Ch17_Bonds2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bonds 2\n",
    "\n",
    "This notebook discusses *duration hedging* as a way to immunize a bond portfolio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, Roots\n",
    "\n",
    "include(\"src/printmat.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Remark on the Code\n",
    "\n",
    "The file included below contains the function `BondPrice3()` which calculates the present value of a cash flow stream. (It's an extract from the notebook on Bonds 1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"src/BondCalculations.jl\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Value of a Bond Portfolio after a Sudden Interest Rate Change\n",
    "\n",
    "The calculations below assume that the *yield curve is flat*, but that it can shift up or down in parallel. This assumption is similar to the classical literature on duration hedging.\n",
    "\n",
    "The initial values are indicated by the subscript $_0$ and the values after the interest rate change by the subscript $_1$. It is assumed that the change is very sudden, so the time to the different cash flows is (virtually) the same before and after. For instance, the subscripts $0$ and $1$ could be interpreted as \"day 0\" and \"day 1\".\n",
    "\n",
    "The next cell sets up the cash flow for a bond portolio $L$ (\"Liability\") that pays the amount 0.2 each year for the next 10 years. The value of $L$ is calculated at an yield to maturity ($\\theta_0$) and at a new yield to maturity ($\\theta_1$). Notice that with a flat yield curve, the yield to maturity equals the (one and only) interest rate.\n",
    "\n",
    "Time to cash flow ($m$) is measured in years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mValue of bond portfolio at θ₀=0.05 and θ₁=0.03:\u001b[22m\u001b[39m\n",
      "PL₀ (at θ₀=0.05)          1.544\n",
      "PL₁ (at θ₁=0.03)          1.706\n",
      "ΔPL/PL₀ (return)          0.105\n",
      "\n",
      "\u001b[31m\u001b[1mNotice that the bond is worth more at the lower interest rate\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "θ₀ = 0.05                   #initial interest rate\n",
    "θ₁ = 0.03                   #interest rate after sudden change\n",
    "\n",
    "cf = ones(10)*0.2            #cash flow of liability\n",
    "m  = 1:10                    #time periods of the cash flows, years\n",
    "\n",
    "PL₀ = BondPrice3(θ₀,cf,m)    #value of bond L at initial interest rate\n",
    "PL₁ = BondPrice3(θ₁,cf,m)    #and after sudden change in interest rate\n",
    "R   = (PL₁ - PL₀)/PL₀        #relative change of the value\n",
    "\n",
    "printblue(\"Value of bond portfolio at θ₀=$θ₀ and θ₁=$θ₁:\")\n",
    "xy = [PL₀, PL₁, R]\n",
    "rowNames = [\"PL₀ (at θ₀=$θ₀)\";\"PL₁ (at θ₁=$θ₁)\";\"ΔPL/PL₀ (return)\"]\n",
    "printmat(xy;rowNames,width=15)\n",
    "\n",
    "printred(\"Notice that the bond is worth more at the lower interest rate\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Macaulay's Duration\n",
    "\n",
    "Let $D^M$ denote Macaulay's duration\n",
    "\n",
    "$D^M = \\sum_{k=1}^{K} m_{k}\\frac{cf_{k}}{\\left(  1+\\theta\\right)  ^{m_{k}}P}$.\n",
    "\n",
    "It can be interpreted as the weighted average time (years) to cash flow.\n",
    "\n",
    "A first-order Taylor approximation gives the (approximate) return\n",
    "\n",
    "$\\frac{\\Delta P}{P} \\approx -D^M \\times \\frac{\\Delta \\theta}{1+\\theta}$, \n",
    "\n",
    "as a function of the change of yield to maturity ($\\theta$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BondDuration"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    BondDuration(P,cf,m,ytm)\n",
    "\n",
    "Calculate Macaulays (bond) duration measure.\n",
    "\n",
    "P:   scalar, bond price\n",
    "cf:  scalar or K vector of cash flows\n",
    "m:   K vector of times of cash flows\n",
    "ytm: scalar, yield to maturity\n",
    "\"\"\"\n",
    "function BondDuration(P,cf,m,ytm)\n",
    "    if length(cf) != length(m)\n",
    "        error(\"cf and m must have the same lengths\")\n",
    "    end\n",
    "    cdisc   = cf.*m./((1+ytm).^m)        #cf1/(1+y) + 2*cf2/(1+y)^2 + ...\n",
    "    Dmac    = sum(cdisc)/P               #Macaulays duration\n",
    "    return Dmac\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Macaulay's duration of the bond portfolio L:     5.099\n",
      "\n",
      "\u001b[34m\u001b[1mRelative price change (return): \u001b[22m\u001b[39m\n",
      "Exact                           0.105\n",
      "Approximate (from duration)     0.097\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Dmac    = BondDuration(PL₀,cf,m,θ₀)\n",
    "printlnPs(\"Macaulay's duration of the bond portfolio L:\",Dmac)\n",
    "\n",
    "Δθ       = θ₁ - θ₀             #change of the ytm\n",
    "R_approx = -Dmac*Δθ/(1+θ₀)\n",
    "\n",
    "printblue(\"\\nRelative price change (return): \")\n",
    "printmat([R,R_approx];rowNames=[\"Exact\",\"Approximate (from duration)\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hedging a Liability Stream\n",
    "\n",
    "Suppose we are short one bond portfolio $L$ (we have a liability) as discussed above, which is worth $P_L$. To hedge against interest rate changes, we buy $v$ units of bond (portfolio) $H$. The balance is put on a money market account $M$ to make the initial value of the portfolio zero ($V=0$)\n",
    "\n",
    "$V=vP_{H}+M-P_{L}$.\n",
    "\n",
    "Over a short time interval, the change (indicated by $\\Delta$) in the overall portfolio value is\n",
    "\n",
    "$\\Delta V=v\\Delta P_{H}-\\Delta P_{L}$.\n",
    "\n",
    "In the cells below, we assume that the yield curve is flat and shifts in parallel. This means that the ytm of both $L$ and $H$ change from one common value ($\\theta_0$) to another common value ($\\theta_1$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Duration Matching\n",
    "\n",
    "Duration matching means that we choose a hedge bond with the *same duration* as the liability and invest same amount in each. Clearly, this gives $\\frac{\\Delta V}{P_{L}}\\approx 0$.\n",
    "\n",
    "The code below uses a zero coupon bond as bond $H$, but that is not important. It has the same maturity as Macaulay's duration of the liability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mHedge bond: a zero coupon bond with m=5.1 and face value of 1.\u001b[22m\u001b[39m\n",
      "\n",
      "\u001b[34m\u001b[1mRecall that the interest rates change from θ₀=0.05 to θ₁=0.03.\u001b[22m\u001b[39m\n",
      "\n",
      "\u001b[34m\u001b[1mResults of the calculations:\u001b[22m\u001b[39m\n",
      "PL₀                     1.544\n",
      "PH₀                     0.780\n",
      "v                       1.981\n",
      "v*PH₀/PL₀               1.000\n",
      "Duration(liability)     5.099\n",
      "Duration(hedge)         5.099\n",
      "Return                 -0.002\n",
      "\n",
      "\u001b[31m\u001b[1mThe duration matching gives a return of -0.2%. Close to zero.\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "PH₀ = BondPrice3(θ₀,1,Dmac)      #value of hedge bond before, here a zero coupon bond\n",
    "PH₁ = BondPrice3(θ₁,1,Dmac)      #value of hedge bond, after\n",
    "\n",
    "v  = PL₀/PH₀                     #so v*PH₀ = PL₀, same amount in L and H\n",
    "\n",
    "ΔV = v*(PH₁-PH₀) - (PL₁-PL₀)     #value change of total portfolio\n",
    "R  = ΔV/PL₀                      #relative value change\n",
    "\n",
    "txt = \"\"\"Hedge bond: a zero coupon bond with m=$(round(Dmac,digits=2)) and face value of 1.\\n\n",
    "Recall that the interest rates change from θ₀=$θ₀ to θ₁=$θ₁.\\n\n",
    "Results of the calculations:\"\"\"\n",
    "printblue(txt)\n",
    "\n",
    "xy = [PL₀,PH₀,v,v*PH₀/PL₀,Dmac,Dmac,R]\n",
    "rowNames = [\"PL₀\",\"PH₀\",\"v\",\"v*PH₀/PL₀\",\"Duration(liability)\",\"Duration(hedge)\",\"Return\"]\n",
    "printmat(xy;rowNames)\n",
    "\n",
    "printred(\"The duration matching gives a return of $(round(R*100,digits=1))%. Close to zero.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Hedging\n",
    "\n",
    "The \"naive\" hedging invests the *same amount in the hedge bond* as the value of the liability, that is, $v P_{H}=P_{L}$ so $v=P_{L}/P_{H}$, but pays no attention to the durations.\n",
    "\n",
    "The effectiveness of this approach depends on the interest rate sensitivities of $L$ and $H$. In particular, it can be shown that the relative value change of the overall portfolio is\n",
    "\n",
    "$\\frac{\\Delta V}{P_{L}}\\approx\\left(  D_{L}^{M}-D_{H}^{M}\\right)  \\times\n",
    "\\frac{\\Delta\\theta}{1+\\theta}$,\n",
    "\n",
    "so it depends on the difference between the durations (of the liability and hedge bond).\n",
    "\n",
    "In particular, if $D_{L}>D_{H}$, and $\\Delta\\theta<0$ (as in the example below), then we will lose money. More importantly, with $D_{L}^{M} \\neq D_{H}^{M}$, we are taking a risk (of losses/gains), that is, we are not hedged.  \n",
    "\n",
    "In contrast, with  $D_{L}=D_{H}$, then we are effectively doing duration matching (see above). Clearly, there are also scenarious"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mHedge bond: zero coupon bond with m=3 and face value of 1\u001b[22m\u001b[39m\n",
      "\n",
      "PL₀                1.544\n",
      "PH₀                0.864\n",
      "v                  1.788\n",
      "v*PH₀/PL₀          1.000\n",
      "Dur(liability)     5.099\n",
      "Dur(hedge)         3.000\n",
      "Return            -0.045\n",
      "\n",
      "\u001b[31m\u001b[1mThe naive hedge here gives a return of -4.5%, which is a bad hedge\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "mH = 3                     #a mH-year zero coupon bond is used as hedge bond\n",
    "\n",
    "PH₀ = BondPrice3(θ₀,1,mH)\n",
    "PH₁ = BondPrice3(θ₁,1,mH)\n",
    "\n",
    "v = PL₀/PH₀                 #so v*PH₀ = PL₀\n",
    "\n",
    "ΔV = v*(PH₁-PH₀) - (PL₁-PL₀)\n",
    "R  = ΔV/PL₀                 #relative value change\n",
    "\n",
    "printblue(\"Hedge bond: zero coupon bond with m=$mH and face value of 1\\n\")\n",
    "xy = [PL₀,PH₀,v,v*PH₀/PL₀,Dmac,mH,R]\n",
    "rowNames = [\"PL₀\",\"PH₀\",\"v\",\"v*PH₀/PL₀\",\"Dur(liability)\",\"Dur(hedge)\",\"Return\"]\n",
    "printmat(xy;rowNames)\n",
    "\n",
    "printred(\"The naive hedge here gives a return of $(round(R*100,digits=1))%, which is a bad hedge\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Illustrating the Problem with the Naive Hedging\n",
    "\n",
    "by plotting the value of the liability ($P_L$) and of the hedge bond position ($v P_H$) at different interest rates.\n",
    "\n",
    "### A Remark on the Code\n",
    "\n",
    "The next cell calculates `PL` and `PH` by a list comprehension. To instead do it with a loop use something like\n",
    "```\n",
    "(PL,PH) = (fill(NaN,length(θ_range)),fill(NaN,length(θ_range)))\n",
    "for i in 1:length(θ_range)\n",
    "    PL[i] = BondPrice3(θ_range[i],cf,m)\n",
    "    PH[i] = BondPrice3(θ_range[i],1,mH)\n",
    "end\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "θ_range = 0:0.01:0.1        #possible ytm values\n",
    "\n",
    "PL = [BondPrice3(θ,cf,m) for θ in θ_range]  #list comprehension,\n",
    "PH = [BondPrice3(θ,1,mH) for θ in θ_range]  #an alternative to a loop\n",
    "\n",
    "txt = \"In our example, the interest rates \\nare $θ₀ (before) and $θ₁ (after)\"\n",
    "\n",
    "p1 = plot( θ_range,[PL v*PH],\n",
    "           linecolor = [:red :green],\n",
    "           linestyle = [:solid :dash],\n",
    "           label = [\"liability\" \"v * hedge bond price\"],\n",
    "           title = \"Naive hedging\",\n",
    "           xlabel = \"Interest rate\",\n",
    "           ylabel = \"Value of the position\",\n",
    "           annotation = (0.005,1.4,text(txt,8,:left)))\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Duration Hedging\n",
    "\n",
    "With $D_{L}^{M}\\neq D_{H}$, we could *adjust the hedge ratio* $v$ to compensate for the difference in interest rate sensitivity (duration). In particular, we could set \n",
    "\n",
    "$v =\\frac{D_{L}^{M}}{D_{H}^{M}}\\times\\frac{P_{L}}{P_{H}}$. \n",
    "\n",
    "The balance $(P_L-v P_H)$ is kept on a money market account ($M$).\n",
    "\n",
    "It can be shown that this gives an (approximate) hedge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mHedge bond: zero coupon bond with m=3 and face value of 1\u001b[22m\u001b[39m\n",
      "\n",
      "PL₀                1.544\n",
      "PH₀                0.864\n",
      "v                  3.039\n",
      "v*PH₀/PL₀          1.700\n",
      "Dur(liability)     5.099\n",
      "Dur(hedge)         3.000\n",
      "M                 -1.081\n",
      "Return            -0.004\n",
      "\n",
      "\u001b[31m\u001b[1mThe duration hedging gives a return of -0.4%. Close to zero.\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "PH₀ = BondPrice3(θ₀,1,mH)\n",
    "PH₁ = BondPrice3(θ₁,1,mH)\n",
    "v   = Dmac/mH * PL₀/PH₀\n",
    "M   = PL₀ - v*PH₀               #on money market account\n",
    "\n",
    "ΔV = v*(PH₁-PH₀) - (PL₁-PL₀)\n",
    "R  = ΔV/PL₀                     #relative value change\n",
    "\n",
    "printblue(\"Hedge bond: zero coupon bond with m=$mH and face value of 1\\n\")\n",
    "xy = [PL₀,PH₀,v,v*PH₀/PL₀,Dmac,mH,M,R]\n",
    "rowNames = [\"PL₀\",\"PH₀\",\"v\",\"v*PH₀/PL₀\",\"Dur(liability)\",\"Dur(hedge)\",\"M\",\"Return\"]\n",
    "printmat(xy;rowNames)\n",
    "\n",
    "printred(\"The duration hedging gives a return of $(round(R*100,digits=1))%. Close to zero.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convexity (extra)\n",
    "\n",
    "A second-order Taylor approximation gives that \n",
    "\n",
    "$\n",
    "\\frac{\\Delta P}{P}\\approx-D^{M}\\times\\frac{\\Delta\\theta}{1+\\theta}+\\frac{1}{2}C\\times(\\Delta\\theta)^{2}, \n",
    "$\n",
    "\n",
    "where \n",
    "$\n",
    "C = \\frac{1}{P} \\frac{d^{2}P}{d\\theta^{2}}\n",
    "$. \n",
    "\n",
    "The function below calculates $C$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BondConvexity"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    BondConvexity(P,cf,m,ytm)\n",
    "\n",
    "Calculate the convexity term `C`. The effect on the bond is 0.5C*(Δytm)^2\n",
    "\"\"\"\n",
    "function BondConvexity(P,cf,m,ytm)\n",
    "    cdisc   = cf.*m.*(1.0.+m)./((1+ytm).^(m.+2))\n",
    "    C       = sum(cdisc)/P\n",
    "    return C\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mConvexity\u001b[22m\u001b[39m\n",
      "C               35.602\n",
      "Δθ              -0.020\n",
      "0.5*C*(Δθ)^2     0.007\n",
      "\n",
      "\u001b[31m\u001b[1mCompare this magnitude to ΔPH/PH: \u001b[22m\u001b[39m\u001b[31m\u001b[1m0.059\u001b[22m\u001b[39m\u001b[31m\u001b[1m. It seems convexity is not important in this case.\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "C = BondConvexity(PL₀,cf,m,θ₀)\n",
    "\n",
    "printblue(\"Convexity\")\n",
    "xy = [C;Δθ;0.5*C*Δθ^2]\n",
    "printmat(xy,rowNames=[\"C\";\"Δθ\";\"0.5*C*(Δθ)^2\"])\n",
    "\n",
    "printred(\"Compare this magnitude to ΔPH/PH: \",round((PH₁-PH₀)/PH₀,digits=3),\". It seems convexity is not important in this case.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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