Basic Interest Rate Calculations - Answers

Transcription

1 Basi Interest Rate Calulations - Answers 1 month Otober = 16 November 22 Total 38 (b) 2 Atual/ th June is Saturday Aording to the modified following onvention: Monday 14 June 4 Aording to the end of month (EOM) onvention, the 3 month value date is Tuesday 31th May (d). 5 b Spot is 30th April Regular 6 months date would be Saturday 30th Otober Aording to the modified following onvention: Friday 29 Otober beause Monday would be 1 November and the value date should not exeed a month ultimo 6 r b = 4,20% + 20/ = 4,40% 7 b The 70 days interpolated rate an be alulated from the 2 months (60 days) and the 3 months (90 days) rates There are 10 days in the broken period 4.20% + 10/30 x 0.30% = 4.30% 1 Lex van der Wielen, August 2015

2 8 d The rate for 15 July an be derived from the 2 month (61 days) and the 3 months (91 days) rates There are 22 days in the broken period: 8 (31-23) + 14 Therefore, the broken rate is 2.30% + 22/30 x 0.10% = 2.37% 9 50M x ( 1+31/360 x ) 10 CHF 15,000,000 ( 1 + 3/360 x ) = CHF 15,001, b 100,000 / 15,500,000 x 360/91 12 Note: dayount onvention on the GBP money market is atual/365 GBP 15,000,000 x (1 + 31/365 x ) = 15,041, ,275 / 5,000,000 x 360 / 91 = % x 46/45 = 4.34% 15 ( / 2) 2-1 = ((1.0287)^0.5-1) x 2 = d First, onvert from semi-annual to annual: 5.27% Next, onvert from atual/ 360 to bond basis: 5.27% x 365/360 2 Lex van der Wielen, August 2015

3 / ( 1-180/360 x 0.025) = The equation to be used is annual yield = (1 + semi annual yield/2) 2-1 Filled in: ( /2) 2-1 = The equation to be used PDR is Yield = # days 360 PDR Yield = = yield = / ( 1-70/360 x 0.021) 22 Present value NOK 20,000,000 = = NOK 19,884, /360 x Prie (present value) SEK 20 mio = = 1 + 0, SEK 19,887, a Prie = USD 5 mio ( ) = USD 4,950, Disounted amount= USD 10,000,000 x ( 1-90/360 x 0.025) = USD 9,937,500 3 Lex van der Wielen, August 2015

4 26 (( /360 x )/(1 + 90/360 x ) - 1) x 360/(180-90) 27 ((1 + 91/360 x )/(1 + 31/360 x ) - 1) x 360/(91-31) 28 1 r , fw 1 + 0, ,01365 = = = 0,0287 1, d The general to alulate a forward rate in the money market is: 1 + r r l d l 360 fw = r s d s ( d l d s ) Here r fw = = The equation to alulate a forward rate in the money market is: Here 1 + r r l d l 365 fw = r s d s ( d l d s ) r fw = = month deposit rate 1.13% (91 days) 3-6 Forward rate 1.25% (92 days) Calulate the future value of one unit amount after the whole term (1 + 91/365 x ) x (1 + 92/365 x ) = Then subtrat one: = Then multiply this outome by the inverse of the dayount fration: 365 / 183 x = %. 4 Lex van der Wielen, August 2015

5 32 ((1 + 31/360 x ) x (1 + 60/360 x ) x ( /360 x ) - 1) x 360/ Lex van der Wielen, August 2015

6 6 Lex van der Wielen, August 2015

7 Cash Money Markets - Answers 1 Annually 2 He will hoose the lowest interest rate The lowest rate with dayount onvention atual/360 is that of Saxo Bank Converted to 30/360, this rate would be 4.16% x 365/360 = 4.22% ABN AMRO s rate would be even higher: 4.18% x 365/360 = 4.24% Therefore, the rate of Den Danske Bank is the most favourable 3 a Use the PV equation, alulate the first FV. Next use the alulated FV as the PV for the next alulation FV s are respetively: 25,205,381.95, 25,429,079.71, 25,695,837.82, 25,962, After the first period, your investment has a value of 10,000,000 x 91/360 x = 10,079, After the seond period, your investment has a value of 10,079, x 90/ 360 x = 10,161, After the third period, your investment has a value of 0,161, x 89/360 x = 10,237, After the last period, your investment has a value of 10,237, x 92/360 x = 10,315, UK treasury bill 6 1 Year 7 Certifiates of Deposit 8 Commerial Paper 1 Lex van der Wielen, August 2015

8 9 All of these 10 Repo 11 Treasury bill 12 Investment bank 13 Corporate 14 BA or bank bill 15 Treasury bill 16 b ECP 17 5 years 18 b More than the fae value 19 Issue Prie EUR 10,000,000 = = EUR 9,920, /360 x Prie = USD 10,000,000 x ( 1-60/360 x 0.06) = USD 9,900, Value at maturity = 10,000,000 x ( /360 x 0.04) = EUR 10,100, GBP 10,000,000 Prie = = GBP 9.914, /365 x Lex van der Wielen, August 2015

9 23 The maturity amount of this CD is 10,000,000 (1 + 90/360 x 0.05) = USD 10,125,000 (FV) The present value of this CD is 10,057, ? = (10,125,000 /10,057, / - 1) x 360/30 = Value at maturity of the CD = 100,000,000 x (1 + 90/360 x 0.005) = 100,125,000 Present value of the value at maturity = 110,125,000 / (1 + 60/360 x ) = JPY 100,083, Purhase prie 50,000,000 Selling prie 50,000,00 x ( /360 x 0.045) / (1 + 30/360 x 0.045) = 50,373, Result: 373,599 ( Capital gain/loss + arued interest) Arued interest = 50,000,000 x 60/360 x 0,045 = 375,000 Capital gain/loss= = ,99 26 Current prie of the CD: PRCD: NOM = 1,500,000, C% = , DT =181, B =360, DR=31, Y% = > PRCD = 1,517, Take this as FV in your PFV equation and take PV as 1,500,000, D=150 and B=360. You will find or Purhase prie = 1,500,000 Selling prie = 1,500,000 x ( /360 x 0,0275) / ( /360 x 0,0260) = 1,517, Result = ,42. Yield= ,42 / 1,500,000 x 360 / 150 = 0, Lex van der Wielen, August 2015

10 27 The prie of the CD is (10,000,000 x 90/360 x 0.03) / (1 + 60/360 x 0.03) = 1,024, You an use the PRCD equation: NOM = 10,000,000, DT = 90, B = 360, C% = 0.03, DR = 60, Y% = 0.03, solve for PRCD. You have bought the CD at 10,000,000 Your total return, therefore is 24, This inludes arued interest, however: 10,000,000 x 30/360 x 0.03 = 25,000,000 Your apital result is negative: 24, ,000, Either party 29 It is immediately transfered to the seller 30 A repo that is not losed in repet to liquidity management 31 Only I and II 32 It is transfered by the third party to the buyer s aount 33 The buyer an liquidate the ollateral 34 The redit risk on the repo ounterparty 35 Either of the above, but usually (b) 36 a Funding 4 Lex van der Wielen, August 2015

11 37 You reverse in repo means that you are the repo buyer. You are the market maker and lend money: the rate is 3.33%. Interest = x 14/360 x = EUR 344, Mat. Cons. = USD 20,300,000 x ( 1 + 7/360 x ) = USD 20,307, Init. Cons. = EUR 15,000,600 / 1.10 = EUR 13,636, Interest Amount = (GBP 50,000,000 x 1.02) x 5/365 x 0.02 = GBP 13, If the bond goes speial, this means that the buyer very muh wants to have the bond Therefore he is willing to lend money at a lower rate than would be the ase with GC rate = 3.25% % = 2.75% 42 b The initial onsideration is equal to the dirty market prie As market user and as buyer of the repo you lend the money at the bid rate USD 20,360,000 x (1 + 4/360 x 0,0130) = USD 20,362, d Interest amount = USD 51,250,000 x 5/360 x = USD 14, d 20,329, x ( /360 x ) = , ( ) x 7/365 x 25M = Lex van der Wielen, August 2015

12 46 The maturities of your deposits given and deposits taken are not the same 47 He has borrowed for a longer period than he has lent has to lend for three months after two months also: long ash in 48 b Break-even rate = (( /360 x 0,0118)/(1+90/360 x ) - 1 ) x 360 / 90 = % 49 You pay a total interest amount of 20,000,000 x 60/360 x ,000,000 x 60/360 x = 104, ,000 = 268, You earn an interest amount of 50,000,000 x 60/360 x = 287,500 You make a profit of 287, , = 18, Lex van der Wielen, August 2015

13 Foreign Exhange - Answers FX spot Your ask prie is therefore 3,000,000 / = 1,868,576 You sell / GBP 6 is overbought in Sterling and oversold in US-dollars 7 EOM onvention: Thursday 31 Marh 8 The most favourable two-way prie is the one with the highest bid prie: You quote 1/ / You want to buy US-dollars and sell Sterling. This means you get the bid prie GBP/USD. The Sterling amount needed is 5,000,000 / 1.65 = GBP 3,030, Lex van der Wielen, August 2015

14 12 You want to buy euro. Therefore the rate is The amount of euro is / = 232, You want to buy GBP, so your bid prie should be high and your ask prie too: therefore: b You buy Japanese Yen, therefore you sell CHF As a market user to will get the market maker s bid prie: ,000,000 / = 1,085, You want to sell GBP and buy euro, so you must quote a high bid rate You don t want to quote either way beause than you run the risk that the ounterparty is going to buy euro from you, whih would inrease your long GBP position Position keeping x GBP 17 The big figure is always 100 pips, therefore: 10,000,000 x 0.01 = 10,000 CAD 18 You have sold at and you now an buy at To lose your position you must buy euro in the market as a market user at the higher rate of , therefore you suffer a loss The result is ( ) x 5,000,000 = minus SGD 6,000 2 Lex van der Wielen, August 2015

15 x ( ) 21 To lose your position you must sell USD in the market as a market user at 8.53 The result is ( ) x 10,000,000 = HKD 1,100,000 The HKD an be sold against USD at a prie of 8.63 Your profit = 1,100,000 / 8.63 = USD 127, If you should lose your position, you should sell your euro. Therefore you would get the bid prie of You would suffer a loss of 10,000,000 x = USD 10, ((5 x x x ) / ( ) ) x 6,000, EUR USD transation 1 + 4,000,000-5,781,200 transation 2-5,000,000 7,237,000 transation 3 + 3,000,000-4,296,300 +2,000,000 2,840,500 Average rate = 2,840,500 / 2,000,000 = d EUR USD transation 1-4,000,000 5,021,200 transation 2-5,000,000 6,337,000 transation 3 + 2,000,000-2,464,200-7,000,000 8,894,000 3 Lex van der Wielen, August 2015

16 The average rate of the position is 8,894,000 / 7,000,000 = The valuation rate is , this means a profit of 7,000,000 x ( ) = 142, Transation 3: sell 3 million euro, Transation 4: buy 7 million euro. Position = = 3 million euro long Average rate = (4 x x x x ) / 3 = FX spot ross rates 27 EUR NOKask = GBP NOK EUR GBPbid ask 28 EUR USDask USD CAD = EUR CAD ask ask Using ommon sense leads to the onlusion that answers and d an not be orret: if one euro is worth approximately 8.30 Norwegian rowns and the euro is worth more than one US dollar, the USD/NOK rate an not be lower than 8.30 Therefore you should divide the EUR/NOK rate by the EUR/USD rate The bid rate an be alulated by dividing the bid rate EUR/NOK by the ask rate USD/NOK 8.30 / = EUR USDbid 1, = = 1,4901 AUD USDask 0, Lex van der Wielen, August 2015

17 33 You must divide the EUR/CHF rate by the EUR/USD rate The ask rate an be alulated by dividing the ask rate EUR/CHF by the bid rate USD/CHF EUR CHFask = USD CHF EUR USDbid / = ask FX Forwards 34 Only for very large movements and longer terms x ( /360 x ) / ( /360 x ) 37 The euro trades at a premium 38 d Selling a low interest rate urreny to invest in a high interest rate urreny should not be profitable if one hedges the urreny risk 39 Full forward exhange rate 40 0,9500 ( ,03) 0,9571 Forward FX rate = = = 0, ,04 1, = Lex van der Wielen, August 2015

18 42 The one month bid prie an be alulated by adding the left hand side of the swap quotation to the spot bid rate Sine the swap quotation is reverse, the EUR trades at a disount: = FXFW = ( ) Forward FX rate ( ) = = You want to sell CHF, whih means that you must buy GBP You are quoted means that you are a market user. Therefore, you will get the ask prie of the spot rate and the right hand side of the swap points GBP trades at a disount and therefore the swap points should de subtrated from the spot rate Therefore: = b The one month ask prie an be alulated by adding the right hand side of the swap quotation to the spot ask rate Sine the quotation is reverse, the EUR trades on a disount: Therefore: = The bid prie GBP/USD for 1.5 months an be alulated by adding the left hand side of the swap quotation to the FX spot bid prie The swap points for 1.5 months an be derived by using interpolation between one month and two months: 1/2 x 50 (102-52) points = 25 points The GBP trades at a disount Therefore: = EUR USDbid USD CAD = ( ) ( ) = 1,2463 bid 6 Lex van der Wielen, August 2015

19 49 The 1 month forward ask prie USD/NOK an be alulated by dividing the EUR/NOK 1 month forward ask prie by the EUR/USD 1 month forward bid prie The EUR/NOK 1 month forward ask prie is = The EUR/USD 1 month forward bid prie is = Therefore, EUR/NOK ask / EUR/USD bid 1 month forward is / = The 1 month forward ask prie CHF/SEK an be alulated by dividing the EUR/SEK 1 month forward ask prie by the EUR/CHF 1 month forward bid prie EUR SEKask = CHF SEK EUR CHFbid ask The EUR/SEK 1 month forward ask prie is The EUR/CHF 1 month forward bid prie is = Therefore, CHF/SEK 1 month forward ask prie is / = /31 x 90 = = 143 Ex ante rates 52 I, II and III 53 GBP trades at a disount, therefore the points should be added with ex ante dates. Beause of the fat that an ask rate should be alulated, the highest number of points should be adde bid spot GBP/USD tom/next 1.3 overnight Lex van der Wielen, August 2015

20 54 The bid prie value 13 April is the bid prie of the FX spot rate adjusted with the tom/next points The GBP is trading at a disount, therefore the tom/next points should be added to the FX spot rate The right hand side of the tom/next quotation is The FX rate value tomorrow is = You must use the spot ask rate and the tom/next left hand side rate Sine is it a reverse quotation, the euro trades at a disount This means that the FX rate value tomorrow is higher than the FX spot rate You add the ask prie of the tom/next quotation = points to the spot rate: = You must use the spot ask rate and the tom/next left side rate Sine is it a normal quotation, the euro trades at a premium This means that the FX rate value tomorrow is lower than the FX spot rate You take the ask prie of the tom/next quotation = points Therefore: = FX swaps 57 A spot sale (purhase) and a forward purhase (sale) of two urrenies agreed simultaneously between two parties Bought and sol As a result of the premium, in the far leg you reeive more US dollars than you have paid in the near leg (buy low, sell high). 60 The swap points are the expression of the interest rate differential between euro and US dollar. Beause the euro is trading at a premium, the euro interest rates are lower than the US dollar interest rates. If the euro interest rates 8 Lex van der Wielen, August 2015

21 stay the same and the US dollar interest rate will derease, the interest rate differential will derease and, as a result, the bid and the ask prie of an FX swap will derease. 61 The swap points are the expression of the interest rate differential between the euro and the Swiss fran Beause the euro is trading at a disount, the euro interest rates are higher than the CHF interest rates. If the euro interest rates stay the same and the CHF interest rates derease, the interest rate differential inreases and, as a result, both the bid and the ask prie of an FX swap will inrease. 62 You have borrowed GBP and have lent US-dollars. Therefore, the most favourable movement is an derease in US-dollar interest rates and a in rease in GBP interest rates. 63 You have lent euro and have borrowed US-dollars. Therefore, the most favourable movement is an inrease in US-dollar interest rates and a derease in euro interest rates. 64 The interest differential will inrease and, as a result, the number of swap points will inrease too. 65 Only the swap points are stated as a prie. This means that the transatio was an FX wap. As a market user the lient gets the most unfavourable rate whih here is This means that he has bougt in the far leg. Therefore, you as market maker have bought and sol 66 You must sell EUR per spot or forwar If you sell them spot, you need to square your liquidity position by either buying and selling the euro or borrowing euro and investing is USD. 67 Sold and bought, beause the FX rate in the far leg is lower than in the near leg and that is favourable for you (buy low, sell high). 9 Lex van der Wielen, August 2015

22 68 You reeive the US dollars from your taken US-dollar deposit This means you mustmust sell and buy the US-dollars This means that you trade on the ask side of the FX swap quotation The points are in your favour, therefore is the most favourable quote for you Alternative explanation: In the swap you lend the US dollars and borrow the Swissies. Sine the US-dollar interest rate is higher than the CHF interest rate, you reeive the interest rate differential (expressed in swap points). This is why the points are in your favour. And of ourse you want as many points in your favour as you an get, i.e. 147 instead of 145. o/n and t/n Swaps 69 If an FX spot dealer is short euro, this means that he has to transfer the euro amount on the spot date. The dealer, however, waits until the next day to roll over his positon for one more day. He then buys the euro value tomorrow and sells them bak on the spot date. 70 If a dealer is long euro, this means that the euro will be transfered to him on a speifi value date. The dealer waits until the day before this value date to roll over his positon for one more day. He then sells the euro value tomorrow and buys them bak value spot. 71 You are long EUR, therefore you have to sell and buy euro in the tom/next swap As a buyer in the forward leg, you will hit the market s right hand side: +2 Sine the euro is trading at a premium, the points are against you You have to make good the tom/next points when losing your position by selling the euro Your new break-even rate, therefore, is = Lex van der Wielen, August 2015

23 72 You are short USD, therefore you have to buy and sell euro in the tom/next swap As a seller in the forward leg, you will hit the market s left hand side: -5 Sine the USD is trading at a disount, the points are against you You have to make good the tom/next points when losing your position by buying the US dollars Your new break-even rate, therefore, is = GBP is trading at a disount against the US dollar and you buy and sell the GBP. This means that the swap points are against you. You lose 2 points in the t/n swap. Your average (selling) rate, therefore, dereases to In the t/n swap you have to sell and buy euro, hene you are quoted (against you). Break-even rate = = In the t/n swap you have to buy and sell JPY, hene you are quoted = (your favour). Break-even rate is = You have to buy GBP per spot to over your FX position. Next you have to sell them spot and buy them tomorrow: buy and sell in the t/n swap. Covered interest arbitrage 77 Borrow euro and sell and buy euro in an FX arbitrage swap 78 Lend euro and buy and sell euro in an FX arbitrage swap 11 Lex van der Wielen, August 2015

24 79 Borrow GBP and sell and buy GBP whih means buy and sell EUR. 80 In this ase, in the ash market the interest rate differential is against you, however in the swap market the interest rfate differential is more in your favour, this means that the euro rate of a syntheti loan will be lower than in a straight ash euro loan. Forward-forward FX swaps 81 d You have to pay USD/ reeive euro after four months and now need them after two months to offset the original trade, you buy and sell euro for four months next, you sell and buy euro in two months 82 a You need to be overborrowed in euro and overlent in US dollars after three months Therefore you have to buy and sell euro in six months and buy and sell them at three months As a result, you an sell and buy euro for three months again. This means lending euro and borrowing US dollars 83 a the trader has bought at 22 and sold at a euro trades at a premium and the lient sells at a later date than (+50) he buys (=30). The points are in his favour. 85 The euro trades at a disount and as a lient you sell at an earlier date ( - 50) than you buy (-60). The points are in your favour and you are quoted Lex van der Wielen, August 2015

25 86 The spot legs will offset eahother; then remain the forward leg of the 3 months FX swap, i.e. buy euro and the forward leg of the 6 month swap, i.e. sell euro 87 b market pratie is to use the FX forward rate at the moment of onluding the transation for the near leg Time options and NDF 88 d Selling USD means buying EUR In these types of ontrats, the lient always is offered the worst possible rate. In this ase, this means the highest ask rate for euro. This is obviously the two month ask rate of a In these types of ontrats, the lient always is offered the worst possible rate. In this ase, this means the lowest bid rate for euro. This is obviously the two month bid rate of = Your lient has to buy 500,000 at the ontrat rate He has to sell them at your bid prie a Your lient has to sell EUR 500,000 at the ontrat rate He has to buy them at your ask prie of He has a profit of 500,000 x ( ) = CHF 6, Lex van der Wielen, August 2015

26 92 d NDF are always settled in the onvertible urreny. Here, this is USD. Sold 100,000,000 TWD in the NDF ontrat: 100,000,000 / USD Bought 100,000,000 TWD to fix the ontrat: 100,000,000 / USD The settlement amount is USD 2,989, USD 3,076, = -/- USD 87, d The seller of a USD/PHP NDF sells USD outright and buys PHP. This market party therefore an be speulating on an appreiation of the Phillipine peso 94 b NDF are always settled in the onvertible urreny. Here, this is USD. The settlement amount is 50,000,000 / ,000,000 / 35 = 67, USD. The USD obviously has inreased in value and the Taiwanese dollar has, in turn, lost value. Therefore, as the buyer of the TWD you must pay. Preious Metals The rate at whih dealers will lend gold against US dollars 97 b Gold Lease Rate = (USD LIBOR ) - (GOFO ) = ( ) - ( ) = = d First you must buy USD against HKD at Then you must buy gold against USD at x x = 966, Lex van der Wielen, August 2015

27 99 Gold mid market lease rate = GOFO basispoints -/- USD LIBOR basispoints GOFO basispoints = 2.75% % = % USD LIBOR basispoints = 4.50% % = % Gold mid market lease rate = % 100 The gold forward prie an be alulated by adding a premium to the spot prie The premium an be alulated by the following equation: Spot midprie x days/360 x GOFO GOFO = 8.75% Gold forward prie = 950 x ( /360 x ) = USD Lex van der Wielen, August 2015

28 16 Lex van der Wielen, August 2015

29 FRAs Answers 1 a loan means that you lend out money whih you need to fun 2 you have a square position from spot until 3 months, then you are overborrowed 3 From June to Otober is 4 months. And from Otober to January (underlying period) is 3 months You are over-borrowed whih means that you have to invest your money and your risk is a derease in interest rates 4 you have a loan whih will be reprised in 1 month for a periode of 3 months (= underlying period), therefore you are exposed to rising interest rates, therefore you have to buy an FRA As a market user you buy at the ask rate 5 6 An adjusted settlement amount is paid at the start of the FRA underlying period that is disounted for early payment Lex van der Wielen, August 2015

30 9 Fixing is on 8th septemer (9 months after the trade date), fixing is two days later 10 His risk is an inrease in interest rates after six months, therefore he should buy a 6s v 9s FRA. 11 You will get an ask prie from the market maker and ABN AMRO s ask prie is the lowest. 12 Hedging against inreasing interest rates 13 If he borrows for nine months and lends for only six months and he proves to be right, after six months, he will be able to give a 3 months deposit at the then higher interest rate. 14 His risk is an derease in interest rates after three months, therefore he should sell a 6s v 9s FRA. 15 You will get a bid prie from the market maker and INGs bid prie is the highest. 16 PV of 40,000,000 x ( ) x 90/360 = 10,000,000, therefore 10,000,000 / (1 + 90/360 x ) = 9, With this parallel shift, all short term interest rates rates will fall To take profit from this movement you must sell FRAs for all maturities 2 Lex van der Wielen, August 2015

31 18 (( /360 x ) / (1 + 90/360 x ) - 1) x 360/90 = , 000, ( 0,047 0,045) FRA settlement amount = ,047 = 4, 996,20 20 PV of 5,000,000 x ( ) x 183/360 = ,83 1, / ( /360 x 0.044) = 16, buy a 3s v 6s FRA and sell a 9s v 12s FRA Money Market Futures Maitaine margin is the amount of money that must be at least at the margin aount. If the value of this futures position beomes negative, the learing house starts to debit the margin aount for the negative value. One the value of the margin aount beomes lower than the maintaine margin, the learing house start demands a margin aal in order to keep the value at the margin aount at the level of the maintainane margin Lex van der Wielen, August 2015

32 I, II and II 33 He is long and the prie went down with 33 points The market value of his position dereases with 20 x JPY 2500 x 33 = JPY 1,650,000 He has to pay the margin all 34 The margin all is 10 x 500,000 x x 1/4= GBP 3,750. Sine the futures prie has inreases and the dealer has a long position, he will reeive this amount. 35 The losing of the short position leaves the dealer with a loss of 20 x 1,000,000 x x 1/4 = 6, sell MM futures of buy FRAs 37 He expeted interest rates to derease and suffered a loss. 38 He expeted interest rates to inrease and suffered a loss. 4 Lex van der Wielen, August 2015

33 39 The market value of the FRA and of the money market futures will develop more or less in the opposite diretion At the moment the money market futures are losed, the implied forward rate apparently was The market value of the FRA then was 25,000,000 x ( ) x 90/360 = EUR 19,375,000 This profit is loked in by losing the position Interest Rate Swaps 40 allable swap 41 The seller of the swap pays 1% alulated over a term of three months. 42 Both oupons are paid at maturity on a netted basis. 43 I, II and III 44 LIBOR 45 Rolleroaster swap 46 Only I and II 47 Compounded interest paid at maturity 48 You pay EUR 10,437,500 and reeive USD 13,260, Sold strip of futures and a reeiver s interest rate swap 5 Lex van der Wielen, August 2015

34 50 after six months: pay 10,000,000 x ( ) x 1/2 = 2,500 after twelve months: reeive 10,000,000 x ( ) x 1/2 = 12,500 After eighteen months: reeive 10,000,000 x ( ) x 1/2 = 17,500 After two years: reeive 10,000,000 x ( )x 1/2= 20, You pay fixe, therefore in the hedge you must reeive fixe = selling an FRA and a 0x6 FRA does not exist 52 The buyer of a swap pays the fixed rate, here 4.75% and the floating oupon payment is 5.75%, therefore the buyer reeives on balane 1% The amount to be reeived by the buyer = 100,000,000 x 1% x 1/2 = EUR 500,000 to be paid by the seller 53 The 1 year aumulation fator an be alulated by multiplying the aumulation fator over the six months period out of spot by the aumulation fator over the 6s v 12s forward period: ( /360 x ) x ( /360 x ) = The orresponding yield an be found by using the following equation: (aumulation fator - 1) x B / D = ( ) x 360/360 = = 1.29% 54 The seller of a swap reeives the fixed rate, here 3.50% With a fully synhronized swap, eah quarterly payment is netted The floating oupon payment is 2.50%, therefore the seller reeives on balane 1% 55 If you want to take profit from dereasing interest rates, you must sell FRAs or sell an interest rate swap 56 The amount to be settled is x 5/360 x 100,000,000 = EUR 694 The fixed rate is higher than the floating rate; therefore the buyer must pay 6 Lex van der Wielen, August 2015

35 Options - answers 1 Amerian style option 2 Bermudan option 3 Falls and rises with the prie of the underlying ommodity, but is always positive 4 The right but not the obligation to buy or sell a ommodity at a fixed prie 5 Asian option 6 Purhasing an JPY/USD put option 7 The prie the buyer of the option pays to the seller when entering into the options ontrat 8 Premium is 3,000,000 x and, unless stated otherwise, must be paid in the quoted urreny 9 d 10 b The premium amount is 2% x 20,000,000 = 400,000 GBP = Lex van der Wielen, August 2015

36 12 The break-even prie of a all option is strike prie + option premium Therefore: = The profit or loss of a sold option at expiry is the reverse of (intrinsi value -/- option premium) Therefore: -/- ( ) = (profit) 14 The equation to alulate the break-even prie of a put option = strike prie - premium Therefore: = The expetations value is the option premium - the intrinsi value The put option is in the money: the intrinsi value is = The expetations value = = b The option is ITM and the intrinsi value is (differene between strike and FX forward rate). Expetations value therefore is The intrinsi value of a put is the strike prie -/- the urrent prie if positive = = The expetations value is the option premium less the intrinsi value = The prie is stated in the quoted urreny Lex van der Wielen, August 2015

37 20 50% probability Costs more than an out-of-the-money all option Delta: underlying value, rho: interest rates, vega: volatility The delta-position of the option position = -/- 100,000,000 x -/- 40% 40,000,000 long in euros. The dealer should, therefore, sell 40,000,000 euros. 28 A all option has a positive delta, therefore a short all position has a negative delt The dealer should buy 0.50% x EUR 100,000,000 = EUR 50,000, A put option has a negative delta, therefore a short position in put options has a positive delta The short put position an be seen as a potential long position in the underlying (British pounds) The dealer should sell 0.30% x GBP 100,000,000 = GBP 30,000,000 3 Lex van der Wielen, August 2015

38 30 A long all option + long put option with the same strike pries 31 To antiipate very high volatility in the prie of the underlying ommodity and b Sell an ATM put and sell an ATM all 34 b With a short EUR all / USD put you suffer from an inrease in the EUR/ USD rate and wirth a long EUR put / USD all you an profit from a derease in this rate. This is exatly the profile of a short position euro against US dollars. 35 The put option will be exerised and the dealer has to pay 100 points. The all options expires worthless. At the start of the onstrution, the dealer reeived a total premium of 400 points. 36 the all is 425 pips ITM and the total premium paid was The break-even levels are: 1. Lowest strike minus total premium and 2. highest strike plus total premium = and = Lex van der Wielen, August 2015

39 The ap level is not reahed: 3.70% % % = 4.30% 43 d 5.30% = 4.20% % % 44 Buy a floor at 3.00% and sell a ap at 5.00% 45 ap level is not reahed: /4 = Lex van der Wielen, August 2015

40 6 Lex van der Wielen, August 2015

41 Asset & Liability Management -ALM answers ICAAP = Internal Capital Adequay Assessment Proes Lex van der Wielen, August 2015

42 Interest immunization is mathing the terms of assets and liabilities and sine with a typial bank the assets have a longer interest-term than theliabilties this bank must derease the term of its assets and inrease the term of its liabilities. 18 Maaulay duration is an indiator for the average term and modified duration is an elastiity between the interest rate and the prie of an interest bearing instrument b The value dereases with 37,000,000 x 0.01 x 7 24 The value inreases with 15,000,000 x x Lex van der Wielen, August 2015

43 25 (100 x 6) - ( 90 x 4) / (100 x 7) - ( 85 x 6) / 15 = 12,67 27 Long term speaks for itself. Low oupons mean that the amortization plays a more important role (the weihtings of the short-term ash flows is relatively low). 28 The duration of a allable bond is lower than the duration of a regular bon 29 If interest rates rise, then the value of the 10 years irs will go up and the value of the 5 years irs will go down The 10 years swap is the most interest sensitive and the value of this irs will, therefore, inrease more than that the value of the 5 years swap will derease. The net exposure (EAD) on this lient, therefore, will rise. If the redit rating of the ounterparty dereases, the PD (probability of default) goes up Beause of the sale of the bond, the redit risk beomes smaller. The bank. however, is now faed with an open position Lex van der Wielen, August 2015

44 34 35 An FX swap does not hange your FX position b Issuing the CDO s in different tranhes dereases the redit risk for the high rated tranhes, however, at the same time it inreases the redit risk for the lower rated tranhes If the PD of the referene entity inreases, the protetion has more value If the PD of the ounterparty dereases, this means that the hane that the ontrat will be honoured inreases d At the start date and during the term of the hedge Lex van der Wielen, August 2015

45 45 46 Ususally the short-term rates are lower than the long-term rates and this effet is larger than the effet of an optionality 47 The linear amortizing loan has the lowest average term 48 The prepayment option is refleted in a surharge to the ost of fund With an interest rate swap there is no liquidity premium 5 Lex van der Wielen, August 2015

46 6 Lex van der Wielen, August 2015

47 Priniples of Risk - answers 1 Fraud is typially lassified operational risk Replaement ost is in the first plae a result of redit risk The seond order effet (the amount of the risk) is a result of market risk 5 d Market risk is related to trader s running an open position. Is speaks for itself that the amount of money that an be lost is influened by market movements. If a trader has a long position of 1,000 Heineken Shares and the prie goes down with 1 euro, he will lose 1,000 euro. If the prie goes down with 5 euro, however, he will lose 5,000 euro. Banks are exposed to pre-settlement risk if they have derivative ontrats with a positive market value. If the ounterparty in suh a ontrat will default, the bank will lose this positive market value. The market value of the ontrat is dependent on the urrent market pries. If a salesperson e.g. enters a sale of US dollars inorretly as a purhase, the trader will lose a sale transation in the market in order to square his position. As a onsequene he now has a short position of twie the amount of the original transation. When the mistake will be disovered, the trader has to loses his position by buying the US amount in the market. If the USD-dollar exhange rate has inreased, he suffers a loss. With small inreases, the loss will also be small. However, with large inreases, the loss will also be large. Other mistakes may be sending inorret settlement instrutions or an inorret valuation of the position. 6 1 Lex van der Wielen, Otober 2015

48 7 a If a dealer has a short position, he has an obligation to deliver the shares. If he buys the shares to be able to fulfill this obligation, as a onsequene he loses his position. This is obviously not his intention. He should borrow the shares by entering into a repo transation as a buyer. 8 Gap analysis is used to measure interest rate risk With the gap analysis, all instruments are ategorized by their remaining interest rate maturity The gap analysis then shows the interest sensitivity of the bank book for future hanges in interest rates 9 10 a Stress tests measure the loss as a result of a pre-defined market event 11 MM futures are exhange traded; the other instruments are OTC 12 Comprehensive Risk Measure. IRC = Inremental Risk Charge is the apital that banks hold as a buffer against the risk of a default or a downgrade of the issuers of seurities that they hold in their trading positions. VaR = Value at Risk EAD = Exposure at Default ,000,000 x x 0.17 x = 787, Lex van der Wielen, Otoberr 2015

49 ,000,000 x x 0.12 x 1.96 = 148, a Vostro aount is the same as a Loro aount 21 Pre-settlement risk or replaement risk is the risk that the bank has to replae a derivative ontrat that eases to exist beause of the default of the ounterparty. The bank has to replae the ontrat in order to keep its position balane 22 ISDA is used for interest rate derivatives and redit derivatives GMSLA is used for seurities lending transations GMRS is used for repos and sell buy bak transations IFXCO is used for FX transations 23 a Aording to the ontrat, the bank has to pay USD 16,000,000 on the value date If the lient will default, the bank has to replae the ontrat for a new ontrat in whih it has to pay USD 16,100,000. The replaement ost, therefore, is USD 100,000 3 Lex van der Wielen, Otober 2015

50 24 Payment netting lowers the settlement risk, whih is part of redit risk 25 The total obligations of the lient to the bank amount to EUR 1,350,000 The bank has an obligation to the lient of EUR 750,000 With a ontratual netting agreement, the mutual obligations are ompensated This results in a netted obligation of EUR 600,000 from the ustomer to the bank 26 a The day to day settlement of hanges in the market value of a ontrat is also alled variation margin The initial deposit that a ounterparty has to plae is also referred to as initial margin 27 b In this ase, you first have to identify the amounts bought with the first and the third transation using the ontrat rates Afterwards you must alulate the equivalent euro amounts and add them up using the urrent rates Amount ontrat rate Amount bought FX rates used for valuation Amount in euros USD sell 10,000, EUR 7,407, ,407,407 GBP 5,000,000 EUR/GBP ,555,556 CHF sell 8,000, USD 5,714,286 EUR/USD ,232,804 total 17,195, With transation with sovereigns, there is normally a unilateral ollateral obligation. 4 Lex van der Wielen, Otoberr 2015

51 29 30 Effeted expeted positive exposure Credit value adjustment, redit spread for expeted loss on derivatives 33 Nominal amount x instrument weighting x ounterparty weighting x 8% 50,000,000 x 0.01 x 0.20 x 0.08 = 8, Nominal amount x instrument weighting x ounterparty weighting x 8% x (return on equity - risk free rate) 10,000,000 x x 1 x 0.08 x 0.06 = 240 euro 5 Lex van der Wielen, Otober 2015

52 6 Lex van der Wielen, Otoberr 2015