Transcript currency swap - the School of Economics and Finance

MFIN6003 Derivative Securities
Lecture Note Six
Faculty of Business and Economics
University of Hong Kong
Dr. Huiyan Qiu
6-1
Outline
Introduction to swaps using an example of a
commodity swap.
• Swap settlement; swap counterparty; market
value of a swap; computing swap price (rate).
Interest Rate Swaps
Currency Swaps
Appendix: more on swaps
• Swaptions
• Total Return Swaps
6-2
Introduction to Swaps
A swap is a contract calling for an exchange of
payments over time
• The swap payments are determined by the
difference in swap price and market price over
time
• A swap provides a means to hedge a stream of
risky payments (lower transaction cost)
• A single-payment swap is the same thing as a
cash-settled forward contract
6-3
An Example of a Commodity Swap
An industrial producer, IP Inc., needs to buy
100,000 barrels of oil 1 year from today and 2
years from today (concern? P↑)
How to hedge against the risk in oil cost?
Relevant information:
• The forward prices for deliver in 1 year and 2
years are $20 and $21/barrel.
• The risk-free 1- and 2-year zero-coupon bond
yields are 6% and 6.5%
6-4
A Commodity Swap (cont’d)
Strategy 1: Long forward contracts for 100,000
barrels in each of the next 2 years
• IP pays $20 in year one and $21 in year two for oil
Strategy 2: Prepaid swap
• A single payment today for multiple deliveries of
oil in the future.
$ 20
$ 21
PV 
1.06

1.065
2
 $37 .383
• IP pays an oil supplier $37.383 per barrel in
exchange for a commitment to delivering one
barrel in each of the next two years. Credit risk?
6-5
A Commodity Swap (cont’d)
Strategy 3: Swap
• Defer payments until the oil is delivered, while still
fixing the total price
• A swap usually calls for equal payment in each year
x
x

 $37 .383  x  $20.483
2
1.06 1.065
• The 2-year swap price is $20.483
Any series of payments that have a PV of $37.383
is acceptable (ignoring the credit risk)
6-6
Time Line – Payments
0
1
2
Unhedged
S1
S2
Strategy 1
20
21
20.483
20.483
Strategy 2
Strategy 3
37.873
All series of payments have a PV of $37.383.
6-7
Swaps, Forwards, and Financing
Swaps are nothing more than forward contracts
coupled with borrowing and lending money
• Compare the swap price and the forward prices, we
are overpaying by $0.483 in the first year, and we
are underpaying by $0.517 in the second year
• We are lending the counterparty money for 1 year.
The interest rate on this loan is
0.517/0.483 – 1 = 7%.
• Given 1- and 2-year zero-coupon bond yields of 6%
and 6.5%, 7% is the 1-year implied forward yield
from year 1 to year 2. (Fair pricing!)
6-8
No-Arbitrage Principle
The present value of future payments for the
same series of future commodity delivery should
be the same. Otherwise, arbitrage!
If the present value of payment using two
forward contracts for the oil delivery in year 1
and in year 2 is lower than that of payment
using two-year swap, one can long the two
forward contracts and short the swap to gain the
arbitrage profit.
6-9
Computing the Swap Price
Suppose there are n swap settlements, occurring
on dates ti, i = 1,… , n. What is the swap price R?
PV (swap price) = PV (forward price)
F0,t
R
n
 i 1

t
t
[1  r (0, ti )]
[1  r (0, ti )]
n
i 1
i
i
i
 RP (0, ti )   F0,t P (0, ti )
n
i 1
n
i 1
i
 F P (0, ti )
P (0, ti )
n
R
 i 1 n
F0,t
 P (0, ti )
 j 1 P (0, t j )
n
i 1 0 ,ti
n
i 1
i
6-10
Physical vs. Financial Settlement
The results for the buyer are the same whether the
swap is settled physically or financially. In both
cases, the net cost of the buyer is fixed at the swap
price of $20.483, whatever the market price of oil.
Physical settlement
6-11
Financial Settlement
The oil buyer, IP, pays the swap counterparty the
difference between $20.483 and the spot price, and the oil
buyer then buys oil at the spot price
100,000 barrels are the notional amount of the swap,
used to determine the magnitude of the payments when
the swap is settled financially
6-12
The Swap Counterparty
The swap counterparty is a dealer, who is, in
effect, a broker between buyer and seller
The fixed price paid by the buyer, usually,
exceeds the fixed price received by the seller.
This price difference is a bid-ask spread, and is
the dealer’s fee
Back-to-back transaction or “matched book”
transaction: the situation where the dealer
matches the buyer and seller.
6-13
Matched Book Transaction
The dealer bears the credit risk of both parties,
but is not exposed to price risk
6-14
Unmatched Book Transaction
In the case that the swap transaction is not
matched, the dealer serves as counterparty to
the oil buyer and is facing future oil price risk:
obligation to receive fixed price and pay
floating price.
Spot price - $20.483
Oil Buyer
Swap
Counterparty
6-15
Unmatched Book Transaction
To hedge the swap transaction with the buyer,
the dealer can enter into long forward or futures
contracts.
Cash flows:
The net cash flow for the hedged dealer is a loan
Thus, the dealer also has interest rate exposure (which
can be hedged by using Eurodollar futures or FRAs)
6-16
The Market Value of a Swap
The market value of a swap is zero at interception
• Once the swap is struck, its market value will
generally no longer be zero (change in forward price,
in interest rate…)
• Even if there is no change in interest rates or the
forward prices, the swap changes value after
payment.
The market value of the swap is the difference in
the PV of payments between the original and new
swap prices
6-17
The Market Value of a Swap
Example: change in forward price
• Assume immediately after the initiation of the swap,
the forward curve for oil rises by $2 in both years
• Assume interest rates are unchanged
• The new swap price will be $22.483, $2 higher than
the old one (check and understand why exactly $2)
• PV of the differences = 2/1.06 + 2/(1.0652) = $3.65
• $3.65 is the market value of the old swap
6-18
Misuse of Swap: Enron’s Case
Energy giant Enron collapsed in 2001.
As charged by SEC, other companies helped
Enron mislead investors.
One case: J.P Morgan Chase had helped Enron
characterize loan proceeds as operating income
by using swaps.
6-19
Enron’s Hidden Debt
Figure
Enron’s swaps
with Mahonia
and Chase.
Source:
Securities and
Exchange
Commission.
6-20
Kinds of Swaps
Interest Rate Swaps: payments are the difference
of interest payments based on floating rate and
fixed rate (swap rate)
• The notional principle of the swap is the amount on
which the interest payments are based
• The life of the swap is the swap term or swap
tenor
Currency Swaps: entail an exchange of payments
in different currencies
• A currency swap is equivalent to borrowing in one
currency and lending in another
6-21
An Example of an Interest Rate Swap
XYZ Corp. has $200M of floating-rate debt at
LIBOR, i.e., every year it pays that year’s LIBOR.
XYZ would prefer to have fixed-rate debt with 3
years to maturity
• Retire the floating-rate and issue fixed rate debt
(Transaction cost? Feasible? )
• Enter a strip of FRAs (FRA rates for each year
varies)
• Enter a swap, in which they receive a floating rate
and pay the fixed rate
6-22
An Example (cont’d)
On net, XYZ pays 6.9548%
XYZ net payment = – LIBOR + LIBOR – 6.9548% = –6.9548%
Floating Payment
Swap Payment
6-23
Questions to Ask
Where does 6.9548% come from? How to
determine this swap rate?
As a counterparty to the swap, the marketmaker receives fixed and pays floating. Thus, the
market-maker is facing the risk of high floating
rate. (The XYZ uses interest rate swap to
transfer the risk to the swap counterparty.)
• The market-maker will hedge the floating rate
payments by using, for example, forward rate
agreements
6-24
Hedge Swap Position
The interest rate for year 0 to year 1 is 6%. Forward
rate for year 1 to year 2 is 7.0024% and for year 2 to
year 3 is 8.0071%.
Cash Flow Table
6-25
Computing the Swap Rate
Suppose there are n swap settlements, occurring
on dates ti, i = 1,… , n. Swap rate is R.
The implied forward interest rate from date ti-1 to
date ti, known at date 0, is r0(ti-1, ti)
The price of a zero-coupon bond maturing on date
ti is P(0, ti)
Using FRAs to hedge or using swap to hedge 
same present value
 P ( 0 , t i ) r0 ( t i  1 , t i )   P ( 0 , t i ) R
n
i 1
n
i 1
6-26
Computing the Swap Rate (cont’d)
Rewrite
P ( 0, ti ) r0 ( ti 1 , ti )

R
n
i 1 P (0, ti )
n
i 1
P ( 0, ti )
 n
r0 ( ti 1 , ti )
i 1  j 1 P ( 0, t j )
n
Thus, the fixed swap rate is as a weighted
average of the implied forward rates, where
zero-coupon bond prices are used to determine
the weights
6-27
Computing the Swap Rate (cont’d)
Note
P(0, ti 1 )
1  r0 (ti 1 , ti ) 
P(0, ti )
An alternative way to express the swap rate is
P(0, ti ) r0 (ti 1 , ti )

R
n
i 1 P(0, ti )
n
i 1
 P(0, ti 1 ) 
 1
 P(0, ti ) 
P(0, ti )
1  P(0,tn )



 n
n
i 1 P(0, ti )
i 1 P(0,ti )
n
i 1
6-28
The Swap Curve
A set of swap rates at different maturities
• The swap curve should be consistent with the
interest rate curve implied by the Eurodollar futures
contract, which is used to hedge swaps
Computing swap rates
• The Eurodollar futures contract provides a set of 3month forward LIBOR rates
• In turn, zero-coupon bond prices can be constructed
from implied forward rates
• We can then use formula to compute swap rates
6-29
The Swap Curve (cont’d)
Table Three-month LIBOR forward rates and swap rates
implied by Eurodollar futures prices with maturity dates given
in the first column. Prices are from November 8, 2007. Source:
Wall Street Journal online.
Maturity
Date of
Eurodollar Price of
Futures
Eurodollar
Contract
Futures
Dec-07
95.250
Mar-08
95.720
Jun-08
95.965
Sep-08
96.075
Dec-08
96.080
3-Month
Forward Rate
Implied by
Eurodollar
Futures Price
0.01201
0.01082
0.01020
0.00992
0.00991
Implied Dec
2007 Price of $1
Paid 3-Months
after Futures
Mat. Date
0.98814
0.97756
0.96769
0.95818
0.94878
Swap Rate (%) for
Loan Made Dec
2007, Ending 3
Months after
Futures Mat. Date
4.8028
4.5664
4.4059
4.2982
4.2326
6-30
Variation of Interest Rate Swaps
A deferred swap is a swap that begins at some date
in the future, but its swap rate is agreed upon today
An amortizing swap is a swap where the notional
value is declining over time (e.g., floating rate
mortgage)
An accreting swap is a swap where the notional
value is growing over time
General formula for the swap rate:
Qt P(0, ti )r0 (ti 1 , ti )

R
n
i k Qt P(0, ti )
n
i k
6-31
Currency Swaps
A currency swap entails an exchange of
payments in different currencies
A currency swap is equivalent to
borrowing in one currency and lending in
another
6-32
Currency Swap: An Example
A dollar-based firm has a 3-year 3.5% eurodominated bond with a €100 par. Current
exchange rate is $0.90/€.
• Use currency forward contracts to hedge
Year
Unhedged
Euro cash flow
Forward
Hedged
Exchange rate Dollar Cash Flow
1
-€3.5
0.9217
-$3.226
2
-€3.5
0.9440
-$3.304
3
-€103.5
0.9668
-$100.064
6-33
Currency Swap Example (cont’d)
Alternatively, the firm can enter into a currency
swap with the market-maker –– making
payments on a dollar-based bond and receiving
payments for its euro-based bond
$, $, $ (how much?)
Market-maker
Firm
€3.5, €3.5, €103.5
Rule: the present value of the payments (from
and to the market-maker) should be the same!
6-34
Currency Swap Example (cont’d)
The euro-based par bond has value €100, which is
equivalent to $90, given the current exchange rate
of $0.90/€.
Therefore, the dollar-based par bond should have
value $90.
Suppose the effective annual dollar-denominated
interest rate is 6%
The payments on dollar-based bond are:
$5.40, $5.40, and $95.40.
6-35
Hedged or Unhedged Cash Flows
Unhedged cash flows and hedged cash flows
using either swap or forward contracts.
Unhedged
€3.5
€3.5
€103.5
Swap-hedged
$5.4
$5.4
$95.4
Forwardhedged
$3.226
$3.304
$100.064
All have PV
= €100 = $90
6-36
Currency Swap
A currency swap is equivalent to borrowing in one
currency and lending in another
$90 now
$5.4, $5.4, $90
Market-maker
Firm
€3.5, €3.5, €103.5
€100 now
6-37
Currency Swap: Market-Maker
Market-maker use currency forward contracts to hedge
the Euro interest. The position of the market-maker is
summarized below
The PV of the market-maker’s net cash flows is
($2.174 / 1.06) + ($2.096 / 1.062) – ($4.664 / 1.063) = 0
6-38
Redundant Information?
Current exchange rate x0 is $0.90/€.
Interest rate on euro is 3.5%.
Interest rate on dollar is 6%.
Question: what determines the forward exchange
rates?
F0,T  x0e
( r  r f )T
(1  r )T
 x0
(1  rf )T
if given rateis effective
Forward exchange rates are given as 0.9217, 0.9440,
and 0.9668.
6-39
Currency Swap Formulas
Consider a swap in which a dollar annuity, R, is
exchanged for an annuity in another currency, R*
• There are n payments
• The time-0 forward price for a unit of foreign
currency delivered at time ti is F0,ti .
• The dollar-denominated zero-coupon bond price is
P0,ti
• Given R*, what is R?
6-40
Currency Swap Formulas (cont’d)
The PV of the two annuities must be the same (in one
currency)
n
n

i 1
RP0 ,ti  i 1 R*F0 ,ti P0 ,ti
• Then,

R
n
i 1
P0 ,t i R*F0 ,t i

n
i 1
P0 ,t i
This equation is equivalent to previous formula, with
the implied forward rate, r0(ti-1, ti), replaced by the
foreign-currency-denominated annuity payment
translated into dollars, R*F0,ti
6-41
Swap Bank
Swap bank is a financial institution that acts as
an intermediary for interest and currency swaps.
• Function: to find counterparties for those who
want to participate in swap agreements.
• The swap bank typically earns a slight premium
for facilitating the swap.
In general, companies do not directly approach
other companies in an attempt to create swap
agreements. In most cases, companies don't even
know the identities of their swap counterparties.
6-42
Swap Bank: Example
Both company A and company B need to take
$5m loan. Company A prefers to pay variable
rate of interest while company B prefers to pay
fixed rate of interest.
Company A is big, well-known, and wellestablished. It is offered with 5% fixed rate or
LIBOR by bank X.
Company B is less well-known and smaller. It is
offered with 8% fixed rate or LIBOR+1% by bank
Y.
How can a swap bank help here?
6-43
Swap Bank: Example (cont’d)
The swap bank offers a swap to company A as
follows:
LIBOR
Swap Bank
Co. A
5.5%
By taking the loan from bank X at 5% and
signing the swap above with the swap bank,
effectively, company A is paying at a variable
rate of LIBOR-0.5%. Great!
6-44
Swap Bank: Example (cont’d)
The swap bank offers a swap to company B as
follows:
6%
Swap Bank
Co. B
LIBOR
By taking the loan from bank Y at LIBOR+1%
and signing the swap above with the swap bank,
efectively, company B is paying at a fixed rate of
7%. Great!
6-45
Swap Bank: Example (cont’d)
Both company A and company B are better off.
The swap bank earns 0.5%
LIBOR
Co. A
LIBOR
Swap Bank
5.5%
Co. B
6%
Concerns: default risk (credit risk) …
6-46
End of the Notes!
6-47
Appendix:
More on Swaps
6-48
Swaptions
A swaption is an option (right) to enter into a
swap with pre-specified terms
• Swaption can be used to speculate on the swap
price in the future
A swaption is analogous to an ordinary option.
• Swaption has a premium.
• Swaptions can be American or European.
6-49
Payer / Receiver Swaption
A payer swaption gives its holder the right, but
not the obligation, to pay the pre-specified price
(strike price) and receive the market swap price
• The holder of a payer swaption would exercise
when the market swap price is above the strike
A receiver swaption gives its holder the right,
but not the obligation to pay the market swap
price and receive the pre-specified strike price
• The holder of a receiver swaption would exercise
when the market swap price is below the strike
6-50
Example: Payer Swaption
Suppose we enter into a 3-month European payer
oil swaption: the strike price = $21 and the
underlying swap commences in 1 year and has 2
settlements
After 3 months, the fixed price on the underlying
swap is $21.50: Exercise the option, obligating us
to pay $21/barrel for 2 years and allowing us to
receive $21.5/barrel for 2 years.
• In year 1 and year 2, we will receive $21.50 and pay
$21, for a certain net cash flow each year of $0.50
6-51
Total Return Swaps
A total return swap is a swap, in which one
party pays the realized total return (dividends
plus capital gains) on a reference asset, and the
other party pays a floating return such as LIBOR
The two parties exchange only the difference
between these rates
The party paying the return on the reference
asset is the total return payer
6-52
Example: Total Return Swap
ABC Asset Management want to sell $1 billion of
investment in S&P index
An alternative is to swap the total stock return
into a floating short-term rate
Table Illustration of cash flows on a total return swap
with annual settlement for 3 years.
6-53
Total Return Swaps (cont’d)
Why to use a total return swap?
• The total return payer gives up the possible risk
premium on the stock index
• The payoff for the swap is equivalent to direct
selling of the stock and buying a floating-rate
note
• However, the total return swap can allow foreign
investors to own stocks without physically holding
them, so as to avoid withholding foreign taxes
• Flexible management of credit risk
6-54