3. Consider the on-the-run, off-the-run arbitrage, made famous by John Meriwether in his Solomon Brothers days....

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3. Consider the on-the-run, off-the-run arbitrage, made famous by John Meriwether in his Solomon Brothers days. Suppose a 3-yr bond was just issued at par to offer a yield of 4% (assume annual coupons w/ discreet discounting). Assume also that another 3 year 4% coupon bond was issued 10 years earlier at par, but now sells for 99.447 per $100 face value and therefore offers a yield of 4.20%. a) Show that there is essentially little or no interest rate risk by showing the impact of an increase of interest rates of 20 basis points on a position that is long $1 Billion dollars of the cheaper bond, and short $1 billion of the more expensive bond (but assuming that the spread between these two bonds REMAINS at 20 basis points). Similarly show the impact of a 20 bp DECLINE in rates without a change in the spread. b) Now, for the same portfolio considered in (a), show the impact of a 20 bp increase in the yield of the cheaper bond and a 40 bp increase in the yield of the more expensive bond (i.e., assume the spread goes to 0). c) Repeat (b) but assume a 40 basis point DECLINE in the yield of the cheaper bond, but a 20 bp decline in the yield of the more expensive bond (again, the spread goes to 0). d) Finally, show what happens if there is no general change in rates, but the spread WIDENS to 50 bp, meaning that the yield of the more expensive bond REMAINS at 4%, but the yield of the cheaper bond rises to 4.50%. 3. Consider the on-the-run, off-the-run arbitrage, made famous by John Meriwether in his Solomon Brothers days. Suppose a 3-yr bond was just issued at par to offer a yield of 4% (assume annual coupons w/ discreet discounting). Assume also that another 3 year 4% coupon bond was issued 10 years earlier at par, but now sells for 99.447 per $100 face value and therefore offers a yield of 4.20%. a) Show that there is essentially little or no interest rate risk by showing the impact of an increase of interest rates of 20 basis points on a position that is long $1 Billion dollars of the cheaper bond, and short $1 billion of the more expensive bond (but assuming that the spread between these two bonds REMAINS at 20 basis points). Similarly show the impact of a 20 bp DECLINE in rates without a change in the spread. b) Now, for the same portfolio considered in (a), show the impact of a 20 bp increase in the yield of the cheaper bond and a 40 bp increase in the yield of the more expensive bond (i.e., assume the spread goes to 0). c) Repeat (b) but assume a 40 basis point DECLINE in the yield of the cheaper bond, but a 20 bp decline in the yield of the more expensive bond (again, the spread goes to 0). d) Finally, show what happens if there is no general change in rates, but the spread WIDENS to 50 bp, meaning that the yield of the more expensive bond REMAINS at 4%, but the yield of the cheaper bond rises to 4.50%.