FIN 684 Fixed-Income Analysis Swaps

Transcription

1 FIN 684 Fixed-Income Analysis Swaps Professor Robert B.H. Hauswald Kogod School of Business, AU Swap Fundamentals In a swap, two counterparties agree to a contractual arrangement wherein they agree to exchange cash flows at periodic intervals exchange of cash flows contractually fixed: dates, size, obligation Single currency interest rate swap: Plain vanilla fixed-for-floating swaps are often just called interest rate swaps Cross-Currency interest rate swap currency swap; fixed for fixed rate debt service in two (or more) currencies 2

2 XFX and Interest Rate Swaps Plain-vanilla swaps: FI risk management 2 segments: FX and interest rate swaps principle: match exposures and positions Generally applicable risk management ideas: build risk management into strategies second chance: deal with risks after the fact Divide and conquer : repackaging risks ex ante: lower your borrowing costs ex post: repackage your risks 3 Origin of Swap Markets New phenomenon: 1970s and 1980s currency transactions between central banks first interest rate swap: 1982 Causes: market segmentation financial arbitrage: comparative borrowing advantages tax and regulatory arbitrage risk management tool financial integration Future: adverse publicity vs. financial needs 4

3 Size of the Swap Market In 2004 the notational principal of: interest rate swaps was $127,570 billion USD. currency swaps was $7,033 billion USD The most popular currencies are: U.S. dollar Japanese yen Euro Swiss franc British pound sterling 5 The Swap Bank A swap bank is a financial institution that facilitates swaps between counterparties. The swap bank (generic term) 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 their risk, or match it with a counterparty. 6

4 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. 7 Interest Rate Swap Quotations Euro- Sterling Swiss franc U.S. $ Bid Ask Bid Ask Bid Ask Bid Ask 1 year year means the swap bank will pay fixed-rate euro payments at 3.82% against receiving euro LIBOR or it will receive fixed-rate euro payments at 3.85% against paying euro LIBOR 3 year year year year year year year year

5 Interest Rate Swap Example Bank A: AAA-rated international bank, needs USD 10m to finance floating-rate Eurodollar loans. considers issuing 5-year fixed-rate USD bonds at 10% better: floating-rate notes at LIBOR to finance floatingrate Eurodollar loans. Firm B: BBB-rated U.S. company, needs USD 10m to finance a project with a 5 year horizon considers issuing 5-year fixed-rate USD bonds at 11.75%: would prefer to borrow at a fixed rate could issue 5-year FRNs at LIBOR + ½ percent. 9 Borrowing Opportunities The borrowing opportunities of the two firms are shown in the following table: COMPANY B BANK A DIFFERENTIAL Fixed rate 11.75% 10% 1.75% Floating rate LIBOR +.5% LIBOR.5% QSD = 1.25% 10

6 Interest Rate Swap Mechanics Bank A 10 3/8% LIBOR 1/8% Swap Bank COMPANY B BANK A DIFFERENTIAL Fixed rate 11.75% 10% 1.75% Floating rate LIBOR +.5% LIBOR.5% QSD = 1.25% The swap bank makes this offer to Bank A: You pay LIBOR 1/8 % per year on $10 million for 5 years and we will pay you 10 3/8% on $10 million for 5 years 11 Interest Rate Swap Mechanics ½ % of $10,000,000 = $50,000. That s quite a cost savings per year for 5 years. 10 3/8% 10% Bank A LIBOR 1/8% Swap Bank Here s what s in it for Bank A: They can borrow externally at 10% fixed and have a net borrowing position of -10 3/ (LIBOR 1/8) = LIBOR ½ % which is ½ % better than they can borrow floating without a swap. COMPANY B BANK A DIFFERENTIAL Fixed rate 11.75% 10% 1.75% Floating rate LIBOR +.5% LIBOR.5% QSD = 1.25% 12

7 Interest Rate Swap Mechanics The swap bank makes this offer to company B: You pay us 10 ½ % per year on $10 million for 5 years and we will pay you LIBOR ¼ % per year on $10 million for 5 years. Swap Bank LIBOR ¼% 10 ½% COMPANY B BANK A DIFFERENTIAL Fixed rate 11.75% 10% 1.75% Floating rate LIBOR +.5% LIBOR.5% QSD = 1.25% Company 13 B Interest Rate Swap Mechanics Here s what s in it for B: Swap Bank They can borrow externally at LIBOR + ½ % and have a net borrowing position of 10½ + (LIBOR + ½ ) - (LIBOR - ¼ ) = 11.25% which is ½ % better than they can borrow floating without a swap. LIBOR ¼% COMPANY B BANK A DIFFERENTIAL Fixed rate 11.75% 10% 1.75% Floating rate LIBOR +.5% LIBOR.5% QSD = 1.25% ½ % of $10,000,000 = $50,000 that s quite a cost savings per year for 5 10 ½% years. Company 14 B LIBOR + ½%

8 Interest Rate Swap Mechanics The swap bank makes money too. 10 3/8 % Swap Bank ¼ % of $10 million = $25,000 per year for 5 years. 10 ½% 10% Bank A A saves ½ % LIBOR 1/8% LIBOR ¼% LIBOR 1/8 [LIBOR ¼ ]= 1/8 10 ½ /8 = 1/8 ¼ COMPANY B BANK A DIFFERENTIAL Fixed rate 11.75% 10% 1.75% Floating rate LIBOR +.5% LIBOR.5% QSD = 1.25% Company LIBOR + ½% B saves ½ % 15 B Interest Rate Swap Mechanics The swap bank makes ¼ % 10 3/8 % Swap Bank 10 ½% 10% Bank A A saves ½ % LIBOR 1/8% LIBOR ¼% Note that the total savings ½ + ½ + ¼ = 1.25 % = QSD COMPANY B BANK A DIFFERENTIAL Fixed rate 11.75% 10% 1.75% Floating rate LIBOR +.5% LIBOR.5% QSD = 1.25% Company 16 B LIBOR + ½% B saves ½ %

9 The QSD Quality Spread Differential represents the potential gains from the 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 In the above example, company B is less creditworthy than bank A, so they probably would have gotten less of the QSD, in order to compensate the swap bank for the default risk 17 Swaps as Portfolio of Bonds If you buy a bond, you receive interest If you issue a bond you pay interest In a plain vanilla swap, you do both You pay a fixed rate You receive a floating rate Or vice versa So, what does a swap correspond to? 18

10 Swaps and Bonds A bond with a fixed rate of 7% sells at a premium when? sells at a discount when? If a firm is involved in a swap and pays a fixed rate of 7% at a time when it would otherwise have to pay a higher rate, the swap is saving the firm money If because of the swap you are obliged to pay more than the current rate, the swap is beneficial to the other party 19 Swaps as a Series of Forward Contracts In a forward contract the parties exchange assets at a particular date in the future An interest rate swap has known payment dates evenly spaced throughout the tenor of the swap A swap with a single payment date six months is simply a 6M forward contract At that date, the party owing the greater amount remits a difference check 20

11 Swap Analysis A plain vanilla fixed-for-floating interest rate swap contract is an agreement between two counterparties one counterparty agrees to make n fixed payments per year at an (annualized) rate c on a notional N up to a maturity date T, the other counterparty commits to make payments linked to a floating rate index r n (t). For T 1, T 2,..., T n = T payment dates, with T i = T i 1 + and = 1/n, the net payment between the two counterparties at each of these dates is Net payment at T i = N [r n (T i-1 ) c] The constant c is called the swap rate 21 Pricing Forwards: Again Consider a forward contract in which one counterparty agrees to buy at a future date T a zero coupon bond P z (T,T*). The forward price is given by the forward discount factor (multiplied by the notional) P fwd z (0,T,T*) = F(0,T,T*) 100 It is useful to look at the arbitrage argument that makes this true Assume P fwd z (0,T,T*) > F(0,T,T*) 100 Recalling that:. Z ( 0, T *) Pz ( 0, T *) F ( 0, T, T *) = = Z 0, T P 0, T ( ) z ( ) 22

12 Valuation of Forward Contracts Forward contract in which one counterparty agrees to purchase at a future date T a Treasury bond with coupon rate c and with maturity T * > T. Let T 1, T 2,..., T n = T* be the coupon dates after T. The value of the forward contract for every t < T is V fwd (t) = Z(t,T) [P c fwd (t,t,t*) K] where K = P c fwd (0, T, T*) is the delivery price agreed upon at initiation 23 Swap Valuation: Series of Forwards The sequence of net cash flows is the same as a portfolio which is long a floating rate bond, and short a fixed rate bond with coupon c V swap (t;c,t) = P FR (t,t) P c (t,t) where V swap (t;c,t) is the value of the swap at time t, with swap rate c and maturity T M ; P FR (t,t) is the value of the floating rate bond and P c (t,t) is the value of the fixed coupon bond with coupon rate c At payment dates T i, we have P FR (t,t) = 100; so: c 2 swap V. ( Ti, c, TM ) = Z ( Ti, Tj ) Z ( Ti, TM ) M j= i+ 1 24

13 The Swap Rate The swap rate c is the number which sets V swap (0;c,T) equal to zero. Rewriting the equation generically for any payment frequency n and payment dates T 1,...,T M, we have c M swap V c T Z n j= 1 T Z T ( 0,, M ) = ( 0, j ) ( 0, M ) Solving this equation for c we find 1 Z ( 0, TM ) c = n M Z ( 0, T ) j= 1 j 25 Pricing Principles The swap price is determined by fundamental arbitrage arguments swap dealers are in close agreement on what this rate should be: otherwise? LIBOR: start date and maturity of a loan Similar to forward rates: A 3 x 6 Forward Rate Agreement (FRA) begins in three months and lasts three months (denoted by 3 f 6 ) A 6 x 12 FRA begins in six months and lasts six months (denoted by ) 6 f 12 26

14 The Forward Curve and LIBOR Assume the following LIBOR interest rates: Spot ( 0 f 3 ) 5.42% Six Month ( 0 f 6 ) 5.50% Nine Month ( 0 f 9 ) 5.57% Twelve Month ( 0 f 12 ) 5.62% 27 Implied Forward Rates (cont d) % LIBOR forward rate curve spot 3 to 6 6 to 9 9 to Months 28

15 At-the-Market Swap An at-the-market swap swap price is set such that the present value of the floating rate side of the swap equals the present value of the fixed rate side The floating rate payments are uncertain Use the spot rate yield curve and the implied forward rate curve why does it work? 29 At-the-Market Swap Example A one-year, quarterly payment swap based on actual days in the quarter and a 360- day year on both the fixed and floating sides. next 4 quarters: days are 91, 90, 92, and 92 the notional principal of the swap is $1. Convert the future values of the swap into present values discounting at the appropriate zero coupon rate contained in the forward rate curve. 30

16 Four Discount Factors What are they? How computed? R3 = = R6 = = R9 = = R12 = = Discount the Floating Leg PV Discount both the fixed and floating rate sides of the swap what cash flow is being discounted? where does it come from? what is the argument? % 5.58% 5.71% 5.77% = = floating =

17 PV fixed Solving for the Swap Rate Solve for the swap fixed rate that equates the two legs: X % X % X % X % = = X X X X = X PVfixed = X = = PVfloating X = c = 5.62% 33 Quoting Swaps Common practice to quote the swap price relative to the U.S. Treasury yield curve Maturity should match the tenor of the swap There is both a bid and an ask associated with the swap price The dealer adds a swap spread to the appropriate Treasury yield 34

18 The LIBOR Yield Curve and the Swap Spread Relationship between the LIBOR Yield curve (swap rate: s.a.) and the Treasury one swap spread: difference between two zero coupon yields with same maturities, from different yield curves: Libor and UST It is generally assumed that unlikely to become negative: default probability of swap dealers is higher than the government s unlikely to move to infinity 35 The Swap Curve The swap market grew so much that market forces now determine the swap rate for every possible future maturity The swap curve at time t is the set of swap rates (at time t) for all maturities T 1, T 2,...,T M. denote the swap curve at time t by c(t,t i ) for i = 1,...,M Given the swap curve we can determine the implicit discount functions through the bootstrap methodology For i = 1 1 Z ( t, T 1 ) = c( t, Ti ) 1 while for i = 2,,M. (, ) Z t T i n (, ) i 1 i n Z ( t Tj ) c t T 1, j= 1 = c( t, Ti ) 1 36 n

19 Forward Swap Contract and Rate In a forward swap contract two parties agree to enter into a swap at a predetermined future date and swap rate f s The forward swap rate f s of a contract to enter into a swap at time T, with maturity T*, payment frequency n, and payment dates T 1,T 2,...,T m (with T m = T*) is given by j= 1 ( T T ) s 1 F 0,, * fn ( 0, T, T *) = n m F ( 0, T, Tj ) 37 Payment Frequency and Day Count Conventions Many swap contracts have payment dates at different frequency Take a common fixed-for-floating swap: 3M LIBOR and pays at quarterly frequency and uses the actual / 360 day count convention fixed rate counterparty pays at semiannual frequency: uses the 360/360 day count convention Usually not a problem for valuation since each leg is priced separately 38

20 Interest-Rate Risk Management A fixed-for-floating swap doesn t cost anything to enter, but can change the duration of a portfolio The dollar duration of a swap corresponds to D $ swap = D $ floating D $ fixed Choosing the adequate notional amount parallel shifts in the term structure won t have an impact on equity value D $ E = D $ A + N D $ swap D $ L 39 Summary: Putting It All Together Swaps: exchanging two liabilities ex-ante: optimize funding and borrowing costs ex-post: manage adverse FX or interest rate shocks Create synthetic instruments and gain twice: issue in preferred market segment swap into needed currency or coupon structure FI financial engineering: repackage cash flows use market imperfections for return enhancements pay only 1.5 times for two or more transactions statistical models: limit exposures, track VAR 40

21 Appendix: Swap Transactions Pricing swaps: fixed income mathematics Foreign currency fixed-for-fixed swap Walt Disney s synthetic JPY bond Fixed-for-floating (plain vanilla) interest rate swap: Radobank and Goodrich synthetic floating rate note and fixed rate bond Floating rate risk: buying insurance caps and floors 41 Notional Amounts Outstanding: USD bn FX contracts Interest rate contracts Equity-linked contracts Commodity contracts Credit default swaps Jun.1998 Dec.1998 Jun.1999 Dec.1999 Jun.2000 Dec.2000 Jun.2001 Dec.2001 Jun.2002 Dec.2002 Jun.2003 Dec.2003 Jun.2004 Dec.2004 Jun.2005 Dec.2005 Jun.2006 Dec.2006

22 7000 Gross Market Value : USD bn FX contracts Interest rate contracts Equity-linked contracts Commodity contracts Credit default swaps Jun.1998 Dec.1998 Jun.1999 Dec.1999 Jun.2000 Dec.2000 Jun.2001 Dec.2001 Jun.2002 Dec.2002 Jun.2003 Dec.2003 Jun.2004 Dec.2004 Jun.2005 Dec.2005 Jun.2006 Dec Fixed-Income Notionals: USD bn Forward rate agreements Interest rate swaps Options Jun.1998 Dec.1998 Jun.1999 Dec.1999 Jun.2000 Dec.2000 Jun.2001 Dec.2001 Jun.2002 Dec.2002 Jun.2003 Dec.2003 Jun.2004 Dec.2004 Jun.2005 Dec.2005 Jun.2006 Dec.2006

23 7000 F-Inc Gross Market Value : USD bn Forward rate agreements Interest rate swaps Options Jun.1998 Dec.1998 Jun.1999 Dec.1999 Jun.2000 Dec.2000 Jun.2001 Dec.2001 Jun.2002 Dec.2002 Jun.2003 Dec.2003 Jun.2004 Dec.2004 Jun.2005 Dec.2005 Jun.2006 Dec.2006 FX Derivatives Notionals: USD bn Forwards and forex swaps Currency swaps Options 46 Jun.1998 Dec.1998 Jun.1999 Dec.1999 Jun.2000 Dec.2000 Jun.2001 Dec.2001 Jun.2002 Dec.2002 Jun.2003 Dec.2003 Jun.2004 Dec.2004 Jun.2005 Dec.2005 Jun.2006

24 FX Gross Market Value : USD bn Forwards and forex swaps Currency swaps Options Jun.1998 Dec.1998 Jun.1999 Dec.1999 Jun.2000 Dec.2000 Jun.2001 Dec.2001 Jun.2002 Dec.2002 Jun.2003 Dec.2003 Jun.2004 Dec.2004 Jun.2005 Dec.2005 Jun.2006 Dec.2006 FX Risk Management Problem Suppose a U.S. MNC wants to finance a GBP 10m expansion of a British plant. They could borrow dollars in the U.S. where they are well known and exchange for dollars for pounds. This will give them exchange rate risk: financing a sterling project with dollars. They could borrow pounds in the international bond market, but pay a lot since they are not as well known abroad. 48

25 From Currency Swaps to Financial Engineering If they can find a British MNC with a mirrorimage financing need they may both benefit from a swap. If the exchange rate is S 0 ($/ ) = $1.60/, the U.S. firm needs to find a British firm wanting to finance dollar borrowing in the amount of USD 16m Financial engineering: create synthetic instruments borrow where one holds an advantage use swap to generate desired cash flow profile 49 International Borrowing Costs Consider two firms A and B: firm A is a U.S. based multinational and firm B is a U.K. based multinational. Both firms wish to finance a project in each other s country of the same size. Their borrowing opportunities are given in the table below. $ Company A 8.0% 11.6% Company B 10.0% 12.0% 50

26 Currency Swap Mechanics Swap Bank $8% $9.4% 12 11% $8% Company % Company 12 A B % $ Company A 8.0% 11.6% Company B 10.0% 12.0% 51 Currency Swap Mechanics Swap Bank $8% $9.4% 12 11% $8% Company % Company 12 A B % A s net position is to borrow at 11% A saves.6% $ Company A 8.0% 11.6% Company B 10.0% 12.0% 52

27 Currency Swap Mechanics Swap Bank $8% $9.4% 12 11% $8% Company % Company 12 A B % B s net position is to borrow at $9.4% $ Company A 8.0% 11.6% Company B 10.0% 12.0% B saves $.6% 53 Putting It All Together The swap bank makes Swap money too: Bank $8% $9.4% 12 11% $8% Company At S % 0 ($/ ) = $1.60/, Company 12 A B % that is a gain of $64,000 or 0.4% on $16m per year for 5 years. $ Company A 8.0% 11.6% Company B 10.0% 12.0% 1.4% of $16 million financed with 1% of 10 million per year for 5 years. The swap bank faces exchange rate risk, but maybe they can lay it off in another swap. 54

28 Comparative Advantage as the Basis for Swaps Which is the more credit-worthy firm? A pays 200 bpts less to borrow in USD than B A pays 40 bpts less to borrow in GBP than B $ Company A 8.0% 11.6% Company B 10.0% 12.0% A has a comparative advantage in borrowing in dollars B has a comparative advantage in borrowing in pounds 55 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 56

29 FX + Interest Rate Swap =? Two currencies, X and Y, have both fixed-rate and floating-rate segments. For example, with an interest rate swap in currency X (AB) and a fixed-fixed currency swap (AC), we can construct a cross currency interest rate swap (BC). Similarly... Currency of Denomination Currency X Currency Y Fixed Rate Asset or Liability Interest Rate Base Interest Rate Swap Floating Rate Asset or Liability A Interest Rate Swap B Fixed-Fixed Currency Swap 57 C Cross Currency Interest Rate Swap Floating-Floating Currency Swap D Funding and Risk Management Distribution and management of risks within security structure: contract design, e.g., covenants: monitoring optionalities: callability, conversion Large, mature company: multinational interest-rate risk foreign-exchange risk Funding and risk management: swaps interaction of capital structure and risks 58

30 Borrowers Objectives Lower your funding costs: optimal distribution of risks between parties look at the project from your lenders perspective Default risk: problematic since almost unhedgeable use the particular structure of investments: collateral Credit Default Swaps: limited number of liquid names guarantee: only as good as the guarantor lender bears cost: spread over benchmark Two easily hedged risks: FX and interest use hedge to lower your borrowing costs! 59 Interest and FX Rate Outlook, Bond Pricing and Issuing Analyze FX and interest rate environment by statistical methods, market analysis reconcile your own opinion with funding needs Levels: security type and structure high interest rates: floating low interest rate: fixed or capped floating Volatility: segment, deal type and timing low volatility: little advantage in repackaging high volatility: funding arbitrage, swaps Risk management includes good judgement 60

31 Basic Toolkit A&L matching: offsetting risks on balance sheet one party s risk might be the other s opportunity trading off risks: FX and default, FX and interest Fixed income security structure: distributes risks embedded options: call (prepayment) or put rights coupon: fixed or floating Derivatives: re-package original financing with swaps: FX, interest rate or FX-interest rate swaps options (insurance) : FX, yield (interest rate) embedded options: structure of bond 61 Risk vs. Exposure Risk: the variability (measured by the standard deviation) of the (domestic-currency) value of an asset, liability or operating income attributable to (unanticipated) changes in a risk factor (price, FX, IR) Exposure: the sensitivity of changes in the (real) value of assets, liabilities or operating income to (surprise) changes in risk factor (input price, etc.) Relation of risk (change) to exposure (sensitivity): change in value = exposure x change in risk factor Caveat: often used as synonyms: risk used in place of exposure - distinction somewhat artificial 62

32 Forward Market Hedge If you are going to owe/need foreign currency, funds, raw materials in the future, buy the asset now now by entering into long position in a forward contract If you are going to own/receive the asset in the future, sell the it now by entering into short position in a forward contract 63 Hedging Recurrent Exposure with Swaps Swap contracts can be viewed as a portfolio of forward contracts. Firms that have recurrent exposure can very likely hedge their (financial) risk at a lower cost with swaps than with a program of hedging each exposure as it comes along. It is also the case that swaps are available in longer-terms than futures and forwards. 64

33 Pricing Swaps A swap is a derivative instrument so it can be priced in terms of the underlying assets: Plain vanilla fixed-for-floating: valued just like a bond. XFX swap: valued just like a nest of currency futures. Swap prices reflect forward prices: swaps are series of forward contracts transaction costs: spreads carry over from the appropriate market segments - tied to benchmark credit risk: similar to FIF; essentially a counterparty (default) risk as measured by spread over benchmark arbitrage: imposes bounds/restrictions on prices 65 Interest Rate Swaps Comparative advantage: Goodrich: Radobank: total savings from swap: Synthetic debt: compare to benchmarks Floating Fixed Rating Goodrich LIBOR BBB Radobank LIBOR AAA Difference Radobank: issue fixed, swap into floating Goodrich: issue floating, swap into fixed rate debt each party keeps track of three cash flows Radobank - B.F. Goodrich, HBS ,

34 X-FX Interest Rate Swaps Comparative advantage: Beirut Power and Light: Deutsche Bank: Synthetic debt: compare to benchmarks BPL: Deutsche Bank: Cash flows: two outflows, one inflow BPL: Deutsche Bank: Floating USD Fixed DEM Rating Beirut P&L LIBOR BBB Deutsche Bank LIBOR 7.00 AA Difference 67 Floating Rate Risk Management Interest rate risk with an attitude: opinions betting on falling rates: floating rate debt buy insurance: cap the rates Interest rate cap: up-front premium an option-like instrument that pays the holder the difference between some index and actual rate floater + cap: rates stay below a certain ceiling Synthetic bonds: instruments plus swaps analyze interest rate sensitivity and pick vehicle combine swap with option: swaption 68