= 0.83658 and 0.5443 × 1.5389 = 0.83762.Therefore AUD/CHF is 0.83658/0.83762. 1 ÷ 0.83762 =1.1939 and 1 ÷ 0.83658 = 1.1953. Therefore CHF/AUD is1.1939/53. The customer sells CHF (i.e. the market-makerbuys CHF, the base currency) on the left at 1.1939.(a)
Chapter 81
2
3
(a) and (c) are true.(b) and (d) are the wrong way round.In (e) the EUR interest rate would be 5.0% if it were on a 365day year, the same as sterling. On a 360-day year as normal,however, it is:3605.0% ×= 4.93%.365In (f) the trader would use only the T/N swap.921 + 0.0275 ×360 = 1.70191.7123 × 921 + 0.0515 ×360 9292− 0.0510 ×0.0280 ×360360= −0.00991.7123 ×921 + 0.0510 ×360 9292− 0.0520 ×0.0270 ×360360= −0.01081.7123 ×921 + 0.0520 ×360The swap price is therefore 108/99
262
Foreign exchange and money markets
4 The quoting bank is selling and buying the base currency,USD. You are buying and selling USD. This is equivalent toborrowing USD and lending CHF. Currently, the USD is at aforward discount to the CHF – i.e. USD interest rates are higherthan CHF interest rates. You are expecting this difference towiden – for example, USD interest rates to rise more than CHFrates or CHF rates to fall more than USD rates.5 The yield curves cross: EUR interest rates are higher than USDrates at 3 months, but lower at 6 months.6
With the customer, you buy and sell EUR, the base currency,on the right at +61. The settlement rates are therefore 0.6215and 0.6276. When you cover the position, the quoting bank isalso buying and selling EUR, on the right at +62. The settlementrates are therefore 0.6205 and 0.6267. Your cashﬂows arisingfrom the two deals are therefore:3 months
Spot+EUR−GBP−EUR+GBP
16,090,104.5910,000,000.0016,116,035.4610,000,000.00
Net cashﬂows: −EUR
25,930.87
Original deal:Original deal:Cover:Cover:
−EUR 15,933,715.74+GBP 10,000,000.00+EUR 15,956,598.05−GBP 10,000,000.00+EUR
22,882.31
You could therefore be said to have a loss of EUR (25,930.87 −22,882.31) = EUR 3,048.56.However, this does not take account of the time value of money(see Chapter 2). The NPV of the net cashﬂows is:EUR 22,882.31 = −EUR 3,502.12−EUR 25,930.87 + 1821 + 0.04 ×3607
(a)
USD/CAD
USD/SEK
spot:swap:
1.5671/1.56770.0030/0.0033
outright:
1.5701/1.5710
spot:swap:
10.3458/10.34680.0070/ 0.0067
outright:
10.3388/10.3401
10.3388 ÷ 1.5710 = 6.581010.3401 ÷ 1.5701 = 6.5856Therefore the CAD/SEK 6-month outright is 6.5810/56The customer can sell CAD at 6.5810
Answers to exercises
(b)
USD/CADUSD/SEK
263
spot:spot:
1.5671/1.567710.3458/10.3468
10.3458 ÷ 1.5677 = 6.599310.3468 ÷ 1.5671 = 6.6025CAD/SEK
outright:spot:swap:
6.5810/6.58566.5993/6.60250.0183/0.0169
Therefore the CAD/SEK 6-month swap is 183/169The customer can sell and buy CAD at −169 points.8
With the customer, you sell and buy the base currency, GBP,on the left at −435 points. The settlement rates are 178.10 and173.75. For the cover, you buy and sell GBP against USD onanother bank’s price on the left at −73 points. The settlementrates are 1.4260 and 1.4187. You also buy and sell USD againstJPY on another bank’s price on the left at −240 points. Thesettlement rates are 124.85 and 122.45. The cashﬂows are asfollows:SpotOriginal deal: −GBP1,000,000Original deal: +JPY 178,100,000Cover:+GBP1,000,000Cover:−USD1,426,000Cover:+USD1,426,000Cover:−JPY 178,036,100Net cashﬂows: +JPY63,900
6 months+GBP1,000,000−JPY 173,750,000−GBP1,000,000+USD1,418,700−USD1,426,000+JPY 174,613,700+JPY863,700−USD7,300
9 173.74. There are four possibilities:(a)
spot: sell GBP against JPYswap: buy and sell GBP against JPYsell GBP against JPY spotbuy and sell GBP against JPYeffective outright rate:
(b)
178.05−4.35173.70
spot: sell GBP against USD; sell USD against JPYswap: buy and sell GBP against USD; buy and sell USDagainst JPYsell GBP against USD spotbuy and sell GBP against USD
1.4255−0.00731.4182
264
Foreign exchange and money markets
sell USD against JPY spotbuy and sell USD against JPY
124.80−2.40122.40
effective outright rate: 1.4182 × 122.40 =(c)
spot: sell GBP against USD; sell USD against JPYswap: buy and sell GBP against JPYsell GBP against USD spotsell USD against JPY spot1.4255 × 124.80 =buy and sell GBP against JPYeffective outright rate:
(d)
173.55
173.59177.90
cross-rate swap:
−4.31
sell GBP against JPY spotcross-rate swap:effective outright rate:
178.05−4.31
spot:S/N:
1.4253 /1.42580.00022 / 0.00017
outright day after spot:
1.42508/1.42563
spot:T/N:
1.4253 /1.42580.00021 / 0.00016
outright tomorrow:
1.42546/1.42601
The customer sells USD at 1.42601(c)
177.90−4.35
To calculate effective cross-rate swap:cross-rate outright (from (b) above)cross-rate spot (from (c) above)
The customer buys GBP at 1.42563(b)
1.4255124.80
spot: sell GBP against JPYswap: buy and sell GBP against USD; buy and sell USDagainst JPY
The last possibility (d) is the best.10 (a)
173.59
spot:T/N:O/N:
1.4253 /1.42580.00021/0.000160.00018 / 0.00013
outright today:
1.42559/1.42619
The customer sells GBP at 1.42559
173.74
Answers to exercises
(d)
(e)
265
S/N:3 months:
0.00022/0.000170.0183 / 0.0178
forward-forward:
0.01813/0.01758
O/N:T/N:3 months:
0.00018/0.000130.00021/0.000160.0183 / 0.0178
forward-forward:
0.01869/0.01809
11 Wednesday 29 October 2003 and Friday 28 November 2003(‘modiﬁed following’ convention because 29 November is aSaturday and the next working day – Monday 1 December – is inthe next month).12
Friday 27 February 2004 (which is the last working day ofFebruary because 29 February is a Sunday) and Wednesday 31March 2004 (‘end-end’ convention).
13
12 − (−11) = 23; 18 − (−15) = 33 The price is therefore23/33(b) The quoting bank is selling and buying the base currency,which it does on the left at +23 points.(c) Middle spot is 1.4240. Middle 2-month swap is −13 points.Therefore middle 2-month outright would be 1.4240 −0.0013 = 1.4227. Therefore set the 2-month settlement rateas 1.4227 and the 5-month settlement rate as 1.4227 +0.0023 = 1.4250. The 2-month settlement rate could beslightly different from this, but must be a current marketrate for two months forward, not the spot rate. Whatever2-month settlement rate is chosen, the 5-month settlementrate must then be 23 points higher.(a)
14 The swap is −8/+18. The outright is 1.4227/63.15
Original transactionat 301.55:Settlement rate 295.71:Proﬁt:
buy HUF 1,000,000,000sell HUF 1,000,000,000
sell USD 3,316,199.64buy USD 3,381,691.52USD
65,491.88
Chapter 91 (a) and (c). In (b), the swap should be ‘sell and buy’ EUR, not ‘buyand sell’ EUR.2
The cashﬂows arising from the original transaction and hedge areas follows:
266
Foreign exchange and money markets
Spot
3 months
Original deal:Original deal:Lend EUR:Borrow USD:
+EUR 10,000,000.00−USD 9,120,000.00−EUR 10,000,000.00+USD 9,120,000.00
−EUR 10,000,000.00+USD 9,163,000.00+EUR 10,075,833.33−USD 9,235,266.67
Net cashﬂows:
–
+EUR−USD
75,833.3372,266.67
In order to remove any risk in USD, you could, for example, buyUSD 72,266.67 3 months forward outright.3
For the hedge, you need to do one of the following:(i) Sell and buy euros forward-forward at −93 points (=−162+69).or (ii) Sell a euro FRA at 4.0% or buy euro futures at 95.96 andbuy a Swiss franc FRA at 1.6% or sell Swiss franc futuresat 98.39.In (ii), buying a euro futures at 95.96 implies a rate of 4.04%. Thisis better than selling an FRA at 4.0%. However, selling Swiss francfutures at 98.39 implies a rate of 1.61%, which is not as good asbuying an FRA at 1.6%. Therefore the strategy would be to buyeuro futures and buy a Swiss franc FRA, if this combination ischeaper than the forward-forward at −93 points.The effective rate achieved through the FRA and futures is:Forward swap= 2-month outright base currency daysvariable currency days−××interest rateinterest rateyearyear×days1 + base currency interest rate ×year 9191− 0.0404 ×0.016 ×360360= 1.5976 ×911 + 0.0404 ×360= −0.0098 = −98 pointsThis is better than the forward-forward at −93 points. Theexpected proﬁt is the difference between the −90 points atwhich you have bought and sold euros in the original dealand the −98 points at which you effectively now sell and
Answers to exercises
267
buy. This 8 points proﬁt on EUR 10 million is worth CHF 8,000(10 million × 0.0008 = 8, 000). In practice, the proﬁt is uncertainbecause it depends on whether the 3-month swap price at whichthe deal will probably be reversed in 2 months’ time is in line withLIBOR at that time (because the FRA and futures contract willsettle against LIBOR then) and on bid/offer spreads at that time.4
Investing via dollars is as follows:Sell EUR 3 million and buy dollars, value spot.Invest the dollars at 4.5%.Sell forward the maturing dollar deposit amount back into euros.The swap involves selling and buying euros, at −1.1 points. If thequoting bank determines 0.9129 as the spot rate, the settlementrates are 0.9129 (spot) and 0.91279 (1 week).The synthetic yield can be calculated using the formula as follows:Dollar interest rate created syntheticallydays=1 + USD rate ×USD yearEUR yearEUR/USD rate for near date−1 ××EUR/USD rate for far datedays0.91293607×−1 ×=1 + 0.045 ×3600.912797= 0.0512 = 5.12%Alternatively, the cashﬂows are as follows:spot
6 months
dollar deposit: −USD 2,738,700swap:+USD 2,738,700−EUR 3,000,000
+USD 2,741,096.36−USD 2,741,096.36+EUR 3,002,986.84
net cashﬂows: −EUR 3,000,000
+EUR 3,002,986.84
The net result is effectively a one-week deposit of EUR 3,000,000with total proceeds of EUR 3,002,986.84 – i.e. effective interestreceived of EUR 2,986.84.This interest earned is for a period of 7 days. It can be expressedas an interest rate per annum of 5.12%:2,986.84360×= 0.0512 = 5.12%3,000,0007
268
Foreign exchange and money markets
5 The dealer borrows euros at 3.3%, then sells and buys eurosagainst sterling at +1.2 points. If the settlement rates are 0.6250(today) and 0.62512 (tomorrow), the effective cost is 5.68%. Thesettlement exchange rates could be slightly different but withouta signiﬁcantly different result as long as the swap points of +1.2are correctly applied:Sterling interest rate created syntheticallydays=1 + EUR rate ×EUR yearGBP yearEUR/GBP rate for far date−1 ××EUR/GBP rate for near datedays36530.62512−1 ×=1 + 0.033 ××3600.62503= 0.0568 = 5.68%An alternative approach is to consider the cashﬂows, based onan arbitrary amount. For example, based on EUR 1 million, thesewould be:Interest on EUR 1 million borrowing= 1,000,000 × 0.033 ×
3= 275360
Principal + interest= 1,000,000.00 + 275 = 1,000,275Fridayeuro borrowing: +EUR 1,000,000swap:−EUR 1,000,000+GBP625,000net cashﬂows:
+GBP
625,000
Monday−EUR 1,000,275.00+EUR 1,000,275.00−GBP 625,291.91−GBP
625,291.91
291.91365×= 0.0568 = 5.68%625,00036 The FX forward-forward price is 178/168. As a price-taker, youwill deal at −168 points (you sell and buy sterling). Based ona middle 2-month outright of 2.3921, this gives 2-month and5-month settlement rates of 2.3921 and 2.3753.
Answers to exercises
269
Swiss franc interest rate created syntheticallydays=1 + GBP rate ×GBP yearGBP/CHF rate for far dateCHF year×−1 ×GBP/CHF rate for near datedays2.375392360×−1 ×=1 + 0.061 ×3652.392192= 0.03226 = 3.226%
Chapter 101
The cashﬂows arising from the original transaction are as follows:2 monthsOriginal deal: −EUR 5,000,000+CHF 7,975,000
6 months+EUR 5,000,000−CHF 7,925,000
The net present value of the euro cashﬂows is:EUR 5,000,000EUR 5,000,000 + −611831 + 0.041 ×1 + 0.043 ×360360= −EUR 72,457The net present value of the Swiss franc cashﬂows is:CHF 7,975,000CHF 7,925,000 − +611831 + 0.022 ×1 + 0.024 ×360360= +CHF 115,901An appropriate hedge could therefore be to buy EUR 72,457 spotagainst sterling and to sell CHF 115,901 spot against sterling.
Chapter 131 There is no risk to the EUR/USD spot rate; if the EUR strengthensor weakens, the two exposures will offset each other. There is,however, an exposure to interest rates. This can be seen either asthe cost of funding the EUR 1 million shortfall from May to June,or as the risk that the forward-forward exchange rate from May toJune will change. To hedge the risk, the company could buy andsell EUR 2v3 forward-forward.
270
2
Foreign exchange and money markets
Suppose that the current GBP/CHF exchange rate is 2.0000 forboth spot and forward and that you have sold all your budgetedincome forward at 2.0000, for expected proceeds of:100 million × 2.0000 = CHF 200 million.If sterling in fact strengthens by 10% to GBP/CHF 2.2000, yoursales receipts would fall in sterling terms from GBP 100 millionto GBP 93 million, because of the fall in ticket prices in sterling terms. After such a change, you would need to buy backGBP 7 million at a rate of 2.2000. The cost of this would be:7 million × 2.2000 = CHF 15.4 millionThis would result in total net receipts from the hedge of:CHF 200 million − CHF 15.4 million = CHF 184.6 millionSimilarly, if sterling had in fact fallen as you expected, you wouldhave ended up with net proceeds of correspondingly more thanCHF 200 million. By selling all the expected sterling, you haveoverhedged, because the true exposure is not entirely a sterling one.Because the sterling amount changes 7% with a 10% movein sterling, the exposure is in fact only around 30% a sterlingexposure and 70% something else (perhaps a euro exposure,depending on what you consider to be the dominant forces inyour particular market). Suppose therefore that you had only soldGBP 30 million forward, for proceeds of:30 million × 2.0000 = CHF 60 millionAfter a 10% strengthening in sterling, your expected total salesreceipts would fall to GBP 93 million, so that it would be necessaryto sell a further GBP 63 million, at the new rate of 2.2000. Theadditional proceeds would therefore be:63 million × 2.2000 = CHF 138.6 millionThe total proceeds would therefore be:CHF 60 million + CHF 138.6 million = CHF 198.6 million– much closer to your expectation.
Appendix A
A summary ofmoney marketday/yearconventionsCountry
Euro-zone (the single‘domestic’ currency forthe European MonetaryUnion countries),Denmark, Switzerland,Australia, Canada, Japan,New ZealandHong Kong, Singapore,South Africa, TaiwanNorway(T-bills)(other money market)Sweden(T-bills)(other money market)
Day/year basisfor domesticinstruments
Day/year basisfor international(‘‘Euromarket’’)instruments
ACT/360
ACT/360
ACT/365
ACT/360
ACT/365
ACT/365
ACT/3651ACT/360
ACT/360
30/360ACT/360
ACT/360(continued overleaf )
272
Foreign exchange and money markets
(continued)Country
UK(BAs and sterling T-bills)(other money market)US(BAs, T-bills anddomestic CP)(other money market)
Day/year basisfor domesticinstruments
ACT/3652ACT/365
Day/year basisfor international(‘‘Euromarket’’)instruments
ACT/365
ACT/3602ACT/360
ACT/360
Notes1 Quoted as an effective (annual equivalent) yield rather than a simple rate.2 Quoted as a discount rate rather than as a true yield.
Appendix B
A summary ofcalculationproceduresThroughout, ‘days’ means the number of days in the period, includingthe ﬁrst date but not the last date; in the money markets, thisgenerally means the number of actual calendar days in the normalway. ‘Year’ means the number of days in a conventional year, whichin the money markets is generally 360 or 365.
Essential ﬁnancial arithmeticDay/year conventions360365365Interest rate on ACT/365 basis = interest rate on ACT/360 basis ×360Interest rate on ACT/360 basis = interest rate on 30/360 basisInterest rate on ACT/360 basis = interest rate on ACT/365 basis ×
×
days in period measured on 30/360 basisdays in period measured on ACT/360 basis
Interest rate on 30/360 basis = interest rate on ACT/360 basis×
days in period measured on ACT/360 basisdays in period measured on 30/360 basis
Present value and yieldamount of future cashﬂowPresent value = days1 + interest rate ×year
274
Foreign exchange and money markets
Yield =
yearcashﬂow at the end−1 ×cashﬂow at the startdays
Creating a stripThe simple interest rate for a period up to one year⎛⎞days in ﬁrst period1+ﬁrstinterestrate×⎜⎟year⎜⎟⎟⎜days in second period ⎟⎜year⎟⎜ × 1 + second interest rate ×=⎜⎟×year⎟ total days⎜⎜ ×..........⎟⎟⎜⎠⎝days in last period× 1 + last interest rate ×−1year
Straight-line interpolationInterpolated rate = the ﬁrst rate⎞⎛(days between the ﬁrst dateand the required date)⎜ (the second rate⎟+⎝×⎠(days between the ﬁrst date− the ﬁrst rate)and the second date)Equivalent interest ratesEquivalent rate with interest paid M times per year⎛ NMrate with interest paid N times per year⎜=⎝ 1+N
⎞⎟− 1⎠ × M
 365daysdays− 1Effective rate = 1 + nominal rate quoted ×year
Deposits and coupon-bearing instrumentsFixed depositsInterest earned = principal amount × interest rate ×Maturity proceeds = principal amountdays+ principal amount × interest rate ×year
daysyear
A summary of calculation procedures
275
or:
daysMaturity proceeds = principal amount × 1 + interest rate ×yearCertiﬁcate of depositMaturity proceeds⎛
⎛
⎞⎞days from issueto maturity ⎟⎟⎜⎜= face value × ⎝1 + ⎝coupon rate ×⎠⎠year⎛
⎛
⎞⎞days from issueto maturity ⎟⎟⎜ ⎜face value × ⎝1 +⎝coupon rate ×⎠⎠yearAmount paid =
days from settlement to maturity1 + yield ×year
Yield over holding period⎛⎛⎛
⎞⎞⎞days from purchaseto maturity⎜⎟⎟⎜⎜⎟⎠⎠⎜⎝1 + ⎝purchase yield ×⎟year⎜⎟⎜⎟year⎟×=⎜−1⎜⎟ days helddaysfromsaletomaturity⎜ 1 + sale yield ×⎟⎜⎟year⎝⎠
To calculate the total amount repayable when a ﬁxed deposit is broken1 Calculate the principal plus interest due on the normal maturity date2 Calculate the present value of this, using the bank’s funding rateTo value a CD with more than one coupon payment outstanding1 Calculate each future cashﬂow2 Discount the ﬁnal cashﬂow back to the previous coupon date,using the current yield as the rate of discount3 Add the coupon on that date and repeat the process until thenearest outstanding coupon4 Add that coupon and discount back to the settlement date
Discount InstrumentsMaturity proceeds = face value
276
Foreign exchange and money markets
Discount instruments quoted on a yieldface value⎞⎞days from settlementto maturity⎜⎜⎟⎟⎝1 + ⎝yield ×⎠⎠year
Amount paid = ⎛
⎛
(the following formula is the same as for a CD)Yield over holding period⎛⎛⎛
⎞⎞⎞days from purchaseto maturity⎟⎟⎜⎜⎜⎟⎠⎠⎜⎝1 + ⎝