IBF/AIBD/FDI:
Sample Exam Questions
Below I list exam questions below have been used in the recent past and do not show up as quizz or
exercises in the textbook. There is, of course, no guarantee whatsoever that future exam questions will be
drawn from this list or from the textbook.
This file covers all chapters of the textbook. You may wish to select the relevant chapters rather than
printing out all pages.
Chapter 1:
Spot markets
Q. Suppose the following rates relative to the USD apply:
DEM/USD
FRF/USD
1.50-1.51
5.00-5.10
•
What are the synthetic FRF/DEM rates?
bid:
ask:
•
What can you say about the (direct) FRF/DEM rate?
Q. a. Would a market maker, when (s)he is being asked for a quote for a very large transaction, increase
the spread or decrease it (relative to spreads that hold for ordinary transactions)?
b.
Are spreads larger in more volatile markets, or smaller? Why?
Q. What is the difference between a market maker and a broker?
Chapter 2:
Perfect-Market Forwards
See also Ch4
Q.
a. What do you think of the following: "At the time you sign the forward contract, hedging does not
affect the market value of the firm because this just adds a zero-value contract to the existing activities."
b.
What do you think of the following: "When forward markets exist, the currency in which you express
export prices is immaterial. If you invoice in FC, you can transform your FCT inflow into a HCT
inflow at no cost; and if you invoice in HC, the customer can transform his/her HCT outflow into a
FCT outflow at no cost. Since at a given moment ther is just one forward rate, it does not matter who
does the transformation from one currency into another."
c.
Suppose you need to value an incoming cashflow of one unit of FC at time T. Three ways are
proposed:
St
1 + r*t,T
(a)
PVt(FCT 1) =
(b)
F
PVt(FCT 1) = 1 +t,Tr
t,T
(c)
PVt(FCT 1) =
Et(S̃T)
1 + E t(R̃t,T )
where Et(R̃t,T ) is the equilibrium expected return on an asset
with the same risk as S̃T.
Discuss each proposal. If you think more than one is acceptable, then demonstrate the equivalence of
these correct proposals.
Q.
Why does it make sense, as a first order approximation, to keep the swap rate constant even though the
spot rate changes slightly?
Q.
Suppose the USD has a higher interest rate than the Euro. Explain, or contradict, the following
statements:
a.
The forward rate (in EUR) will be above the spot because the USD, with its interest-rate advantage,will
appreciate.
b.
The forward rate (in EUR per USD) will be above par because of IRP.
c.
The forward rate (in USD per EUR) will be below par because of IRP.
d.
Because of the higher USD interest rate, investors prefer to invest in USD while bowwowers prefer to
borrow EUR. Therefore there cannot be equilibrium, and the rates will have to change.
e.
With IRP, there can be no money machines (arbitrage opportunities), but in general it would be more
interesting to borrow EUR, rather than to borrow USD and cover the USD outflow forward.
Chapter 3:
Value Forward & implications
Q.
List the arguments in favor of, and the arguments against, using the spot rate when you convert
foreign-currency-denominated invoices into home currency for accounting purposes.
Q. a.
Which is the correct way to value of forward contract? (please check the correct answer(s):)
the replication approach
the binomial approach
the hypallagic utility approach
the hedging approach
none of the above
Explain your choice(s). (No need to to say anything about the box(es) you did not check.)
b.
In perfect markets, the initial value of a forward contract is zero. Does that mean that hedging does not
affect the value of the firm? [If you see many reasons why hedging does matter, then just mention them
briefly, without explaining a lot: you have preciously little space.]
Q.
Unless stated otherwise, assume that markets are perfect: no spreads, no discrininatory taxes, no
default, no information asymmetries.
The value of a forward contract is zero at the moment you sign it. Explain, or contradict, the following
statements:
a.
If the firm's cashflows (other than the ones stemming from the forward contract) are totally unaffected,
a forward hedge will not affect the firm's value.
b.
If the firm's cashflows (other then the ones stemming from the forward contract) are totally unaffected,
a speculative forward transaction will not affect the firm's value.
c.
Since the firm's cashflows (other then the ones stemming from the forward contract) are probably
affected by its decision (not) to hedge, such a decision will affect the firm's value.
d.
Given a HC price offered by the exporter, the customer can always hedge and vice versa. Thus, for any
HC pricing strategy there always exists a FC pricing strategy that is as good. That is, the currency of
pricing does not matter.
e.
Given any HC loan taken up by a firm, there always exists a hedged FC loan with the same proceeds
and the same future outflows. That is, the currency of borrowing does not matter.
f.
In international tenders it does not matter whether the customer asks for own-currency prices, or prices
in the currency of the supplier(s).
g.
It does not matter whether one books FC-denominated assets (or liabilities) at the spot rate or at the
forward rate.
h.
Suppose taxes are discriminatory in the sense that capital gains are not taxed and capital losses are not
tax-deductible, while interest income (expenses) are fully taxable (deductible) Then an investor prefers
to invest in a currency with a low interest rate.
i.
Suppose taxes are discriminatory in the sense that capital gains are not taxed and capital losses are not
tax-deductible, while interest income (expenses) are fully taxable (deductible) Then a borrower prefers
to borrow in a currency with a low interest rate.
Q.
Indicate, in two lines each, five interesting insights, related to corporate finance issues, that can be
obtained from the formula for the valuation of a forward contract.
Q.
The Chief Accountant of your company worries how one should translate a foreign-currency invoice
into home currency. He is pondering the following memo sent by a colleague. How would you advise
him?
"What we want is accuracy—as far as possible, of course. The current spot rate is a better predictor
of the future spot rate than is the current forward rate. [This bit is true—don't argue with this.] It follows
that, for the purpose of translating a foreign-currency invoice, the best rate is the current spot rate. A
related advantage of translating at the current spot rate is that this approach makes clear how
expensive or profitable a forward hedge actually is. The argument goes as follows. Given that—
approximately at least—Et(ST) = St, it follows that the expected gain on a forward contract, Ft,T –
Et(ST), is equal to Ft,T – St, the forward premium. Thus, in accounting for the hedge, one should
show the forward premium as the expected effect (cost or gain) from hedging. This is obtained by
(1) translating at the current spot rate, and (2) showing the forward premium as the cost or gain from
hedging."
Q.
You work for a large and very creditworthy Italian firm, and you need to borrow ITL 1b for 12 months.
A friend advises you to borrow DEM and convert the proceeds into ITL, because the DEM interest
rates are so low:
ITL/DEM: St = 1,000 ; ITL: rt,T = 10% ;
DEM: r*t,T = 4%
There are no spreads, as you can see.
a.
•
Assume the tax rate is 40% (on interest items as well as capital gains or losses). If any of your three
answers, below, depends on an unknown future spot rate, denote it by S̃T.
What will you pay, in 1 year, if you borrow ITL?
•
What will you pay, in 1 year, if you borrow DEM?
•
Which of the two future outlays has the higher present value? Why?
b.
Q.
Suppose that taxes are discriminatory: capital gains on loans are untaxed but capital losses and interest
payments are tax-deductible. What is now your favored currency of borrowing? Why? What is the
(present) value gained by chosing the best currency?
Your firm's list price for product X is BEF 610,000, payable cash on delivery. A French prospective
customer asks your firm to quote a FRF price, with three months' credit (as standard in France), for
immediate delivery. On the foreign-exchange page of this afternoon's Echo de la Bourse you find:
FRF spot 6.1, 30 days 6.05, 90 days 6.00, 120 days 5.98, 180 days 5.95, 360 days 5.92.
a.
Your colleague says that you should just translate at the current rate, 6.10: "This guarantees that this
export deal is as profitable as domestic sales." Why does s/he think that?
b.
What's wrong with this argument?
c.
What's your suggestion and why?
Q. a.
In the text, the following equation plays a major role:
W =
Ft0 ,T
St
–
1+r t,T
1+r *t,T
•
What is "W"?
•
Briefly indicate, using words rather than math, by which (equivalent) arguments the above expression
can be obtained.
•
•
Interpret each of the terms on the right hand side:
St
is …
1+r *t,T
•
Ft0 ,T
1+r t,T is …
b.
In the text we see the following expressions:
=
CEQt(S̃T) (1 + r*t,T) – St (1 + rt,T)
1 + rt,T
[b]
=
Ft,T (1 + r*t,T)
– St
1 + rt,T
[c]
=0.
[a]
[d]
PV[S̃T (1 + r*t,T) – St (1 + rt,T)]
⇒
PVt{[S̃T r*t,T – St rt,T] τ – [St – S̃T] τ} = 0
•
What is the issue? That is, what is being proven here?
•
What is the logic behind equation [a]?
•
What is the logic behind equation [b]?
•
What is the logic behind equation [c]?
•
What is the assumption made to obtain equation [d]?
•
Suppose that the assumption made in [d] is not met. What is the implication?
Chapter 4:
Imperfect forwards
Q.
•
•
b.
a. Interpret the following expressions—for instance, is this a synthetic cross-rate, or what?— and
indicate the corresponding series of transactions on the diagram:
1 + rbid,t,T
Sbid,t
is …
1 + r*ask,t,T
1 + rask,t,T
Sask,t
1 + r*bid,t,T
is …
Home curr.
at t
Foreign curr.
at t
Home curr.
at T
Foreign curr.
at T
Home curr.
at t
Foreign curr.
at t
Home curr.
at T
Foreign curr.
at T
Indicate, for each of the relations below, whether the relation is a no-arbitrage condition, a least-costdealing condition, or neither of these. If you check answer 1 or 2, also describe the transaction(s) you
would undertake if the condition is NOT fulfilled.
no-arbitrage bound
"least cost dealing" bound
•
neither of these.
If the above is some rational bound and the condition is not met, I will …
1 + rbid,t,T
Sbid,t
≤ Fask,t,T is a
1 + r*ask,t,T
no-arbitrage bound
"least cost dealing" bound
•
neither of these.
If the above is some rational bound and the condition is not met, I will …
1 + rbid,t,T
Sbid,t
≤ Fbid,t,T is a
1 + r*ask,t,T
no-arbitrage bound
"least cost dealing" bound
•
neither of these.
If the above is some rational bound and the condition is not met, I will …
1 + rask,t,T
Sask,t
≥ Fbid,t,T is a
1 + r*bid,t,T
no-arbitrage bound
"least cost dealing" bound
•
neither of these.
If the above is some rational bound and the condition is not met, I will …
1 + rask,t,T
Sask,t
≤ Fask,t,T is a
1 + r*bid,t,T
c.
Which bounds from question 1.b does one need to obtain IRP? What additional assumption is made
to obtain the standard form of IRP (the equality, rather than two inequalities)?
d.
What is direction of causality in IRP? That is, which term is caused by which?
Q.a. At 10.00 p.m. a bank offer the following quotes:
BEF/DEM spot 20.500 \ 20.550
BEF interest 90d 4% \ 4.125% (simple annualization)
DEM interest 90d
4.125% \ 4.250%
(simple annualization)
swap quotes 90d –0.64 \ –0.63
(in cents per DEM)
•
is it normal that there is a discount? Isn't the DEM normally at a premium against the BEF?
•
is it normal that the bid discount is larger, in absolute value than the ask discount? Or does one usually
see the opposite?
•
are there any arbitrage possibilities?
b.
By 10.05 p.m. the spot quote has changed to BEF/DEM 20.52 - 20.57. Interest rates have not moved.
Should the bank change its swap rates?
Q. a.
Which is the correct way to value of forward contract? (please check the correct answer(s):)
the replication approach
the binomial approach
the hypallagic utility approach
the hedging approach
none of the above
Explain your choice(s). (No need to to say anything about the box(es) you did not check.)
b.
•
•
•
Q.
Assume the following data:
Spot DEM (in BEF) 20.500 - 20.510
Forward 90 days
20.507 - 20.523
90-day Interest rate (simple, p.a.) BEF
3.80 - 3.925
90-day Interest rate (simple, p.a.) DEM
3.60 - 3.725
What can you say about the value of an outstanding forward purchase contract that still has exactly 90
days to go, and stipulates that you will pay 20.60 per DEM?
Would it have a positive value or a negative one?
Can you also come up with an exact number? If not, why not?
If you can't come up with an exact number, what range of numbers is not unreasonable?
Data:
Spot DEM (in BEF)
Forward DEM 90 days
20.507 - 20.523
90-day Interest rate (simple, p.a.) BEF
3.80 - 3.925
90-day Interest rate (simple, p.a.) DEM
3.60 - 3.725
20.500 - 20.510
In questions a.-e. below, you can ignore taxes.
a.
At 90 days, the DEM trades above par. Does that mean that the market expects the DEM to rise relative
to the BEF? Answer from two perspectives:
•
•
from a theoretical point of view
from an empirical point of view (Chapter 15)
b.
Suppose a Belgian company wants to invest in DEM 90 days. For this and the next question, ignore
the forward quotes above.
At what forward rate would the company be indifferent between the two ways of doing so?
Is this critical forward rate a bid or an ask?
•
•
c. Suppose a Belgian company wants to borrow DEM 90 days.
• At what forward rate would the company be indifferent between the two ways of doing so?
• Is this critical forward rate a bid or an ask?
d.
In b. and c. above, is it possible to be indifferent between the two ways, for both lending and for
borrowing transactions simultaneously?
Is this a freak result due to carefully selected numbers, or is this almost always the case? Why (not)?
e.
Given the forward rates mentioned on top of the page, … [check the correct answer:]
It is expensive to hedge a DEM account receivable (or any asset denominated in DEM)
It is expensive to hedge a DEM account payable (or any liability denominated in DEM)
There is no cost whatsoever associated with hedging either A/P not A/R.
Explain you answer:
f.
In questions a.-e. below, you were asked to ignore taxes.Suppose there are taxes. Under what
conditions are the above answers still valid? (no proof)
Q. You are given the following data:
Spot rates
a.
DEM/USD: 1.500-1.510
USD/GBP
0.600-0.605
180-day interest rate
DEM
6.00-6.25%
(simple p.a. percentage) USD
6.00-6.25%
GBP
6.00-6.25%
What are the bounds on the DEM/USD forward rate for 180 days? (It is all right to count 180 days as
half a year.)
bid:
ask:
b.
What are the bounds on the USD/GBP forward rate for 180 days?
bid:
ask:
c.
Given your excellent answers to questions 1.a. and 1.b., I'm sure you could derive bounds on the
DEM/GBP 180-day forward rate using spot and interest data. But one could also set bounds (on the
forward rate) using a kind of triangular arbitrage approach. Spell out the logical steps, explain clearly
whether you use pure arbitrage or least-cost-dealing arguments, and do the actual computations:
bid:
ask:
Q.
Use the following data:
Spot rates
180-day interest rate
(simple p.a. percentage)
DEM/USD:
USD/GBP
DEM
USD
GBP
1.500-1.510
0.600-0.605
6.00-6.25%
6.00-6.25%
6.00-6.25%
a.
Suppose there are no taxes. Compute the forward rate that would make you indifferent between a
DEM loan and a covered USD loan.
b.
Could one conclude, on the basis of an efficient-markets argument, that the actual forward rate should
be equal to the rate you computed in question 2.a.? Why, or why not?
d.
Evaluate the following statement: "Since interest income is taxable and interest costs are deductible
from your taxable profits, the rates relevant for corporate decision-making are after-tax interest rates.
However, corporate tax rates differ across countries. As after-tax interest rates are different to players
from different countries, the usual arbitrage argument breaks down, and there is no easy way to predict
how the forward rate differs from the spot rate."
Q. The data for this question are:
Interest rate (simple, per annum)
BEF/AUD rate
BEF
spot
25.00-25.05
—
90days
24.87-24.93
3.00-3.25
180days
24.68-24.76
3.50-3.75
AUD
—
5.00-5.25
6.00-6.25
a.
Compute, to four decimal digits, the synthetic forward rates, 90 days:
b.
Compute, to four decimal digits, the synthetic forward rates, 180 days:
c.
Check the correct answer(s). Check at least two boxes.
there are arbitrage opportunities in the 90-day markets;
there are arbitrage opportunities in the 180-day markets;
there always are arbitrage opportunities in markets with spreads; arbitrage opportunities can be absent
only in perfect markets;
there are no least-cost dealing opportunities al all, with these data;
none of the above are true;
the sun is probably shining on some spot on earth. (You get no marks for this one, but it probably
helps that you know you've got at least one answer right.)
d
Keep this question for last, as it is probably the trickiest one. For your convenience, I repeat the data:
Interest rate (simple, per annum)
BEF/AUD rate
BEF
AUD
spot
25.00-25.05
—
—
90days
24.87-24.93
3.00-3.25
5.00-5.25
180days
24.68-24.76
3.50-3.75
6.00-6.25
You have just received AUD 1m from a customer. You need to pay AUD 500,000 in 90 days, and you
also need to make a large payment in BEF in 180 days. You don't want to incur any exchange risk, but
you don't know what to do best:
• convert the entire AUD 1m into BEF, spot,
• keep all of the AUD for 90 days,
• keep all of the AUD for 180 days,
• keep some of the AUD for 90 days and convert the rest into BEF, spot
What is your decision, and why?
Q. You know that, in perfect markets, the value of a forward (purchase) contract at an 'old' contract price is
given by
St
X
1+r t,T - 1+r *t,T
How would you identify the bounds on the market value if there are bid-ask spreads in the exchange
markets, and bid-offer spreads in the interest rates? Hint: apply the Law of the Worst Possible
Combination to the above formula, and carefully spell out the transactions that correspond to each
extreme version.
Q. (This question is far less tricky than it looks at first sight.) You know that, in perfect markets, the value
S
X
of a forward (purchase) contract at an 'old' contract price is given by 1+rt
. In this
t,T
1+r *t,T
question, we are looking for the bounds on the value when there are spreads. Suppose you want to get
out of an ‘old’ forward purchase contract. One way to settle the value is to figure out the cost to you, if
you close out in the money market.
•
•
•
The purchase means that you receive FC 1 and pay HC X at time T. To close out, you could form an
offsetting money-market position that generates a FC 1 outflow and a HC X inflow. You can compute
the immediate cashflow implications as follows
invest
to generate a FC 1 outflow at time T, you
{OO borrow
} an amount FCt = ..........
bid,t
which can be converted into HC at
{OO SSask,t
O inflow
and generates a HC { O outflow} of ..............
O invest
to generate a HC X inflow at time T you { O borrow} an amount HCt = ...........
so the net (combined) time-t flow from all this is .................................
•
You could also close out in the forward market.
•
to generate a FCT = 1 outflow, you
•
at the forward rate
•
The time-T net cashflows are
old contract
new contract
buy forward
{OO sell
forward }
bid,t,T
{OO FFask,t,T
.....
in FC
in HC
=====
=====
units of FC
total
•
How can you make the time-t flow of the first alternative comparable with the time-T flow of the
second alternative?
Q.
The following quotes are given to you (with the DEM as home currency):
DEM/USD
spot
1.600-1.650
180d
1.615-1.670
DEM interest rate 180d 6-6.5
(simple p.a. rate)
USD interest rate 180d 4-4.5
(simple p.a. rate)
a.
Suppose you need to invest some DEM for 6 months. What is the best alternative? Ignore taxes.
b.
Suppose capital gains and interest income are taxable (and capital losses or interest expenses taxdeductible) at 40%. How does this change your answer?
c.
Suppose that capital gains are no longer taxable (and capital losses no longer tax-deductible), but that
interest income is still taxed at 40%. How does this change your answer?
Q.
Data: DEM banker's discount rate 8% p.a.; exchange rates spot 20.5-20.55, 90 days 20.7-20.76;
BEF borrowing rate on the secured loan 9.25% p.a. simple interest; BEF deposit rate 8.75% p.a.,
simple interest.
You have drawn a DEM 100,000 90-day trade bill on a customer, which you want to convert into cash
money (BEF).
a.
•
•
in the absence of credit risks, will you
discount the DEM bill and convert the proceeds, or
sell forward the DEM 100,000, use the bill and the forward contract as security for a BEF loan against
the future proceeds?
b.
Is there any difference as far as credit risk is concerned? Exchange risk?
Q.
Data:
DEM/USD
FRF/USD
Spot bid/ask
1.5
1.505
5.0
5.010
USD
Interest rates (simple, per annum) 90 days
DEM 4%
4.125%
FRF 4.125%
4.25%
3.75% 3.875%
a.
You are asked to compute bounds on the 90-day DEM/FRF rate. Colleague X tells you to compute
bounds on the DEM/FRF spot rate and then to derive, from these, the bounds on the forward rate.
Colleague Y, in contrast, says that you should first compute bounds on the DEM/USD and FRF/USD
forward rates, and then use triangular arbitrage to obtain bounds on the DEM/FRF rate.
•
Does X's suggestion make sense? If so, implement it.
•
Does Y's suggestion make sense? If so, implement it.
•
If both suggestions make sense, what is the difference (if any) and where is it coming from?
b.
A German firm wants to borrow USD to finance a DEM expense. How would it identify the best
way? (If you need an actual forward quote, just write the appropriate symbol, Fbid or Fask, and indicate
how your decision would be made.)
b.
A German firm wants to invest USD. How would it identify the best way? (If you need an actual
forward quote, just write the appropriate symbol, Fbid or Fask, and indicate how your decision would be
made.)
Q.
Suppose you face the following data:
Spot rate BEF/CAD
Forward 180 days
Interest 180d (p.a.) BEF
Interest 180d (p.a.) CAD
19.95
19.75
4%
6%
- 20.00
- 19.81
- 4.125%
- 6.125%
a.
Verify that there are no arbitrage opportunities to a normal tax-paying player.
b.
Suppose you pay taxes on interest received, and that interest paid is tax-deductible, but that capital
gains (losses) are not taxed (tax-deductible). Are there any arbitrage opportunities?
c.
Go back to the situation with normal (non-discriminatory) taxes. You have an old forward purchase
contract outstanding, maturing in 180 days, at a historic forward rate of 23 BEF/CAD. You want to
close out this old contract. In light of the above data, how would you do this—by selling forward, or by
synthetically selling forward?
Chapter 9:
Bond & Money Markets
Q. Briefly list the roles that banks could play in a eurobond issue (not a syndicated euroloan).
Q. Briefly list the roles that banks could play in a syndicated euroloan.
Q. Suppose that, six months ago, the 6 against 9 month forward rate on GBP was 10% (simple, p.a.).
a.
•
•
You signed a FF for a deposit of GBP 1m. Today, 3-month LIBOR is 9%. What cashflows will take
place
now?
within three months?
b.
•
•
Suppose you contract was a FRA rather than an FF. What cashflows will take place
now?
within three months?
c.
What would have been the price, six months ago, of a forward contract, expiring at T1 = six months
from that date, on a CD maturing at T2 = nine months from that date?
d.
What would have been the quote, six months ago, of a standard Euro-GBP futures contract, expiring at
T1 = six months from that date, on a CD maturing at T2 = nine months from that date?
e.
Is there any role for all these contracts, given that we can construct synthetic FFs from 6- and 9-month
money market operations?
Chapter 10:
Swaps
Q. How does one price the floating-rate leg of a swap?
Q.
Below, please find three tentative definitions for a modern currency swap. None of them is perfect.
Point out what is missing or wrong in each definition.
a.
A swap is a simultaneous spot and forward contract, both for the same currency and the same amount,
but in opposite directions.
b.
A swap is a simultaneous spot and forward contract, both for the same currency and the same amount,
but in opposite directions; in addiition, also the interest on the two amounts is being paid.
c.
A swap is something that transforms a currency-A loan into a currency-B loan.
Q. You work for a small, highly specialized Belgian engineering company. Your firm has just signed an
export contract with a new US customer for a turn-key plant, valued at USD 10m spot. However,either
you or your customer needs a loan to finance the investment. You can borrow BEF for 5 years at 10%
or USD at 8%, while the customer can borrow USD at 9%. Being a small firm without many
diversification opportunities, you want to avoid exchange rate exposure—that is, you prefer BEF
inflows, or, if the customer pays USD, you prefer a USD loan. The 5-year swap interest rates are 8%
and 6% on BEF and USD, respectively, and the spot rate us BEF/USD 30.
a.
Assuming that you extend 5 years credit to the customer and get a loan to finance the contract, is there
any useful role for a swap? In explaining your answer, please show the cashflows that arise when you
use a swap.
b.
Given the above data, should you get the loan, or should the customer be the party that borrows?
Carefully weigh pros and cons of each alternative.
Q. You can borrow BEF for 5 years at 7%, and AUD at 9%. The 5-year swap rates are 6% (BEF) and 7%
(AUD). The spot rate is BEF/AUD 25.
a.
Will you be interested in a swap if you have a preference for BEF loans? Why? No calculations,
please.
b.
Will you be interested in a swap if you have a preference for AUD loans? Why? No calculations,
please.
c.
Suppose you do want to borrow BEF and swap. Before seeing your swap dealer you prepare the
following table:
BEF loan
Initial principal
annual interest
swap: BEF leg Swap: AUD leg
BEF 100m
<BEF 100m>
<BEF 7m>
BEF 6m
final amortization <BEF 100m>
BEF 100m
total
AUD 4m
<AUD 0.28>
+ <BEF 1m>
<AUD 4m>
AUD 4m
<AUD 0.28>
<AUD 4m>
But your swap dealer laughs heartily. "I see that Sercu did not hand out the correction to the above
solution that he has promised during the class. In practice, one often swaps the entire BEF loan into
AUD, that is, the BEF leg of the swap stipulates a payment of BEF 7m in annual interest, not 6m; and
the AUD interest income from the swap is increased to"—she quickly punches some numbers on her pocket
calculator—"8.0273563. So your table becomes
BEF loan
swap: BEF leg Swap: AUD leg
total
Initial principal
BEF 100m
<BEF 100m>
AUD 4m
annual interest
<BEF 7m>
BEF 7m
<AUD 321.094>
final amortization <BEF 100m>
BEF 100m
<AUD 4m>
AUD 4m
<AUD 321.094>
<AUD 4m>
As you see, this messy BEF 1m in the total interest payments is nor gone."
•
Is the proposed swap a fair deal? Why? (Hint: think of a crucial property that a swap shares with a
forward contract.)
•
In the above example, the BEF interest payments under the swap contract have been increased by 1%
(from 6 to 7%), and the AUD interest payments by somewhat more than 1% (from 7 to 8.0273563%).
Is it always the case that the foreign-currency interest payment is increased by more than the domestic
one? If so, why? If not, what kind of data would mean that the change in the AUD interest payments is
lower than the change in the BEF interest payments?
Q. A friend in the Domus (a Leuven café) claims that a fixed-for-fixed currency swap is just a combination
of many forward contracts plus, often, a spot contract. You decide that your friend either does not
know exactly what a swap is, or has had too much beer. (The Domus boasts a beer list with about 80
different entries). That is, you disagree. Why?
Q. Swap dealers set their swap rates close to the riskfree yields at par for the currency and maturity of each
leg of the (fixed-for-fixed) swap. Yet the companies they are dealing with cannot borrow at nearriskless rates. Is this way of setting the swap rates irrational?
Q. You can borrow DEM 1m for five years, with a single final amortization, at 10% per year, and BEF at
9%. The swap rates are 8.5% in DEM and 9% in BEF. De spot rate is BEF/DEM 20. Show that its is
advantageous to borrow BEF, and then swap, rather than to borrow DEM.
Cash flows if
Cash flow when borrowing BEF and swapping to DEM
borrowing DEM BEF-loan Swap: BEF Swap: DEM Total
Gain
initial
principal
annual
interest
final
principal
Q. You company wants to borrow DEM 1m for 5 years (annual interest payments, 1 amortization at
expiration). It can get a DEM loan at 10% (the spot rate is BEF/DEM 20), and a BEF loan also at
10%.
a.
Assuming the swap rates are 8% in DEM and 9% in BEF, is there any point in borrowing BEF and
swapping? What are the annual savings, if any, if the spot rate is BEF/DEM 20?
b.
If you think there are savings, do these reflect a money machine, or a market inefficiency, or something
else?
Q. Suppose you borrow BEF 50m for 5 years at 10%, with a single amortization at the end, and then swap
this loan into DEM at the swap rates of 9% (BEF) and 7% (DEM). The current spot rate is BEF/DEM
20.
a.
What are the annual cashflows?
loan
swap:BEF
swap:DEM
total
at inception (t)
interest payments
final amortization (T)
b.
Do you think it could actually be interesting to swap this BEF loan into DEM, rather than taking out a
DEM loan? More precisely, for what DEM borrowing rates would this be interesting?
c.
Are there any reasons why DEM borrowing rates could actually be such that s swapped BEF loan is
better than a DEM loan?
Q. A fixed-for-floating swap is usually valued using a formula

1 + R

1 – (1 + yt,T )–n
Value = Vnom  1 + (s – yt,T )
(1+yt,T )τ – Vnom  1 + Rt0,T1 

y


t,T

t,T1 
where Vnom is the nominal or notional value, s is the effective swap rate paid per interest period (one
year, or six months, etc.), t is the date of valuation (current time), yt,T is the effective per-period yieldat-par for near-riskless investments at time t maturing at T, n is the number of remaining interest
payments, τ is the fraction of a period elapsed since the last interest payment, Rt0,T1 is the effective
short-term riskfree rate at the most recent re-set date (t0) until the next re-set date (T1), and R t,T1 is the
current effective risk-free return until the next re-set date.
a.
Why is the principal of such a swap called notional (theoretical, hypothetical)?
b.
How can the first part of the formula (that relates to the fixed-rate leg of the swap) be reconciled with
the modern approach to bond valuation, where one uses a different interest rate for each payment date
rather than a single, flat internal-rate-of-return-type discount rate like yt,T ? Just state the result in
words, you don't need proofs or numerical examples.
c.
What is the link between s and the initial yield at par (that is, the yield at par when the swap is initiated,
or started)?
d.
How is it possible that the second part of the formula (that relates to the floating-rate leg of the swap)
totally ignores the interest payments beyond date T1?
e.
How would you modify the formula for the case of a fixed-for-floating currency swap? Assume that
the floating-rate leg is in foreign currency, and indicate the changes, below:

1 + R

1 – (1 + yt,T )–n
Value = Vnom  1 + (s – yt,T )
(1 + yt,T )τ – Vnom  1 + Rt0,T1 

y


t,T

t,T1 
Q. Your (Belgian) company has just signed an export contract where the foreign customer pays USD 10m
five years from now. The customer agrees to pay either USD LIBOR+2% as annual interest, or 11%
fixed; you have a few days to make up your mind about that 'detail', as he calls it. You need (BEF) cash
now, to finance production; also, you want to hedge this rather big and long-term USD position. You
can borrow fixed-rate BEF from Copromex at 8%, and fixed-rate USD from your bank at 10% (these
rates are for 5-year loans, amortized at the end). You can also borrow floating-rate BEF at BEF LIBOR
+ 2%. You can, finally, swap 5-year USD vs BEF fixed-to-fixed at USD 9% and BEF 10%, or fixedto-floating at the above swap rates (BEF or USD) and LIBOR (USD or BEF).
a.
Why is it clear that you should borrow 5-year fixed-rate BEF from Copromex, even though such a
loan would not hedge the USD A/R.
b.
Suppose we hedge with a swap; should we opt for a fixed-rate or a floating-rate interest scheme for the
customer, and which swap is 'best' (in the sense of minimizing uncertainty about the BEF cashflows):
fixed-to-floating, or floating-to-floating, or fixed-to-fixed?
•
suppose you instruct the customer to pay a floating-rate interest (USD LIBOR + 2%): the best swap
then is ........... to .........., and it works out as follows:
Loan
incoming
Swap
outgoing
A/R
Total
principal
interest
principal
•
suppose you instruct the customer to pay a fixed-rate interest (11%): the best swap then is ........... to
.........., and it works out as follows:
Loan
incoming
Swap
outgoing
A/R
Total
principal
interest
principal
•
your conclusion:
Q. Suppose you borrow BEF 50m for 5 years at 10%, with a single amortization at the end, and then swap
this loan into DEM at the swap rates of 9% (BEF) and 7% (DEM). The current spot rate is BEF/DEM
20.
a.
What are the annual cashflows?
loan
at inception (t)
interest payments
final amortization (T)
swap:BEF
swap:DEM
total
b.
Do you think it could actually be interesting to swap this BEF loan into DEM, rather than taking out a
DEM loan? More precisely, for what DEM borrowing rates would this be interesting?
c.
Are there any reasons why DEM borrowing rates could actually be such that s swapped BEF loan is
actually better than a DEM loan?
Q. You want to borrow DEM 5m for 5 years with one single amortization of the principal at the end. You
can do this at 7% (payable annually). You can borrow BEF at 6.5% (payable annually). The swap rates
are 6% (DEM) and 5.5% (BEF). The spot rate is 20. The 5-year annuity factors are: a(5 year, 5%) =
4.3294766 ; a(5 year, 5.5%) = 4.2702844 ; a(5 year, 6%) = 4.2123638 ; a(5 year, 7%) = 4.1001974.
a.
Why should you borrow BEF 100m and swap rather than borrowing DEM 5m?
b.
What interest rate would the swap dealer ask on a DEM loan if you swap the entire BEF loan into
DEM (that is, the swap should eliminate all BEF liabilities)?
c.
Suppose you are offered an outstanding swap contract that has exactly 5 years to go. This old contract
stipulates 7% interest on BEF 100m, and a 5% interest on DEM 5m.
Will you have to pay for this old contract, or will you be paid? Why? (you can answer this without any
computations) (just use your common sense) (sorry for making things difficult)
What is the value of the old contract?
•
•
Q. a.
b.
Under what circumstances can it be useful to borrow home currency and then swap the loan into foreig
currency, instead of immediately borrowing foreign currency?
How does one discover and quantify whether it is advantageous to borrow home currency and then
swap the loan into foreign currency, instead of immediately borrowing foreign currency?
Chapter 11:
PPP
Q. In the end-August 1995 issue of The Economist there was a graph showing that Big Macs tend to be
more expensive in countries with a current-account surplus, and vice versa. Is this a coincidence, or do
you think there is (are) economic mechanism(s) behind this empirical observation?
Q. We see that periods of low (real) exchange rates of the USD relative to the DEM and the JPY tend to
trigger direct foreign investment into the US, and vice versa. Does this suggest that businesspersons
have a strong belief in PPP or not?
Are we talking about Absolute PPP or Relative PPP?
Q. As a business man, would you rather live in a world where PPP holds all the time, or in a world where
there are substantial and long-lived deviations from PPP?
Q. Suppose the UN proposes to replace all currencies by a single world currency. As a business man,
would you be in favour of such a plan? Why or why not? (Give pros and cons, and your overall
opinion.)
Q. We observe, empirically, that periods of low (real) exchange rates of the USD relative to the DEM and
the JPY tend to trigger foreign direct investment into the US, and vice versa. Does this suggest that
businesspersons have a strong belief in PPP or not? Are we talking about Absolute PPP or Relative
PPP?
Q. Check the correct answer(s).
Purchasing power parity (PPP) is a joke. In reality, exchange rates are not at all attracted towards the
PPP level.
The above statement is roughly equivalent to saying that the direction of the next change in the real
exchange rate is independent of the current value of the real exchange rate.
PPP does not hold in the short run, but it does hold in the long run. Specifically, over very long
intervals, the percentage exchange rate change equals the inflation difference between the two countries'
inflation rate over that entire period.
PPP does not hold in the short run, but it does hold in the long run. Specifically, over very long
intervals, the percentage exchange rate change equals the ratio of [unity plus domestic inflation over
that entire period] and [unity plus foreign inflation over that entire period].
PPP does not hold in the short run, but it does hold in the long run. Specifically, over very long
intervals, the variance of the difference between the percentage exchange rate change and the inflation
difference (between the two countries' inflation rate over that entire period) increases less than
proportionally with time.
None of the above are true.
If you think that none of the above three definitions of long-run PPP is correct, write down, below, a correct
definition of long-run PPP, using bits and pieces from the above.
Q. Suppose that the USD is currently undervalued by PPP standards.
a.
What are the implications for short-term portfolio investments: should I buy USD T-bills?
b.
What are the implications for long-term portfolio investments: should I buy USD bonds?
c.
What are the implications for direct investments: should I build a factory in the US?
Q. The PPP-rate fluctuates far less than the actual rate. Can we conclude from this that financial markets
are crazy, and generate excess volatility?
Q. PPP is a hypothesis that says that the average price for a large number of goods should be similar
across countries, after translation into a common base currency.
a.
Is this this a more reasonable assumption than Commodity Price Parity (which says that there should
be such a parity for individual goods)?
b.
Mention some reasons why PPP may fail in practice.
c.
Does PPP work in practice? In what sense (not)?
Q.
Explain or contradict: "In many ways, relative PPP is more general than absolute PPP."
See also under "miscellania" at the end.
Chapter 14:
Risk and return
Q. Your banker tells you that, in the past, the total
a.
b.
return on CHF (capital gains plus interest) were
significantly below the returns on BEF deposits.
can you conclude from this that the CHF forward rate on average overestimates the future spot rate?
Why (not)?
Does the above have any implications as to the relevance of hedging CHF A/R? A/P?
Q. a.
If there is a 1% forward premium, then on the basis of past empirical evidence you best bet is that
the currency will
rise by far more than 1%
rise, but by less than 1%
drop
none of the above
b.
One of the explanations of the above empirical finding is that it is caused on transaction costs. In the
view, people bet in the forward markets only if there is a clear and large signal about what the spot rate
will do. Suppose you want to test this explanation. How would you do it?
Chapter 15:
Predicting Exchange Rates
Chapter 16:
Relevance of Hedging
Q. a. What do you think of the following: "Because interest payments are tax-deductable, borrowing in a
high-interest currency brings with it a larger tax shield than borrowing in a low-interest currency.
Therefore, the PV of a firm that borrows in a high-interest currency is higher."
b.
What do you think of the following: "A firm with a progressive tax rate will pay more taxes, on
average, the higher the variability of the profit; therefore, hedging reduces average taxes and increases
the firm's market value. But in practice firms are facing a flat tax rate rather than an increasing one, so
that in practice hedging does not affect taxes at all."
See also under "miscellania" at the end.
Chapter 17:
Transaction Exposure
Q. Suppose you hold an option on USD as a speculative investment. There clearly is exposure. Would
you classify it as "operating" or "transaction" exposure?
Q.
a. What is transaction exposure?
b.
How do you measure it?
c.
Suppose a firm covers all of its transaction exposure. Is it now totally immune to changes in exchange
rate changes?
Q.
Suppose you want to hedge, with a single forward contract or money-market hedge, a number of FCdenominated cashflows that do not all have the same expiry date. What problem does arise—or, what
extra risk needs to be taken care of?
Chapter 18:
Economic Exposure
Q. Suppose that, today, you have to submit a bid for an international tender, in BEF. Your only competitor
is a French company, and you know the (FRF) bid they have submitted. The buyer will decide one
month from now, and then pay immediately.
•
•
If next month's BEF/FRF rate were fully known, your decision would be easy. The problem is that the
FRF may devalue (to BEF/FRF 5.8), or stay at its current level (BEF/FRF 6). Thus, you hesitate
between two possible bids:
either you submit a low BEF price, so that you surely win the tender even if the FRF devalues. This
gives you a sure profit of BEF 1m on the transaction.
or you submit a higher BEF price. Then you win (and make a profit of BEF 2m) if the FRF does not
devalue between now and next month, but you lose (and make no profit) if the FRF does devalue.
a.
Check the answer that looks most true to you. If you hestitate between two answers, you can check two
boxes, and then use the space below (and only the space below) to explain why you hesitate.
If you submit the high (risky) bid, you are not exposed: the price is in BEF.
If you submit the high (risky) bid, there is transaction exposure.
If you submit the high (risky) bid, there is operating exposure.
b.
Check the answer that looks most true to you. If you hestitate between two answers, you can check
two boxes, and then use the space below (and only the space below) to explain why you hesitate.
Suppose you submit the higher BEF price, so that there is uncertainty. To hedge against the
uncertainty, you should use a forward contract rather than an option.
Suppose you submit the higher BEF price, so that there is uncertainty. To hedge against the
uncertainty, you should use a an option rather than forward contract.
In this particular case it does not matter whether one uses an option or a forward contract.
Neither an option nor a forward hedge will do, because the bid is in BEF.
You actually need a forward-to-tender contract.
c.
The one-month riskfree interest rate in BEF is 6% per annum (simple interest), and in FRF the rate is
9% p.a.. The current spot rate is BEF/FRF 6.00. What is the decision with the highest value: to submit
the high (risky) bid, or the low (safe) bid? Why?
d.
In the example above, do you see any reason why the firm should hedge? If there is no clue in the text,
what possible reasons could prompt the firm to hedge? (A brief list of key words suffices.)
Q. We all know that hedging contractual exposure is not generally sufficient, one needs to think about
operating exposure, too. However, the hedging of transactions exposure is much easier than the
hedging of operation exposure.
Q.
What are the practical problems you encounter when trying to hedge operating exposure?
Mini-minicase. You are taking part in an international tender. The buyer will take a decision three
months from now, and will pay one week later (that is, you van ignore the time difference between the
decision date and the payment date). Your production cost is BEF 5m, payable three months from now
(at the time of production) if you do win.
•
•
•
a.
b.
c.
d.
By means that I will not reveal to you, you happen to know that your only competitor has submitted a
price of FRF 1m. You can submit prices in any currency. The FRF currently trades at BEF/FRF 6, and
per annum simple 3-month riskfree interest rates are 4% on BEF and 7.395% on FRF, respectively, so
that the three-month forward rate is below par. Bankers tell you that the FRF may, in fact devalue to
BEF/FRF 5.75. Thus, the only two possible rates at time T are 6 and 5.75. You hesitate between the
following:
submit a price of FRF 999,999 and win for sure
submit a price in BEF, FRF 999,999 × BEF/FRF 5.75 = BEF 5,749,994, and win for sure (even if the
FRF devalues)
submit a price of BEF 5,999,999 and win when the FRF does not devalue / lose when the FRF does
devalue.
Questions:
In what case is there an exposure?
How could you hedge e
What is the value-maximizing strategy?
If you chose the first or third, what about the risk?
Q. a. Which should you be more worried about, accounting exposure or transaction exposure? Why?
b.
Suppose that the exposure of your firm's cashflows is summarized as follows:
If ST =
20
20.5 21.0 21.5
then Et[CFT|ST)
100
120
160
220
Discuss verbally the ways you can hedge this, with pros and cons. No computations needed.
Miscellanea
Q. Check the statements that you agree with. If you do not agree (or do not quite agree), explain why (in
no more than two lines).
O
Hedging matters because it reduces the risk of the operating cashflows at a low or zero cost
O
Hedging does not matter because adding a zero-value contract cannot possibly alter the value of the
firm
O
Hedging does not matter because the forward rate equals the expected future spot rate
O
Hedging matters because the forward rate is a biased predictor of the future spot rate
O
It is possible that Absolute Purchasing Power Parity holds while Relative Purchasing Power Parity
does not hold.
O
An increase in the money supply strengthens the currency of the country, everything else held
constant.
O
An increase in economic activity stimulates inflation, everything else held constant.
O
An increase in the value of the stock market due to an exogenous event has a negative effect on foreign
exchange rates, because people sell foreign exchange in order to buy more of the stock.
O
Exchange risk does not matter, because purchasing power parity holds quite well.
Q. Each of the following claims is not generally correct. Give, however, an example where the claim is
correct indeed.
a.
Claim: hedging is never relevant because adding a contract with zero value cannot change the value of
the firm.
Your example:
b.
Claim: If you quote a price, payable within 90 days, to a German customer, it does not matter whether
you quote a BEF price or a DEM price.
Your example:
c.
If the interest rate on BEF is lower than on ITL, you should borrow ITL rather than BEF because it
produces a higher corporate tax shield from deductible interest.
Your example:
d.
It is quite normal to show, in the financial statements, the asset and the liability implicit in a forward
contract at a zero net value. After all, the value of a forward contract is zero.
Your example:
e.
In case of an international tender, it does not matter whether bids are to be expressed in the buyer's
currency or not,
Your example:
Q.
Check the statements that you agree with. If you do not agree (or do not quite agree), explain why (in
no more than two lines).
O
Hedging matters because it reduces the risk of the operating cashflows at a low or zero cost
O
Hedging does not matter because adding a zero-value contract cannot possibly alter the value of the
firm
O
Hedging does not matter because the forward rate equals the expected future spot rate
O
Hedging matters because the forward rate is a biased predictor of the future spot rate
O
Hedging does not matter because the forward rate is the certainty-equivalent of the future spot rate
Q.
Each of the following claims is not generally correct. Give an example where the claim is wrong
indeed.
a.
Claim: hedging is never relevant because adding a contract with zero value cannot change the value of
the firm.
Your counter-argument:
b.
Claim: If you quote a price, payable within 90 days, to a German customer, it does not matter whether
you quote a BEF price or a DEM price.
Your counter-argument:
c.
If the interest rate on BEF is lower than on ITL, you should borrow ITL rather than BEF because it
produces a higher corporate tax shield from deductible interest.
Your counter-argument:
d.
It is quite normal to show, in the financial statements, the asset and the liability implicit in a forward
contract at a zero net value. After all, if there's default on your liability, your asset disappears, too,
because of the right of offset.
Your counter-argument:
e.
In case of an international tender, it does not matter whether bids are to be expressed in the buyer's
currency or not, because a forward hedge is available at no cost.
Your counter-argument:
f.
Options are superior, as hedging instruments, relative to forward contracts because they leave open the
possibility of gains while eliminating the downside risk.
Your counter-argument:
Q.
[This question requires a fair amount of computations; you can however get most of the grades by first
showing what you would compute and how, and then working out the actual computations afterwards
if and when you have enough time left.]
Suppose you are a banker, and you want to hedge an investment in an annuity loan that pays out four
equal annuities of ATS 10m, in years t+1, t+2, t+3, and t+4 respectively. You also need cash. In short,
you want cash BEF instead of future ATS.
a.
•
•
•
b.
The spot rate is BEF/ATS 2. The forward rates are
maturity
(spot)
T=t+1
t+2
t+3
t+4
BEF/ATS (2.00)
1.923
1.850
1.780
1.711
Assume that, for 4-year annuity-type loans, your bank can borrow, in the interbank market, BEF at
13% compound per annum, and ATS at 17.5% per annum. Swap rates for 4-year annuity-type loans
are 12% in BEF, and 16% in ATS. Four-year annuity factors — i.e.
4
a(4 years, R) ≡ ∑ j=1
(1+R)–j — are as follows:
R=
8%
12%
13%
16%
17.5%
21%
a(4, R) =
3.31212
3.03735
2.97447
2.79818
2.71643 2.54044
Which of the following is the best way to raise cash BEF against the future ATS income?
Hedge each of the ATS in the forward market, and borrow BEF against the proceeds:
Borrow ATS in the interbank market, and convert spot
Exchange the ATS annuity for a BEF annuity through a swap contract, and then borrow BEF in the
interbank market against the BEF proceeds from that swap.
If the customer to which you granted the ATS annuity loan is not perfectly risk free (that is, there is
credit risk), does this affect you choice?