Price Discount Factor Spot Rate 0.999692 0.062 0.999075 0.093 0.998150 0.123 0.997538 0.123 0.996673 0.133 0.994572...

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Price Discount Factor Spot Rate 0.999692 0.062 0.999075 0.093 0.998150 0.123 0.997538 0.123 0.996673 0.133 0.994572 0.182 0.991521 0.243 0.987230 0.322 0.982406 0.395 0.975940 0.488 Maturity Coupon 8/15/21 2.750 101.34375 2/15/22 2.000 101.90625 8/15/22 1.625 2/15/23 1.375 8/15/23 2.500 105.90625 2/15/24 2.750 107.6875 8/15/24 2.375 107.4375 2/15/25 2.000 106.6875 8/15/25 2.000 107.1875 2/15/26 1.625 105.65625 Coupon and spot rate in %/year, price as percent of par. 102.25 102.5 4. Using Excel or your favorite software: (a) A 5-year Treasury newly issued on February 15, 2021 would have a coupon equal to the 5-year par coupon and would have been priced at par. Confirm that your par coupon results in a par price for this bond. (b) Calculate the 6-month forward rates for all the cash-flow dates of your 5-year bond. Confirm that a 5-year floating rate bond with coupons equal to the forward rates prices at par. (c) Consider the case where the Federal Reserve increases rates in a way that results in an increase of all forward rates by 200 basis points: i. Recalculate the price of the fixed-rate bond using the par coupon you calcu- lated in part 4(a) above. Note that the discount factors will have changed because of the parallel shift in the forward curve. Briefly explain the price change or lack thereof. ii. Recalculate the price of the 5-year floating-rate bond. Briefly explain the price change or lack thereof. (d) A security known as an interest-rate swap can be modeled as a portfolio consisting of either (i) a long position in a floating-rate bond and a short position in a fixed- rate bond (a payer swap) or (ii) a long position in a fixed-rate bond and a short position in a floating-rate bond (a receiver swap). Briefly explain: The price of the swap when the swap is created. How changes in the yield curve after the swap is created result in changes to the swap price. In both cases the par coupon (also known as the swap rate) is set when the swap is created and the onstituent bonds have the same payment frequency (annual, semi-annual, etc.) and the same maturity. Price Discount Factor Spot Rate 0.999692 0.062 0.999075 0.093 0.998150 0.123 0.997538 0.123 0.996673 0.133 0.994572 0.182 0.991521 0.243 0.987230 0.322 0.982406 0.395 0.975940 0.488 Maturity Coupon 8/15/21 2.750 101.34375 2/15/22 2.000 101.90625 8/15/22 1.625 2/15/23 1.375 8/15/23 2.500 105.90625 2/15/24 2.750 107.6875 8/15/24 2.375 107.4375 2/15/25 2.000 106.6875 8/15/25 2.000 107.1875 2/15/26 1.625 105.65625 Coupon and spot rate in %/year, price as percent of par. 102.25 102.5 4. Using Excel or your favorite software: (a) A 5-year Treasury newly issued on February 15, 2021 would have a coupon equal to the 5-year par coupon and would have been priced at par. Confirm that your par coupon results in a par price for this bond. (b) Calculate the 6-month forward rates for all the cash-flow dates of your 5-year bond. Confirm that a 5-year floating rate bond with coupons equal to the forward rates prices at par. (c) Consider the case where the Federal Reserve increases rates in a way that results in an increase of all forward rates by 200 basis points: i. Recalculate the price of the fixed-rate bond using the par coupon you calcu- lated in part 4(a) above. Note that the discount factors will have changed because of the parallel shift in the forward curve. Briefly explain the price change or lack thereof. ii. Recalculate the price of the 5-year floating-rate bond. Briefly explain the price change or lack thereof. (d) A security known as an interest-rate swap can be modeled as a portfolio consisting of either (i) a long position in a floating-rate bond and a short position in a fixed- rate bond (a payer swap) or (ii) a long position in a fixed-rate bond and a short position in a floating-rate bond (a receiver swap). Briefly explain: The price of the swap when the swap is created. How changes in the yield curve after the swap is created result in changes to the swap price. In both cases the par coupon (also known as the swap rate) is set when the swap is created and the onstituent bonds have the same payment frequency (annual, semi-annual, etc.) and the same maturity.

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4 Bond pricing calculations a For a 5year Treasury issued on 2152021 the par coupon would be the 5ye... View the full answer