1 - Money Market.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import bond_pricing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Day Count Convention"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relevant time period in most financial markets is based on the number of days between the starting and ending dates. In other words, “parking lot rules”(whereby both the starting and ending dates count) do not apply."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datetime import date\n",
    "from pandas import to_datetime, Timedelta, DateOffset\n",
    "from importlib import import_module\n",
    "\n",
    "daycount_dict = {'actual/360': 'actual360', \n",
    "                 'actual/365': 'actual365',\n",
    "                 'actual/actual': 'actualactual', \n",
    "                 'thirty/360': 'thirty360'}\n",
    "\n",
    "settle = to_datetime('2024-1-12')\n",
    "mat = to_datetime('2024-03-12')\n",
    "convention = 'actual/365'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "days = 60\n",
      "year = 365\n"
     ]
    }
   ],
   "source": [
    "def days_year(settle, mat, convention='actual/360'):\n",
    "    name = 'isda_daycounters.'+ daycount_dict[convention]\n",
    "    days = import_module(name).day_count(settle, mat)\n",
    "    if convention == \"actual/360\" or convention == \"thirty/360\":\n",
    "      year = 360\n",
    "    elif convention == \"actual/365\":\n",
    "      year = 365\n",
    "    else:\n",
    "      oneyear = settle + DateOffset(years=1)\n",
    "      year = (oneyear - settle).days\n",
    "    return days, year\n",
    "    \n",
    "days, year = days_year(settle, mat, convention=convention)\n",
    "print(f'{days = }\\n{year = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dayYear = 6.083333333333334\n",
      "6.083333333333333\n",
      "yearDay = 0.1643835616438356\n",
      "0.1643835616438356\n"
     ]
    }
   ],
   "source": [
    "def year_frac(settle, mat, convention='actual/360', inverse=False):\n",
    "    name = 'isda_daycounters.'+ daycount_dict[convention]\n",
    "    fraction = import_module(name).year_fraction(settle, mat)\n",
    "    if inverse:\n",
    "      return fraction\n",
    "    else:\n",
    "      return 1/fraction\n",
    "\n",
    "dayYear = year_frac(settle, mat, convention=convention, inverse=False)\n",
    "print(f'{dayYear = }')\n",
    "print(year/days)\n",
    "\n",
    "yearDay = year_frac(settle, mat, convention=convention, inverse=True)\n",
    "print(f'{yearDay = }')\n",
    "print(days/year)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Add-On Rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following rates are generally quoted on an add-on rate basis:\n",
    "- Commercial bank loans and deposits\n",
    "- Certificates of deposit (CD)\n",
    "- Repos\n",
    "- Fed funds\n",
    "- LIBOR\n",
    "- SOFR\n",
    "- Commercial paper (CP) in Euromarkets\n",
    "\n",
    "Quoted at 'present value' or current price."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add-on rates follow a simple interest calculations. The **interest is added on to the principal amount** to get the **redemption payment** at maturity.\n",
    "\n",
    "$$FV=PV+\\left[PV \\times AOR \\times \\frac{Days}{Year}\\right]$$\n",
    "$$FV=PV\\times\\left[1 + \\left(AOR \\times \\frac{Days}{Year}\\right)\\right]$$\n",
    "$$\\frac{FV}{PV}=\\left[1 + \\left(AOR \\times \\frac{Days}{Year}\\right)\\right]$$\n",
    "$$PV=\\frac{FV}{\\left[1 + \\left(AOR \\times \\frac{Days}{Year}\\right)\\right]}$$\n",
    "$$AOR=\\left(\\frac{Year}{Days}\\right)\\times\\left(\\frac{FV-PV}{PV}\\right)$$\n",
    "$$AOR\\times\\left(\\frac{Days}{Year}\\right)=\\left(\\frac{FV-PV}{PV}\\right)$$\n",
    "\n",
    "- AOR is the quoted add-on rate (annual percentage rate (APR))\n",
    "- PV the present value (the initial principal amount)\n",
    "- FV the future value (the redemption payment including interest)\n",
    "- Days the number of days until maturity, and \n",
    "- Year the number of days in the year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fv = 1,019,500.0\n",
      "periodicity = 2.0\n"
     ]
    }
   ],
   "source": [
    "def addon_fv(pv, aor, days, year=360):\n",
    "    return pv * (1 + (aor * days  / year))\n",
    "\n",
    "pv = 1_000_000\n",
    "aor = 0.039\n",
    "days = 180\n",
    "year = 360\n",
    "\n",
    "fv = addon_fv(pv, aor, days, year)\n",
    "print(f'fv ={round(fv, 2): ,}')\n",
    "periodicity = year/days\n",
    "print(f'{periodicity = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pv = 1,007,013.04\n",
      "periodicity = 3.0\n"
     ]
    }
   ],
   "source": [
    "def addon_pv(fv, aor, days, year=360):\n",
    "    return fv / (1 + (aor * days  / year))\n",
    "\n",
    "fv = 1_019_500\n",
    "aor = 0.0372\n",
    "days = 120\n",
    "year = 360\n",
    "\n",
    "pv = addon_pv(fv, aor, days, year)\n",
    "print(f'pv ={round(pv, 2): ,}')\n",
    "periodicity = year/days\n",
    "print(f'{periodicity = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aor =  0.0421\n",
      "periodicity = 6.0\n"
     ]
    }
   ],
   "source": [
    "def addon_rate(pv, fv, days, year=360):\n",
    "    return (year/days) * (fv - pv)/pv\n",
    "\n",
    "pv = 1_000_000\n",
    "fv = 1_007_013.04\n",
    "days = 60\n",
    "year = 360\n",
    "\n",
    "aor = addon_rate(pv, fv, days, year)\n",
    "print(f'{aor = : 0.4f}')\n",
    "periodicity = year/days\n",
    "print(f'{periodicity = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    }
   ],
   "source": [
    "def periodicity(days, year):\n",
    "    return year / days\n",
    "\n",
    "days = 90\n",
    "year = 360\n",
    "\n",
    "print(periodicity(days, year))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discount Rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following rates are generally quoted on a discount rate basis:\n",
    "- T-Bills\n",
    "- Commercial paper (CP) \n",
    "- Banker's acceptance\n",
    "\n",
    "Quoted at 'face value' or 'redemption' value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The price of the security is a **discount from the face value**. The future (or face) value times the annual discount rate times the fraction of the year. Interest is not “added on” to the principal; instead it is included in the face value.\n",
    "\n",
    "$$PV = FV - \\left[FV \\times DR \\times \\frac{Days}{Year}\\right]$$\n",
    "$$PV = FV \\times \\left[1 - \\left(DR \\times \\frac{Days}{Year}\\right)\\right]$$\n",
    "$$\\frac{PV}{FV} = \\left[1 - \\left(DR \\times \\frac{Days}{Year}\\right)\\right]$$\n",
    "$$FV = \\frac{PV}{\\left[1 - \\left(DR \\times \\frac{Days}{Year}\\right)\\right]}$$\n",
    "$$DR=\\left(\\frac{Year}{Days}\\right)\\times\\left(\\frac{FV-PV}{FV}\\right)$$\n",
    "$$DR\\times\\left(\\frac{Days}{Year}\\right)=\\left(\\frac{FV-PV}{FV}\\right)$$\n",
    "\n",
    "- DR is the discount rate\n",
    "- PV the present value (the initial principal amount)\n",
    "- FV the future value (the redemption payment including interest)\n",
    "- Days the number of days until maturity, and \n",
    "- Year the number of days in the year\n",
    "\n",
    "The “amount” of a transaction is the face value (the FV) for instruments quoted on a discount rate basis. In contrast, the “amount” is the original principal (the PV at issuance) for money market securities quoted on an add-on rate basis.\n",
    "\n",
    "Note:\n",
    "$$PV = FV - \\left[FV \\times DR \\times \\frac{Days}{Year}\\right]$$\n",
    "Can be simplified to:\n",
    "$$PV = FV - \\text{Dollar Discount}$$\n",
    "where $\\text{Dollar Discount} = FV  \\times DR \\times \\frac{Days}{Year}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pv = 981,000.0\n",
      "periodicity = 2.0\n"
     ]
    }
   ],
   "source": [
    "def dr_pv(fv, dr, days, year=360):\n",
    "    return fv * (1 - (dr * days  / year))\n",
    "\n",
    "fv = 1_000_000\n",
    "dr = 0.038\n",
    "days = 180\n",
    "year = 360\n",
    "\n",
    "pv = dr_pv(fv, dr, days, year)\n",
    "print(f'pv ={round(pv, 2): ,}')\n",
    "periodicity = year/days\n",
    "print(f'{periodicity = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pv = 997,208.33\n",
      "periodicity = 12.0\n"
     ]
    }
   ],
   "source": [
    "def dr_pv(fv, dr, days, year=360):\n",
    "    return fv * (1 - (dr * days  / year))\n",
    "\n",
    "fv = 1_000_000\n",
    "dr = 0.0335\n",
    "days = 30\n",
    "year = 360\n",
    "\n",
    "pv = dr_pv(fv, dr, days, year)\n",
    "print(f'pv ={round(pv, 2): ,}')\n",
    "periodicity = year/days\n",
    "print(f'{periodicity = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fv = 1,032,300.53\n"
     ]
    }
   ],
   "source": [
    "def dr_fv(pv, dr, days, year=360):\n",
    "    return pv / (1 - (dr * days  / year))\n",
    "\n",
    "pv = 1_019_500\n",
    "dr = 0.0372\n",
    "days = 120\n",
    "year = 360\n",
    "\n",
    "fv = dr_fv(pv, dr, days, year)\n",
    "print(f'fv ={round(fv, 2): ,}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dr =  0.0367\n"
     ]
    }
   ],
   "source": [
    "def dr_rate(pv, fv, days, year=360):\n",
    "    return (year/days) * (fv - pv)/fv\n",
    "\n",
    "pv = 1_007_013\n",
    "fv = 1_019_500\n",
    "days = 120\n",
    "year = 360\n",
    "\n",
    "dr = dr_rate(pv, fv, days, year)\n",
    "print(f'{dr = : 0.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing Discount Rate and Add-on Rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "General conversion formula between discount rates and addon rates (and vice versa) when quoted for the **same assumed number of days in the year**:\n",
    "\n",
    "$$AOR = \\frac{Year \\times DR}{Year - (Days \\times DR)}$$\n",
    "$$DR = \\frac{Year \\times AOR}{Year + (Days \\times AOR)}$$\n",
    "\n",
    "Note that the DR, unlike an AOR, is **not an APR** because the $\\frac{FV - PV}{FV}$ is not the periodic interest rate, it is the interest earned relative to the future value. This is not the way we think about an interest rate — the growth rate of an investment should be measured by the increase in value (FV − PV) given where we start (PV), not where we end (FV). The discount rate systematically understate the investor’s rate of return, as well as the borrower’s cost of funds. AOR will always be greater than the DR for the same cash flows, the more so the greater the number of days in the time period and the higher the level of interest rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aor = 0.03873598369011213\n",
      "dr = 0.038\n"
     ]
    }
   ],
   "source": [
    "def equiv_rate_mm(rate, days, year, aor=True):\n",
    "    if aor:\n",
    "        return (year * rate) / (year - (days * rate))\n",
    "    else:\n",
    "        return (year * rate) / (year + (days * rate))\n",
    "    \n",
    "\n",
    "dr = 0.038\n",
    "days = 180\n",
    "year = 360\n",
    "\n",
    "aor = equiv_rate_mm(dr, days, year, aor=True)\n",
    "print(f'{aor = }')\n",
    "\n",
    "dr = equiv_rate_mm(aor, days, year, aor=False)\n",
    "print(f'{dr = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Converting Between Rate Periodicity "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Converting between discrete periodicities:\n",
    "$$\\Big(1+\\frac{APR_{m}}{m}\\Big)^{m} = \\Big(1+\\frac{APR_{n}}{n}\\Big)^{n}$$\n",
    "$$n\\times\\Big[\\Big(1+\\frac{APR_{m}}{m}\\Big)^{m/n}-1\\Big] = APR_{n}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.04039999999999999\n"
     ]
    }
   ],
   "source": [
    "quoted_apr = 0.04\n",
    "m = 360/180\n",
    "n = 1\n",
    "\n",
    "print(bond_pricing.equiv_rate(rate=quoted_apr, from_freq=m, to_freq=n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bond Equivalent Yield (BEY) or Investment Rate (IR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intent of *bond equivalent yield* (BEY) is to report to investors an interest rate for the security that is more meaningful than the discount rate and that allows a comparison to Treasury note and bond yields.\n",
    "\n",
    "A **bond equivalent yield** (BEY) is a money market rate stated on a **365-day add-on rate basis**. \n",
    "\n",
    "$$BEY=\\left(\\frac{365}{Days}\\right)\\times\\left(\\frac{FV-PV}{PV}\\right)$$\n",
    "$$BEY=\\left(\\frac{365}{Days}\\right)\\times\\left(\\frac{\\text{Dollar Discount}}{PV}\\right)$$\n",
    "$$BEY=\\left(\\frac{365}{Days}\\right)\\times\\left(\\frac{FV  \\times DR \\times \\frac{Days}{Year}}{PV}\\right)$$\n",
    "$$BEY = \\frac{365 \\times DR}{Year_{\\text{DR Convention}} - (Days \\times DR)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The U.S. Treasury uses a different method to calculate its official Investment Rate (i.e., the bond equivalent yield) when the time to **maturity exceeds six months**. The BEY for the 52-week T-bill is based on the following formula:\n",
    "\n",
    "$$BEY=\\frac{-\\frac{2\\times Days}{365} + 2 \\times \\sqrt{\\left(\\frac{Days}{365}\\right)^{2}-\\left(\\frac{2\\times Days}{365}-1\\right)\\left(1-\\frac{100}{PV}\\right)}}{\\frac{2\\times Days}{365}-1}$$\n",
    "\n",
    "derived from:\n",
    "$$100=PV\\times \\left(1+\\frac{182.5}{365}\\times BEY\\right)\\times \\left(1+\\frac{Days - 182.5}{365}\\times BEY\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Term    | Maturity Date | Discount Rate | Investment Rate | Price (per $100 in par value) |\n",
    "| ------- | ------------- | ------------- | --------------- | ----------------------------- |\n",
    "| 4 week  | 31/07/2008    | 1.850%         | 1.878%           | 99.856111                      |\n",
    "| 13 week | 02/10/2008    | 1.900%         | 1.936%           | 99.519722                      |\n",
    "| 26 week | 02/01/2009    | 2.135%         | 2.188%           | 98.914708                      |\n",
    "| 52 week | 03/07/2009    | 2.295%         | 2.368%           | 97.679500                       |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price = 99.85611, days = 28, bey = 0.01878\n",
      "price = 99.51972, days = 91, bey = 0.01936\n",
      "price = 98.91471, days = 183, bey = 0.02188\n",
      "price = 97.67312, days = 365, bey = 0.02382\n",
      "\n",
      "bey = 0.01878\n",
      "bey = 0.01936\n",
      "bey = 0.02188\n",
      "bey = 0.02382\n"
     ]
    }
   ],
   "source": [
    "settle = to_datetime(\"2008-7-3\")\n",
    "convention = 'actual/360'\n",
    "mat_dr = {'2008-7-31': 0.0185,\n",
    "             '2008-10-2': 0.019,\n",
    "             '2009-1-2': 0.02135,\n",
    "             '2009-7-3': 0.02295}\n",
    "\n",
    "days_pv = {}\n",
    "for mat, dr in mat_dr.items():\n",
    "    days, year = days_year(settle, to_datetime(mat), convention=convention)\n",
    "    price = dr_pv(100, dr, days, year)\n",
    "    days_pv[days] = price\n",
    "    bey = (365 * dr) / (360 - (days * dr)) # DR to BEY conversion formula\n",
    "    print(f'{price = :0.5f}, {days = }, {bey = :0.5f}')\n",
    "    \n",
    "print()\n",
    "\n",
    "for days, price in days_pv.items():\n",
    "    bey = addon_rate(price, 100, days, year=365) # AOR Cash flow formula set to 365 year\n",
    "    print(f'{bey = :0.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.019263888888888886"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def bey_short(rate, days, year, from_dr_rate=True):\n",
    "    if from_dr_rate:\n",
    "        return (365 * rate) / (year - (days * rate))\n",
    "    else:\n",
    "        premium = rate * (days/year) \n",
    "        return (365 / days) * premium \n",
    "    \n",
    "days = 91\n",
    "year = 360\n",
    "rate = 0.019\n",
    "from_dr_rate = False\n",
    "\n",
    "bey_short(rate, days, year, from_dr_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02368170792870403"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def bey_long(days, pv):\n",
    "    D = (2*days)/365\n",
    "    num = -D + 2 * ((days/365)**2 - (D - 1) * (1 - (100/pv)))**(1/2)\n",
    "    return num / (D - 1)\n",
    "\n",
    "days = 364\n",
    "pv = 97.6795\n",
    "\n",
    "bey_long(days, pv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Semiannual Bond Basis (SABB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For comparability of Treasury securities such as bills, notes, and bonds across maturities, it is often advisable to convert rates to semiannual compounding because that is how yields to maturity on Treasury notes and bonds are calculated and presented. T-bill discount rates can be first converted to a **365-day add-on** basis and then converted to a **semiannual bond basis (SABB)**.\n",
    "\n",
    "Note that $SABB = APR_{2}$\n",
    "\n",
    "Step 1:\n",
    "$$BEY = \\frac{365 \\times DR}{Year_{\\text{DR}} - (Days \\times DR)}$$\n",
    "Step 2:\n",
    "$$\\left(1+\\frac{BEY}{Year/Days}\\right)^{Year/Days} = \\Big(1+\\frac{SABB}{2}\\Big)^{2}$$\n",
    "$$2\\times\\left[\\left(1+\\frac{BEY}{Year/Days}\\right)^{(Year/Days)/2}-1\\right] = SABB$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sabb(rate, days, year, from_dr_rate=True):\n",
    "    bey = bey_short(rate, days, year, from_dr_rate)\n",
    "    year_frac = 365/days\n",
    "    return 2 * ((1 + bey/year_frac)**(year_frac/2) - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "semiannual = 0.01886, bey = 0.01878, days = 28\n",
      "semiannual = 0.01940, bey = 0.01936, days = 91\n",
      "semiannual = 0.02188, bey = 0.02188, days = 183\n",
      "semiannual = 0.02368, bey = 0.02368, days = 365\n"
     ]
    }
   ],
   "source": [
    "mat_dr = {'2008-7-31': 0.0185,\n",
    "             '2008-10-2': 0.019,\n",
    "             '2009-1-2': 0.02135,\n",
    "             '2009-7-3': 0.02295}\n",
    "\n",
    "convention = 'actual/360'\n",
    "\n",
    "for mat, dr in mat_dr.items():\n",
    "    days, year = days_year(settle, to_datetime(mat), convention=convention)\n",
    "    bey = bey_short(dr, days, year) if days < 183 else bey_long(days, dr_pv(100, dr, days, year))\n",
    "    semiannual = sabb(dr, days, year)\n",
    "    print(f'{semiannual = :0.5f}, {bey = :0.5f}, {days = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that a money market security can be purchased on January 12 for $64,000. The security matures on March 12, paying $65,000. Calculate the interest rate on the security to the nearest one-tenth of a basis point, given the following quotation methods and day-count conventions:\n",
    "- Add-on Rate, Actual/360\n",
    "- Add-on Rate, Actual/365\n",
    "- Add-on Rate, 30/360\n",
    "- Add-on Rate, Actual/370\n",
    "- Discount Rate, Actual/360"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "days = 59\n",
      "year = 360\n",
      "aor =  0.09534\n"
     ]
    }
   ],
   "source": [
    "pv = 64_000\n",
    "fv = 65_000\n",
    "settle = to_datetime('2025-1-12')\n",
    "mat = to_datetime('2025-3-12')\n",
    "convention = 'actual/360'\n",
    "\n",
    "days, year = days_year(settle, mat, convention)\n",
    "print(f'{days = }\\n{year = }')\n",
    "aor = addon_rate(pv, fv, days, year)\n",
    "print(f'{aor = : 0.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "days = 59\n",
      "year = 365\n",
      "aor =  0.09666\n"
     ]
    }
   ],
   "source": [
    "pv = 64_000\n",
    "fv = 65_000\n",
    "settle = to_datetime('2025-1-12')\n",
    "mat = to_datetime('2025-3-12')\n",
    "convention = 'actual/365'\n",
    "\n",
    "days, year = days_year(settle, mat, convention)\n",
    "print(f'{days = }\\n{year = }')\n",
    "aor = addon_rate(pv, fv, days, year)\n",
    "print(f'{aor = : 0.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "days = 60\n",
      "year = 360\n",
      "aor =  0.09375\n"
     ]
    }
   ],
   "source": [
    "pv = 64_000\n",
    "fv = 65_000\n",
    "settle = to_datetime('2025-1-12')\n",
    "mat = to_datetime('2025-3-12')\n",
    "convention = 'thirty/360'\n",
    "\n",
    "days, year = days_year(settle, mat, convention)\n",
    "print(f'{days = }\\n{year = }')\n",
    "aor = addon_rate(pv, fv, days, year)\n",
    "print(f'{aor = : 0.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "days = 60\n",
      "year = 370\n",
      "aor =  0.09635\n"
     ]
    }
   ],
   "source": [
    "pv = 64_000\n",
    "fv = 65_000\n",
    "settle = to_datetime('2025-1-12')\n",
    "mat = to_datetime('2025-3-12')\n",
    "convention = 'thirty/360'\n",
    "\n",
    "days = days_year(settle, mat, convention)[0]\n",
    "year = 370\n",
    "print(f'{days = }\\n{year = }')\n",
    "aor = addon_rate(pv, fv, days, year)\n",
    "print(f'{aor = : 0.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "days = 59\n",
      "year = 360\n",
      "dr =  0.09387\n"
     ]
    }
   ],
   "source": [
    "pv = 64_000\n",
    "fv = 65_000\n",
    "settle = to_datetime('2025-1-12')\n",
    "mat = to_datetime('2025-3-12')\n",
    "convention = 'actual/360'\n",
    "\n",
    "days, year = days_year(settle, mat, convention)\n",
    "print(f'{days = }\\n{year = }')\n",
    "dr = dr_rate(pv, fv, days, year)\n",
    "print(f'{dr = : 0.5f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that sometime in the not-so-distant future the fastest-growing financial institution in the world is **Bank 24/7/52**. Its success owes to pioneering use of hourly interest rates for loans and deposits, an idea borrowed from the success of the hourly car rental businesses. Its (add-on) rates on short term large time deposits (>$1,000,000) are shown in table below. The APR quoted by Bank 24/7/52 assumes a 364-day year. For instance, 3.4944% is calculated as 0.0004% * 24 * 7 * 52.\n",
    "\n",
    "To see how hourly interest rates might work, suppose a corporation makes a 52-hour, $5,000,000 time deposit at Bank 24/7/52. The redemption amount on the deposit can be calculated using an hourly version of the below equation. The corporation will receive $5,001,560 when the deposit\n",
    "matures.\n",
    "\n",
    "$$FV=PV\\times\\left[1 + \\left(AOR \\times \\frac{Days}{Year}\\right)\\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Time Period | Rate per Hour | APR     |\n",
    "| ----------- | ------------- | ------- |\n",
    "| 1–8 Hours   | 0.0004%       | 3.4944% |\n",
    "| 9–24 Hours  | 0.0005%       | 4.3680% |\n",
    "| 25–72 Hours | 0.0006%       | 5.2416% |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.4944, 4.368000000000001, 5.2416]\n",
      "fv = 5_001_560\n"
     ]
    }
   ],
   "source": [
    "rate_per_hour = [4e-6, 5e-6, 6e-6]\n",
    "apr = [rate_per_hour[i] * 24 * 7 * 52 * 100 for i in range(len(rate_per_hour))]\n",
    "print(apr)\n",
    "\n",
    "pv = 5_000_000\n",
    "hours = 52\n",
    "days = hours/24\n",
    "year = 364\n",
    "\n",
    "fv = round(addon_fv(pv, apr[2]/100, days, year)) \n",
    "print(f'{fv = :_}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose that 30 hours after making the time deposit, the corporation has sudden need for liquidity. Bank 24/7/52’s policy is to buy back time deposits as a service to its regular corporate customers. The redemption amount is fixed once the deposit is issued. The present value of the time deposit after 30 hours have passed and 22 hours remain is computed using the equation used earlier.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pv_sold = 5_001_010\n"
     ]
    }
   ],
   "source": [
    "sold_hour = 22\n",
    "sold_days = sold_hour/24\n",
    "\n",
    "pv_sold = round(addon_pv(fv, aor=apr[1]/100, days=sold_days, year=year))\n",
    "print(f'{pv_sold = :_}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How did the corporation do on its short-term investment? The realized rate of return for its 30-hour holding period can be calculated with an hourly version of the equation below. That turns out to be 5.8822% on a 364-day add-on basis.\n",
    "\n",
    "$$AOR=\\left(\\frac{Year}{Days}\\right)\\times\\left(\\frac{FV-PV}{PV}\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aor = 5.8822399999999995\n",
      "periodicity = 291.2\n"
     ]
    }
   ],
   "source": [
    "hours_held = 30\n",
    "days_held = hours_held/24\n",
    "\n",
    "aor = addon_rate(pv, pv_sold, days_held, year)*100\n",
    "print(f'{aor = }')\n",
    "periodicity = year/days_held\n",
    "print(f'{periodicity = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that, for consistency, the money manager likes to convert all rates of return to a semiannual bond basis. Equation below can be used to convert that AOR to an SABB, but first one additional step is needed.\n",
    "\n",
    "$$2\\times\\left[\\left(1+\\frac{BEY}{Year/Days}\\right)^{(Year/Days)/2}-1\\right] = SABB$$\n",
    "\n",
    "In general, interest rates should be put on a full-year, 365-day basis before carrying out the periodicity conversion. That is because an SABB having a periodicity of 2 implicitly assumes two evenly spaced periods in the 365-day year, each period having 182.5 days. (Notice that this assumption is implicit in equation below)\n",
    "\n",
    "$$100=PV\\times \\left(1+\\frac{182.5}{365}\\times BEY\\right)\\times \\left(1+\\frac{Days - 182.5}{365}\\times BEY\\right)$$\n",
    "\n",
    "So, first we need to convert 5.8822% to an addon rate for 365 days in the year by multiplying by 365/364.\n",
    "\n",
    "$$AOR_{start}=\\left(\\frac{Year_{start}}{Days}\\right)\\times\\left(\\frac{FV-PV}{PV}\\right)$$\n",
    "$$\\left(\\frac{365}{Year_{start}}\\right)\\times AOR_{start}=\\left(\\frac{\\cancel{Year_{start}}}{Days}\\right)\\times\\left(\\frac{FV-PV}{PV}\\right)\\times \\left(\\frac{365}{\\cancel{Year_{start}}}\\right)$$\n",
    "$$AOR_{365}=\\left(\\frac{365}{Year_{start}}\\right)\\times AOR_{start}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.8984\n",
      "periodicity_new = 292.0\n"
     ]
    }
   ],
   "source": [
    "year_new = 365\n",
    "aor_365 = (year_new/year) * aor\n",
    "print(aor_365)\n",
    "periodicity_new = year_new/days_held\n",
    "print(f'{periodicity_new = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This rate is now an APR for 292 periods in the year: (365 * 24)/30 = 292. The holding-period rate of return converted to an SABB is 5.9856%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.985625711839848\n"
     ]
    }
   ],
   "source": [
    "semiannual = sabb(aor_365/100, days_held, year_new, from_dr_rate=False)\n",
    "\n",
    "print(semiannual*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://www.youtube.com/watch?v=ufO_BScIHDQ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare Rates - Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2855954aab0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1280x960 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fv = 100\n",
    "days = 90\n",
    "year = 360\n",
    "\n",
    "rate_x = np.linspace(0.005, 1, num=1000)\n",
    "addon_price_y = addon_pv(100, rate_x, days, year)\n",
    "dr_price_y = dr_pv(100, rate_x, days, year)\n",
    "\n",
    "plt.figure(num=0, dpi=200)\n",
    "plt.plot(rate_x, addon_price_y, label=\"Add-On Rate\")\n",
    "plt.plot(rate_x, dr_price_y, label=\"Discount Rate\")\n",
    "plt.title('Money Market Rate Comparison')\n",
    "plt.xlabel('Rate')\n",
    "plt.ylabel('Present Value')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def addon_fv(pv, aor, days, year=360):\n",
    "    return pv * (1 + (aor * days  / year))\n",
    "\n",
    "def addon_pv(fv, aor, days, year=360):\n",
    "    return fv / (1 + (aor * days  / year))\n",
    "\n",
    "def addon_rate(pv, fv, days, year=360):\n",
    "    return (year/days) * (fv - pv)/pv\n",
    "\n",
    "def periodicity(days, year):\n",
    "    return year / days\n",
    "\n",
    "def dr_pv(fv, dr, days, year=360):\n",
    "    return fv * (1 - (dr * days  / year))\n",
    "\n",
    "def dr_fv(pv, dr, days, year=360):\n",
    "    return pv / (1 - (dr * days  / year))\n",
    "\n",
    "def dr_rate(pv, fv, days, year=360):\n",
    "    return (year/days) * (fv - pv)/fv\n",
    "\n",
    "def bey_short(rate, days, year, from_dr_rate=True):\n",
    "    if from_dr_rate:\n",
    "        return (365 * rate) / (year - (days * rate))\n",
    "    else:\n",
    "        premium = rate * (days/year) \n",
    "        return (365 / days) * premium \n",
    "    \n",
    "def bey_long(days, pv):\n",
    "    D = (2*days)/365\n",
    "    num = -D + 2 * ((days/365)**2 - (D - 1) * (1 - (100/pv)))**(1/2)\n",
    "    return num / (D - 1)\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)\n",
    "\n",
    "def sabb(rate, days, year, from_dr_rate=True):\n",
    "    bey = bey_short(rate, days, year, from_dr_rate)\n",
    "    year_frac = 365/days\n",
    "    return 2 * ((1 + bey/year_frac)**(year_frac/2) - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) The add-on rate on a USD100,000, 3-month bank CD (certificate of deposit) is 1.75%. Interest on the CD is based on an actual/360 day count. If there are 92 days in the 3-month time period, the redemption amount at maturity including interest for the CD is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "redemption = 100,447.22\n"
     ]
    }
   ],
   "source": [
    "redemption = round(addon_fv(pv=100_000, aor=0.0175, days=92, year=360),2)\n",
    "print(f'{redemption = :,}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. The discount rate on a USD10,000, 13-week T-bill (Treasury bill) is 0.745%. The T-bill uses an actual/360 day count. If there are 91 days in the 13-week time period, the purchase price for the T-bill is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price = 9,981.17\n"
     ]
    }
   ],
   "source": [
    "price = round(dr_pv(fv=10_000, dr=0.00745, days=91, year=360),2)\n",
    "print(f'{price = :,}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Three money market securities have the same cash flows, meaning the same purchase price (PV) and redemption amount including interest (FV), and the same number of days to maturity. Their quoted annual rates differ by type, discount rate or add-on rate, and by day-count convention, actual/360 or actual/365. Which security has the highest quoted annual rate?\n",
    "\n",
    "    -  Discount rate, actual/360\n",
    "    -  Add-on rate, actual/360\n",
    "    -  **Add-on rate, actual/365**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Security (b) will have a higher quoted rate than (a) because for the same cash flows, PV and FV, a discount rate understates an add-on rate. The discount rate is based on FV – PV divided by FV, whereas the add-on rate is based on FV – PV divided by PV. Assuming a non-negative interest rate, PV < FV. Security (c) will have a higher quoted rate than (b) because the quoted add-on rate is (FV – PV) divided by PV, times the assumed periodicity, which is Year/Days. \n",
    "\n",
    "$$\\frac{365}{Days}\\times\\left(\\frac{FV-PV}{PV}\\right)>\\frac{360}{Days}\\times\\left(\\frac{FV-PV}{PV}\\right)>\\frac{360}{Days}\\times\\left(\\frac{FV-PV}{FV}\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0909090909090908\n",
      "1.2\n",
      "1.2166666666666666\n"
     ]
    }
   ],
   "source": [
    "price = 100\n",
    "redemption = 110\n",
    "days = 30\n",
    "\n",
    "d_actual_360 = dr_rate(price, redemption, days, 360)\n",
    "print(d_actual_360)\n",
    "aor_actual_360 = addon_rate(price, redemption, days, 360)\n",
    "print(aor_actual_360)\n",
    "aor_actual_365 = addon_rate(price, redemption, days, 365)\n",
    "print(aor_actual_365)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. The face value of 28-day commercial paper (CP) is USD1,000,000. The purchase price for the CP is USD994,500. The quoted discount rate for a 360-day year is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quoted_rate = 7.0714%\n"
     ]
    }
   ],
   "source": [
    "price = 994_500\n",
    "redemption = 1_000_000\n",
    "days = 28\n",
    "quoted_rate = dr_rate(price, redemption, days, 360)\n",
    "print(f'{quoted_rate = :.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. The discount rate on USD100,000, 91-day T-bills is 1.443%, quoted for a 360-day year. The bond-equivalent yield (i.e., an add-on rate for a 365-day year) for the T-bills is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bey =  1.468%\n"
     ]
    }
   ],
   "source": [
    "rate = 0.01443\n",
    "days = 91\n",
    "year = 360\n",
    "from_dr_rate = True\n",
    "\n",
    "bey = bey_short(rate, days, year, from_dr_rate=True)\n",
    "print(f'{bey = : 0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6. An investor buys a 2.50%, USD1,000,000, 3-month bank CD. Interest on the CD is paid at redemption using a 30/360 day-count convention. One month later, the investor sells the CD to a dealer at its bid rate of 2.40% (on 2-month CDs having comparable risk). The investor’s realized rate of return, stated as an add-on rate for a periodicity of 12, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "redemption = 1006250.00\n",
      "price_sell = 1002241.04\n",
      "aor_return = 2.689%\n"
     ]
    }
   ],
   "source": [
    "price_buy = 1_000_000\n",
    "rate_buy = 0.025\n",
    "rate_sell = 0.024\n",
    "days_buy = 30*3\n",
    "days_sell = 30*2\n",
    "year = 360\n",
    "\n",
    "redemption = addon_fv(pv=price_buy, aor=rate_buy, days=days_buy, year=year)\n",
    "print(f'{redemption = :.2f}')\n",
    "\n",
    "price_sell = addon_pv(fv=redemption, aor=rate_sell, days=days_sell, year=year)\n",
    "print(f'{price_sell = :.2f}')\n",
    "\n",
    "aor_return = addon_rate(pv=price_buy, fv=price_sell, days=30, year=360)\n",
    "print(f'{aor_return = :.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7. A money manager buys a USD10,000,000, 6-month Treasury bill at the regular weekly auction. The T-bill discount rate is 1.22% using an actual/360 day-count convention. The time between settlement and maturity is 182 days. Sixty days later, the T-bill is sold to a dealer at the bid (discount) rate of 1.25%. The money manager’s realized rate of return, stated on an add-on rate basis for 60 days in a 365-day year (i.e., a bond equivalent yield, or BEY), is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price_buy = 9938322.22\n",
      "price_sold = 9957638.89\n",
      "bey_return = 1.182%\n"
     ]
    }
   ],
   "source": [
    "redemption = 10_000_000\n",
    "disc_rate = 0.0122\n",
    "days = 182\n",
    "year = 360\n",
    "days_sell = 182-60\n",
    "disc_rate_sell = 0.0125\n",
    "\n",
    "price_buy = dr_pv(fv=redemption, dr=disc_rate, days=days, year=year)\n",
    "print(f'{price_buy = :.2f}')\n",
    "\n",
    "price_sold = dr_pv(fv=redemption, dr=disc_rate_sell, days=days_sell, year=360)\n",
    "print(f'{price_sold = :.2f}')\n",
    "\n",
    "bey_return = addon_rate(pv=price_buy, fv=price_sold, days=60, year=365)\n",
    "print(f'{bey_return = :.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8. Which of these three money market securities offers the highest rate of return on a bond equivalent yield basis assuming the investor holds to maturity and there is no default by the issuer:\n",
    "\n",
    "    - 2.75%, 90-day banker’s acceptance quoted on a discount rate basis and an actual/360 day count.\n",
    "    - 2.80%, 90-day commercial paper quoted on a discount rate basis and an actual/360 day count.\n",
    "    - 2.85%, 90-day bank time deposit quoted on an add-on rate basis and an actual/360 day count."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bey_a = 2.8075%\n",
      "bey_b = 2.8589%\n",
      "bey_c = 2.8896%\n"
     ]
    }
   ],
   "source": [
    "days = 90\n",
    "year = 360\n",
    "dr_rate_1 = 0.0275\n",
    "dr_rate_2 = 0.0280\n",
    "aor_rate_1 = 0.0285\n",
    "\n",
    "bey_a = bey_short(dr_rate_1, days, year, True)\n",
    "print(f'{bey_a = :.4%}')\n",
    "bey_b = bey_short(dr_rate_2, days, year, True)\n",
    "print(f'{bey_b = :.4%}')\n",
    "bey_c = bey_short(aor_rate_1, days, year, False)\n",
    "print(f'{bey_c = :.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "9. A security offers an annual percentage rate (APR) of 6.36% for monthly payments (a periodicity of 12). The APR converted to quarterly payments (a periodicity of 4) is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "apr_4 =  6.394%\n"
     ]
    }
   ],
   "source": [
    "apr_12 = 0.0636\n",
    "from_freq = 12\n",
    "to_freq = 4\n",
    "\n",
    "apr_4 = equivRate(apr_12, from_freq, to_freq)\n",
    "print(f'{apr_4 = : .3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10. A security offers an annual percentage rate (APR) of 5.70% for semiannual payments (a periodicity of 2). The APR converted to daily payments (a periodicity of 365) is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "apr_365 =  5.621%\n"
     ]
    }
   ],
   "source": [
    "apr_2 = 0.057\n",
    "from_freq = 2\n",
    "to_freq = 365\n",
    "\n",
    "apr_365 = equivRate(apr_2, from_freq, to_freq)\n",
    "print(f'{apr_365 = : .3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11. A money market mutual fund buys a 3.50%, USD1,000,000, 6-month bank CD at par value (i.e., for USD1,000,000). Interest on the CD is paid at redemption using an actual/360 day-count convention. There are 181 days in the 6-month time period. Sixty days later, the mutual fund sells the CD to a dealer at its bid rate of 3.45% (on 4-month CDs having comparable risk). The fund’s realized rate of return on the purchase and sale of the CD, stated on a semiannual bond basis, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "redemption =  1017597.22\n",
      "price_sell =  1005932.60\n",
      "aor_return = 3.56%\n",
      "sabb_return =  3.63%\n"
     ]
    }
   ],
   "source": [
    "pv = 1_000_000\n",
    "aor = 0.035\n",
    "days = 181\n",
    "year = 360\n",
    "days_sold = 181-60\n",
    "aor_sold = 0.0345\n",
    "\n",
    "redemption = addon_fv(pv, aor, days, year)\n",
    "print(f'{redemption = : 0.2f}')\n",
    "\n",
    "price_sell = addon_pv(redemption, aor_sold, days_sold, year)\n",
    "print(f'{price_sell = : 0.2f}')\n",
    "\n",
    "aor_return = addon_rate(pv, price_sell, 60, year)\n",
    "print(f'{aor_return = :0.2%}')\n",
    "\n",
    "sabb_return = sabb(aor_return, 60, 360, False)\n",
    "print(f'{sabb_return = : 0.2%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12. A problem with quoted investment rates on U.S. Treasury bills having maturities above 182 days is that:\n",
    "    1. The derivation of the formula for the investment rate involves the “quadratic rule” and therefore is an approximation.\n",
    "    2. The quoted investment rate is a discount rate and therefore understates the true rate of return to an investor.\n",
    "    3. The quoted rate assumes a 360-day year when in reality years have 365 or 366 days.\n",
    "    4. **The quoted investment rate does not have a well-defined periodicity and therefore cannot be easily compared to rates on other securities.**\n",
    "    \n",
    "The quoted investment rate for T-bills having maturities over 182 days has a “hybrid” periodicity, a combination of semiannual compounding and something more frequent than semiannual. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "13. Which of the following statements best summarizes the effect of a periodicity conversion:\n",
    "    1. **Compounding a lower APR for a higher periodicity provides the same total return as compounding a higher APR for a lower periodicity.**\n",
    "    2. Compounding a lower APR for a lower periodicity provides the same total return as compounding a higher APR for a higher periodicity.\n",
    "    3. Compounding a higher APR for a higher periodicity provides the same total return as compounding a lower APR for a lower periodicity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "14. Suppose that the interest rate on time deposits at Bank 24/7/52 is an APR of 8.7360%, quoted on a 364-day basis. The rate per hour is 0.0010%, so that 0.0010% * 24 * 7 * 52 = 8.7360%. The interest earned on a USD100,000 deposit for 84 hours is closest to:\n",
    "\n",
    "The annual interest rate is adjusted by the “hour count” rather than by the day count. Another way to do the calculation of interest earned is: \n",
    "\n",
    "0.0010% per hour * 84 hours * 100,000 = 84.00\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rate_over_year =  8.7360%\n",
      "84.0\n",
      "84.0\n"
     ]
    }
   ],
   "source": [
    "deposit = 100_000\n",
    "rate_per_hour = 0.000010\n",
    "rate_over_year = rate_per_hour * 24 * 7 * 52\n",
    "print(f'{rate_over_year = : 0.4%}')\n",
    "\n",
    "redemption = deposit * (1 + (rate_over_year * (84/24)/364))\n",
    "print(redemption - deposit)\n",
    "\n",
    "redemption = deposit * (1 + (rate_per_hour * 84))\n",
    "print(redemption - deposit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "15. The discount rate on 270-day commercial paper is 8.112% for an actual/360 day count. That rate converted to a semiannual bond basis, i.e., an APR for a periodicity of 2, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "apr_2 =  8.6681%\n",
      "apr_2 =  8.6681%\n",
      "apr_2 =  8.6681%\n"
     ]
    }
   ],
   "source": [
    "rate = 0.08112\n",
    "days = 270\n",
    "year = 360\n",
    "\n",
    "apr_2 = sabb(rate, days, year, True)\n",
    "print(f'{apr_2 = : 0.4%}')\n",
    "\n",
    "redemption = dr_fv(100, rate, days, year)\n",
    "aor_rate = addon_rate(100, redemption, 270, 365)\n",
    "apr_2 = 2 * ((1 + aor_rate/(365/days))**((365/days)/2) - 1)\n",
    "print(f'{apr_2 = : 0.4%}')\n",
    "\n",
    "apr_2 = sabb(aor_rate, days, 365, False)\n",
    "print(f'{apr_2 = : 0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "16. A money manager acquires a USD25,000,000 position in 13-week (91-day) Treasury bills at the regular weekly auction. The T-bill discount rate is 1.118% using an actual/360 day-count convention. Seven days later, the T-bills are sold to a dealer at the bid (discount) rate of 1.127%. The money manager’s realized rate of return, stated on an add-on rate basis for the 7 days in a 360-day year is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price_buy = 24929348.61\n",
      "price_sell = 24934258.33\n",
      "ar_return = 1.01%\n"
     ]
    }
   ],
   "source": [
    "redemption = 25_000_000\n",
    "days = 91\n",
    "disc_rate = 0.01118\n",
    "year = 360\n",
    "days_sell = 91 - 7\n",
    "disc_rate_sell = 0.01127\n",
    "\n",
    "price_buy = dr_pv(redemption, disc_rate, days, year)\n",
    "print(f'{price_buy = :0.2f}')\n",
    "price_sell = dr_pv(redemption, disc_rate_sell, days_sell, year)\n",
    "print(f'{price_sell = :0.2f}')\n",
    "\n",
    "ar_return = addon_rate(price_buy, price_sell, 7, 360)\n",
    "print(f'{ar_return = :0.2%}')"
   ]
  }
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