RALEIGH 2024
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: rikkyriks
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 5.13 Ko KB
Mis en ligne Uploaded: 18/12/2024 - 19:06:01
Uploadeur Uploader: rikkyriks (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4420067
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 5.13 Ko KB
Mis en ligne Uploaded: 18/12/2024 - 19:06:01
Uploadeur Uploader: rikkyriks (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4420067
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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EXAMEN 2024 1. A US Treasury bond with a 4% coupon matures on March 31, 2030 and yields 5 %. You wish to purchase, today (exam date which is December 5th)) $200,000 FV of this bond. What is your total cost (including accrued) in dollars. (4pts) Bond in $, so coupon paid semi-annually. US Treasury bond so ACT/ACT convention (=365 days in a year). If the bond is paid semi-annually, then you do : r/2, c/2, t*2 in the PV formulas. t = 2030-2025 + (31+30+5)/365 =5.2 AI = annual coupon * days/365 = 0.04*200 000 * 66/365 =1 600 PV notional = FV/ (1+r)^t = 200 000 / ( 1 + 0.05/2)^(2*5.2) = 155 802.58 PV coupons = c/r * ( 1 1/(1+r)^t ) = (0.04/2*200 000)/(0.05/2) * ( 1-1/(1+0.05/2)^(2*5.2) ) = 35 360 To conclude : Full price = AI + PV notional + PV coupons = $ 192 762.58 2. A swap involves paying 6-month Sofr and receiving 4 % on a notional of $50 million. The swap has a remaining life of 9 months. What is the value of the swap ? We assume yield curve is flat and all necessary maturities yield 5%. (4 points) FRA 0X6: 4.5% FRA 2X8 : 3.60% FRA 3X9 : 4.50% FRA 1x7: 4.2% FRA 3X6: 3.9% FRA 5 x 11: 4.40% Formula : =SUM [ notional * fixed rate * frequency of payment * exponential (- r *remaining days) ] Frequency of payment : for annual c =12/12, for semi annual c =6/12, for quarterly c= 3/12 for monthly c =1/12 Remaining days : for the 2nd exponential it is the remaining life of the swap (given, here 9/12), for the first exponential it is the difference between the remaining life and the frequency of payment (example here : = 9/12 6/12). Cash flow from fixed leg : =50*0.04/2*exp(-0.05*3/12) + 50*0.04/2*exp(-0.05*9/12) = $1 950 800 Cash flow from floating leg : =50*FRA0x6/2*exp(-0.05*3/12) + 50*FRA3x9/2*exp(-0.05*9/12) =$2 192 200 Value of the swap from the party paying the floating rate : Receiving leg Paying leg = 1.9M 2.1M = - $241 400 of swap market value 3. What is the total dollar cost of purchasing $50 million face value of a Treasury bill yielding 4% and maturing July 30th 2025. (apply adequate convention) (2 points) By definition : Treasury bill à ZC bond, in $, ACT/360. By definition, for discount instruments like Treasury bills, the yield is applied to the time remaining until maturity because that's when the instrument pays its face value. We count the day between the today date and the end date, and note the opposite (which is done usually with non ZC bonds). T= (26+31+28+31+30+31+30+30)/360 = 247/360 =0.69 AI = 0 because there is no coupon PV coupons = 0 because there is no coupon PV notional = FV/(1+r)^t = 50 000 000 /(1+0.04)^247/360 = $ 48 665 116 4. A trader bought 5 Bund futures at 137,80 and sold them at 139,10. The same trader shorted 5 Treasury bond futures at 119-16. At what price did he cover his 5 T-Bonds (in USD) futures, considering he broke even with both trades. The EUR/USD trades at 1.0530 ( 3 points) Cash flow from the 1st operation : Long/Short Bund = (139.1-137.8)*5*1000 = ¬ 6 500 We convert the result in $ : 6 500 * 1.053 = $ 6 845 From the first trade, the trade made $6 845. In order to be at breakeven (0), he needs to be down of this amount. To do this, lets solve the equation to find the buying price : (119.5 x)*5*1000=-6 845 ó x = 120.87 Price = 120.87 5. Explain, in maximum 6 lines, what fixed income strategy you would adopt in an upcoming steepening yield curve environment and why. (4 points) Barbell strategy : focus on short and long term bonds to avoid intermediate maturities. Why ? - Short term bonds : provide liquidity + lower interest rate risk - Long term bonds : provide higher yield Additionally : Considering floating rate bonds to benefit from the rising short-term rates. Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
EXAMEN 2024 1. A US Treasury bond with a 4% coupon matures on March 31, 2030 and yields 5 %. You wish to purchase, today (exam date which is December 5th)) $200,000 FV of this bond. What is your total cost (including accrued) in dollars. (4pts) Bond in $, so coupon paid semi-annually. US Treasury bond so ACT/ACT convention (=365 days in a year). If the bond is paid semi-annually, then you do : r/2, c/2, t*2 in the PV formulas. t = 2030-2025 + (31+30+5)/365 =5.2 AI = annual coupon * days/365 = 0.04*200 000 * 66/365 =1 600 PV notional = FV/ (1+r)^t = 200 000 / ( 1 + 0.05/2)^(2*5.2) = 155 802.58 PV coupons = c/r * ( 1 1/(1+r)^t ) = (0.04/2*200 000)/(0.05/2) * ( 1-1/(1+0.05/2)^(2*5.2) ) = 35 360 To conclude : Full price = AI + PV notional + PV coupons = $ 192 762.58 2. A swap involves paying 6-month Sofr and receiving 4 % on a notional of $50 million. The swap has a remaining life of 9 months. What is the value of the swap ? We assume yield curve is flat and all necessary maturities yield 5%. (4 points) FRA 0X6: 4.5% FRA 2X8 : 3.60% FRA 3X9 : 4.50% FRA 1x7: 4.2% FRA 3X6: 3.9% FRA 5 x 11: 4.40% Formula : =SUM [ notional * fixed rate * frequency of payment * exponential (- r *remaining days) ] Frequency of payment : for annual c =12/12, for semi annual c =6/12, for quarterly c= 3/12 for monthly c =1/12 Remaining days : for the 2nd exponential it is the remaining life of the swap (given, here 9/12), for the first exponential it is the difference between the remaining life and the frequency of payment (example here : = 9/12 6/12). Cash flow from fixed leg : =50*0.04/2*exp(-0.05*3/12) + 50*0.04/2*exp(-0.05*9/12) = $1 950 800 Cash flow from floating leg : =50*FRA0x6/2*exp(-0.05*3/12) + 50*FRA3x9/2*exp(-0.05*9/12) =$2 192 200 Value of the swap from the party paying the floating rate : Receiving leg Paying leg = 1.9M 2.1M = - $241 400 of swap market value 3. What is the total dollar cost of purchasing $50 million face value of a Treasury bill yielding 4% and maturing July 30th 2025. (apply adequate convention) (2 points) By definition : Treasury bill à ZC bond, in $, ACT/360. By definition, for discount instruments like Treasury bills, the yield is applied to the time remaining until maturity because that's when the instrument pays its face value. We count the day between the today date and the end date, and note the opposite (which is done usually with non ZC bonds). T= (26+31+28+31+30+31+30+30)/360 = 247/360 =0.69 AI = 0 because there is no coupon PV coupons = 0 because there is no coupon PV notional = FV/(1+r)^t = 50 000 000 /(1+0.04)^247/360 = $ 48 665 116 4. A trader bought 5 Bund futures at 137,80 and sold them at 139,10. The same trader shorted 5 Treasury bond futures at 119-16. At what price did he cover his 5 T-Bonds (in USD) futures, considering he broke even with both trades. The EUR/USD trades at 1.0530 ( 3 points) Cash flow from the 1st operation : Long/Short Bund = (139.1-137.8)*5*1000 = ¬ 6 500 We convert the result in $ : 6 500 * 1.053 = $ 6 845 From the first trade, the trade made $6 845. In order to be at breakeven (0), he needs to be down of this amount. To do this, lets solve the equation to find the buying price : (119.5 x)*5*1000=-6 845 ó x = 120.87 Price = 120.87 5. Explain, in maximum 6 lines, what fixed income strategy you would adopt in an upcoming steepening yield curve environment and why. (4 points) Barbell strategy : focus on short and long term bonds to avoid intermediate maturities. Why ? - Short term bonds : provide liquidity + lower interest rate risk - Long term bonds : provide higher yield Additionally : Considering floating rate bonds to benefit from the rising short-term rates. Made with nCreator - tiplanet.org
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