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F r a n k f u r t S c h o o l . d e
Akademische Programme
Berufsbegleitende Programme
Seminare
Executive Education
Unternehmensprogramme & Services
Forschung
Internationale Beratung
F r a n k f u r t S c h o o l . d e
Basics of CurrencySwaps
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2 F r a n k f u r t S c h o o l . d e
Fundamentals
In its simplest form, a currency swap iseconomically equivalent to an exchange ofinterest and principal payments in onecurrency for interest and principal payments in
another. A currency swap requires that the principalamount is specified in each of the two currenciesinvolved.
The principal is usually exchanged at thebeginning and at the end of the swap.
Usually, the principal amounts are chosen to be(almost) equivalent, using the exchange rate
prevailing at the initiation of the swap. Dr. Sikandar Siddiqui
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3 F r a n k f u r t S c h o o l . d e
Illustration
Dr. Sikandar Siddiqui
Suppose a U.S. company A, wants to finance a
10,000,000 expansion of a British plant.
They could borrow dollars in the U.S. where theyare well known and exchange USD for GBP. Thisresults in exchange rate risk.
OR
They could borrow pounds in the internationalbond market, but pay a lot more in interest thancompanies of comparable credit quality, since they
are not well known abroad.
If Company A can find a company with a mirror-image financing need, both may benefit from aswap.
If the exchange rate is s0
= 1.60 USD/GBP, Company
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4 F r a n k f u r t S c h o o l . d e
The borrowing opportunities for both companiesare given below:
Illustration
Dr. Sikandar Siddiqui
$
Company A . %88 . %888
Company B . %888 . %111
In this example, A is rated as being more credit-worthy by the market than B:
- A pays 2% less to borrow in dollars than B.
- A pays 0.4% less to borrow in pounds than B.
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5 F r a n k f u r t S c h o o l . d e
However, B has a comparative advantage inborrowing in GBP:
The difference in borrowing cost between B andA
- amounts to 2% when borrowing in USD but
- is only 0.4% when borrowing in GBP:
Illustration
Dr. Sikandar Siddiqui
$
Company A . %88 . %888
Company B. %888 . %111
Potential Savings = 2.0% - 0.4% = 1.6%
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6 F r a n k f u r t S c h o o l . d e
Therefore, both companies can lower theirinterest expense by
Illustration
Dr. Sikandar Siddiqui
- borrowing in the currency where they have acomparative advantage,
- and then entering into a currency swap to
obtain the currency they actually need in thisparticular situation.
$
Company A . %88 . %888
Company B . %888 . %111
Differential (B-A) . %88 . %11
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Illustration
Dr. Sikandar Siddiqui
In this example, a specialised intermediary theSwap Bank arranges the transaction and isassumed to claim an amount equivalent to 0.4%for itself as a compensation for this service.
The remaining part of the total advantage (1.6% -0.4% = 1.2%) is split equally between A and B, sothat
- Company A pays 11.6% - 0.5 x 1.2% =11.0%, and
- Company B pays 10.0% - 0.5 x 1.2% =9.4%
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8/388 F r a n k f u r t S c h o o l . d e
Illustration
Dr. Sikandar Siddiqui
Company
A
Swap
Bank
i$=8%
i$=8%
i=11%
i=12%
i$=9.4%
Company
B
i=12%
$
Company A . %88 . %888 Company B . %888 . %111
Differential (B-A) . %88 . %11
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Illustration
Dr. Sikandar Siddiqui
Company
A
Swap
Bank
i$=8%
i$=8%
i=11%
i=12%
i$=9.4%
Company
B
i=12%
$
Company A . %88 . %888
Company B . %888 . %111
Differential (B-A) . %88 . %11
As net position is to borrow at i=11%
A saves i=0.6%
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$
Company A . %88 . %888
Company B . %888 . %111
Illustration
Dr. Sikandar Siddiqui
Company
A
Swap
Bank
i$=8%
i$=8%
i=11%
i=12%
i$=9.4%
Company
B
i=12%
Bs net position is to borrow at i$=9.4%
B saves i$=0.6%
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Illustration
Dr. Sikandar Siddiqui
Company
A
Swap
Bank
i$=8%
i$=8%
i=11%
i=12%
i$=9.4%
Company
B
i=12%
$
Company A . %88 . %888
Company B . %888 . %888
The swap bank makes
money too:
1.4% of $16 millionfinanced with 1% of 10
million per year for 5
years.
At S0 = 1.60 $/, that is a
gain of $64,000 per year
for 5 years.The swap bank
faces exchange raterisk, which it may
or may not choose
to hedge with
another
transaction.
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12/3812 F r a n k f u r t S c h o o l . d e
In the absence of credit risk, entering into a currencyswap is economically equivalent to simultaneously
(1) issuing a bond in currency X (e.g. GBP) at par
(2) exchanging the proceeds from (1) into currency Y
(e.g. USD) at the spot exchange rate, and(3) using the proceeds from (2) to buy a bonddenominated in
currency Y at face value.
At the end of the swaps tenor, the party underconsideration repays the principal of hypothetical bondissued under (1) and receives the principal of thehypothetical bond bought under (3).
Valuation of Currency Swaps
Dr. Sikandar Siddiqui
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13/3813 F r a n k f u r t S c h o o l . d e
In terms of currency Y, the calculational market valueof such a swap can thus be determined according tothe following pattern:
Valuation of Currency Swaps
Dr. Sikandar Siddiqui
=YSwapV ,
Value of
hypothetical bondbought (in units of
the referencecurrency, Y)
Value of
hypothetical bondissued (in units of
currency X)
Spot exchange rate
(price of one unit ofX in terms ofcurrency Y)
VBond, Y VBond, XsY/X-
.
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Valuation of Currency Swaps
Dr. Sikandar Siddiqui
Depending on whether the coupon paymentspertaining to the two components of the swap arefixed or floating, we can distinguish between fourbasic types of currency swaps:
- fixed for fixed,
- fixed for floating,
- floating for fixed, and
- floating for floating.
For the sake of simplicity, only fixed-for-fixedcurrency swaps will beexplicitly dealt with here.
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Example: Cash Flow Profile of a Fixed for Fixed
USD/GBP Currency Swap
Key data:
Payment frequency = Semi-annual
Spot rate at inceptions0 = 1.60 USD/GBP,
Face value = USD 100 = GBP 62.5 (= 100/1.60)
Term = 3 years.
Fixed swap rate (USD) = 1.43%
Fixed swap rate (GBP) = 2.21%
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
As before, we describe the situation from theperspective of the party which has syntheticallyissued GBP debt and invested in USD.
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16 F r a n k f u r t S c h o o l . d e
Example: Cash Flow Profile of a Fixed for Fixed
USD/GBP Currency Swap (continued)
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
. 0.5 . 100 . (-0.5) . 62.5
Proceeds fromsynthetic GBPbond issuance
Outlay forsynthetic USDbond purchase
Principal + lastcoupon from
synthetic bondinvestment
Principal + lastcoupon from
synthetic bondissue
. 0.5 . 100.
(-0.5).
62.5
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17 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Valuation of Currency Swaps
Market values at and after the starting date
At the starting date, the swap described here has amarket value of zero because the values of the USDand the GBP legs cancel out exactly.
During the life of the swap, however, its calculationalmarket value changes because both the currency-specific interest rates and the exchange rate change
over time, and the values of both legs of the swapreact differently to these developments.
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18 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Valuation of Currency Swaps
Example: Computation of the calculational market
valueWe now move forward in time and arrive at apoint where
the remaining tenor of the swap is only 2.5 moreyears,
sterling has depreciated to s0.5
= 1.50 USD/GBP,
and
the calculational USD and GBP spot rates,
deduced from thecorresponding par yield curves viabootstrapping, are
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19 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Valuation of Currency Swaps
Example: Computation of the calculational market
value
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20 F r a n k f u r t S c h o o l . d e
Example (continued):
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
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21 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Example (continued):
Valuation of Currency Swaps
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22 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Example (continued):
Valuation of Currency Swaps
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23 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Example (continued):
Valuation of Currency Swaps
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24 F r a n k f u r t S c h o o l . d e
Example (continued):
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
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25 F r a n k f u r t S c h o o l . d e
Example (continued):
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
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26 F r a n k f u r t S c h o o l . d e
Example (continued):
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
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27 F r a n k f u r t S c h o o l . d e
Example (continued):
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
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28 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Example (continued):
Valuation of Currency Swaps
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29 F r a n k f u r t S c h o o l . d e
Example (continued):
Valuation of Currency Swaps
Dr. Sikandar Siddiqui
asassumed
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30 F r a n k f u r t S c h o o l . d e
Example (continued):
Dr. Sikandar Siddiqui
Valuation of Currency Swaps
x
=
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31 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Example (continued):
Valuation of Currency Swaps
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32 F r a n k f u r t S c h o o l . d e Dr. Sikandar Siddiqui
Example (continued):
Valuation of Currency Swaps
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33 F r a n k f u r t S c h o o l . d e
A currency swap thus consists of
a synthetic liability in one currency (currency X) and
an (initially equally valued) asset in another(currency Y).
It thus
gains in value if... loses in valueif...
Risk Analysis
Dr. Sikandar Siddiqui
currency X declines invalue
the spot interest rates
used to value thesynthetic liability(currency X leg) increase,
the spot interest rates
used to value the
currency X increases invalue
the spot interest rates
used to value thesynthetic liability(currency X leg) decline,
the spot interest rates
used to value the
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34 F r a n k f u r t S c h o o l . d e
Risk Analysis
Dr. Sikandar Siddiqui
Impact of a GBP appreciation in the example
An appreciation of the GBP causes thesynthetic liablilty to gain in value, leading to alower swap value
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35 F r a n k f u r t S c h o o l . d e
Risk Analysis
Dr. Sikandar Siddiqui
Impact of an increase in GBP spot interest rates
in the example
Higher GBP spot rates cause the syntheticliablilty to lose in value, leading to a higherswap value
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36 F r a n k f u r t S c h o o l . d e
Risk Analysis
Dr. Sikandar Siddiqui
Impact of an increase in USD spot interest rates
in the example
Higher USD spot interest rates cause thesynthetic asset to lose in value, leading to alower swap value
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37 F r a n k f u r t S c h o o l . d e
Credit Risks of CurrencySwaps
In the absence of risk mitigation measures likenetting and collateralisation, the counterparties in acurrency swap will be subject to greater credit riskthan in the case of an interest rate swap.
This is due to the fact that in the case of a currencyswap, there is an exchange of principal at the end.
This implies a higher probability of a large buildup invalue, exposing one of the parties (the one which
has been winning) to a correspondingly highpotential loss if other one defaults.
Dr. Sikandar Siddiqui
Credit Risks of Swaps d
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Three measures are commonly taken in order to mitigatecounterparty risks
in the field of derivatives trading:
Netting agreements: Claims from different involving thesame counterparties are counted up against each other,
and only the net amount is actually paid when due. Collateralisation: The particular counterparty which
currently is in the position of a net debtor is contractuallybound to provide collateral in the form of cash or liquid,tradeable securities. Very often, the market value of thecollateral posted is calculationally reduced by a haircutin order to further protect the net creditor againstpotential losses.
Regular mark-to-market valuation: The market values of
ll iti i l d i l l t d l l t
Credit Risks of Swaps andother Derivatives