the ﬁnance department, there is beneﬁt in a reportingsystem from the ﬁnance department back to the divisions. The ﬁnancedepartment should be responsible for setting budget exchange ratesand providing the operating divisions with a regular update to theseexchange rates as the year unfolds.Different rates might be used for each quarter, and the rates shouldpreferably be based on the forward market rates available at the time.These rates are for planning and reporting purposes and do notrepresent a commitment by the ﬁnance department to provide actualtransactions at these rates. Companies often use forecasts as budgetrates. A forecast, however, does not necessarily represent either a
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Foreign exchange and money markets
rate which it is possible for the company to achieve, or a rate whichwould result in proﬁtable commercial business if it did achieve it.
Evaluating the success oftreasury managementEvaluation is something that comes after the event and in ﬁnancedepartments with few resources is often overtaken by more immediateproblems. Much depends on the objective of the ﬁnance department.If the objective is to be a proﬁt centre rather than a cost centre, thendetailed evaluation is essential to justify the continued contributionof the ﬁnance department to the company.There are two stages to evaluation. How successful are we currentlyon our outstanding exposures? How successful have we been inthe past? The ﬁrst question has already been mentioned above in‘Setting short-term dealing targets’ and in ‘Internal reporting withinthe ﬁnance department’. The second question can be answered invarious ways as follows. A combination of these ways might benecessary to give a fair appraisal:1 Compare the exchange rate achieved with the spot rate availableat the time the exposure is ﬁrst managed.2 Compare the exchange rate achieved with the exchange rate atwhich the exposure is booked in the accounts – often the spot rateavailable at the time of booking, and possibly the same as in (1).3 Compare the exchange rate achieved with the forward rate available at the time the exposure is ﬁrst managed. This is equivalentto comparing against a very conservative policy of hedging 100%when the exposure is ﬁrst managed. Some companies hedge whenthey can secure foreign exchange proﬁts relative to this initialforward rate. Such an approach might encourage a company toplace emphasis on a short-term perspective rather than managethe exposure over its whole life.4 Compare the exchange rate achieved with the spot rate at maturity. This is equivalent to comparing against a policy of hedgingnothing and might indeed encourage a company to take a verypassive approach to risk management.5 Compare the exchange rate achieved with the average forwardrate available from the creation of the exposure until maturity.6 Compare the exchange rate achieved with the highest and lowestforward rates available from the creation of the exposure untilmaturity. This is evaluating against the best- and worst-case
Corporate risk management
249
situations and highlights the impossibility of always achievingthe best available rate. A progressive hedging strategy implies anaveraging approach, but comparison with the highest and lowestrates provides a useful method of assessing relative success orfailure.7 Compare the exchange rate achieved with the budget rate. Thisis probably the most common system of evaluation but dependson the relationship of budget rates to the underlying commercialbusiness. Many companies use forecast average rates for theaccounting period as their budget rates, and many take no explicitaccount of the forward market in budgeting. Rarely are the budgetrates related to the break-even rates necessary for proﬁt on thesale of receivables, or minimum acceptable proﬁt levels. Althoughbudget rates are usually set annually, some companies adopt aquarterly or bi-annual planning period and revise budget rates ifthe market situation dictates.(1) and (2) represent rates which the currency manager is not in aposition to obtain – because they do not relate to the forward ratesat which he can deal – and are therefore not generally satisfactory asmeasures of performance.(3), (4) and (5) are useful measures of performance, in that theycompare what was actually achieved with what could have beenachieved in practice. (3) compares performance against a policy ofautomatically hedging everything, (4) against hedging nothing, and (5)against a random policy over a long time. If, on average, a company’streasury department cannot do better than each of these 3, it raisesthe question of whether it is worthwhile having an active treasurydepartment at all. (3) and (4) are relatively simple to record but (5) ismore complicated.(7) can be an extremely important measure by which to take action,but should not be used alone as a measure of performance. As with (1)and (2), it does not necessarily relate to rates which are achievable inpractice. If too much emphasis is placed on these, it might encouragethe currency manager to suggest unrealistic budget exchange rates.
Exercises1
2
In March, a US company reports that it has an outﬂowof EUR 1 million which will occur in May and an inﬂow ofEUR 1 million which will occur in June. In March, to what risk isthe company exposed?You are a Swiss airline company. Tickets which you sell in the UKfor scheduled ﬂights all over Europe are sold in sterling. However,
250
Foreign exchange and money markets
your competitors in this industry are European, not UK ones. Ifsterling weakens or strengthens, these competitors will ensurethat the price of a ticket in the UK goes up or down in sterlingterms to compensate partly for the weaker or stronger pound. Youhave analysed that a 10% fall (or rise) in sterling against all othercurrencies unilaterally would result in a 7% increase (or decrease)in UK ticket prices in sterling terms, but no change in the volumeof ticket sales. You have budgeted that your sales to the UK overthe next 12 months will be GBP 100 million. You are worried thatsterling will fall sharply, and wish to hedge against that risk. Howmuch of what do you sell to hedge the risk?
Answers toexercisesChapter 21 ACT/365 basis:ACT/360 basis:30/360 basis:2
136= 124,821.923651365,000,000 × 0.067 ×= 126,555.56360133= 123,763.895,000,000 × 0.067 ×3605,000,000 × 0.067 ×
Interest rate on ACT/360 basis= interest rate on 30/360 basisdays in period measured on 30/360 basisdays in period measured on ACT/360 basis133= 6.552%= 6.7% ×136
×
Interest rate on ACT/365 basis= interest rate on ACT/360 basis ×= 6.552% ×
365360
365= 6.643%360
amount of future cashﬂow3 Present value = days1 + interest rate ×yearEUR 5, 327.21 = EUR 5, 161.02= 2761 + 0.042 ×360
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Foreign exchange and money markets

4
56
cashﬂow at the endyearYield =−1 ×cashﬂow at the startdays2,350,000.00365=−1 ×= 0.0961 = 9.61%2,345,678.917(193 − 183)9.00% + (9.15% − 9.00%) ×= 9.0484%(214 − 183)Equivalent rate with interest paid four times per year⎞⎛⎛⎛⎞⎞ 124ratewithinterestpaid12⎜⎟⎜⎜⎟times per year⎜⎟⎟⎜− 1⎟= ⎜⎝1 + ⎝⎠⎠⎟×412⎠⎝⎛
⎞ 1240.0735⎜⎟=⎝ 1+− 1⎠ × 4 = 0.07395 = 7.395%127 6.7% annual bond basis. 365daysdays8 Effective rate = 1 + nominal rate ×−1year 3654545− 1 = 0.0476 = 4.76%= 1 + 0.046 ×3609
 92360183× 1 + 0.053 ×−1 ×1 + 0.051 ×360360275= 0.05213 = 5.213%
Chapter 412
273= GBP 2,067,315.07GBP 2,000,000 × 1 + 0.045 ×365The net position is short of EUR 4 million at an average rate of4.31%:−10,000,000 × 0.0428 = −428,000− 3,000,000 × 0.0423 = −126,900+ 9,000,000 × 0.0425 = +382,500− 4,000,000
−172,400
− 172,400= 0.0431 = 4.31%−4,000,000
Answers to exercises
3
(a)
253
181Maturity proceeds = USD 5,000,000 × 1 + 0.047 ×360= USD 5,118,152.78
USD 5,118,152.78(b) Purchase amount = 1291 + 0.048 ×360= USD 5,031,609.10USD 5,118,152.78 = USD 5,031,196.93(c) Sale amount = 1221 + 0.051 ×360360USD 5,031,196.93−1 ×(d) Yield over holding period =USD 5,031,609.107= −0.0042 = −0.42%or:
⎛⎞1291 + 0.048 ×⎜⎟ 360360 − 1⎟yield over holding period = ⎜⎝⎠× 71221 + 0.051 ×360= −0.0042 = −0.42%This is a negative yield because the value of the investmenthas fallen.(e)
To achieve 4.80%, we would need:⎛ ⎞1291 + 0.048 ×⎜⎟ 360360⎜ − 1⎟⎝⎠ × 7 = 0.0481221 + sale yield ×360This can be rearranged to give:⎛⎞1291 + 0.048 ×⎜⎟ 360360 − 1⎟Sale yield = ⎜⎝⎠ × 12271 + 0.048 ×360= 0.04796 = 4.796%
4
The maturing proceeds of the deposit, if it is not broken, would be:92EUR 5,000,000 × 1 + 0.0464 ×= EUR 5,059,288.89360
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Foreign exchange and money markets
If you repay the cash early, you would need to reﬁnance at around1-month LIBOR plus 5 basis points, which is 4.85%. The presentvalue of the maturing deposit at this rate of discount is:
EUR 5,059,288.89 = EUR 5,038,247.21311 + 0.0485 ×360
This is therefore the most that you would repay. In practice, youmight take a more pessimistic view on the rate at which you couldrefund yourself in the market.
Chapter 51
2
3
4
5
USD 10 million = USD 9,971,083.86241 + 0.0435 ×36024= USD 9,971,000,00USD 10 million × 1 − 0.0435 ×3604.97% = 5.073%1471 − 0.0497 ×360365= 5.143%5.073% ×3604.5567% = 4.51%831 + 0.045567 ×365GBP 10,000,000 = GBP 9,777,318.23Purchase price = 1631 + 0.051 ×365GBP 10,000,000 = GBP 9,784,630.89Sale price = 1561 + 0.0515 ×365GBP 9,784,630.89365−1 ×= 0.0390 = 3.90%Yield =GBP 9,777,318.237or:
⎛ ⎞1631 + 0.051 ×⎜⎟ 365365 − 1⎟Yield = ⎜⎝⎠ × 7 = 0.0390 = 3.90%1561 + 0.0515 ×365
Answers to exercises
6
255
163Purchase price = USD 10,000,000 × 1 − 0.051 ×360= USD 9,769,083.33156Sale price = USD 10,000,000 × 1 − 0.0515 ×360= USD 9,776,833.33Yield =
360USD 9,776,833.33−1 ×= 0.0408 = 4.08%USD 9,769,083.337
or:
⎛⎞1561 − 0.0515 ×⎜⎟ 360360 − 1⎟Yield = ⎜⎝ ⎠ × 7 = 0.0408 = 4.08%1631 − 0.051 ×3607
8
9
Bond-equivalent yield⎛⎞0.5⎜ 190 2⎟190⎜⎟− 0.5+ 2×⎜⎟366⎜ 366⎟⎞⎟⎜ ⎛⎜⎟⎜ ⎜⎟⎟⎜ ⎜1190⎟⎟⎜× ⎟ −−1⎠⎠⎝ ⎝1903661 − 0.0499 ×360=190− 0.5366= 0.05205 = 5.205%⎞⎛ 365103 ⎟⎜ 100Effective yield = ⎝⎠ − 1 = 0.07112 = 7.112%98.08
Norwegian bill:Simple yield (365-day basis)119365365= 0.05594 = 5.594%−1 ×= 1.057119Simple yield (360-day basis)= 5.594% ×
360= 0.05517 = 5.517%365
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Foreign exchange and money markets
US bill:Simple yield (360-day basis)0.055 = 0.05602 = 5.602%=1191 − 0.055 ×360The US bill has the higher yield.10 For comparison, convert each rate to the same method of quotation – for example, a yield on a 360-day basis:UK sterling Treasury bill at 4.98% (discount rate on 365-daybasis):4.98% = 5.0426%Yield on a 365-day basis = 911 − 0.0498 ×365Yield on a 360-day basis = 5.0426% ×
360= 4.97%365
UK euro Treasury bill at 4.98% (yield on 360-day basis):Yield on a 360-day basis = 4.98%Sterling domestic CP at 5.10% (yield on 365-day basis):Yield on a 360-day basis = 5.10% ×
360= 5.03%365
Sterling ECP at 5.10% (yield on 365-day basis):Yield on a 360-day basis = 5.10% ×
360= 5.03%365
US dollar Treasury bill at 4.81% (discount rate on 360-daybasis):4.81% = 4.87%Yield on a 360-day basis = 911 − 0.0481 ×360US dollar domestic CP at 4.93% (discount rate on 360-daybasis):4.93% = 4.99%Yield on a 360-day basis = 911 − 0.0493 ×360
Answers to exercises
257
US dollar ECP at 4.93% (yield on 360-day basis):Yield on a 360-day basis = 4.93%Therefore in ascending order:US dollar Treasury billUS dollar ECPUK sterling Treasury billUK euro Treasury billUS dollar domestic CPSterling domestic CPSterling ECP
4.87%4.93%4.97%4.98%4.99%5.03%5.03%
Chapter 61
Use the bid side for 9 months and the offered side for 6 months:⎛ ⎞2731 + 0.05 ×⎜⎟ 360360 − 1⎟Forward-forward rate = ⎜⎝⎠ × 911821 + 0.0525 ×360= 0.0438 = 4.38%
2
This is a forward-forward calculation. Overnight on Friday is3 days.⎛ ⎞71 + 0.043 ×⎜⎟ 360360⎟×Break-even rate = ⎜−1⎝⎠341 + 0.0425 ×360= 0.04336 = 4.336%
3
You sell the FRA at 7.30%FRA settlement amount91(0.073 − 0.0715) ×365 = GBP 734.85= GBP 2,000,000 × 911 + 0.0715 ×365You receive this amount because you sold the FRA and LIBOR isﬁxed lower than the FRA rate.
4
(a)(b)
You need to protect the rate at which you can lend again in3 months’ time. You therefore sell an FRA.4.80%
258
Foreign exchange and money markets
(c)
Cover exactly the amount which you will need to lend again.This is the maturing amount (principal plus interest) ofthe 3-month loan you have already made. This is EUR7,087,655.55:92EUR 7,000,000 × 1 + 0.049 ×360= EUR 7,087,655.55
(d)
LIBOR is ﬁxed at 5.05%. You pay the settlement becauseyou have sold the FRA and LIBOR is ﬁxed higher than theFRA rate. The amount is EUR 8,688.19:181(0.048 − 0.0505) ×360EUR 7,087,655.55 × 1811 + 0.0505 ×360= −EUR 8,688.19
(e)
After 3 months, you receive the maturing amount ofthe 3-month loan (EUR 7,087,655.55) but pay the FRAsettlement of EUR 8,688.19. You therefore receive a netEUR 7,078,967.36. You therefore lend out this amount atLIBID, which is 4.95%, to give you total proceeds at the endof 9 months of EUR 7,255,145.16:181EUR 7,078,967.36 × 1 + 0.0495 ×360= EUR 7,255,145.16Also at the end of 9 months, you will repay EUR7,260,108.33 as the principal and interest on the 9-monthborrowing:273EUR 7,000,000 × 1 + 0.049 ×360= EUR 7,260,108.33There is therefore a total net loss of EUR 4,963.17 (=EUR 7,255,145.16 − EUR 7,260,108.33)
5
You expect interest rates to rise. The size of a euro futurescontract is EUR 1 million. You have made a loss of 11 basispoints on each contract.10 × EUR 1,000,000 × 0.0011 ×or 10 × 11 × EUR 25 = EUR 2,750
3= EUR 2,75012
Answers to exercises
6
(a)
(b)
259
If the 3v6 period is covered separately, it is cheaper to buyan FRA at 5.39% than to sell June futures at 94.60 (impliedinterest rate 5.40%).If the 6v9 period is covered separately, it is cheaper to sellSeptember futures at 94.57 (implied interest rate 5.43%)than to buy an FRA at 5.45%.
Combining (a) and (b) in a strip, the 3v9 period can be coveredat 5.447%. This is cheaper than buying a 3v9 FRA at 5.47%:
 9136092× 1 + 0.0543 ×−1 ×1 + 0.0539 ×360360183
= 0.05447 = 5.447%
The choices are therefore reduced to:• Borrow 9-month cash at 5.45%• Borrow 6-month cash at 5.35% and sell September futuresat 5.43% to give a combined strip cost of 5.43%:
 91360184× 1 + 0.0543 ×−1 ×1 + 0.0535 ×360360275
= 0.0543 = 5.43%
• Borrow 3-month cash at 5.20%, buy a 3v6 FRA at 5.39% andsell September futures at 5.43% to give a combined strip costof 5.41%: 9292× 1 + 0.0539 ×1 + 0.0520 ×36036036091−1 ×× 1 + 0.0543 ×= 0.0541 = 5.41%360275

Of these, the last is the cheapest.7 The FRA is from May to October. You therefore use a combinationof futures contracts which overlap this period – March, June andSeptember.8 You are overborrowed. You therefore need to lend again in thefuture. You therefore need to sell an FRA at 6.51% or buy afutures at 93.51 (implied interest rate 6.49%). The better choiceis to sell an FRA at 6.51%.9 Strip together the June and September futures to give 4.30%:
 9136092× 1 + 0.0416 ×−1 ×1 + 0.0439 ×360360183
= 0.0430 = 4.30%
10
Buy June futures and sell December futures for example, or sella near-dated FRA and buy a longer-dated FRA
260
Foreign exchange and money markets
Chapter 712
34
56
7
8
The number of Norwegian kroner equal to 1 Singapore dollar.You will deal on the right-hand side because you are buyingthe base currency and the market-maker is selling the basecurrency. You therefore want the best possible right-hand side,which is 1.4361.You have bought EUR 5 million, at 0.9503.For AUD/USD, one point on a deal of AUD 1 million is worthUSD 100. For USD/JPY, one point on a deal of USD 1 million isworth JPY 10,000.You have a loss of 6 points which is CAD 6,000 (10,000,000 ×0.0006 = 6,000).You should quote 0.9502/07. You are currently long of EUR andtherefore wish to sell them. You therefore want to encourage thecounterparty to deal on the right-hand side of the price you arequoting. You must therefore make that side of the price moreattractive to the counterparty than the current general marketprice.You sell the customer CHF 5 million at CHF/USD 0.6338. Youtherefore receive USD (5,000,000 × 0.6338) = USD 3,169,000.To cover this, you buy CHF 5 million at USD/CHF 1.5783. Youtherefore pay USD (5,000,000 ÷ 1.5783) = USD 3,167,965.53.You therefore make a proﬁt of USD (3,169,000.00 −3,167,965.53) = USD 1,034.47.The position is short EUR 2 million. The average rate is 0.93055.The loss is GBP 3,054.99EUR
USD
−5,000,000+2,000,000+4,000,000−3,000,000Position:
at 0.9320:at 0.9325:at 0.9330:at 0.9327:
−2,000,000
+1,861,1001,861,1002,000,000= 0.93055
Average rate:+2,000,000
at 0.9328:
−Loss:
+4,660,000−1,865,000−3,732,000+2,798,100
−1,865,600−4,500
−4,5001.4730= −3,054.99
Answers to exercises
261
9
1 ÷ 1.0528 = 0.9498 and 1 ÷ 1.0523 = 0.9503. Therefore the ratefor NOK/SEK is 0.9498/03.
10
2.3895 ÷ 1.5389 = 1.5527 and 2.3905 ÷ 1.5384 = 1.5539.Therefore CHF/SGD is 1.5527/39. The customer sells SGD(i.e. the market-maker sells CHF, the base currency) on theright at 1.5539.(b) 0.9678 ÷ 0.5443 = 1.7781 and 0.9683 ÷ 0.5438 = 1.7806.Therefore EUR/AUD is 1.7781/06. The customer buys EUR(i.e. the market-maker sells EUR, the base currency) on theright at 1.7806.(c) 0.9678 × 1.5384 = 1.4889 and 0.9683 × 1.5389 = 1.4901.Therefore EUR/CHF is 1.4889/01. The customer buys CHF(i.e. the market-maker buys EUR, the base currency) on theleft at 1.4889.(d) 0.5438 × 1.5384