SOPHIA 2019
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: rikkyriks
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 8.49 Ko KB
Mis en ligne Uploaded: 18/12/2024 - 19:33:34
Uploadeur Uploader: rikkyriks (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4420190
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 8.49 Ko KB
Mis en ligne Uploaded: 18/12/2024 - 19:33:34
Uploadeur Uploader: rikkyriks (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4420190
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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EXAMEN SOPHIA 2019 1. JP Morgan (USD ) 2.5% of May 31, 2027 yields 2%. You wish to purchase, today (define the date today please) $200,000 FV of this bond what is your total cost (including accrued) in dollars. (4pts) Bond in $ so coupon paid semi-annually. JP Morgan =corporate bonds, so ACT/360. If the bond is paid semi-annually, then you do : r/2, c/2, t*2 in the PV formulas. t=2027-2020 + (30+13)/360 =7.12 AI = annual coupon * days/360 = 0.025*200 000 *43/360 = 597.22 PV notional = FV/(1+r)^t = 200 000 (1+0.02/2)^(2*7.12) = 229 600 PV coupons = c/r * (1 1/(1+r)^t) = (0.025/2*200000)/(0.02/2) * (1-1/(1+0.02/2)^(2*7.12)) =32 750 Full bonds price = AI + PV notional + PV coupons =$ 262 947.22 2 .A swap involves paying 6-month Libor and receiving 2% on anotional of $30 million. The swap has a remaining life of 9 months. What is thevalue of the swap to the party paying fixed? Assume all discounting rate at 1.5%. Last 6-month Libor stands at 1.90% (4 points) FRA 0X3:1.87% FRA 3X6 : 1.71% FRA 6x9: 1.60% FRA 3X9: 1.70% Formula : =SUM [ notional * fixed rate * frequency of payment * exponential(- r * remaining days) ] Frequency of payment : for annual c =12/12, for semiannual c =6/12, for quarterly c= 3/12 for monthly c =1/12 Remaining days : for the 2 nd exponential it isthe remaining life of the swap (given, here 9/12), for the first exponential itis the difference between the remaining life and the frequency of payment(example here : = 9/12 6/12). CashFlow from the Fixed leg : =30*(0.02/2)*exp(-0.015*3/12) + 30*(0.02/2)*exp(-0.015* 9/12) = $0.5955M Cashflow from the floating leg : =30*(6monthsLIBOR/2)*exp(-0.015* 3/12) + 30*(FRA 3x9/2)*exp(-0.015 * 9/12) =$0.5359M Swapvalue from the point of view of the party who pay the fixed rate : =Receiving leg paying leg = 0.53 0.6 = -0.0596 = - $59 600 of marketvalue 3. What is your P&L in USD when going short 5 US Tbond futures at 157-16 and covering it later at 154-8 and going long 5 Bund futures at 172.14 and covering them back at 169.20? Euro dollar stands at 1.1050. Transaction fees is $6.5(2 points) First transaction(long/short T-Bond futures): = (157.5 154.25)*5*1000 -6.5 = $16 250 Secondtransaction (long/short Bund futures): = [ (169.2 172.14)*5*1000 ] *1.105 -6.5 = - $ 16 250 Total P&L : =16243.5-16250= - $ 6.50 (loss) 4. The December 2020 Eurodollar futures contract trades at 98.42/98.44 and the equivalent FRA 9X12 quotes 1.59% / 1.60%. Indicate what possible arbitrage trade if any and resulting P&L on a notional of $100 million. (2 points) By definition, if not indicated, theEurodollar futures and FRA pay quarterly coupons, and ACT/360. Eurodollarfutures : bid/ask =1.58%/1.56% FRA 9x12 :bid/ask = 1.59%/1.60% Arbitrage :long futures (1.56%) + short FRA (1.60%) P&L = ratespread * notional * Days/360 = (0.0156-0.016) * 100 000 000 * 90/360= $7 500 90/360 à 90 corresponds to 3months (quarterly payments) 5. Define and Calculate the implied repo of a cash and carry trade when the March 2020 Tbond futures trades at 157-24 and the CDT Treasury bond is the 4 1/2 02/15/2036 trading at 134-16 with a 0.8484 conversion factor. The future expires March 20 th 2020. Today is Friday 13 th 2019 (3 points) First, lets compute the invoice price : AI = annual coupon * days/360 =4.5 +120/360 = 1.5 120 corresponds to the number of daysbetween August 15 th and December 13 th . Invoice price = future price * conversionfactor + Accrued Interest (on the delivery) = 157.75*0.8484 + 1.5 = 136.11 Then, lets calculate the repo rate : Dirty price = clean price + AI = 134.5 +1.5 = 136 Days to delivery = 18 + 31 +29 +20 =98from December 13 th to March 20 th . Repo rate = (invoice price/dirty price-1) * (360/days to delivery) = (136.11/136) * 360/98 = 0.297% 6. What is my total dollar cost of purchasing $10 million of a Treasury bill yielding 1.51% and maturing March 15 th 2020. (Watch convention calculation) (2 points) By definition aTreasury bill is ZC, in $, with ACT/360. By definition, for discount instruments like Treasury bills , the yield is applied to thetime remaining until maturity because that's when the instrument paysits face value. We count the day between the today date and the end date, andnote the opposite (which is done usually with non ZC bonds). T =(18+31+29+15)/360=93/360=0.26 AI = 0 because itis a ZC bond PV coupons = 0because it is a ZC bond PV notional = FV/(1+r)^t = 10 000 000 / (1+0.0151)^93/360 = $ 9,961,318.26 7. What is the next coupon dollar amount ($) , on a $200,000 Face v
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Compatible OS 3.0 et ultérieurs.
<<
EXAMEN SOPHIA 2019 1. JP Morgan (USD ) 2.5% of May 31, 2027 yields 2%. You wish to purchase, today (define the date today please) $200,000 FV of this bond what is your total cost (including accrued) in dollars. (4pts) Bond in $ so coupon paid semi-annually. JP Morgan =corporate bonds, so ACT/360. If the bond is paid semi-annually, then you do : r/2, c/2, t*2 in the PV formulas. t=2027-2020 + (30+13)/360 =7.12 AI = annual coupon * days/360 = 0.025*200 000 *43/360 = 597.22 PV notional = FV/(1+r)^t = 200 000 (1+0.02/2)^(2*7.12) = 229 600 PV coupons = c/r * (1 1/(1+r)^t) = (0.025/2*200000)/(0.02/2) * (1-1/(1+0.02/2)^(2*7.12)) =32 750 Full bonds price = AI + PV notional + PV coupons =$ 262 947.22 2 .A swap involves paying 6-month Libor and receiving 2% on anotional of $30 million. The swap has a remaining life of 9 months. What is thevalue of the swap to the party paying fixed? Assume all discounting rate at 1.5%. Last 6-month Libor stands at 1.90% (4 points) FRA 0X3:1.87% FRA 3X6 : 1.71% FRA 6x9: 1.60% FRA 3X9: 1.70% Formula : =SUM [ notional * fixed rate * frequency of payment * exponential(- r * remaining days) ] Frequency of payment : for annual c =12/12, for semiannual c =6/12, for quarterly c= 3/12 for monthly c =1/12 Remaining days : for the 2 nd exponential it isthe remaining life of the swap (given, here 9/12), for the first exponential itis the difference between the remaining life and the frequency of payment(example here : = 9/12 6/12). CashFlow from the Fixed leg : =30*(0.02/2)*exp(-0.015*3/12) + 30*(0.02/2)*exp(-0.015* 9/12) = $0.5955M Cashflow from the floating leg : =30*(6monthsLIBOR/2)*exp(-0.015* 3/12) + 30*(FRA 3x9/2)*exp(-0.015 * 9/12) =$0.5359M Swapvalue from the point of view of the party who pay the fixed rate : =Receiving leg paying leg = 0.53 0.6 = -0.0596 = - $59 600 of marketvalue 3. What is your P&L in USD when going short 5 US Tbond futures at 157-16 and covering it later at 154-8 and going long 5 Bund futures at 172.14 and covering them back at 169.20? Euro dollar stands at 1.1050. Transaction fees is $6.5(2 points) First transaction(long/short T-Bond futures): = (157.5 154.25)*5*1000 -6.5 = $16 250 Secondtransaction (long/short Bund futures): = [ (169.2 172.14)*5*1000 ] *1.105 -6.5 = - $ 16 250 Total P&L : =16243.5-16250= - $ 6.50 (loss) 4. The December 2020 Eurodollar futures contract trades at 98.42/98.44 and the equivalent FRA 9X12 quotes 1.59% / 1.60%. Indicate what possible arbitrage trade if any and resulting P&L on a notional of $100 million. (2 points) By definition, if not indicated, theEurodollar futures and FRA pay quarterly coupons, and ACT/360. Eurodollarfutures : bid/ask =1.58%/1.56% FRA 9x12 :bid/ask = 1.59%/1.60% Arbitrage :long futures (1.56%) + short FRA (1.60%) P&L = ratespread * notional * Days/360 = (0.0156-0.016) * 100 000 000 * 90/360= $7 500 90/360 à 90 corresponds to 3months (quarterly payments) 5. Define and Calculate the implied repo of a cash and carry trade when the March 2020 Tbond futures trades at 157-24 and the CDT Treasury bond is the 4 1/2 02/15/2036 trading at 134-16 with a 0.8484 conversion factor. The future expires March 20 th 2020. Today is Friday 13 th 2019 (3 points) First, lets compute the invoice price : AI = annual coupon * days/360 =4.5 +120/360 = 1.5 120 corresponds to the number of daysbetween August 15 th and December 13 th . Invoice price = future price * conversionfactor + Accrued Interest (on the delivery) = 157.75*0.8484 + 1.5 = 136.11 Then, lets calculate the repo rate : Dirty price = clean price + AI = 134.5 +1.5 = 136 Days to delivery = 18 + 31 +29 +20 =98from December 13 th to March 20 th . Repo rate = (invoice price/dirty price-1) * (360/days to delivery) = (136.11/136) * 360/98 = 0.297% 6. What is my total dollar cost of purchasing $10 million of a Treasury bill yielding 1.51% and maturing March 15 th 2020. (Watch convention calculation) (2 points) By definition aTreasury bill is ZC, in $, with ACT/360. By definition, for discount instruments like Treasury bills , the yield is applied to thetime remaining until maturity because that's when the instrument paysits face value. We count the day between the today date and the end date, andnote the opposite (which is done usually with non ZC bonds). T =(18+31+29+15)/360=93/360=0.26 AI = 0 because itis a ZC bond PV coupons = 0because it is a ZC bond PV notional = FV/(1+r)^t = 10 000 000 / (1+0.0151)^93/360 = $ 9,961,318.26 7. What is the next coupon dollar amount ($) , on a $200,000 Face v
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