1. Currency and equity swap
Institute of Economic Studies
Faculty of Social Sciences
Charles University in Prague
Currency and equity swap
Ztlumené efekty: 2,3,4
Odstranit srážku kamionu: snímek 8, 1:33 – 1:45
Financial Instruments

2. Exchange rate conventions
Exchange rate is the price of one currency in terms of other currency (1 EUR = 1.25 USD, 1 GBP = 1.32 EUR)
Base currency (BAC) is the measured currency ; BAC is represented by one unit in the exchange rate quotation
Variable currency (VAC) is the measuring currency; VAC is represented by a number of units in the exchange rate quotation
Possible exchange rate notations of 1 BAC = x VAC (1 EUR = 1.25 USD): x VAC/BAC (1.25 USD/EUR), x BAC/VAC (1.25 EUR/USD), x BACVAC (1.25 EURUSD)
Quotation conventions
Indirect quotation uses foreign currency as the base currency (a number of units of domestic currency per one unit of foreign currency)
Direct quotation uses domestic currency as the base currency (a number of units of foreign currency per one unit of domestic currency)
Conversion formula: x VAC/BAC ⇔ 1/x BAC/VAC
1.25 USD/EUR ⇔ 1/1.25 EUR/USD = 0.8 EUR/USD
Currency and equity swap

3. Discounts and premiums
Classification of exchange rates
Spot exchange rate is a rate agreed now for outright purchase or sale of one currency for another currency (with delivery of up to two working days)
Forward exchange rate is a rate agreed now for purchase or sale of one currency for another currency in a fixed date in the future
Covered interest rate parity
Cash-and-carry transaction should generate neither a profit nor a loss
VAC
BAC ① ② ③ ⑤ ④
① Borrow one unit of BAC
② Convert BAC to VAC at a given spot rate 𝑆
③ Deposit S units of VAC at VAC-interest rate to get S× 1+ 𝑖 𝑉𝐴𝐶 × days units of VAC
𝐹=𝑆× 1+ 𝑖 𝑉𝐴𝐶 × days 𝑖 𝐵𝐴𝐶 × days 365
④ Convert the deposit balance back to BAC at a given forward rate 𝐹 to get S× 1+ 𝑖 𝑉𝐴𝐶 × days /𝐹 units of BAC
⑤ Repay the BAC loan 1+ 𝑖 𝐵𝐴𝐶 × days 365
To eliminated arbitrage opportunities, a higher interest rate must be offset by weaker forward rate
The currency with the higher interest rate is at a discount to the currency with lower interest rate and the currency with the lower interest rate is at a premium to the currency with the higher interest rate
Currency and equity swap

4. Related currency instruments
Outright forward
Outright forward is the exchange of principal amounts denominated in two different currencies on a given future date
EA Bank
US Bank
USD
EUR
time
The exchange will take place at a current forward exchange rate
Forward swap
Forward swap is a temporary exchange of principal amounts denominated in two different currencies to be reversed on a given future date
EA Bank
US Bank
USD
EUR
time
The initial exchange is made at a spot rate and the re-exchange is made at a forward rate in accordance with the covered interest rate parity
Forward swap can be seen as a combination of a spot deal and an outright forward
Currency and equity swap

5. Currency swap Definition Types of currency swaps
Currency swap commits two counterparties to exchange:
a) over an agreed period two streams of interest payments in different currencies
b) usually at the end of the contract corresponding principal amounts at an exchange rate agreed at the start of the contract
EA Bank
US Bank
USD interest
USD
EUR
time
EUR interest
Principal amounts can be exchange at the start of the swap as well, usually in connection with a new borrowing
Types of currency swaps
Currency coupon swap involves an exchange of interest streams of which both are derived from a fixed rate of interest
Cross-currency swap involves an exchange of interest streams of which at least one is derived from a floating rate of interest
Currency swap is not a derivative instrument because there is an eventual movement of principal amounts on which interest payments are based
Currency and equity swap

6. Hedged borrowing in foreign currency
Using cross-currency coupon swap
Borrower
FC interest
Swap dealer
DC interest
DC revenues
FC principal
DC principal
FC repayment
FC borrowing
Cross-currency coupon swap hedges fixed rate foreign loan against exchange rate risk and benefits from falling domestic interest rates
In net terms the borrower pays DC interest and repays the DC debt from earnings generated by its domestic business
Using currency coupon swap
Borrower
FC interest
Swap dealer
DC interest
DC revenues
FC principal
DC principal
FC repayment
FC borrowing
Currency coupon swap hedges fixed rate foreign loan against exchange rate risk and protects against rising domestic interest rates
Currency and equity swap

7. Hedged investment in foreign currency
Using currency coupon swap
Borrower
FC interest
Swap dealer
DC interest
DC outlays
FC principal
DC principal
FC repayment
FC investment
Currency coupon swap hedges fixed rate foreign investment against exchange rate risk and protects against rising domestic interest rates
In net terms the investor receives DC fixed interest and DC principal which are used for financing DC expenditures
Using cross-currency coupon swap
Borrower
FC interest
Swap dealer
DC interest
DC outlays
FC principal
DC principal
FC repayment
FC investment
Currency coupon swap hedges fixed rate foreign investment against exchange rate risk and benefits from falling domestic interest rates
Currency and equity swap

8. New-issues arbitrage Properties Example of new-issues arbitrage
An arbitrage trade with a currency swap involves bond issues in two different currencies
EUR
USD
Company AA
6.5%
4.0%
Company 𝐁𝐁
7.0%
5.2%
Differential
50 EUR bp
120 USD bp
Arbitrage potential
120 USD bp – 50 EUR bp
AA has a comparive advantage in USD
but needs EUR funds
BB has a comparive advantage in EUR
but needs USD funds
= 75 USD bp = EUR bp
Comparison of basis points in different currencies is achieved by using covered interest rate parity (i.e. 1 EUR bp = 0.9 USD bp)
Example of new-issues arbitrage
Co AA
Co BB
USD 4%
EUR 6.0%
EUR 7%
AA net borrowing cost: USD 4% — USD 4% +EUR 6.0% = EUR 6.0%
BB net borrowing cost: EUR 7% — EUR 6% + USD 4.0% = USD 4.9%
EUR bp
USD bp
Company AA 50 45
Company BB
33.33 30
Currency and equity swap

9. Warehousing Risks of unhedged position Warehousing strategy
Later
customer
Swap
dealer
5Y EUR + spread
Earlier
5Y EUR
6M USD Libor
USD
EUR
A fall in EUR long-term interest rates will result in a lower rate received than paid out during the whole term of the swap
A rise of USD Libor will result in a higher rate paid out than received until the next refixing date
A USD depreciation will result in a smaller USD principal amount received than paid out at maturity of the swap pair
Warehousing strategy
Buying 5-year EUR denominated government bonds
A fall in EUR interest rate will increase the selling price of the bonds that will offset the income loss on EUR legs of the swap pair
A USD depreciation will increase the USD equivalent of the EUR bonds that will offset the loss from the imbalance between USD principal amounts at maturity of the swap pair
Currency and equity swap

10. Valuation of currency swaps
Valuation formulas
Value of the currency swap is the difference between net present values of cash flows to be paid and received in the swap which are expressed in the same currency by using the market exchange rate
Swap value (in units of CUR A) =
NPV(CUR A)−NPV CUR B × exchange rate (CUR A/CUR B)
Swap value (in units of CUR B) =
NPV(CUR A)/ exchange rate (CUR A/CUR B)−NPV CUR B
The swap value, based on current market interest and exchange rates, should be zero when the deal is originated
The swap may acquire non-zero values after it is transacted as a result of market movements in the underlying interest and exchange rates
Currency and equity swap 10

11. Equity swap Description
Equity swap is a contract which commits the counterparties to exchange over an agreed period two streams of payments
1. payments linked to a change in a agreed stock market index
2. payments linked to an agreed short-term interest rate
Investor
Swap dealer
Libor + spread
Stock index payment
Both income streams are applied to an agreed notional principal amount (ES with a fixed notional principal)
Market practice is to net payments so only one payment is actually made between counterparties
Equity swap is a derivative instrument because it derives its payments from underlying cash instruments
Equity swap is an over-the-counter instrument whose specifications are negotiated by the swap counterparties
Currency and equity swap

12. Application of equity swap
Synthetic equity investment
Equity swap can simulate investment in a stock market without the need to invest in this market (transformation of money market investment into a synthetic equity investment)
Money
market
Investor
Libor
Swap
dealer
Index payment
Libor + spread
Repayment
Cash investment
Equity swap can circumvent regulatory restrictions on direct investment on the stock market
Equity swap with a variable notional principal amount
Equity-linked payments are reinvested in money market and equity-linked losses are funded by disinvestment in money market
Principal is either increased by the amount equal to the index payment received or reduced by the amount equal to the index payment paid
Trading strategy simulates stock market investment in which profits and losses are capitalised
Currency and equity swap

13. Swaption Definition Application of swaptions
Swaption is an option to enter into a forward coupon swap
Call swaption is the right to buy a forward swap (fixed interest is paid), put swaption is the right to sell a forward swap (fixed interest is received)
Application of swaptions
Company can put a ceiling on future borrowing rate by buying a call swaption
Bank
Company
Loan
Swap
dealer
Swaption
Libor
exercise rate 11%
6M Libor +1%
If the swaption has a premium of 1% then the company can fix its effective borrowing cost at 13%
13% = 11% (fixed leg of the swap) + 1% (spread in the bank loan) + 1% (swaption premium)
Any increase in borrowing rate up to 13% will be absorbed by the company
Currency and equity swap

14. See you in the next lecture
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See you in the next lecture
Currency and ekvity swap