Currency Swaps
1
Currency Swap: Definition
 A currency swap is an exchange of a liability in one
currency for a liability in another currency.
 Nature:
• US corporation with operations in France can
obtain comparatively better terms by borrowing
dollars, but prefers a loan in euros.
• French corporation with operations in the US can
obtain comparatively better terms by borrowing
euros, but prefers a loan in dollars.
• The two companies could go to a swap bank who
could arrange for a loan swap.
2
Example
 As a example, suppose the British Petroleum Company
plans to issue five-year bonds worth £100 million at
7.5% interest, but actually needs an equivalent amount
in dollars, $150 million (current $/£ rate is $1.50/£), to
finance its new refining facility in the U.S.
 Also, suppose that the Piper Shoe Company, a U. S.
company, plans to issue $150 million in bonds at 10%,
with a maturity of five years, but it really needs £100
million to set up its distribution center in London.
3
Example
 To meet each other's needs, suppose that both
companies go to a swap bank that sets up the following
agreements:
4
Example
Agreement 1:
1. The British Petroleum Company will issue 5-year £100
million bonds paying 7.5% interest. It will then
deliver the £100 million to the swap bank who will
pass it on to the U.S. Piper Company to finance the
construction of its British distribution center.
2. The Piper Company will issue 5-year $150 million
bonds. The Piper Company will then pass the $150
million to swap bank that will pass it on to the British
Petroleum Company who will use the funds to finance
the construction of its U.S. refinery.
5
Example
Agreement 2:
1. The British company, with its U.S. asset (refinery),
will pay the 10% interest on $150 million ($15
million) to the swap bank who will pass it on to the
American company so it can pay its U.S. bondholders.
2. The American company, with its British asset
(distribution center), will pay the 7.5% interest on
£100 million ((.075)( £100m) = £7.5 million), to the
swap bank who will pass it on to the British company
so it can pay its British bondholders.
6
Example
Agreement 3:
1. At maturity, the British company will pay $150 million
to the swap bank who will pass it on to the American
company so it can pay its U.S. bondholders.
2. At maturity, the American company will pay £100
million to the swap bank who will pass it on to the
British company so it can pay its British bondholders.
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Valuation
Equivalent Bond Position
Equivalent Bond Position
 In the above swap agreement, the American company
will receive $15 million each year for five years and a
principal of $150 million at maturity and will pay £7.5
million each year for five years and £100 million at
maturity.
8
Valuation
Equivalent Bond Position
Equivalent Bond Position
 To the American company, this swap agreement is
equivalent to a position in two bonds:
1. A long position in a dollar-denominated, five-year,
10% annual coupon bond with a principal of $150
million and trading at par
2. A short position in a sterling-denominated, fiveyear, 7.5% annual coupon bond with a principal of
£100 million and trading at par
9
Valuation
Equivalent Bond Position
 The dollar value of the American company’s swap
position where dollars are received and sterling is paid
is
SV  B$  E0 B£
where:
B$ = Dollar-Denominated Bond Value
B£ = Sterling-Denominated Bond Value
E0 = Spot Exchange Rate = $/BP
10
Valuation
Equivalent Bond Position
 The dollar value of the swap to the American Company
in terms of equivalent bond positions is zero:
SV = $150 million – ($1.50/£)(£100 million) = 0
11
Valuation
Equivalent Bond Position
 The British company’s swap position in which it will
receive sterling and pay dollars is just the opposite of
the American’s position.
 It is equivalent to a long position in a sterlingdenominated bond and short position in a dollar
denominated bond. In this example, it likewise has a
value of zero.
12
Valuation
Equivalent Bond Position
 If a dealer had been warehousing swaps and provided a
swap to just the American company, then it could have
hedged its swap position of paying $15 million and
receiving £7.5 million by shorting the 7.5% sterlingdenominated bond and buying the 10% U.S. dollardenominated bond.
 Given this hedge, a currency swap, like an interest rate
swap, generally has an economic value of zero when it
is created.
13
Valuation
Equivalent Bond Position
 The zero economic value of the swap positions will
change over time with changes in U.S. rates, British
rates, and the spot exchange rate.
 The value of a dollar received/foreign currency paid
swap is inversely related to U.S. interest rates and the
exchange rate and directly related to the foreign rate.
 The value of a foreign currency received/dollar paid
swap, valued in dollars, is directly related to U.S. rates
and the exchange rate and inversely related to the foreign
rate.
14
Valuation
Equivalent Forward Exchange Position
Equivalent Forward Exchange Position
 Instead of viewing its swap as a bond position, the British company
could alternatively view its interest agreement to pay $15 million for
£7.5 million each year for five years and it principal agreement to
pay $150 million for £100 million at maturity as a series of long
currency forward contracts in years 1, 2, 3, 4, and 5.
 In contrast, the American company could view its swap agreements
to sell £7.5million each year for $15 million and sell £100 million at
maturity for $150 million as a series of short currency forward
contracts.
15
Valuation
Equivalent Forward Exchange Position
Equivalent Forward Exchange Position
 In the absence of arbitrage, the value of the American
company’s swap of dollar’s received/British pounds paid
should be equal to:
1.
The sum the present values of $15 million received each year from
the swap minus the dollar cost of buying £7.5 million at the
forward exchange rate (Eft).
2.
The present value of the $150 million received at year five minus
the dollar cost of buying £100 million at the five-year forward
exchange rate.
 The dollar value of the British position is just the opposite.
16
Valuation
Equivalent Forward Exchange Position
Equivalent Forward Exchange Position
 Note that in the absence of arbitrage, the values of the
swap positions as forward contracts are equal to their
values as bond positions:
($ Re ceived)  E ft (FC Paid)
SV  
 B$  E 0 BFC
t
(1  R US )
t 1
M
17
Comparative Advantage
 The currency swap in the above example
represents an exchange of equivalent loans.
 Most currency swaps, though, are the result of
financial and non-financial corporations
exploiting a comparative advantage resulting from
different rates in different currencies for different
borrowers.
18
Comparative Advantage: Example
Example
 Suppose the American and British companies have
access to both British (BP) and American ($)
lending markets.
 Suppose the American company is more
creditworthy and can obtain lower rates than the
British company in both the US and British
markets.
19
Comparative Advantage: Example
Example:
 Suppose the American company can obtain 10%
U.S. dollar-denominated loans in the U.S. market
and 7.25% sterling-denominated loans in the
British market, whereas the best the British
company can obtain is 11% in the U.S. market and
7.5% in the British market
20
Comparative Advantage: Example
Loan Rates for American and British
Companies in Dollars and Pounds
Spot: E0 = $/£ = $1.50/£
American Company
British Company
Dollar Market
(rate on $)
Pound Market
(rate on £)
10%
11%
7.25%
7.5%
21 21
Comparative Advantage: Example
Example
 The American company has a comparative advantage in
the US market:
 It pays 1% less than the British company in the US
market, compared to only .25% less in the British
market.
 The British company has a comparative advantage in the
British market:
 It pays .25% more than the American company in the
British market, compared to 1% more in the US
market.
22
Comparative Advantage: Example
 When a comparative advantage exist, a swap
bank is in a position to benefit one or both
parties.
23
Comparative Advantage: Example
Example:
 Suppose in this case a swap bank sets up the following
swap arrangement:
1. The American company borrows $150 million at
10%, and then agrees to swap it for £100 million
loan at 7%.
2. The British company borrows £100 million at
7.5%, and then agrees to swap it for $150 million
loan at 10.6%.
24
Comparative Advantage: Example
 The next three exhibit slides show the
initial swap of the principals, annual cash
flows of interest, and final exchange of the
principals.
25
Comparative Advantage: Example
(a) Initial Cash Flow
Brit ish
American
Bondholder
Bondholder
£100 m
British
Company
$150 m
£100 m
$150 m
$150 m
British Company' s
American Asset
Swap
Bank
£100 m
$150 m
American
Company
£100 m
American Company' s
British Asset
26
Comparative Advantage: Example
(b) Annual Interest Cash flow
Brit ish
American
Bondholder
Bondholder
£7.5m
$15m
(£100m)(.075)  £7.5m
British
Company
(.106)($150)  $15.9m
$15.9m
British Company' s
American Asset
Swap
Bank
(£100m)(.07)  £7m
(.10)($150m)  $15m
American
Company
£7.5m
American Company' s
British Asset
27
Comparative Advantage: Example
(c) Principal Payment at Maturity
Brit ish
American
Bondholder
Bondholder
£100 m
British
Company
$150 m
£100 m
$150 m
$150 m
British Company' s
American Asset
Swap
Bank
£100 m
$150 m
American
Company
£100 m
American Company' s
British Asset
28
Comparative Advantage:
Swap Bank’s Position
 In this swap arrangement:

The American company benefits by paying
0.25% less than it could obtain by borrowing
British pounds directly in the British market

The British company gains by paying 0.4% less
than it could obtain directly from the U.S. market.
29
Comparative Advantage:
Swap Bank’s Position

The swap bank in this case will receive $15.9 million
each year from the British company, while only
having to pay $15 million to the American company,
for a net dollar receipt of $ 0.9 million.

On the other hand, the swap bank will receive only
£7 million from the American company, while
having to pay £7.5 million to the British company,
for a net sterling payment of £0.5 million.
30
Comparative Advantage:
Swap Bank’s Position
Swap Bank’s Position:
Swap Bank’s $ Position
Swap Bank’s £ Position
Receives: (.106)($150,000,000) = $15,900,000 Receives: (.07)(£100,000,000) = £7,000,000
= −£7,500,000
Pays: −(.10)($150,000,000)
= −$15,000,000 Pays: (.075)(£100,000,000)
Net £ Payment:
−£500,000
Net $ Receipt:
$900,000
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Comparative Advantage:
Swap Bank’s Position

Thus, the swap bank has a position equivalent to a
series of long currency forward contracts in which it
agrees to buy £500,000 for $900,000 each year. The
swap bank's implied forward rate on each of these
contracts is $1.80/£:
$900,000 $1.80
Ef 

£500,000
£
32
Comparative Advantage:
Swap Bank’s Position

The swap bank can hedge its position with currency
forward contracts.

If the forward rate is less than $1.80/£, then the bank
could gain from hedging the swap agreement with
forward contracts to buy £500,000 each year each
year for the next five years.
33
Comparative Advantage:
Swap Bank’s Position

For example, suppose the yield curves applicable for the swap bank are
flat at 9.5% in the U.S. dollars and 7% in pounds (assume annual
compounding). Using the interest rate parity relation, the one-, two-,
three-, four-, and five-year forward exchange rates would be:
1
E fT
 1 R $ 

 E 0 
 1  R BP 
T
 1.095
T 1 : E f  ($1.50 / £)
  $1.535047/ £
 1.07 
2
 1.095
T  2 : E f  ($1.50 / £)
  $1.570912/ £
 1.07 
3
 1.095
T  3 : E f  ($1.50 / £)
  $1.607616/ £
 1.07 
4
 1.095
T  4 : E f  ($1.50 / £)
  $1.645177/ £
 1.07 
5
 1.095
T  5 : E f  ($1.50 / £)
  $1.683616/ £
1
.
07


34
Comparative Advantage:
Swap Bank’s Position

The swap bank could enter into forward contracts to buy
£500,000 each year for the next five years at these
forward rates.

With all of the forward rates less than implied forward
rate of $1.80/£, the bank’s dollar costs of buying
£500,000 each year would be less than its $900,000
annual inflow from the swap.

By combining its swap position with forward contracts,
the bank would be able to earn a total profit from the
deal of $478,816.
35
Comparative Advantage:
Swap Bank’s Hedge
 Swap Bank’s Hedged Position
1
Year
2
$ Cash Flow
3
£ Cash Flow
1
2
3
4
5
$900,000
$900,000
$900,000
$900,000
$900,000
£500,000
£500,000
£500,000
£500,000
£500,000
4
Forward Exchange: $/£
Column (2) X Column (3)
$1.535047
$1.570912
$1.607616
$1.645177
$1.683616
5
$ Cost of Sterling
Column (4) X Column (3)
-$767,524
-$785,456
-$803,808
-$822,589
-$841,808
6
Net $ Revenue
Column (2) - Column (5)
$132,477
$114,544
$96,192
$77,412
$58,192
$478,816
36
Comparative Advantage:
Swap Bank’s Hedge
 Instead of forward contracts, the swap bank also could hedge its swap
position by using a money market position.
 For example, on its first sterling liability of £500,000 due in one year, the
bank would need to create a sterling asset worth £500,000 one year later
(current value of £467,290M = £500,000/1.07) and a dollar liability worth
$764,524 (based on the forward contract).
 The bank could do this by borrowing $700,935 (= ($1.50/£) (£467,290)) at
9.5%, converting it to £467,290, and investing the sterling at 7% interest for
the next year.
 One year later, the bank would have £500,000 (= £467,290(1.07)) from the
investment to cover its sterling swap liability and would have a dollar
liability of $767,524 (= $700,935(1.095)), which is less than the $900,000
dollar inflow from the swap.
 The bank would thus earn a profit of $132,476 (= $900,000 −$767,524)
from the hedged cash flow – the same profit it would earn from hedging
with the forward exchange contracts if the interest rate parity relation holds.
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Summary
 The presence of comparative advantage creates a currency swap
market in which swap banks look at the borrowing rates offered
in different currencies to different borrowers and at the forward
exchange rates and money market rates that they can obtain for
hedging.
 Based on these different rates, they will arrange swaps that
provide each borrower with rates better than the ones they can
directly obtain and a profit for them that will compensate them
for facilitating the deal and assuming the credit risk of each
counterparty.
38
Non-Generic Currency Swaps
 The generic currency swap has been modified to
accommodate different uses.
 Of particular note is the cross-currency swap that is a
combination of the currency swap and interest rate
swap.
• This swap calls for an exchange of floating-rate payments in
one currency for fixed-rate payments in another.
39
Non-Generic Currency Swaps
 Non-Generic Currency Swaps:
1.
2.
3.
4.
Currency swaps with amortizing principals
Cancelable and extendable currency swaps
Forward currency swaps
Options on currency swaps
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