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1 International Fixed Income Topic 7A:SWAPS

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2 Outline F Description of a Swap F Motivation for Swaps F Graphical Analysis F Valuation and Interest Rate Sensitivity F Credit Risk F Currency Swaps

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3 I. Description F An interest rate swap is a contract which commits two counterparties to exchange, over an agreed period, two streams of interest payments, each calculated using a different interest rate index, but applied to a common notional principal amount.

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4 Plain Vanilla Swap F A plain vanilla or generic swap is a fixed-for-floating swap with: »constant notional principal »constant fixed interest rate »floating interest rate such as 6-month LIBOR (London Interbank Offer Rate), a Treasury bill rate, Prime rate, Fed Funds,... »semi-annual payments of fixed and floating. F The swap rate quoted is the fixed rate.

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5 Swap Jargon F The fixed-rate payer is »paying fixed and receiving floating »long the swap »short the bond market F The floating-rate payer is »paying floating and receiving fixed »short the swap »long the bond market

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6 Importance of Swaps Market

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7 II. Motivation for Swaps F Risk Taking »Arbitrage due to market imperfections? F Risk Management »Hedging interest rate risks F Financing »Low transaction costs »Off-balance sheet

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8 Example: Using swaps to take advantage of market imperfections? F Company A has an AAA credit rating »Borrows fixed at 10% or at LIBOR+20bp F Company B has a BBB credit rating »Borrows at 11.20% or at LIBOR+75bp F Their spreads allow for swap market arbitrage »A borrows fixed and swaps to pay LIBOR with dealer, while B borrows floating, and swaps to pay fixed 10.20% with dealer.

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9 Example continued...

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10 Example continued... F Is this really arbitrage? »The conventional wisdom is that B is reducing its borrowing costs and sharing some of the savings with A. »On the other hand, if B is achieving the floating debt by rolling over short term debt, which has a lower spread than long term debt, then B is at risk if its credit quality deteriorates.

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11 Example: Mortgage Lending Institution F Typically invests in fixed-rate assets (mortgages) funded by liabilities on which it pays a floating rate (deposits). »How can the bank hedge its interest rate risk? u Go long a swap u It pays fixed and receives floating u It funds the fixed from its mortgage payments, and uses the floating to pay its deposits. »Why? It makes money from the business side, not in taking interest rate risk.

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12 Hedging Interest Rate Risk

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13 III. Graphical Analysis

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14 3 ways to view the cash flow from a swap - #1

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15 #2 - short a fixed, long a floater

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16 #3 - a portfolio of forward contracts

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17 Swaps as a portfolio of forward contracts F The 2-year (annual reset) swap is like a portfolio of 4 forwards of maturities.5-2 years. »Since swaps have a present value of zero, the portfolio is also PV zero. »However, because the obligated payment is fixed each period with the swap, the fixed swap rate will not equal the time-zero forward rates unless the term structure is flat. u Thus, each individual forward embedded in the swap will not have the usual zero present value, only their sum will. u If the term structure is upward (downward) sloping, then the payer of fixed initially expects to have losses (gain) before eventual gains (losses).

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18 IV. Valuation & Interest Rate Sensitivity F Three Components: »Distribution of Cash Flows »Valuation of Swap »Interest Rate Sensitivity of Swap F Illustration using an example of a 2-year swap of fixed against 6-month Libor.

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19 A. Cash Flow Rule F Every six months until maturity, the party who is long the swap receives the 6-month rate set 6-months earlier minus a fixed rate k. F If the notional amount of the swap is N and the maturity is T, the time t cash flow to this party for t = 0.5, 1, 1.5,..., T can be written as

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20 Example: Cash Flows to Long Position in 5.5% 2- Year Swap with $100 Notional Amount

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21 B. Valuation F As shown earlier, the cash flows from a swap are equivalent to a long position in a floater (indexed to Libor) minus a fixed-rate bond (with rate k). »The difference between the coupons of the two notes equals the swap payment, and the difference between their principal payments is zero. F Thus, default risk aside, the value of a swap is just the difference between the value of the floater and the fixed rate bond:

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22 Valuation continued... F Since it is standard to set the initial value of the swap to zero, this means the swap rate is the fixed rate that sets the floater equal to the fixed-rate bond. F Thus, the swap rate is chosen such that

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23 Example F What is the value of a 5.5% plain, vanilla interest rate 2- year swap; »assuming the current zero curve is 5.54%, 5.45%, 5.47% and 5.5% for the 6 mth through 2 year zeroes (cocnistent with previous classes), that is, discount factors of.973,.9746,.9222 and,8972, respectively. F The 2-year swap with fixed rate 5.5% is worth -0.0019 per $100 notional amount: »The 2-yr 5.5% bond is worth 100.0019 »The floater is worth 100 (see below) F swap value = 100 - 100.0019

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24 Review: Floaters F A floating rate note (FRN) is a bond with a coupon that is adjusted periodically to a benchmark interest rate, or indexed to this rate (e.g., LIBOR) F Consider a semi-annual coupon floating rate note, with the coupon indexed to the 6-month interest rate. Each coupon date, the coupon paid is equal to the par value of the note times one-half the 6-month rate quoted 6 months earlier, at the beginning of the coupon period. The note pays par value at maturity. F Valuation (See next two pages) F What is the duration of a floater? »The note is always worth par on the next coupon date with certainty. So a floater is equivalent to a zero that matures on the next coupon date with face value equal to the par value of the floater plus the current coupon.The duration of the floater is therefore equal to the duration of a zero maturing on the next coupon date. Their convexities are the same, too.

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27 Calculating the Swap Rate F The swap rate is the fixed rate that sets the swap's value equal to zero. »If the swap is fixed-against-LIBOR, then the swap rate should be above the Treasury rate. u Why? F Because LIBOR is appropriate for A-rated banks; and the default risk on swaps is much lower; it must be the case that the fixed rate should reflect the default-free rate plus the LIBOR spread (TED spread).

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28 Swap rate continued... F For each maturity T, the swap rate k(T) is the coupon rate that sets the fixed-rate component equal to the floater. With no default risk, the floater's value is par plus the present value of the spread over Treasuries. Denote s as the spread, and d as the discount factors; then for a semi-annual swap, we have

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29 Example F Assume a spread of zero, so that we are working off treasuries, then »The 2-year swap with fixed rate 5.5% is worth -0.0019 (per $100 notional amount). »To make the swap worth exactly zero, the swap rate must be set equal to the par rate for 2 year maturity: u 2-year par rate = 2(1-0.897166)/ (0.973047+0.947649+0.922242+0.897166) = 5.499%

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30 The Swap Curve F Recall that the swap curve relates the generic swap rate to the maturity of the swap. (It refers to dealer rates for fixed- against-six month Libor). »The swap spread is the spread between the swap rate and a U.S. Treasury of similar maturity. F This curve generally coincides with what a dealer would pay/receive in a swap with a AAA (or AA) party. F The variation in the swap spread across maturities is empirically related to: »demand/supply factors (price pressure) »credit spreads in the corporate bond market

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31 April 1,2000 Swap Curve & Treasury Curve

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32 January 1,2000 Swap Curve & Treasury Curve

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33 Swap Spreads (1997-2000)

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34 C. Interest Rate Sensitivity F The dollar duration (or, the price value of a basis point [DV01]) and the dollar convexity of the swap respectively is simply the dollar duration and dollar convexity of a floating rate note minus the fixed-rate bond. »Since a floater faces only interest rate risk between reset dates, the duration then is primarily that of the underlying fixed-rate bond. u Note that the surprising charateristic here is that a swap has no principal amount at stake (i.e., it's a levered position in the underlying bond). »A long position in a swap has, therefore, negative duration, as it is primarily a negative position in a long-term fixed rate bond. F Increasing (decreasing) interest rates increase (decrease) the swap's value.

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35 Example

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36 V. Credit Risk F The swap curve generally indicates what a dealer would pay/receive in a swap with a AAA (or AA) counterparty. However, spreads for lower quality counterparties are about the same. F How important is credit risk? Many regulators argue that credit risk is underpriced in the swaps market, e.g., swap spreads much lower than corporate credit spreads. However, swaps have many special features, which substantially reduce their credit risk.

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37 Are the concerns warranted? F Loan »Full principal at risk »Full interest payments at risk »Defaults always matter »Covenants apply F Swap »No principal at risk »Only a spread payment is at risk »Default matters only if in the money »Long maturity contracts often have rating-related unwind/settlement triggers and advanced credit enhancement collateralization features

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38 Characteristics of Swaps: Credit Risk Issues #1 F Although the cash flows of long a floater, short a fixed-rate bond are equal to a swap; note that only the difference between their coupons are at risk. »Thus, the capital at risk is of a much smaller magnitude than the underlying fixed income market.

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39 Characteristics of Swaps: Credit Risk Issues #2 F Rational default occurs only when the swap's value is negative. »In our example, this happens only when interest rates have fallen (from the perspective of being long the swap), thus reducing the incidence of default. »This also highlights the importance of the term structure of interest rates, as displayed by thinking of swaps as a portfolio of forwards.

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40 Characteristics of Swaps: Credit Risk Issues #3 F Credit Enhancement Vehicles »The most "matured" setting can be found on organized exchanges »The OTC market provides a variety of standard (ISDA master agreement) and new (asset/counterparty-specific) additions

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41 Credit Enhancement (Exchanges) F Options and futures margin requirements »margin serves as a collateral F Daily mark-to-market and possible liquidation of a position »margin is proportional to avg. vol »margin may be related to the nature of the trade (hedging or speculative) F Position limits vis-a-vis each counterparty helps diversify default risk F Cross-clearing agreements

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42 Credit Enhancement (OTC Derivatives) F Netting Arrangements »bilateral close-out is now standard in the ISDA master swap agreement F Position Limits »RM group monitors the "exposure profile" for each counterparty »each trade is considered for its portfolio effect F Margins and Collateral »common to require dynamic margining F Derivative Product Companies »dynamically capitalized »AAA-rated SPVs »Often a requirement for sovereigns F Recouponing »periodic change of coupon +payment to bring the transaction to market F Credit Triggers »if a counterparty falls below investment grade, the other counterparty may require an immediate cash settlement (of questionable effectiveness) »common for long-dated swaps

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43 VI. Currency Swaps F A contract by which two counterparties exchange, over an agreed period, two streams of interest payments in different currencies and, at the end of the period, the corresponding principal amounts at an exchange rate agreed at the start of the contract. F Different from an interest rate swap in that »the interest and principal are denominated in different currencies »exchange of principal at maturity

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44 Currency Swap: fixed/fixed $/DM

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45 Other types of currency swaps F Cross-Currency Coupon Swap »Fixed-against-floating: counterparty A pays fixed DM interest and principal in exchange for floating $ interest and principal at maturity F Cross-Currency Basis Swap »Floating-against-floating: counterparty A pays floating DM interest and principal in exchange for floating $ interest and principal at maturity.

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46 Interest Rate and Cross-Currency Swaps: Notional Principal, Trillions $, 1995

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47 Currency Swap Pricing F We can think of a currency swap as an exchange of notes, one denominated in each currency: »Price of swap = price of DM note - price of $ note »For the fixed/fixed swap here, it can be written as Price of swap = price of fixed rate DM bond - price of fixed rate $ bond F The interest rate sensitivity of the swap, however, is different. To see this note that the change in the swap's value can be approximated by Swap= p $ -s p Dm -p Dm s, where s is the exchange rate ($ per DM) »The duration of the swap then depends on the interest rate sensitivity of three factors: US rates, German rates, and the exchange rate. Since the exchange rate is roughly 8 times more variable than the underlying interest rates, much of a swap's risk comes from currency changes.

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48 Comparison of Currency Swaps and Forwards F Currency Swaps »Involves exchange of interest and principal amounts of currencies »Exchange of principal takes place at an exchnage rate agreed at start of swap, usually the spot rate »E.G., exchange streams of dollar and DM payments, and principal amounts at maturity at current spot rate. F Forwards »Only principal amounts at maturity »Exchange of principal takes place at the forward exchange rate (at start of swap) »E.G., transaction takes place at forward rate F agreed at start of swap,i.e., simple exchange of principal amount at maturity

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49 VII. Other Types of Swaps F Amortizing and Accreting Swaps »Notional declines (increases) through time F Step Up/Down Swaps »Coupon starts low (high) then steps up (down) F Basis Swaps »Exchange of two floating rates, e.g., T-bill rate versus LIBOR F CMT Swaps »Floating rate is tied to a long-treasury yield

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50 LTCM Example Reviewed: European credit spreads F Swap spreads represent the spread between future LIBOR (bank offer rates) and future T-bills. During the 1996-1997 period, UK swap spreads began to rise relative to German swap spreads. In other words, UK swaps (relative to their treasuries) were cheap compared to German swaps (relative to their treasuries). F LTCM went long UK swap spreads and short German swap spreads, betting they would eventually converge.

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51 Swap Spreads: UK & Germany

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52 Swap Spreads: UK & Germany

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© 2004 South-Western Publishing 1 Chapter 13 Swaps and Interest Rate Options.

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