UNIVERSITY OF PORTSMOUTH
Portsmouth Business School
INTERNATIONAL FINANCIAL MANAGEMENT
U05753
Level 3, Semester 2
MAY/JUNE2012
Formulae/PV tables provided
This examination contains 6 questions students should attempt 4 questions
Write your answers on the answer sheet provided.
Remember to enter your Student Number on your answer sheet but NOT your
name.
Time Allowed: 2 hours
Calculators that are capable of holding text are not permitted in examinations
(for the purposes of identification calculators capable of holding text will have
an alpha-numeric keypad, i.e. a-z letters)
Specialist dictionaries such as Legal, Business, Technical or Accounting
Dictionaries etc. are not allowed in the exam. International students for whom
English is a second language are allowed to take into the exam one bilingual
paper based dictionary containing no annotations. Otherwise the normal
University of Portsmouth Examination Regulations will apply.
Unit Co-ordinator: Annette Gillies
Department: Accounting & Finance
Question 1 Transaction Exposure
San Ramon Inc a U.S. based company has concluded a sale of telecommunications equipment to
Royal plc (U.K.). A total payment of £3,000,000 is due in 90 days. The Financial Controller has
discovered that San Ramon Inc will only be able to borrow in the United Kingdom at 14% per
annum (due to credit concerns of the British banks). The following exchange rates and interest
rates are available:
Assumptions
90-day A/R in pounds
Spot rate, US$ per pound ($/£)
Financial Controller's expected spot rate in 90-days, US$ per
pound ($/£)
90-day forward rate, US$ per pound ($/£)
3-month U.S. dollar investment rate
3-month U.S. dollar borrowing rate
3-month UK investment interest rate
3-month UK borrowing interest rate
Put option on the British pound: Strike rate, US$/pound ($/£)
Put option premium 1.500%
Put option on the British pound: Strike rate, US$/pound ($/£)
Put option premium 1.000%
San Ramon's WACC
Value
£3,000,000.00
$1.7620
$1.7850
$1.7550
6.000%
8.000%
8.000%
14.000%
$1.75
$1.71
12.000%
Required:
(a) Calculate the proceeds of each alternative in hedging a £3,000,000 accounts receivable in
90days:
(i) Remain uncovered
(ii) Forward Hedge
(iii) Money Market Hedge
(iv) Options Hedge(if exercised)
(3 marks)
(2 marks)
(5 marks)
(10 marks)
(b) What are the risks associated with each of the above alternatives? (5 Marks)
Total 25 marks
/Continued……
Question 2 Interest Rate Exposure
CamilloFashions of Italy recently took out a 4-year €5 million loan on a floating rate basis. It is
now worried, however, about rising interest costs. Although it had initially believed interest rates
in the Eurozone would be trending downward when taking out the loan, recent economic
indicators show growing inflationary pressures. Analysts are predicting that the European
Central Bank will slow monetary growth driving interest rates up.
Camillo is now considering whether to seek some protection against a rise in euro-LIBOR, and is
considering a Forward Rate Agreement (FRA) with an insurance company. According to the
agreement Camillo would pay to the insurance company at the end of each year the difference
between its initial interest cost at LIBOR + 2.50% (6.50%) and any fall in interest cost due to a
fall in LIBOR. Conversely, the insurance company would pay to Camillo 70% of the difference
between Camillo’s initial interest cost and any increase in interest costs caused by a rise in
LIBOR.
Purchase of the floating Rate Agreement will cost €100,000, paid at the time of the initial loan.
Required
(a) What are Camillo’s all in costs (AIC) if LIBOR rises by 50 basis points per year and if
LIBOR falls by 50 basis points per year? (20 marks)
(b) Do you recommend that Camillo purchase the FRA? (5 marks)
Total 25 marks
/Continued......
2
Question 3 Global Cost of Capital
Sicilia Pharmaceutical’s cost of debt is 7%. The risk-free rate of interest is 3%. The expected
return on the market portfolio is 8%. After effective taxes, Sicilia’s effective tax rate is 25%. Its
optimal capital structure is 60% debt and 40% equity.
Required:
(a) If Sicilia’s beta is estimated at 1.1, what is its weighted average cost of capital?
(10 marks)
(b) If Sicilia’s beta is estimated at 0.8, significantly lower because of the continuing profit
prospects in the global energy sector, what is its weighted average cost of capital?
(10 marks)
(c) A national capital market is segmented if the required rate of returnon securities in that
market is different from the required rate of return on securities of a comparable
expected return and riskthat are traded on other national securities market. What are the
main reasons that markets become segmented?
(5 marks)
Total 25 marks
/Continued……
3
Question 4 Futures
RobertAdams, a currency trader for Chicago-based Black River Investments, uses the following
futures quotes on the British pound to speculate on the value of the British pound.
British Pound Futures, US$/£
Contract = £62,500
Maturity
Open
High
Low
Settle
Change
High
March
June
1.4246
1.4164
1.4268
1.4188
1.4214
1.4146
1.4228
1.4162
0.0032
0.0030
1.4700
1.4550
(a)
(b)
(c)
(d)
(e)
Open
Interest
25,605
809
If Robert buys 5 June pound futures, and the spot rate at maturity is $1.3980/£, what is
the value of his position? (4 marks)
If Robert sells 12 March pound futures, and the spot rate at maturity is $1.4560/£, what is
the value of his position? (4 marks)
If Robert buys 3 March pound futures, and the spot rate at maturity is $1.4560/£, what is
the value of his position? (4 marks)
If Robert sells 12 June pound futures, and the spot rate at maturity is $1.3980/£, what is
the value of his position?(4 marks)
Compare and contrast the features of the following two types of contract: the Foreign
currency Future and the Forward contract (9 marks)
Total 25 marks
/Continued……
4
Question 5 Purchasing Power Parity
You are based on the USA but are planning a summer holiday Sorrento, Italy one year from now.
You are negotiating the rental of a villa. The villa's owner wishes to preserve his real income
against both inflation and exchange rate changes, and so the present weekly rent of €9,800 will
be adjusted upward or downward for any change in the Italian cost of living between now and
then. You are basing your budgeting on purchasing power parity (PPP). Italian inflation is
expected to average 3.5% for the coming year, while U.S. dollar inflation is expected to be 2.5%.
The current spot rate is $1.3620/€.
(a)
(b)
What should you budget as the U.S. dollar cost of the one week rental? (10 marks)
Define the following terms:
Law of one price (5 marks)
Absolute Purchasing Power Parity (5 marks)
Relative Purchasing Power Parity (5 marks)
Total 25 marks
Question 6 Foreign Exchange Rate Determination
(a) Define the Fisher effect. To what extent do empirical test confirm that the Fisher effect
exists in practice? (5 marks)
(b) Define the international Fisher effect. To what extent do empirical tests confirm that the
international Fisher effect exists in practice? (7 marks)
(c) Cho-Cho-San, a foreign exchange trader at Credit Suisse (Tokyo), is exploring covered interest
arbitrage possibilities. She wants to invest $5,000,000 or its yen equivalent, in a covered interest
arbitrage between U.S. dollars and Japanese yen. She faced the following exchange rate and
interest rate quotes:
Spot Exchange Rate
¥ 118.60/$
180 day dollar interest rate
4.8% per year
180 Yen interest rate
3.4% per year
180 day forward exchange rate
¥ 117.80/$
The bank does not calculate transaction costs on any individual transactions because these costs are
part of the overall operating budget of the arbitrage department.
Explain and diagram the specific steps that Cho-Cho-San must take to make a covered interest
arbitrage profit. (13 marks)
Total 25marks
/Continued……
5
Present value of £1 receivable in n years time
Years
n
1
2
3
4
5
6
7
8
9
10
1
0.9901
0.9803
0.9706
0.9610
0.9515
0.9420
0.9327
0.9235
0.9143
0.9053
2
0.9804
0.9612
0.9423
0.9238
0.9057
0.8880
0.8706
0.8535
0.8368
0.8203
3
0.9709
0.9426
0.9151
0.8885
0.8626
0.8375
0.8131
0.7894
0.7664
0.7441
Discount rate as a percentage
4
5
6
7
0.9615 0.9524 0.9434 0.9346
0.9246 0.9070 0.8900 0.8734
0.8890 0.8638 0.8396 0.8163
0.8548 0.8227 0.7921 0.7629
0.8219 0.7835 0.7473 0.7130
0.7903 0.7462 0.7050 0.6663
0.7599 0.7107 0.6651 0.6227
0.7307 0.6768 0.6274 0.5820
0.7026 0.6446 0.5919 0.5439
0.6756 0.6139 0.5584 0.5083
8
0.9259
0.8573
0.7938
0.7350
0.6806
0.6302
0.5835
0.5403
0.5002
0.4632
9
0.9174
0.8417
0.7722
0.7084
0.6499
0.5963
0.5470
0.5019
0.4604
0.4224
10
0.9091
0.8264
0.7513
0.6830
0.6209
0.5645
0.5132
0.4665
0.4241
0.3855
1
2
3
4
5
6
7
8
9
10
11
0.9009
0.8116
0.7312
0.6587
0.5935
0.5346
0.4817
0.4339
0.3909
0.3522
12
0.8929
0.7972
0.7118
0.6355
0.5674
0.5066
0.4523
0.4039
0.3606
0.3220
13
0.8850
0.7831
0.6931
0.6133
0.5428
0.4803
0.4251
0.3762
0.3329
0.2946
14
0.8772
0.7695
0.6750
0.5921
0.5194
0.4556
0.3996
0.3506
0.3075
0.2697
18
0.8475
0.7182
0.6086
0.5158
0.4371
0.3704
0.3139
0.2660
0.2255
0.1911
19
0.8403
0.7062
0.5934
0.4987
0.4190
0.3521
0.2959
0.2487
0.2090
0.1756
20
0.8333
0.6944
0.5787
0.4823
0.4019
0.3349
0.2791
0.2326
0.1938
0.1615
Present value of an annuity of £1 payable at the end of each of n years
Years
Discount rate as a percentage
n
1
2
3
4
5
6
7
8
1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259
2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833
3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771
4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121
5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927
6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229
7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064
8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466
9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469
10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101
9
0.9174
1.7591
2.5313
3.2397
3.8897
4.4859
5.0330
5.5348
5.9952
6.4177
10
0.9091
1.7355
2.4869
3.1699
3.7908
4.3553
4.8684
5.3349
5.7590
6.1446
19
0.8403
1.5465
2.1399
2.6386
3.0576
3.4098
3.7057
3.9544
4.1633
4.3389
20
0.8333
1.5278
2.1065
2.5887
2.9906
3.3255
3.6046
3.8372
4.0310
4.1925
1
2
3
4
5
6
7
8
9
10
11
0.9009
1.7125
2.4437
3.1024
3.6959
4.2305
4.7122
5.1461
5.5370
5.8892
12
0.8929
1.6901
2.4018
3.0373
3.6048
4.1114
4.5638
4.9676
5.3282
5.6502
13
0.8850
1.6681
2.3612
2.9745
3.5172
3.9975
4.4226
4.7988
5.1317
5.4262
14
0.8772
1.6467
2.3216
2.9137
3.4331
3.8887
4.2883
4.6389
4.9464
5.2161
15
0.8696
0.7561
0.6575
0.5718
0.4972
0.4323
0.3759
0.3269
0.2843
0.2472
15
0.8696
1.6257
2.2832
2.8550
3.3522
3.7845
4.1604
4.4873
4.7716
5.0188
16
0.8621
0.7432
0.6407
0.5523
0.4761
0.4104
0.3538
0.3050
0.2630
0.2267
16
0.8621
1.6052
2.2459
2.7982
3.2743
3.6847
4.0386
4.3436
4.6065
4.8332
17
0.8547
0.7305
0.6244
0.5337
0.4561
0.3898
0.3332
0.2848
0.2434
0.2080
17
0.8547
1.5852
2.2096
2.7432
3.1993
3.5892
3.9224
4.2072
4.4506
4.6586
18
0.8475
1.5656
2.1743
2.6901
3.1272
3.4976
3.8115
4.0776
4.3030
4.4941
6
International Financial Management - Formulae
i = r + π + rπ
S1 − S2
× 100 = i $ − i ¥ ,
S2
kd x ( 1 - t )
E(Ra) = Rf + [Ba x (E(Rm) - Rf)]
WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ]
PV =
A
(1 + r ) n
7
ANSWERS
8
Question 1 - Transaction Exposure
a)
(i) Remain Uncovered
San Ramon may decide to accept the transaction risk. If they believe that the future spot rate in
90 days will be the same as current ($1.7620/₤), then San Ramon will receive ₤3,000,000 x
$1.7620/₤= $5,286,000 in 3 months’ time. However, if the future spot rate in 90 days is the same
as the 90-day forward rate ($1.7550/₤), San Ramon will receive ₤3,000,000 x $1.7550/₤=
$5,265,000. If the future spot rate in 90 days is the same as the Financial Controller's expected
spot rate in 90-days ($1.7850/€), the proceeds would be ₤3,000,000 x $1.7850/₤= $5,355,000.
If spot rate in 90 days is same as current
If spot rate in 90 days is same as forward rate
If spot rate in 90 days is controller’s expected spot rate
Values
$5,286,000
$5,265,000
$5,355,000
Assessment
Risky
Risky
Risky
(ii) Forward Market Hedge
Should San Ramon want to cover their exposure with a forward contract, then they would sell
₤3,000,000 forward at the 3-month forward rate ($1.7550/₤). The forward contract will be
entered upon the creation of the ₤3,000,000 A/R, and fulfilled in 90 days when San Ramon will
receive ₤3,000,000 from Royal plc and exchange those for US$ with the financial institution that
is the counter-party to the forward contract, receiving $5,265,000 (₤3,000,000 x $1.7550/₤).
Settlement amount at the forward rate
Values
$5,265,000
Assessment
Certain
(iii) Money Market Hedge
To hedge in the money market, San Ramon will borrow British pounds, convert the pounds to
US$ and repay the pound loan with the proceeds from the sale of equipment to Royal plc. To
calculate how much to borrow, San Ramon needs to discount the FV of the ₤3,000,000 to be
received in 90 days to today (i.e. when A/R is created):
Loan proceeds = ₤3,000,000/(1+ 90 day UK borrowing rate) = ₤3,000,000/[1+(14% x 90/360)] =
₤2,898,551.
San Ramon should borrow ₤2,898,551 upon the A/R creation, exchange those at the current spot
rate of $1.7620/₤, receiving $5,107,246 at once, and in 90 days repay the ₤2,898,551 plus
£101,449 in interest (₤3,000,000 in total) from the proceeds of the equipment sale.
In order to compare the forward hedge with the money market hedge, San Ramon must analyze
the use of the US$ loan proceeds of $5,107,246.
Received today
$5,107,246
$5,107,246
$5,107,246
Invested in
US Treasury
Bill
San Ramon’s
debt
substitution
San Ramon’s
operations
Rate
90-day US$ investment
rate (6.0% p.a.)
FV in 3 months
$5,107,246 x [1+(6% x 90/360)] =
$5,183,855
Assessment
90-day US$ borrowing
rate (8.0% p.a.)
$5,107,246 x [1+(8% x 90/360)] =
$5,209,391
Certain
Cost of capital (12%
p.a.)
$5,107,246 x [1+(12% x 90/360)] =
$5,260,463
Certain
Certain
9
(iv) Options Hedge (if exercised)
Given the quotes earlier, San Ramon could buy one of the two 3-month put options, one with a
$1.75/₤ strike price and 1.5% premium, and the other with a $1.71/₤ strike price and 1.0%
premium. The cost of these options would be:
Cost of option = Size of option x Premium x Spot rate
Cost of the $1.75/₤ option = ₤3,000,000 x 1.5% x $1.7620/₤ = $79,290
Cost of the $1.71/₤ option = ₤3,000,000 x 1.0% x $1.7620/₤ = $52,860
Because San Ramon is using future value to compare the various hedging alternatives, it is
necessary to project the cost of the option in 3 months’ time. Using the cost of capital of 12%
p.a., the premium cost of the option in 90 days will be:
FV Cost of the $1.75/₤ option = $79,290 x [1+(12% x 90/360)] = $81,669
FV Cost of the $1.71/₤ option = $52,860 x [1+(12% x 90/360)] = $54,446
San Ramon would exercise the options only if the spot rates in 90 days are <$1.75/£ and
<$1.71/£, respectively.
Net Proceeds of the $1.75/₤ option = (₤3,000,000 x $1.75/$) - $81,669 = $5,168,331 (certain)
Net Proceeds of the $1.71/₤ option = (₤3,000,000 x $1.71/$) - $54,446 = $5,075,554 (certain)
Analysis: The Financial Controller would receive the most certain US$ from the forward
contract, $5,265,000; the money market hedge is less attractive as result of the higher borrowing
costs in the UK now. The two put options yield unattractive amounts if they had to be exercised.
(b)
Remain Uncovered - this is highly risky, the amount received is dependent upon the spot rate on
the day the payment is made. In addition, there is a risk of non- or late payment by the customer
Forward Hedge - you have guaranteed the amount to be received with a forward hedge. The
forward contract is entered into at the time the transaction exposure is created. There is still a
risk of non- or late payment by the customer.
Money Market Hedge - you have the advantage of receiving the proceeds immediately. The net
proceeds are certain, but there is still a risk of non- or late payment by the customer.
Options Hedge - you do not have to exercise the option if exchange rates on the spot market are
more favorable but you would still have to pay the option premium. So you can benefit from any
upside of this transaction whilst limiting the down side to the strike price. There is still a risk of
non- or late payment by the customer.
10
Question 2 - Interest Rate Exposure
a)
Interest Rate Exposure - Camillo
Assumptions
Principal borrowing need
Maturity needed, in years
Current LIBOR
Camillo 's bank spread
Proportion of differential paid by FRA
Cost of FRA
If LIBOR Falls 50 Basis Pts Per
Year
Values
€ 5,000,000
4.00
4.000%
2.500%
70%
€ 100,000
Year 0
Year 2
Year 3
Year 4
3.500%
2.500%
6.000%
3.000%
2.500%
5.500%
2.500%
2.500%
5.000%
2.000%
2.500%
4.500%
-€ 300,000
-€ 25,000
-€ 275,000
-€ 50,000
-€ 250,000
-€ 75,000
€ 4,900,000
7.092%
-€ 325,000
-€ 325,000
-€ 325,000
-€ 225,000
-€ 100,000
-€ 5,000,000
-€ 5,325,000
Year 0
Year 1
Year 2
Year 3
Year 4
4.500%
2.500%
7.000%
5.000%
2.500%
7.500%
5.500%
2.500%
8.000%
6.000%
2.500%
8.500%
-€ 100,000
-€ 350,000
€ 17,500
-€ 375,000
€ 35,000
-€ 400,000
€ 52,500
€ 4,900,000
-€ 332,500
-€ 340,000
-€ 347,500
-€ 425,000
€ 70,000
-€ 5,000,000
-€ 5,355,000
Expected annual change in LIBOR
LIBOR
Bank spread
Interest rate
Funds raised, net of fees
Expected interest (interest rate x principal)
Forward Rate Agreement
Repayment of principal
Total cash flows
All-in-cost of funds (IRR)
If LIBOR Rises 50 Basis Pts Per
Year
-0.500%
4.000%
2.500%
6.500%
€ 5,000,000
-€ 100,000
Expected annual change in LIBOR
LIBOR
Bank spread
Interest rate
Funds raised, net of fees
Expected interest (interest rate x principal)
Forward Rate Agreement
Repayment of principal
Total cash flows
All-in-cost of funds (IRR)
Year 1
0.500%
4.000%
2.500%
6.500%
€ 5,000,000
7.458%
b)
This rather unusual forward rate agreement is somewhat one-sided in the favor of the insurance company.
When Camillo is correct in its predictions that interest rates are to go down, Camillo pays the full
difference in rates to the insurance company. But when interest rates move against Camillo, the insurance
company pays Camillo only 70% of the difference in rates. And all of that is after Camillo paid €100,000
up-front for the agreement regardless of outcome. Not a very good deal. A final note of significance is
that since Camillo receives only 70% of the difference in rates, its total cost of funds is not effectively
"capped"; they could in fact rise with no limit over the period as interest rates rose.
11
Question 3 - Global Cost of Capital
(a) & (b)
Assumptions
Sicilia's beta
Cost of debt, before tax
Risk-free rate of interest
Corporate income tax rate
General return on market portfolio
Optimal capital structure:
Proportion of debt, D/V
Proportion of equity, E/V
Calculation of the WACC
Cost of debt, after-tax
kd x ( 1 - t )
Cost of equity, after-tax
ke = krf + β x ( km - krf )
WACC
WACC = [ ke x E/V ] + [ ( kd x ( 1 - t ) ) x D/V ]
a)
Values
b)
Values
1.10
7.0%
3.0%
25.0%
8.0%
0.80
7.0%
3.0%
25.0%
8.0%
60%
40%
60%
40%
5.250%
5.250%
8.500%
7.000%
6.550%
5.950%
(c)
The main reasons that markets become segmented are: (i) regulatory controls; (ii) perceived
political risk; (iii) foreign exchange risk; (iv) lack of transparency; (v) asymmetric information;
and (vi) insider trading
12
Question 4 - Futures
a)
By buying future contracts, Robert is taking a long position, i.e. betting on the British pound to
appreciate (i.e. rise above $1.4162/£). Therefore, the value of her position at maturity will be
determined using the following formula:
Value at maturity = Notional principal x (End Spot rate– Future rate)
Value at maturity = (5 x £62,500) x ($1.3980 - $1.4162) = -$5,688 (loss)
b)
By selling future contracts, Robert is taking a short position, i.e. betting on the British pound to
depreciate (i.e. fall below $1.4228/£). Therefore, the value of her position at maturity will be
determined using the following formula:
Value at maturity = -Notional principal x (End Spot rate– Future rate)
Value at maturity = -(12 x £62,500) x ($1.4560 - $1.4228) = -$24,900 (loss)
c)
Value at maturity = (3 x £62,500) x ($1.4560 - $1.4228) = $6,225 (gain)
d)
Value at maturity = -(12 x £62,500) x ($1.3980 - $1.4162) = $13,650 (gain)
e)
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Question 5 - Purchasing Power Parity
а)
Assumptions
Spot exchange rate ($/€)
Expected US inflation for coming year
Expected Italian inflation for coming year
Current chateau nominal weekly rent (€)
Value
$1.3620
2.500%
3.500%
€ 9,800
Forecasting the future rent amount and
exchange rate:
Value
Purchasing power parity exchange rate forecast ($/€)
Spot (one year) = Spot x ( 1 + US$ inflation ) / ( 1 + Italy inflation )
Nominal monthly rent, in Euros, one year from now
Rent now x ( 1 + inflation Italy )
Cost of rent one year from now in US dollars
Rent one year from now x PPP forecasted spot rate
$1.3488
€ 10,143
$ 13,681
b)
The law of one price. The law of one prices states that producers’ prices for goods or services of
identical quality should be the same in different markets, i.e., different countries (assuming no
restrictions on the sale and allowing for transportation costs). If a country has higher inflation
than other countries, its currency should devalue or depreciate so that the real price remains the
same as in all countries. Application of this law results in the theory of purchasing power parity
(PPP).
Absolute purchasing power parity. If the law of one price were true for all goods and services,
the purchasing power parity (PPP) exchange rate could be found from any individual set of
prices. By comparing the prices of identical products denominated in different currencies, one
could determine the “real” or PPP exchange rate that should exist if markets were efficient. This
is the absolute version of the theory of purchasing power parity. Absolute PPP states that the spot
exchange rate is determined by the relative prices of similar baskets of goods.
Relative purchasing power parity. If the assumptions of the absolute version of PPP theory are
relaxed a bit more, we observe what is termed relative purchasing power parity. This more
general idea is that PPP is not particularly helpful in determining what the spot rate is today, but
that the relative change in prices between two countries over a period of time determines the
change in the exchange rate over that period. More specifically, if the spot exchange rate
between two countries starts in equilibrium, any change in the differential rate of inflation
between them tends to be offset over the long run by an equal but opposite change in the spot
exchange rate.
14
Question 6 - Foreign Exchange Rate Determination
a)
The Fisher effect, named after economist Irving Fisher, states that nominal interest rates in each
country are equal to the required real rate of return plus compensation for expected inflation.
More formally, this is derived from (1  r)(1  π )  1:
i = r + π + rπ
where i is the nominal rate of interest, r is the real rate of interest, and π is the expected rate
of inflation over the period of time for which funds are to be lent. The final compound term, r times
π, is frequently dropped from consideration due to its relatively minor value. The Fisher effect then
reduces to (approximate form):
i = r +π
The Fisher effect applied to two different countries, like the United States and Japan, would
be:
i $ = r $ + π $;
i¥ = r ¥ + π ¥
where the superscripts $ and ¥ pertain to the respective nominal (i), real (r), and expected
inflation (π) components of financial instruments denominated in dollars and yen, respectively. We
need to forecast the future rate of inflation, not what inflation has been. Predicting the future can be
difficult.
b)
Irving Fisher stated that the spot exchange rate should change in an equal amount but opposite in
direction to the difference in nominal interest rates. Stated differently, the real return in different
countries should be the same, so that if one country has a higher nominal interest rate, the gain from
investing in that currency will be lost by a deterioration of its exchange rate.
The relationship between the percentage change in the spot exchange rate over time and the
differential between comparable interest rates in different national capital markets is known as
the international Fisher effect. “Fisher-open,” as it is often termed, states that the spot exchange rate
should change in an equal amount but in the opposite direction to the difference in interest rates
between two countries. More formally:
S1 − S2
× 100 = i $ − i ¥ ,
S2
where i$ and i¥ are the respective national interest rates, and S is the spot exchange rate using
indirect quotes (an indirect quote on the dollar is, for example, ¥/$) at the beginning of the period (S1)
and the end of the period (S2). This is the approximation form commonly used in industry.
The precise formulation is:
S1 − S2 i $ − i ¥
.
=
S2
1+ i¥
Empirical tests using ex-post national inflation rates have shown the Fisher effect usually
exists for short-maturity government securities such as treasury bills and notes. Comparisons based
on longer maturities suffer from the increased financial risk inherent in fluctuations of the market
value of the bonds prior to maturity. Comparisons of private sector securities are influenced by
unequal creditworthiness of the issuers. All the tests are inconclusive to the extent that recent past
rates of inflation are not a correct measure of future expected inflation.
15
c)
Cho-Cho-San should compare the forward premium/discount to the difference in national rates:
f$ =
¥117.8 − ¥118.6 360
×
= −1.349% (the US$ is selling forward at a discount of 1.349%)
¥118.6
180
Difference in interest rates =
(3.4% − 4.8%)
= −1.367%
180 ⎤
⎡
⎢1 + (4.8% × 360 )⎥
⎣
⎦
As those are not equal, the covered interest rate parity does not hold and there is an arbitrage
profit opportunity. Since the difference in interest rates is negative, change the signs of both the
forward discount and the differential in interest rates from the equations above to their opposite
ones. As interest rate difference (1.367%) > forward discount (1.349%), Cho-Cho-San should
make a CIA by investing in the currency with the higher interest rate, the US$, starting with the
Yen equivalent of $5m ($5m x ¥118.6 = ¥593,000,000). The Japanese yen is the funding
(borrowing) currency, while the US dollar is the investment currency.
Japanese yen interest (6-month)
3.4% p.a.
START
¥593,000,000
↓
↓
↓
↓
↓
Spot (¥/$)
118.60
↓
↓
↓
$5,000,000
Sign forward
contract
→
→
(1+3.4% x 180/360 = 1.017)
END
→
→
---------------> 180 days ---------->
→
→
(1+4.8% x 180/360 =1.024)
→
→
¥603,081,000
¥603,136,000
¥55,000
↑
↑
↑
F-180 (¥/$)
117.80
↑
↑
↑
$5,120,000
4.8% p.a.
U.S. dollar interest (6-month)
The arbitrage profit potential is ¥55,000.
16