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Interest Rate & Currency Swaps Chapter Fourteen Copyright © 2012 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

Chapter Outline Types of Swaps Size of the Swap Market The Swap Bank Swap Market Quotations Interest Rate Swaps Currency Swaps Variations of Basic Interest Rate and Currency Swaps § Risks of Interest Rate and Currency Swaps § Is the Swap Market Efficient? § § § § 14 -2

Definitions § In a swap, two counterparties agree to a contractual arrangement wherein they will exchange cash flows at periodic intervals. § There are two types of interest rate swaps. – Single currency interest rate swap • “Plain vanilla” fixed-for-floating swaps are often just called interest rate swaps. – Cross-currency interest rate swap • This is often called a currency swap; fixed for fixed rate debt service in two (or more) currencies. 14 -3

Size of the Swap Market § In 2009 the notational principal of: – Interest rate swaps was $349. 2 trillion USD. – Currency swaps was $16. 5 trillion USD. § The most popular currencies are: – U. S. dollar – Japanese yen – Euro – Swiss franc – British pound sterling 14 -4

The Swap Bank § Swap bank is a generic term to describe a financial institution that facilitates swaps between counterparties. § The swap bank can serve as either a broker or a dealer. – As a broker, the swap bank matches counterparties but does not assume any of the risks of the swap. – As a dealer, the swap bank stands ready to accept either side of a currency swap and then later lay off the risk, or match it with a counterparty. 14 -5

Swap Market Quotations § Swap banks will tailor the terms of interest rate and currency swaps to customers’ needs. § They also make a market in “plain vanilla” swaps and provide quotes for these. Since the swap banks are dealers for these swaps, there is a bid-ask spread. 14 -6

Interest Rate Swap Quotations The convention is to quote against U. S. dollar LIBOR. Euro-€ Bid Ask £ Sterling Bid Ask Swiss franc U. S. $ Bid Ask 1 year 2. 34 2. 37 5. 21 5. 22 0. 98 3. 54 3. 57 2 year 2. 62 2. 65 5. 14 5. 18 1. 23 1. 31 3. 90 3. 94 3 year 2. 86 2. 89 3. 82– 3. 85 means 1. 50 5. 13 5. 17 the 4 year 3. 06 5 year 3. 23 6 year 3. 38 7 year 3. 52 1. 58 4. 11 4. 13 swap bank will pay 3. 09 fixed-rate 5. 17 payments at 3. 82% 5. 12 4. 25 4. 28 euro 1. 73 1. 81 3. 26 against receiving 1. 93 LIBOR or it will 5. 11 5. 16 4. 37 4. 39 euro 2. 01 3. 41 receive fixed-rate euro payments at 4. 50 5. 11 5. 16 2. 10 2. 18 4. 46 euro 4. 55 3. 85% against receiving 2. 33 LIBOR. 4. 58 5. 10 5. 15 2. 25 8 year 3. 63 3. 66 5. 10 5. 15 2. 37 2. 45 4. 62 4. 66 9 year 3. 74 3. 77 5. 09 5. 14 4. 48 2. 56 4. 70 4. 72 10 year 3. 82 3. 85 5. 08 5. 13 2. 56 2. 64 4. 75 4. 79 14 -7

Swap Quotations 3. 82– 3. 85 means the swap bank will pay fixed-rate euro payments at 3. 82% against receiving dollar LIBOR or it will receive fixed-rate euro payments at 3. 85% against paying dollar LIBOR. Firm B € 3. 85% $LIBOR Swap Bank € 3. 82% $LIBOR Firm A While most swaps are quoted against “flat” dollar LIBOR, “off-market” swaps are available where one party pays LIBOR plus or minus some number. 14 -8

Example of an Interest Rate Swap § Consider Firms A and B; each firm wants to borrow $40 million for three years. – Firm A wants to finance an interest-rate-sensitive asset and therefore wants to borrow at a floating rate. A has good credit and can borrow at LIBOR. – Firm B wants to finance an interest-rate-insensitive asset and thus wants to borrow at a fixed rate. B has less-than-perfect credit and can borrow fixed at 5. 5%. Fixed A 5% Floating LIBOR B 5. 50% LIBOR +. 20% § The swap bank quotes a three-year swap as 5. 1— 5. 2 (against dollar LIBOR). 14 -9

Example of an Interest Rate Swap 5. 0 % Firm 5. 10% Swap A LIBOR Bank X If Firm A borrows from their bank at 5. 0% fixed and takes up the swap bank on their offer of 5. 1 — 5. 2, they can convert their fixed rate 5% debt into a floating rate debt at LIBOR – 0. 10%. A’s all-in-cost = 5. 0% + LIBOR – 5. 10% = LIBOR – 0. 10%. 14 -10

Example of an Interest Rate Swap Bank Firm B LIBOR 5. 20% R BO +. 2% B’s all-in-cost = –LIBOR + 0. 20% + 5. 20% = 5. 40%. LI If Firm B borrows floating from their bank at LIBOR + 0. 20% and takes up the swap bank on their offer of 5. 1— 5. 2, they can convert their floating rate debt into a fixed rate debt at 5. 40%. Bank Y 14 -11

Example of an Interest Rate Swap Firm 5. 10% Swap A LIBOR Bank Firm B LIBOR 5. 20% The swap bank makes 10 basis points on the deal. The swap bank’s all-in-cost = –LIBOR + LIBOR – 5. 20% + 5. 10% = – 0. 10% 14 -12

Example of an Interest Rate Swap R + The notional size is $40 million. The tenor is for 3 years. BO 5. 0 Firm B LIBOR 5. 20% LI % Firm 5. 10% Swap A LIBOR Bank A earns $40, 000 per year on the swap. . 2% Bank X B earns $40, 000 per year on the swap. The swap bank earns $40, 000 per year. Bank Y 14 -13

Using a Swap to Transform a Liability § Firm A has transformed a fixed rate liability into a floater. – A is borrowing at LIBOR –. 10% – A savings of 10 bp. Firm 5. 10% Swap Bank 5. 0% A LIBOR Bank X § Firm B has transformed a floating rate liability into a fixed rate liability. – B is borrowing at 5. 40% – A savings of 10 bp. Swap Bank Firm LIBOR +. 2% B LIBOR 5. 20% Bank Y 14 -14

What about the Principal? § In our “plain vanilla” interest-only interest rate swap, we did not mention swapping the Notational Principal. § It could be the case that Firm A exchanged principal with their lender, Bank X, and Firm B exchanged principal with their outside lender, Bank Y. 14 -15

Cash Flows of an Interest-Only Swap: T = 0 0 , 00 00 0, 0 00 $4 Firm B 0, 0 Bank X Swap Bank $4 0 Firm A Bank Y 14 -16

Cash Flows of an Interest-Only Swap: T = 1 Assume LIBOR = 3%. Swap Bank Firm B $1, 200, 000 $2, 080, 000 Bank X Firm B saves $40, 000 per year relative to borrowing at 5. 5%. 00 Firm A saves $40, 000 per year relative to borrowing at LIBOR = 3%. , 0 80 $2 , 00 The swap bank earns $40, 000 per year. , 2 $1 0, 0 00 Firm $2, 040, 000 A $1, 200, 000 Bank Y 14 -17

Cash Flows of an Interest-Only Swap: T = 2 Assume LIBOR = 4%. $2 , 00 0, 0 $1, 600, 000 Swap Bank Firm B $1, 600, 000 $2, 080, 000 The swap bank earns $40, 000 per year. Firm A saves $40, 000 per year relative to borrowing at LIBOR = 4%. Firm B saves $40, 000 per year relative to borrowing at 5. 5%. 00 0, 0 Bank X $2, 040, 000 , 68 $1 00 Firm A Bank Y 14 -18

Cash Flows of an Interest-Only Swap: T = 3 Assume LIBOR = 5%. $2, 040, 000 $2, 000 Swap Bank Firm B $2, 000 $2, 080, 000 $4 2, 0 0 The swap bank earns $40, 000 per year. Firm A saves $40, 000 per year relative to borrowing at LIBOR = 4%. 0 , 00 80 2, 0 $4 0, 0 00 Firm A Bank X Firm B saves $40, 000 per year relative to borrowing at 5. 5%. Bank Y 14 -19

Example of a Currency Swap § Consider Firms A and B: – Firm A is a U. S. MNC who wants to finance a euro denominated asset in Italy, and therefore wants to borrow € 40 million for 3 years. A can borrow euros at 6%. – Firm B is a French MNC who wants to finance a dollar denominated asset, and therefore wants to borrow $60 million for 3 years. B can borrow dollars at 8%. $ € A $7% € 6% B $8% € 5% § The current exchange rate is $1. 50 = € 1. 00. 14 -20

Example of a Currency Swap Suppose that the Swap Bank publishes these quotes. The convention is to quote against U. S. dollar LIBOR. Euro-€ Bid Ask 3 year 5. 00 5. 20 U. S. $ Bid Ask 7. 00 7. 20 Firm A wants to finance a eurodenominated asset in Italy and wants to borrow euros. It can borrow euros at 6% or it can borrow euros at 5. 2% by using a currency swap. $ € A $7% € 6% B $8% € 5% 14 -21

Example of a Currency Swap Euro-€ Bid Ask 5. 00 5. 20 $ $7. 0% $60 m Firm A $60 m Suppose that Firm A borrows $60 m locally at $7% and then trades $60 m for € 40 m at spot. Firm A then enters into 2 fixed for floating swaps. € 6% $8% € 5% LIBOR € 40 m Bank X $7% B (The convention is to quote against U. S. dollar LIBOR. ) € A U. S. $ Bid Ask 7. 00 7. 20 $7. 0% € 5. 2% Swap Bank LIBOR FOREX Market 14 -22

Example of a Currency Swap Euro-€ Bid Ask 5. 00 5. 20 U. S. $ Bid Ask 7. 00 7. 20 $ € A $7% € 6% B $8% € 5% (The convention is to quote against U. S. dollar LIBOR. ) LIBOR Firm B € 5. 0% $7. 2% € 40 m LIBOR € 40 m € 5% $60 m Swap Bank FOREX Market Bank Y Suppose that Firm B borrows € 40 m locally at € 5%, then trades € 40 m for $60 m. Firm B then enters into 2 fixed for floating swaps. 14 -23

Example of a Currency Swap The swap bank earns 40 bp per year (20 bp in $ and 20 bp in €). $7 Bank X $7. 0% € 5. 2% Swap Bank Firm B € 5. 0% $7. 2% The notional size is $60 m. The tenor is for 3 years. . 0% € 5 . 0% Firm A earns 80 bp per year on the swap and hedges exchange rate risk. Bank Firm B earns 80 bp per year on the swap and Y hedges exchange rate risk. 14 -24

Cash Flows of the Swaps: T = 0 00 , 00 0 0, 0 , 00 00 00 0, 0 € 4 0 $6 0 , 00 0, 0 00 0 , 00 00 $6 0, 0 , 00 00 Foreign Exchange Spot Market € 4 0, 0 $6 Bank X Firm B 0 Swap Bank 0 Firm A Bank Y 14 -25

Cash Flows of the Swaps: T = 1 Assume LIBOR = 3%. $1. 8 m Firm A $4. 2 m € 2. 08 m $1. 8 m Swap Bank $1. 8 m $4. 32 m € 2 m Firm B $1. 8 m Firm A’s all-in-cost = € 2. 08 m or 5. 2% of € 40 m Firm B’s all-in-cost = $4. 32 or 7. 2% of $60 m m Bank X € 2 m $ The swap bank earns € 80, 000 + $120, 000 or. 002×€ 40 m +. 002×$60 m per year. . 2 4 Bank Y 14 -26

Cash Flows of the Swaps: T = 2 Assume LIBOR = 4%. $2. 4 m Firm A $4. 2 m € 2. 08 m $2. 4 m Swap Bank $2. 4 m $4. 32 m € 2 m Firm B $2. 4 m Firm A’s all-in-cost = € 2. 08 m or 5. 2% of € 40 m Firm B’s all-in-cost = $4. 32 or 7. 2% of $60 m m Bank X € 2 m $ The swap bank earns € 80, 000 + $120, 000 or. 002×€ 40 m +. 002×$60 m per year. . 2 4 Bank Y 14 -27

Cash Flows of the Swaps: T = 3 Assume LIBOR = 5%. $3 m Firm A $4. 2 m € 2. 08 m $3 m Swap Bank $4. 32 m € 2 m $3 m m € 4 2 4. 0 m $6 0 m € 4 0 m 2 m $6 Bank X Firm B Bank Y Foreign Exchange Forward Market 14 -28

Equivalency of Currency Swap Debt Service Obligations § We can assume that IRP holds between the € 5% euro rate and the $7% dollar rate. – This is reasonable since these rates are, respectively, the best rates available for each counterparty who is well known in its national market. (1 + i$)t – According to IRP: St($/€) = S 0($/€) × t (1 + i€) $1. 50×(1. 07)1 $1. 5286 S 1($/€) = 1 = € 1. 00×(1. 05) € 1. 00 $ € A $7% € 6% B $8% € 5% 14 -29

IRR 7. 00% 0 –$60. 00 1 2 $4. 20 3 $64. 20 5. 00% –€ 40. 00 € 2. 75 € 2. 70 € 40. 44 The swap bank could borrow $60 m at 7% and use a set of 3 forward contracts to redenominate the bond as a 5% euro bond. € 1. 00×(1. 05) –€ 40 m = –$60 m× € 2. 75 m = $4. 20 m × $1. 50×(1. 07) € 1. 00×(1. 05)2 € 2. 70 m = $4. 20 m × $1. 50×(1. 07)2 € 1. 00×(1. 05)3 € 40. 44 m = $64. 20 m × $1. 50×(1. 07)3 14 -30

IRR 0 7. 00% 5. 00% –$60. 00 –€ 40. 00 1 2 $3. 06 € 2. 00 $3. 12 € 2. 00 3 $66. 67 € 42. 00 The swap bank could borrow € 40 m at 5% and use a set of 3 forward contracts to redenominate the bond as a 7% dollar bond. $1. 50×(1. 07) –$60 m = –€ 40 m× $3. 06 m = € 2 m × × € 1. 00×(1. 05) $1. 50×(1. 07)2 $3. 12 m = € 2 m ×× € 1. 00×(1. 05)2 $1. 50×(1. 07)3 $66. 67 m = € 42 m× € 1. 00×(1. 05)3 14 -31

The Quality Spread Differential § The Quality Spread Differential (QSD) represents the potential gains from a swap that can be shared between the counterparties and the swap bank. § There is no reason to presume that the gains will be shared equally. § The QSD is calculated as the difference between the differences. $ € A $7% € 6% B $8% € 5% QSD 1% – – 1% = 2% 14 -32

Variations of Basic Currency and Interest Rate Swaps § Currency swaps: – Fixed for fixed – Fixed for floating – Floating for floating – Amortizing § Interest rate swaps: – Zero-for floating – Floating for floating § For a swap to be possible, a QSD must exist. Beyond that, creativity is the only limit. 14 -33

Risks of Interest Rate and Currency Swaps § Interest rate risk – Interest rates might move against the swap bank after it has only gotten half of a swap on the books, or if it has an unhedged position. § Basis risk – Basis risk may occur if the floating rates of the two counterparties are not pegged to the same index. § Exchange rate risk – In the example of a currency swap given earlier, the swap bank would be worse off if the pound appreciated. 14 -34

Risks of Interest Rate and Currency Swaps (continued) § Credit risk – This is the major risk faced by a swap dealer, the risk that a counterparty will default on its end of the swap. § Mismatch risk – It’s hard to find a counterparty that wants to borrow the right amount of money for the right amount of time. § Sovereign risk – The risk that a country will impose exchange rate restrictions that will interfere with performance on the swap. 14 -35

Valuation of an Existing Swap § A swap is a derivative security, so it can be priced in terms of the underlying assets. § How to valuate a swap: – Any swap’s value is the difference in the present values of the payment streams that are incoming and outgoing. – Plain vanilla, fixed for floating swaps get valued just like a pair of bonds. – Currency swaps get valued just like two nests of currency forward contracts. 14 -36

Swap Valuation Example § A currency swap has a remaining life of 18 months. § It involves exchanging interest at 14% on £ 20 million for interest at 10% on $30 million once a year. § The term structure of interest rates is currently flat in both the U. S. and the U. K. If the swap were negotiated today, the interest rates exchanged would be $8% and £ 11%. All rates were quoted with annual compounding. § The current exchange rate is $1. 65 = £ 1. § What is the value of the swap (in USD) to the party paying dollars? 14 -37

Swap Valuation Example (continued) 18 6 £ 2. 8 m –$3 m Value of the swap to the party paying dollars: 0 £ 2. 8 m $1. 65 $8, 335, 659 = (1. 11)½ + (1. 11)3/2 × £ 1 –$5, 559, 669 = –$3 m ½ + –$3 m 3/2 (1. 08) $2, 775, 990 14 -38

Second Swap Valuation Example § Find the dollar value today to the party paying dollars of a 7 -year old swap with 3 years remaining maturity. § The swap calls for exchanging interest only on € 10 m at 5% for $15 m at 3%. – Semiannual payments, and the last payment was yesterday. – Today’s exchange rate is $1. 30/€ and the AAA rate is 2% in the U. S. and 2. 5% in the euro zone. 14 -39

Swap Valuation Example 2 (continued) Find the value of the swap as the net N 6 value of a portfolio of two bonds: I/Y 2. 5% 1. Long a euro-denominated bond and CPT PV -€ 1, 436, 502. 48 2. Short a dollar-denominated bond PMT € 250, 000 = (€ 10 m ×. 05) /2 (semi-annual pay bond) FV € 0 (NOT € 10 m since this is an interest-only swap. ) dollar value = € 1, 436, 502. 48 × $1. 30/€ 1 = $1, 867, 453. 22 N 6 I/Y 2. 0% CPT PV -$1, 303, 982. 21 PMT $225, 000 = ($15 m ×. 03) /2 (semi-annual pay bond) FV $0 (NOT $15 m since this is an interest-only swap. ) The value of this swap to the party paying dollars is $563, 471. 02 (= $1, 867, 453. 22 – $1, 303, 982. 21). 14 -40

Swap Market Efficiency § Swaps offer market completeness, and that has accounted for their existence and growth. § Swaps assist in tailoring financing to the type desired by a particular borrower. Since not all types of debt instruments are available to all types of borrowers, both counterparties can benefit (as well as the swap dealer) through financing that is more suitable for their asset maturity structures. 14 -41