454 – 63.145). The key point is that, in principle, interest income is the change in price associated with the **passage of time**.\n",
    "\n",
    "Capital gains and losses are the changes in price related to **changes in value**—for bonds that means a **change in the yield** and a **price above or below the carrying value**. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that the investor does not sell after two years and instead holds on to the bond for seven years. At that time, the now 3-year corporate zero is sold for 83 because it is being priced to yield 6.308% (s.a.)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.308432926101526\n"
     ]
    }
   ],
   "source": [
    "# Yield at which the bond is sold\n",
    "pv = 83\n",
    "fv = 100\n",
    "years = 3 # remaining years\n",
    "per = 2\n",
    "\n",
    "ytm = ((fv/pv)**(1/(years*per)) - 1) * per\n",
    "print(ytm*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The investor’s realized 7-year holding-period rate of return is 4.690% (s.a.), which is less than 5.174% because the sale price is below the trajectory.\n",
    "\n",
    "In this case, there is a capital loss even though the investor buys at 60 and sells later at the much higher price of 83. The relevant comparison is between 83 and 85.792, the carrying value on the constant-yield price trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.689798589683569\n"
     ]
    }
   ],
   "source": [
    "# Realized return \n",
    "pv = 60\n",
    "fv = 83\n",
    "years = 7 # remaining years\n",
    "per = 2\n",
    "\n",
    "ytm = ((fv/pv)**(1/(years*per)) - 1) * per\n",
    "print(ytm*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There in an important investment lesson in these scenarios. Suppose the buyer of the 10-year corporate zero actually has an investment horizon of 10 years and plans to hold the bond to maturity. Then the unrealized gain in year 2 caused by the lower yield at that time, as well as the unrealized loss in year 7 caused by the higher yield, has no impact on the realized total return. The bull market prevailing in year 2 and the bear market in year 7 are irrelevant news\n",
    "stories to this investor. The bond buyer achieves a locked-in yield to maturity of 5.174% (s.a.) regardless of the path that the price takes to its destination of par value—before taxes and inflation and assuming no default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.791720044409516 25.791720044409516 0.06308432926101526\n",
      "0.04689798589683569\n"
     ]
    }
   ],
   "source": [
    "# Horizon Yield & Capital Gains\n",
    "\n",
    "def horizon_yield(purchase_price, current_price, years, per):\n",
    "  return ((current_price/purchase_price)**(1/(years*per)) - 1) * per\n",
    "\n",
    "def capital_gains(purchase_price, current_price, par_value, years_to_maturity_purchase, years_to_mat, per):\n",
    "  purchase_ytm = ((par_value/purchase_price)**(1/(years_to_maturity_purchase*per)) - 1) * per\n",
    "  constant_yield_price = par_value / ((1 + purchase_ytm/per)**(years_to_mat*per))\n",
    "  current_ytm = ((par_value/current_price)**(1/(years_to_mat*per)) - 1) * per\n",
    "  return (current_price - constant_yield_price), (constant_yield_price - purchase_price), current_ytm\n",
    "\n",
    "purchase_price = 60\n",
    "current_price = 83\n",
    "par_value = 100\n",
    "years_to_maturity_purchase = 10\n",
    "years_to_mat = 3\n",
    "per = 2\n",
    "\n",
    "capital_gain, interest_earned, current_ytm = capital_gains(purchase_price, current_price, par_value, years_to_maturity_purchase, years_to_mat, per)\n",
    "print(capital_gain, interest_earned, current_ytm)\n",
    "print(horizon_yield(purchase_price, current_price, years_to_maturity_purchase-years_to_mat, per))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Breakeven Curve & Rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This breakeven curve represents the rate changes required over a one year time horizon such that investors in all maturities have the same realized return; specifically the current 1-year yield.\n",
    "\n",
    "The mechanics of the break-even curve are easily revealed – with an upward sloping curve, an investor earns a higher yield by investing in longer duration securities. As such, if rates were to remain unchanged, an investor holding the 10-year Treasury note would outperform an investor holding the 1-year Treasury bill. The *break-even curve simply solves for the rate increase required for the return on the 10-year Treasury to equal that of the 1-year Treasury.* \n",
    "\n",
    "Of course, if the yield curve is perfectly flat, the break-even curve would be identical to the current yield curve. If the yield curve is inverted, break-even rates would be below the prevailing curve. Additionally, break-even curves can be calculated for a range of horizons – in each case the yield changes correspond to rate changes required to break-even with that horizon’s zero coupon Treasury security.\n",
    "\n",
    "The importance of the break-even curve for investors considering tactical interest rate investing is that it provides a framework for implementing interest rate views. For an investor to profit from a bearish view on bonds over a given time horizon, the investor must expect rates to rise more than the break-even level over that period. For an investor to profit from a bullish view on bonds, the investor must expect rates to rise less than the horizon break-even level.\n",
    "\n",
    "A breakeven rate is very useful in assessing the risk in the “maturity extension” strategy.\n",
    "\n",
    "Reference: [The Break-Even Yield Curve - NISA](https://nisa.com/wp-content/uploads/2011/08/NISA-Break-Even-Yield-Curve.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Break-even yield curves are calculated to understand the yield you need to earn on an investment to equate it to another investment over different maturities. It's a way to compare the attractiveness of investments.\n",
    "\n",
    "Here’s a simplified view:\n",
    "1. **Select Short and Long Maturity**: Choose the starting point (e.g., 1 year) and the ending point (e.g., 2 years).\n",
    "2. **Discount Factors**: Compute the discount factors for both short and long maturities. Discount factor = $(1 + yield)^{maturity}$.\n",
    "3. **Ratio of Discount Factors**: Divide the long maturity discount factor by the short maturity discount factor.\n",
    "4. **Adjust for Time**: Calculate the *geometric average rate over the difference in maturities*.\n",
    "5. **Compute Break-Even Yield**: Adjust the geometric rate to find the break-even yield.\n",
    "In mathematical terms, for short maturity $S$ with yield $Y_{S}$, and long maturity $L$ with yield $Y_{L}$:\n",
    "$$\\text{Short Discount} = (1 + Y_S)^{S}$$\n",
    "$$\\text{Long Discount} = (1 + Y_L)^{L}$$\n",
    "$$\\text{Break-Even Yield} = \\left( \\frac{\\text{Long Discount}}{\\text{Short Discount}} \\right)^{\\frac{1}{L-S}} - 1$$\n",
    "This process allows you to see the required yield for different maturities to make investments equivalent in terms of returns.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17b5aad4fe0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For ease of comparison, this description approximates the break-even calculation for a “constant maturity” 10-year security. \n",
    "# A similar result would apply to a bond that is allowed to age over the horizon.\n",
    "\n",
    "# June 30th, 2011 - Daily Treasury Par Yield Curve Rates\n",
    "yield_curve = {1: 0.0019,\n",
    "               2: 0.0045,\n",
    "               3: 0.0081,\n",
    "               5: 0.0176,\n",
    "               7: 0.0250,\n",
    "               10: 0.0318,\n",
    "               20: 0.0409,\n",
    "               30: 0.0438}\n",
    "\n",
    "mat_x = [year for year in yield_curve.keys() if year != 1]\n",
    "\n",
    "def breakeven_rate(short_maturity, short_yield, long_maturity, long_yield, per):\n",
    "  short_discount = (1 + short_yield/per)**(short_maturity*per)\n",
    "  long_discount = (1 + long_yield/per)**(long_maturity*per)\n",
    "  return ((long_discount / short_discount)**(1/((long_maturity - short_maturity)*per)) - 1) * per\n",
    "\n",
    "breakeven_y = [breakeven_rate(short_maturity=1,short_yield=yield_curve[1], long_maturity=year, long_yield=yield_curve[year], per=1) for year in mat_x]\n",
    "\n",
    "plt.figure(num=0, dpi=150)\n",
    "plt.plot(yield_curve.keys(), yield_curve.values(), label='Yield Curve')\n",
    "plt.plot(mat_x, breakeven_y, label='Break-Even Yield Curve')\n",
    "plt.ylim(ymin=0, ymax=0.05)\n",
    "plt.gca().yaxis.set_major_formatter(PercentFormatter(xmax=1, decimals=0))\n",
    "plt.title('Daily Treasury Par Yield Curve Rates & Break-Even Yield Curve')\n",
    "plt.xlabel('Maturity (Years)')\n",
    "plt.ylabel('Yield, %')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mat. = 2 short_fv = 99.29, long_sale = 99.29, yield_diff = 26bps\n",
      "Mat. = 3 short_fv = 97.79, long_sale = 97.79, yield_diff = 31bps\n",
      "Mat. = 5 short_fv = 91.82, long_sale = 91.82, yield_diff = 40bps\n",
      "Mat. = 7 short_fv = 84.29, long_sale = 84.29, yield_diff = 39bps\n",
      "Mat. = 10 short_fv = 73.26, long_sale = 73.26, yield_diff = 34bps\n",
      "Mat. = 20 short_fv = 44.94, long_sale = 44.94, yield_diff = 21bps\n",
      "Mat. = 30 short_fv = 27.69, long_sale = 27.69, yield_diff = 15bps\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(breakeven_y)):\n",
    "  long_purchase = 100 / (1 + yield_curve[mat_x[i]])**mat_x[i]\n",
    "  short_fv = long_purchase * (1 + yield_curve[1])\n",
    "  long_sale = 100 / (1 + breakeven_y[i])**(mat_x[i] - 1)\n",
    "  yield_diff = (breakeven_y[i] - yield_curve[mat_x[i]])*10_000\n",
    "  print(f'Mat. = {mat_x[i]} {short_fv = :0.2f}, {long_sale = :0.2f}, {yield_diff = :0.0f}bps')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For calculating break-even yields above a Treasury yield curve:\n",
    "1. **Rate Changes Over One Year**: The break-even curve indicates how rates need to adjust over one year so that all investors, regardless of the bond's maturity, realize the same return as if they had invested in a 1-year Treasury bill.\n",
    "2. **Short and Long Maturities**:\n",
    "   - **Short Maturity**: This is typically the 1-year Treasury yield, which serves as the baseline or starting point for the break-even calculations.\n",
    "   - **Long Maturity**: This can be any maturity in the yield curve (2, 3, 5, 7, 10, 20, 30 years).\n",
    "3. **Calculating Break-Even Yield**: For each maturity on the curve (2 years, 3 years, etc.), you need to determine the rate change required so that the yield of the longer-maturity bond, adjusted over one year, matches the yield of the 1-year Treasury bill.\n",
    "\n",
    "In essence, you’re figuring out what yield (i.e., what rate change) is needed for different maturities so investors get the same return as they would from a 1-year Treasury. That’s how these yields are plotted against the Treasury yield curve. It’s an elegant way to compare the returns of different maturities with a constant short-term benchmark.\n",
    "\n",
    "This makes it possible to visualize, at a glance, how yields across various maturities would need to change for investors to remain indifferent between long-term and short-term bonds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "long_pv = 74.409, Year = 0, YTM = 3.00%\n",
      "short_fv = 82.154, Year = 0, YTM = 2.00%\n",
      "\n",
      "long_pv = 86.261, Year = 5, YTM = 3.00%\n",
      "long_pv = 82.154, Year = 5, Break-Even YTM = 4.009804%\n"
     ]
    }
   ],
   "source": [
    "short_yield = 0.02\n",
    "short_mat = 5\n",
    "long_yield = 0.03\n",
    "long_mat = 10\n",
    "\n",
    "breakeven = breakeven_rate(short_maturity=short_mat, short_yield=short_yield, long_maturity=long_mat, long_yield=long_yield, per=1)\n",
    "\n",
    "long_pv = 100 / (1+long_yield)**(long_mat)\n",
    "print(f'{long_pv = :0.3f}, Year = 0, YTM = 3.00%')\n",
    "short_fv = long_pv * (1+short_yield)**(short_mat)\n",
    "print(f'{short_fv = :0.3f}, Year = 0, YTM = 2.00%')\n",
    "print()\n",
    "long_pv = 100 / (1+long_yield)**(long_mat - short_mat)\n",
    "print(f'{long_pv = :0.3f}, Year = 5, YTM = 3.00%')\n",
    "long_pv = 100 / (1+breakeven)**(long_mat - short_mat)\n",
    "print(f'{long_pv = :0.3f}, Year = 5, Break-Even YTM = {breakeven :%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a 2-year corporate zeros are priced at 95 to yield only 2.581% (s.a) and a 10-year zero yielding 5.174%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "short_ytm = 0.025811789959920173\n",
      "short_fv = 63.15789473684209\n",
      "short_interest = 3.1578947368420884\n",
      "\n",
      "long_ytm = 0.051740509078987085\n",
      "long_fv = 66.45398059489737\n",
      "long_interest = 6.453980594897374\n",
      "\n",
      "profit = 3.296085858055285\n",
      "breakeven_yield = 0.05827437795383439\n"
     ]
    }
   ],
   "source": [
    "# Short Bond\n",
    "short_years = 2\n",
    "short_pv = 95\n",
    "# Long Bond\n",
    "long_years = 10\n",
    "long_pv = 60\n",
    "\n",
    "fv = 100\n",
    "per = 2\n",
    "\n",
    "short_ytm = ((fv/short_pv)**(1/(short_years*per)) - 1) * per\n",
    "print(f'{short_ytm = }')\n",
    "# Short FV if brought at Long PV\n",
    "short_fv = long_pv * (1 + (short_ytm/per))**(short_years * per)\n",
    "print(f'{short_fv = }')\n",
    "short_interest = short_fv - long_pv\n",
    "print(f'{short_interest = }')\n",
    "print()\n",
    "\n",
    "long_ytm = ((fv/long_pv)**(1/(long_years*per)) - 1) * per\n",
    "print(f'{long_ytm = }')\n",
    "# Value of Long Bond when Short Bond Matures\n",
    "long_fv = long_pv * (1 + (long_ytm/per))**(short_years * per)\n",
    "print(f'{long_fv = }')\n",
    "# Interest Earned During The period\n",
    "long_interest = long_fv - long_pv\n",
    "print(f'{long_interest = }')\n",
    "print()\n",
    "\n",
    "profit = long_interest - short_interest\n",
    "print(f'{profit = }')\n",
    "\n",
    "breakeven_yield = ((100/short_fv)**(1/((long_years-short_years)*per)) - 1) * per\n",
    "print(f'{breakeven_yield = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "long_pv = 60.000, Year = 0, YTM = 5.174051%\n",
      "short_fv = 63.158, Year = 0, YTM = 2.581179%\n",
      "\n",
      "long_pv = 66.454, Year = 2, YTM = 5.174051%\n",
      "\n",
      "long_pv = 63.158, Year = 2, Break-Even = 5.827438%\n"
     ]
    }
   ],
   "source": [
    "short_mat = 2\n",
    "short_yield = ((100/95)**(1/(short_mat*2)) - 1) * 2\n",
    "long_mat = 10\n",
    "long_yield = ((100/60)**(1/(long_mat*2)) - 1) * 2\n",
    "\n",
    "\n",
    "breakeven = breakeven_rate(short_maturity=short_mat, short_yield=short_yield, long_maturity=long_mat, long_yield=long_yield, per=2)\n",
    "\n",
    "long_pv = 100 / (1+long_yield/2)**(long_mat*2)\n",
    "print(f'{long_pv = :0.3f}, Year = 0, YTM = {long_yield :%}')\n",
    "short_fv = long_pv * (1+short_yield/2)**(short_mat*2)\n",
    "print(f'{short_fv = :0.3f}, Year = 0, YTM = {short_yield :%}')\n",
    "print()\n",
    "long_pv = 100 / (1+long_yield/2)**((long_mat - short_mat)*2)\n",
    "print(f'{long_pv = :0.3f}, Year = 2, YTM = {long_yield :%}')\n",
    "print()\n",
    "long_pv = 100 / (1+breakeven/2)**((long_mat - short_mat)*2)\n",
    "print(f'{long_pv = :0.3f}, Year = 2, Break-Even = {breakeven :%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def breakeven_rate(short_maturity, short_yield, long_maturity, long_yield, per):\n",
    "  long_pv = 100 / (1 + long_yield/per)**(long_maturity*per)\n",
    "  short_fv = long_pv * (1 + short_yield/per)**(short_maturity*per)\n",
    "  return ((100/short_fv)**(1/((long_years-short_years)*per)) - 1) * per"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Changes in Bond Prices and Yields"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bond prices change from day to day because of the **passage of time**, changes in **benchmark** and **spread** over (or under) the benchmark. Think of the yield as the investor’s **required rate of return** for holding the bond to its maturity and bearing the default risk. If for some reason investors require a higher (or lower) return for the bond, the price must fall (or rise).\n",
    "\n",
    "It is useful for analysis to break a corporate bond yield into a **benchmark** and a **spread** over (or, perhaps, under) that benchmark. Then changes in the corporate yield are due to changes in the benchmark, changes in the spread, or some combination thereof. \n",
    "\n",
    "**Changes in Benchmark (Macroeconomic)**:\n",
    "- Expected inflation\n",
    "- Foreign exchange rates\n",
    "- International capital flows\n",
    "- Business cycles\n",
    "- Monetary and fiscal policy\n",
    "\n",
    "**Changes in Spread (Microeconomic)**\n",
    "- Liquidity\n",
    "- Tax status\n",
    "- Potential losses if issuer defaults"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Credit Spreads and the Implied Probability of Default"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A bondholder’s rate of return depends on when the default occurs and on any remaining value to the bond. Given all the possible outcomes for the realized rates of return, the mean of the probability distribution—that is, the *expected value*—will be less than the yield to maturity.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "Probability Distribution for Rates of Return on a Corporate Bond to a Buy-and-Hold Investor\n",
    "\n",
    "The key feature of the figure above is that the probability distribution is highly *skewed*. That’s because the yield to maturity is the maximum rate the hold-to-maturity investor will ever experience. As we’ve seen, the horizon yield could be higher or lower if the bond is sold prior to maturity, but now we’re assuming the intent is to the hold the bond for its full lifetime.\n",
    "\n",
    "A nice application of bond math is to infer the probability of default given the prices on the risky zero-coupon corporate bond and an otherwise comparable risk-free security."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An approximation for the implied default probability directly uses the credit spread.\n",
    "\n",
    "$$\\text{Default Probability}=\\frac{\\text{Credit Spread}}{1-\\text{Recovery Rate}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "per = 2\n",
    "\n",
    "# 10-year zero-coupon corporate bond\n",
    "cop_mat = 10\n",
    "cop_pv = 60\n",
    "cop_yield = ((100/cop_pv)**(1/(cop_mat*per)) - 1) * per\n",
    "\n",
    "# Equivalent 10-year zero-coupon government bond\n",
    "gov_mat = 10\n",
    "gov_pv = 64\n",
    "gov_yield = ((100/gov_pv)**(1/(gov_mat*per)) - 1) * per\n",
    "\n",
    "credit_spread = cop_yield - gov_yield\n",
    "price_spread = gov_pv - cop_pv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------+------------------+-----------------+----------+--------------+--------------------+---------------+\n",
      "| Year | Prob. of Default | Risk-Free Value | Recovery | Default Loss | PV of Default Loss | Expected Loss |\n",
      "+------+------------------+-----------------+----------+--------------+--------------------+---------------+\n",
      "|  1   |        Q         |      66.921     |  26.768  |    40.153    |        38.4        |    38.4 * Q   |\n",
      "|  2   |        Q         |      69.975     |  27.99   |    41.985    |        38.4        |    38.4 * Q   |\n",
      "|  3   |        Q         |      73.169     |  29.268  |    43.901    |        38.4        |    38.4 * Q   |\n",
      "|  4   |        Q         |      76.508     |  30.603  |    45.905    |        38.4        |    38.4 * Q   |\n",
      "|  5   |        Q         |       80.0      |   32.0   |     48.0     |        38.4        |    38.4 * Q   |\n",
      "|  6   |        Q         |      83.651     |  33.46   |    50.191    |        38.4        |    38.4 * Q   |\n",
      "|  7   |        Q         |      87.469     |  34.988  |    52.481    |        38.4        |    38.4 * Q   |\n",
      "|  8   |        Q         |      91.461     |  36.584  |    54.877    |        38.4        |    38.4 * Q   |\n",
      "|  9   |        Q         |      95.635     |  38.254  |    57.381    |        38.4        |    38.4 * Q   |\n",
      "|  10  |        Q         |      100.0      |   40.0   |     60.0     |        38.4        |    38.4 * Q   |\n",
      "+------+------------------+-----------------+----------+--------------+--------------------+---------------+\n",
      "Q = 1.041667%\n",
      "approx_implied_default_prob = 1.101691%\n"
     ]
    }
   ],
   "source": [
    "from prettytable import PrettyTable\n",
    "\n",
    "# Probability of Default Calculation - Unconditional Probability\n",
    "year = np.arange(1, cop_mat+1)\n",
    "probability_default = ['Q' for _ in year]\n",
    "\n",
    "# Risk-Free Value (value of the corporate bond if it were risk free) - constant-yield price trajectory\n",
    "riskfree_value = np.array([round(100 / (1+gov_yield/per)**((gov_mat-i)*per), 3) for i in year])\n",
    "\n",
    "# Recovery assuming a recovery rate of 40% of risk-free value\n",
    "recovery_rate = 0.4 # Depending on the industry and the rank of the bond in the debt structure\n",
    "recovery = np.array([round(value * recovery_rate, 3) for value in riskfree_value])\n",
    "\n",
    "# Loss Severity\n",
    "loss_severity = np.array([100 - value for value in recovery])\n",
    "\n",
    "# Default Loss - loss at that time if default occurs—it is the riskfree value minus recovery\n",
    "default_loss = np.array([round(riskfree_value[i-1] - recovery[i-1], 3) for i in year])\n",
    "\n",
    "# Present value of default loss - risk-free rate is used to discount the losses\n",
    "pv_default = np.array([round(default_loss[i-1]/((1+gov_yield/per)**(i*per)),3) for i in year])\n",
    "# Here the present values turn out to be the same for each year—that’s because the bond is zero-coupon \n",
    "# and the recovery rate is assumed to be a constant share of the loss.\n",
    "\n",
    "# Present Value of Expected Loss\n",
    "expected_loss = np.array([str(default) + ' * Q' for default in pv_default])\n",
    "\n",
    "# Output Table\n",
    "table = PrettyTable()\n",
    "table.add_column(\"Year\", year)\n",
    "table.add_column(\"Prob. of Default\", probability_default)\n",
    "table.add_column(\"Risk-Free Value\", riskfree_value)\n",
    "table.add_column(\"Recovery\", recovery)\n",
    "table.add_column(\"Default Loss\", default_loss)\n",
    "table.add_column(\"PV of Default Loss\", pv_default)\n",
    "table.add_column(\"Expected Loss\", expected_loss)\n",
    "print(table)\n",
    "\n",
    "Q = price_spread/np.sum(pv_default)\n",
    "print(f'{Q = :%}')\n",
    "\n",
    "approx_implied_default_prob = credit_spread/(1 - recovery_rate)\n",
    "print(f'{approx_implied_default_prob = :%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+------+------------------+-----------------+----------+--------------+--------------------+---------------+\n",
      "| Year | Prob. of Default | Risk-Free Value | Recovery | Default Loss | PV of Default Loss | Expected Loss |\n",
      "+------+------------------+-----------------+----------+--------------+--------------------+---------------+\n",
      "|  1   |      0.0104      |      66.921     |  26.768  |    40.153    |        38.4        |      0.4      |\n",
      "|  2   |      0.0104      |      69.975     |  27.99   |    41.985    |        38.4        |      0.4      |\n",
      "|  3   |      0.0104      |      73.169     |  29.268  |    43.901    |        38.4        |      0.4      |\n",
      "|  4   |      0.0104      |      76.508     |  30.603  |    45.905    |        38.4        |      0.4      |\n",
      "|  5   |      0.0104      |       80.0      |   32.0   |     48.0     |        38.4        |      0.4      |\n",
      "|  6   |      0.0104      |      83.651     |  33.46   |    50.191    |        38.4        |      0.4      |\n",
      "|  7   |      0.0104      |      87.469     |  34.988  |    52.481    |        38.4        |      0.4      |\n",
      "|  8   |      0.0104      |      91.461     |  36.584  |    54.877    |        38.4        |      0.4      |\n",
      "|  9   |      0.0104      |      95.635     |  38.254  |    57.381    |        38.4        |      0.4      |\n",
      "|  10  |      0.0104      |      100.0      |   40.0   |     60.0     |        38.4        |      0.4      |\n",
      "+------+------------------+-----------------+----------+--------------+--------------------+---------------+\n",
      "4.0\n"
     ]
    }
   ],
   "source": [
    "probability_default = [round(Q,4) for _ in year]\n",
    "expected_loss = np.array([default * Q for default in pv_default])\n",
    "\n",
    "\n",
    "# Output Table\n",
    "table = PrettyTable()\n",
    "table.add_column(\"Year\", year)\n",
    "table.add_column(\"Prob. of Default\", probability_default)\n",
    "table.add_column(\"Risk-Free Value\", riskfree_value)\n",
    "table.add_column(\"Recovery\", recovery)\n",
    "table.add_column(\"Default Loss\", default_loss)\n",
    "table.add_column(\"PV of Default Loss\", pv_default)\n",
    "table.add_column(\"Expected Loss\", expected_loss)\n",
    "print(table)\n",
    "\n",
    "print(np.sum(expected_loss))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability calculated above is an unconditional probability of default. An alternative approach (which is harder to illustrate but more theoretically correct) is to estimate the probability of default for each year conditional on no prior default.\n",
    "\n",
    "An important choice in this calculation is the risk-free rate. Using Treasury rates may not necessarily be the appropriate choice as Treasury bonds are more liquid (unlike corporate bonds that are illiquid and require liquidity premiums) and exempt from state and local income taxes. Ideally, the risk-free rate in this analysis is the yield on a bond having the same maturity, liquidity, and taxation as the corporate but default risk that approaches zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The advantage of the tabular method of calculating expected loss from default is its flexibility and explicit use of the time value of money. You can make the following modification to improve the computation:\n",
    "- You can easily **vary the recovery rate** across the years, for example, if it is assumed that the current fixed assets of the issuer depreciate over time, or if there is an impending legal change that could affect creditors’ rights in bankruptcy court. \n",
    "- Also, you could **introduce a term structure of risk-free rates** instead of the flat yield curve assumed in the example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def zero_bond_ytm(n, pv, fv=100, freq=2):\n",
    "    if freq == np.inf:\n",
    "        return np.log(fv/pv) * (1/n)\n",
    "    return ((fv/pv)**(1/(n*freq)) - 1) * freq\n",
    "\n",
    "def zero_bond_pv(n, rate, fv=100, freq=2):\n",
    "    if freq == np.inf:\n",
    "        return fv / np.exp(rate*n)\n",
    "    return fv / ((1 + rate/freq)**(n*freq))\n",
    "\n",
    "def zero_bond_fv(n, rate, pv, freq):\n",
    "    if freq == np.inf:\n",
    "        return pv * np.exp(rate*n)    \n",
    "    return pv * ((1 + rate/freq)**(n*freq))\n",
    "\n",
    "def equivRate(rate, from_freq=1, to_freq=1):\n",
    "  if from_freq == np.inf:\n",
    "    return (np.exp(rate / to_freq) - 1) * to_freq\n",
    "  elif to_freq == np.inf:\n",
    "    return np.log(1 + rate / from_freq) * from_freq\n",
    "  else:\n",
    "    return to_freq * ((1 + rate/from_freq)**(from_freq/to_freq) - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. A buy-and-hold institutional investor expects market interest rates to be going up in the next few years. Which types of securities, differentiated only by coupon rate and time to maturity, are mostly likely to be preferred by the investor?\n",
    "   1. High coupon rate, long-term securities\n",
    "   2. **High coupon rate, short-term securities**\n",
    "   3. Low coupon rate, long-term securities\n",
    "   4. Low coupon rate, short-term securities\n",
    "\n",
    "Buy-and-hold investors are concerned with cash flow reinvestment risk arising from coupon payments and the redemption of principal. If market rates are expected to be rising, the investor would prefer high coupon rates over low coupon rates because there is more cash flow to be reinvested at the higher rates. Also, the investor would prefer short-term over long-term securities because the principal can be reinvested sooner at the higher rates. Of course, this question neglects concerns over credit risk, liquidity, and transactions costs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Coupon-stripping is the fixed-income arbitrage strategy of buying a coupon bond and selling its interest and principal cash flows separately as zero-coupon bonds as in the creation of TIGRS, CATS, and LIONS in the 1980s. Suppose a 3-year, 5% annual payment bond can be purchased at par value. Which pattern of zero-coupon bond prices allows an arbitrageur to carry out the strategy of coupon stripping, neglecting transactions costs? [Note that the bond prices are given per one unit of future or face value, i.e., they are discount factor.]\n",
    "   1. **1 year, 0.97; 2-year, 0.92; 3-year, 0.87**\n",
    "   2. 1 year, 0.96; 2-year, 0.91; 3-year, 0.86\n",
    "   3. 1 year, 0.95; 2-year, 0.90; 3-year, 0.85\n",
    "   4. 1 year, 0.94; 2-year, 0.89; 3-year, 0.84\n",
    "\n",
    "Hint: Calculate the value of the stripped coupon bond by multiplying each cash flow by the zero-coupon bond price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.95238095 0.90702948 0.8638376 ]\n",
      "100.0\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "coupon = 5\n",
    "ytm = 0.05\n",
    "cash_flows = np.full(n, coupon)\n",
    "cash_flows[-1] += 100\n",
    "# Discount Factor of Purchased Coupon Bond\n",
    "discount_factor = np.full(n, (1 + ytm))**(-np.arange(1,n+1)) \n",
    "print(discount_factor)\n",
    "# Price Paid for the Coupons\n",
    "price = np.sum(cash_flows * discount_factor)\n",
    "print(price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100.8   99.65  98.5   97.35]\n"
     ]
    }
   ],
   "source": [
    "# Discount Factor of Selling Coupon Bonds\n",
    "factors = np.array([[0.97, 0.92, 0.87],\n",
    "                    [0.96, 0.91, 0.86],\n",
    "                    [0.95, 0.90, 0.85],\n",
    "                    [0.94, 0.89, 0.84]])\n",
    "# Calculate the value of the stripped coupon bond for each pattern of zero-coupon bond prices.\n",
    "prices = np.sum(cash_flows * factors, axis=1)\n",
    "print(prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Bond reconstitution is the fixed-income arbitrage strategy of buying a series of zero-coupon bonds such as C-STRIPS and P-STRIPS and selling the rebuilt coupon bond. Suppose a 3-year, 4% annual payment bond can be sold at par value. Which pattern of zero-coupon bond prices allows an arbitrageur to carry out the strategy of bond reconstitution, neglecting transactions costs?\n",
    "   1. 1 year, 0.99; 2-year, 0.95; 3-year, 0.90\n",
    "   2. 1 year, 0.98; 2-year, 0.94; 3-year, 0.89\n",
    "   3. **1 year, 0.99; 2-year, 0.94; 3-year, 0.88**\n",
    "   4. 1 year, 0.97; 2-year, 0.95; 3-year, 0.90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[101.36 100.24  99.24 101.28]\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "coupon = 4\n",
    "cash_flows = np.full(n, coupon)\n",
    "cash_flows[-1] += 100\n",
    "factors = np.array([[0.99, 0.95, 0.90],\n",
    "                    [0.98, 0.94, 0.89],\n",
    "                    [0.99, 0.94, 0.88],\n",
    "                    [0.97, 0.95, 0.90]])\n",
    "prices = np.sum(cash_flows * factors, axis=1)\n",
    "print(prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Suppose that a 2-year, USD10 million par value, 2% annual coupon payment government bond can be bought or sold at 101. Zero-coupon government bonds can be bought or sold at 99.20 for a maturity of one year and at 96.50 for two years. Each price is the percentage of par value. Which statement is best describes the arbitrage opportunity that is available?\n",
    "   1. The potential profit from coupon stripping is $58,600.\n",
    "   2. The potential profit from bond reconstitution is $58,600.\n",
    "   3. The potential profit from coupon stripping is $100,000.\n",
    "   4. The potential profit from bond reconstitution is $100,000."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cash flows on the 2-year, $10 million par value, 2% annual coupon payment government bond are $200,000 at the end of the first year (0.02 * $10,000,000) and $10,200,000 at the end of the second year when the principal is redeemed. The purchase or sale price for the bond is $10,100,000, which is 1.01 * $10,000,000. The break-even, or no-arbitrage, value for the 2-year, 2% government bond is the amount based on the prices of the zero-coupon bonds. \n",
    "\n",
    "($200,000 * 0.9920) + ($10,200,000 * 0.9650) = $10,041,400\n",
    "\n",
    "The arbitrage strategy that is available, neglecting transactions costs, is bond reconstitution. Buy the zero-coupon bonds—the 1-year zero for a face value of $200,000 and 2-year zero for a face value of $10,200,000. The total cost is $10,041,400. Sell the reconstituted 2-year, 2% coupon bond for $10,100,000. The profit is the difference, $58,600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profit = 58_600.0\n"
     ]
    }
   ],
   "source": [
    "# Zero-coupon gov. bonds stated as discount factor\n",
    "discount_factor = np.array([0.992, 0.965])\n",
    "# Cash flow from gov. coupon bond\n",
    "cash_flows = np.array([200_000, 10_200_000])\n",
    "coupon_bond_price = 10_100_000\n",
    "\n",
    "# Price to reconstitute the zero-coupons\n",
    "price_reconstitution = np.sum(cash_flows * discount_factor)\n",
    "# Profit/Loss\n",
    "profit = coupon_bond_price - price_reconstitution\n",
    "\n",
    "print(f'{profit = :_}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. Which statement best explains why long-term P-STRIPS usually are priced a bit higher than C-STRIPS maturing on the same date?\n",
    "   1. C-STRIPS are more liquid than P-STRIPS.\n",
    "   2. **P-STRIPS are available in greater supply.**\n",
    "   3. C-STRIPS have greater “optionality” because they can be used in a bond reconstitution arbitrage strategy.\n",
    "   4. P-STRIPS are federal tax-exempt whereas C-STRIPS are taxable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Long-term P-STRIPS are more liquid than C-STRIPS because they are available in greater supply; hence the price of P-STRIPS is usually higher than C-STRIPS having the same maturity date. Also, owning P-STRIPS can facilitate bond reconstitution because only the sequence of C-STRIPS is needed to rebuild the coupon bond. The taxation of P-STRIPS and C-STRIPS is the same"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6. A 10-year zero-coupon bond is priced at 57.5 (per 100 of par value). The bond’s yield to maturity, stated as an annual percentage rate for semiannual compounding (i.e., a semiannual bond basis having a periodicity of 2) is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm = 5.611%\n"
     ]
    }
   ],
   "source": [
    "pv = 57.5\n",
    "n = 10\n",
    "freq = 2\n",
    "ytm = zero_bond_ytm(n=n, pv=pv, fv=100, freq=freq)\n",
    "print(f'{ytm = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7. A 20-year zero-coupon bond is priced at 30 (per 100 of par value). The bond’s yield to maturity, stated as an annual percentage rate for daily compounding (a periodicity of 365) is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm = 6.020%\n"
     ]
    }
   ],
   "source": [
    "pv = 30\n",
    "n = 20\n",
    "freq = 365\n",
    "ytm = zero_bond_ytm(n=n, pv=pv, fv=100, freq=freq)\n",
    "print(f'{ytm = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8. A 5-year zero-coupon bond is priced at 80 (per 100 of par value). The bond’s yield to maturity, stated as an annual percentage rate for continuous compounding (a periodicity of infinity) is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm = 4.463%\n"
     ]
    }
   ],
   "source": [
    "pv = 80\n",
    "n = 5\n",
    "freq = np.inf\n",
    "ytm = zero_bond_ytm(n=n, pv=pv, fv=100, freq=freq)\n",
    "print(f'{ytm = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "9. The annual yield to maturity on a 30-year zero-coupon bond is stated to be 6.824% on a continuously compounded basis. That yield converted to a semiannual bond basis (a periodicity of 2) is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "apr_2 = 6.942%\n"
     ]
    }
   ],
   "source": [
    "continous_rate = 0.06824\n",
    "apr_2 = equivRate(continous_rate, from_freq=np.inf, to_freq=2)\n",
    "print(f'{apr_2 = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10.\tSuppose an investor buys a $100,000, 15-year zero-coupon bond at a price of $48,000. Two years later, the investor sells the bond at a price of $55,000. In principle, the capital gain associated with this investment is:\n",
    "    1. 0, the difference between the sale price of $55,000 and the purchase price of $48,000 is all interest income to the investor.\n",
    "    2. **$2,065, the difference between the sale price of $55,000 and $52,935, the carrying value at the time of sale, is the capital gain to the investor.**\n",
    "    3. $7,000, the difference between the sale price $55,000 and the purchase price of $48,000 is all capital gain to the investor.\n",
    "\n",
    "Note that this is the economic capital gain; the taxable capital gain might differ depending on the tax rules that are in effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2065.0623685145474"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def capital_gains(purchase_price, current_price, par_value, years_to_maturity_purchase, years_to_mat, per):\n",
    "    purchase_ytm = ((par_value/purchase_price)**(1/(years_to_maturity_purchase*per)) - 1) * per\n",
    "    constant_yield_price = par_value / ((1 + purchase_ytm/per)**(years_to_mat*per))\n",
    "    current_ytm = ((par_value/current_price)**(1/(years_to_mat*per)) - 1) * per\n",
    "    return (current_price - constant_yield_price), (constant_yield_price - purchase_price), current_ytm\n",
    "\n",
    "capital_gains(purchase_price=48_000, current_price=55_000, par_value=100_000, years_to_maturity_purchase=15,years_to_mat=13, per=1)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11.\tA 3-year, zero-coupon corporate bond is priced at 78 (percent of par value) to yield 8.4559% (s.a.). A 3-year, zero-coupon government bond, which is assumed to be (default) risk-free, is priced at 82.5 (percent of par value) to yield 6.5163% (s.a.). Assume that the recovery rate if the corporate bond defaults would be 30% of the risk-free value. Using the tabular method, the probability of default for each year is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Probability of Default Calculation - Unconditional Probability\n",
    "per = 2\n",
    "mat = 3\n",
    "\n",
    "# Zero-coupon corporate bond\n",
    "cop_pv = 78\n",
    "cop_yield = ((100/cop_pv)**(1/(mat*per)) - 1) * per\n",
    "\n",
    "# Zero-coupon government bond\n",
    "gov_pv = 82.5\n",
    "gov_yield = ((100/gov_pv)**(1/(mat*per)) - 1) * per\n",
    "\n",
    "credit_spread = cop_yield - gov_yield\n",
    "price_spread = gov_pv - cop_pv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q = 2.597403%\n",
      "+------+----------+----------+--------------+--------------------+---------------+\n",
      "| Year | Rf Value | Recovery | Default Loss | PV of Default Loss | Expected Loss |\n",
      "+------+----------+----------+--------------+--------------------+---------------+\n",
      "|  1   |  87.964  |  26.389  |    61.574    |       57.75        |      1.5      |\n",
      "|  2   |  93.789  |  28.137  |    65.652    |       57.75        |      1.5      |\n",
      "|  3   |  100.0   |   30.0   |     70.0     |       57.75        |      1.5      |\n",
      "+------+----------+----------+--------------+--------------------+---------------+\n"
     ]
    }
   ],
   "source": [
    "year = np.arange(mat) + 1\n",
    "\n",
    "# Risk-Free Value - constant-yield price trajectory\n",
    "riskfree_value = np.full(mat, 100) * (1 + gov_yield/per)**(-(year[::-1]-1)*per)\n",
    "\n",
    "# Recovery of 30% of risk-free value\n",
    "recovery_rate = 0.3\n",
    "recovery = riskfree_value * recovery_rate\n",
    "\n",
    "# Default Loss - loss at that time if default occurs\n",
    "default_loss = riskfree_value - recovery\n",
    "\n",
    "# Present value of default loss - risk-free rate is used to discount the losses\n",
    "pv_default = default_loss * (1 + gov_yield/per)**(-year*per)\n",
    "Q = price_spread/np.sum(pv_default)\n",
    "expected_loss = pv_default * Q\n",
    "\n",
    "print(f'{Q = :%}')\n",
    "\n",
    "table = PrettyTable()\n",
    "table.add_column(\"Year\", year)\n",
    "table.add_column(\"Rf Value\", riskfree_value.round(3))\n",
    "table.add_column(\"Recovery\", recovery.round(3))\n",
    "table.add_column(\"Default Loss\", default_loss.round(3))\n",
    "table.add_column(\"PV of Default Loss\", pv_default.round(3))\n",
    "table.add_column(\"Expected Loss\", expected_loss.round(3))\n",
    "print(table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12.\tSuppose an investor buys a $50,000, 10-year zero-coupon bond for a price of $33,500. One year later, the investor sells the bond at a price of $38,000. In principle, the interest income for the 1-year holding period is:\n",
    "    1. 0, there is no interest income on a zero-coupon bond.\n",
    "    2. $4,500, the difference between the purchase and sale prices is the interest income.\n",
    "    3. **$1,369, the difference between the carrying value at the time of sale and the purchase price is the interest income.**\n",
    "    4. $3,131, the difference between the sale price and carrying value at the time of sale is the interest income."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "interest_income = 1369\n"
     ]
    }
   ],
   "source": [
    "def capital_gains(purchase_price, current_price, par_value, years_to_maturity_purchase, years_to_mat, per):\n",
    "    purchase_ytm = ((par_value/purchase_price)**(1/(years_to_maturity_purchase*per)) - 1) * per\n",
    "    constant_yield_price = par_value / ((1 + purchase_ytm/per)**(years_to_mat*per))\n",
    "    current_ytm = ((par_value/current_price)**(1/(years_to_mat*per)) - 1) * per\n",
    "    return (current_price - constant_yield_price), (constant_yield_price - purchase_price), current_ytm\n",
    "\n",
    "interest_income = capital_gains(purchase_price=33_500, current_price=38_000, par_value=50_000, years_to_maturity_purchase=10,years_to_mat=9, per=1)[1]\n",
    "print(f'{interest_income = :0.0f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "13.\tA 5-year, zero-coupon corporate bond is priced at 75.75 (percent of par value). A 5-year, zero-coupon government bond, which is assumed to be (default) risk-free, is priced at 78.25 (percent of par value). Assume that the recovery rate if the corporate bond defaults would be 40% of the risk-free value. Using the tabular method, the probability of default for each year is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q = 1.064963%\n",
      "+------+----------+----------+--------------+--------------------+---------------+\n",
      "| Year | Rf Value | Recovery | Default Loss | PV of Default Loss | Expected Loss |\n",
      "+------+----------+----------+--------------+--------------------+---------------+\n",
      "|  1   |  82.184  |  32.874  |    49.31     |       46.95        |      0.5      |\n",
      "|  2   |  86.316  |  34.526  |    51.79     |       46.95        |      0.5      |\n",
      "|  3   |  90.655  |  36.262  |    54.393    |       46.95        |      0.5      |\n",
      "|  4   |  95.213  |  38.085  |    57.128    |       46.95        |      0.5      |\n",
      "|  5   |  100.0   |   40.0   |     60.0     |       46.95        |      0.5      |\n",
      "+------+----------+----------+--------------+--------------------+---------------+\n"
     ]
    }
   ],
   "source": [
    "# Probability of Default Calculation - Unconditional Probability\n",
    "per = 1\n",
    "mat = 5\n",
    "\n",
    "# Zero-coupon corporate bond\n",
    "cop_pv = 75.75\n",
    "cop_yield = ((100/cop_pv)**(1/(mat*per)) - 1) * per\n",
    "\n",
    "# Zero-coupon government bond\n",
    "gov_pv = 78.25\n",
    "gov_yield = ((100/gov_pv)**(1/(mat*per)) - 1) * per\n",
    "\n",
    "credit_spread = cop_yield - gov_yield\n",
    "price_spread = gov_pv - cop_pv\n",
    "\n",
    "year = np.arange(mat) + 1\n",
    "\n",
    "# Risk-Free Value - constant-yield price trajectory\n",
    "riskfree_value = np.full(mat, 100) * (1 + gov_yield/per)**(-(year[::-1]-1)*per)\n",
    "\n",
    "# Recovery of 30% of risk-free value\n",
    "recovery_rate = 0.4\n",
    "recovery = riskfree_value * recovery_rate\n",
    "\n",
    "# Default Loss - loss at that time if default occurs\n",
    "default_loss = riskfree_value - recovery\n",
    "\n",
    "# Present value of default loss - risk-free rate is used to discount the losses\n",
    "pv_default = default_loss * (1 + gov_yield/per)**(-year*per)\n",
    "Q = price_spread/np.sum(pv_default)\n",
    "expected_loss = pv_default * Q\n",
    "\n",
    "print(f'{Q = :%}')\n",
    "\n",
    "table = PrettyTable()\n",
    "table.add_column(\"Year\", year)\n",
    "table.add_column(\"Rf Value\", riskfree_value.round(3))\n",
    "table.add_column(\"Recovery\", recovery.round(3))\n",
    "table.add_column(\"Default Loss\", default_loss.round(3))\n",
    "table.add_column(\"PV of Default Loss\", pv_default.round(3))\n",
    "table.add_column(\"Expected Loss\", expected_loss.round(3))\n",
    "print(table)"
   ]
  }
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