Swaps. Chapter 6. Nature of Swaps. Uses of Swaps: Transforming a Liability (Figure 6.2, page 136) Typical Uses of an Interest Rate Swap

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1 Swaps Chapter 6 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to specified rules Example: A Plain Vanilla Interest Rate Swap The agreement on March 5, 2001: $100m nominal principal on a 3-year loan Microsoft will pay Intel a fixed rate of 5% per annum for 3 years Microsoft will receive from Intel 6-month Both interest payments to be made every 6 months With semi-annual compounding year duration of swap Cashflows to Microsoft under Swap (See Table 6.1, page 135) Floating rate pa Millions of Dollars FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.5, % 4.2/2=6-mnth inflow Sept. 5, % Mar.5, % Sept. 5, % Mar.5, % Sept. 5, % Mar.5, % /2=6-mnth outflow =6- mnth net cash flow Converting a liability from fixed rate to floating rate or floating rate to fixed rate Typical Uses of an Interest Rate Swap Converting an investment from fixed rate to floating rate or floating rate to fixed rate 6.5 Intel s payments before SWAP (fixed rate) Uses of Swaps: Transforming a Liability (Figure 6.2, page 136) 5% FIXED 5.2% INTEL MSOFT +0.1% (wants floatg, has fixed) swap (wants fixed, has floatg) NCFs AFTER SWAP MSOFT : L ( L+ 0.1) 5 = 5.1 (Fixed rate) INTEL: 5.2 L+ 5 = ( L+ 0.2) (Floatingrate) 6.6 Msoft s s payments before SWAP (floating rate)

2 Intel s payments before SWAP (fixed) 5.2% INTEL (wants fixed, has floating) Intermediary in Swap (Figure 6.4, page 137) Rate received by Intel is LESS: = 5% / % Institution collects 0.03%=0.015x2 FINANCIAL INSTITUTION 5.015% Rate paid by MSOFT is MORE: = 5% /2 MSOFT (wants floatg, has fixed) NCFs AFTER SWAP MSOFT : L ( L+ 0.1) = 5.115(Fixed rate) INTEL: 5.2 L = ( L ) (Floatingrate) BANK : 0.015x 2= 0.03% 6.7 Msoft s s payments before SWAP (floating) +0.1% -0.25% Intel s investment returns before SWAP (variable) Uses of Swaps: Transforming an Asset (Figure 6.3, page 137) Intel (Has floatg, wants fixed) swap 5% NCFs AFTER SWAP MS (Has fixed, wants floatg) Intel: L L = 4.75(Fixed) MS: L = L 0.3(Variable) Msoft s s investment returns before SWAP (fixed) 4.7% 6.8 Intermediary in the Swap (See Figure 6.5, page 138) 6.9 Reasons for Swaps: The Comparative Advantage Argument (Table 6.4, page 140) % Institution collects 0.03%=0.015x % Intel F.I. MS -0.25% 4.7% AAA Corp wants to borrow floating BBB Corp wants to borrow fixed AAA s comparative Advantage in Fixed Fixed Floating BBB s comparative Advantage in Variable AAA Corp 10.00% 6-month % BBB Corp 11.20% 6-month % Comparative vs. absolute advantage Note that AAA has an absolute advantage in both markets It pays less in both fixed and floating But AAA has a comparative advantage in Fixed It pays 1.2% less in fixed vs. 0.7% less in floating BBB has a comparative advantage in Floating It pays only 0.7% more in floating vs. 1.2% more in fixed 6.11 AAA specialises according to comp. adv., borrowing Fixed 10% The Swap (Figure 6.6, page 140) AAA Swap enables both to profit 9.95% BBB Profit from SWAP AAApays ( L+ 0.05) < ( L + 0.3) without swap BBBpays 10.95% < 11. 2% without swap % BBB specialises according to comp. adv., borrowing Variable

3 Gains from trade Note that the total gain from the swap is Division of the spoils Note that in our example this gain is divided equally: a b= difference in fixed- differencein floating AAA s floating rate in market AAA s floating rate under swap = ( ) (1 0.3) = % = 0.5% AAAgains : ( L + 0.3) ( L ) = 0.25% BBB gains : = 0.25% BBB s fixed rate in market BBB s fixed rate under swap Exercise What factors in practice might mean that the gains from trade might not be divided equally? 6.15 The Swap when a Financial Institution is Involved (Figure 6.7, page 141) 10% 9.93% 9.97% AAA F.I. BBB % Criticism of the Comparative Advantage Argument Criticism cont d Arbitrage opportunities Genuine differences in the value of the two contracts (fixed and floating)? Should be arbitraged away quite quickly But in fact, the differences in value persist Suggests other factors at work The differences in the rates of the two contracts reflect The relative flexibility (to the lender) of floating rates If default probability changes rate can be revised up/down The relative inflexibility to lenders of fixed rates No revisions are possible in the light of new information

4 Criticism cont d The two rates traded are not comparable The fixed rates are 5-year rates The floating rates are six-month rates BBB s fixed rate depends on the spread above it borrows at in the future 6.19 Valuation of an Interest Rate Swap Interest rate swaps can be valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bond Alternatively, they can be valued as a portfolio of forward rate agreements (FRAs) 6.20 Valuation in Terms of Bonds The fixed rate bond is valued in the usual way The floating rate bond (FRB) is valued by noting that it is worth par immediately after the next payment date 6.21 Swap pricing formula For a party receiving floating paying fixed the value of the swap, V swap, is: where Swap pricing formula B fl =price of floating ratebond under swap V swap t = timewhen ith paymentsareexchanged i r = ratefor period t i i = B B fl fix B fix =price of the fixed rate bond under swap L=Notional principal Under swap B fl = ( L + k*) e k* = known floating rate payment to be made on next payment date t 1 r1 t1 t = timewhen next payment is exchanged 1 r = rate for period t 1 1 B fix n = ke i= 1 r t i i + Le r t n n k=fixed periodic payment Under swap

5 Example Swap valuation A bank has agreed to pay 6-month receive 8% pa, semiannual On a notional principal of 100m The swap has a remaining life of 1.25 years rates are 3 months = 10% 9 months = 10.5% 15 months = 11% month at last payment date = 10.2% sa comp). Hence k = (8 / 2)100m = 4m k* = (10.2 / 2)100m = 5.1m 6.26 Timeline of the swap rates for swap: 10% 10.5% 11% This gives (from timeline) Time (years) t 1 =next payment date Remaining life of swap B = 4e fix = $98.24m B = ( ) e fl = $102.51m V = swap 0. 1x = $4.27m + 4e x x e 0.11x e t 1 =next payment date 0. 11x1. 25 Exercise 2: Valuation of swaps Look back to the Microsoft example on slide 6.4 Assume that the zero rates for maturities of 6mths, 1 year,1.5years..3 years are 5%, 6%, 10% pa. continuous What is the value of the swap to Microsoft as of March 5, 2001? March 6, 2003? (Assume that the zero curve doesn t change over time) 6.29 Proof of FRB pricing formula A proof of this can be found in Cuthbertson and Nitzsche, Financial Engineering, Wiley It involves the use of forward rates 6.30

6 Valuation in Terms of FRAs 6.31 An Example of a Currency Swap 6.32 Each exchange of payments in an interest rate swap is an FRA The FRAs can be valued on the assumption that today s forward rates are realized An agreement to pay 11% on a sterling principal of 10m & receive 8% on a US$ principal of $15m every year for 5 years Exchange of Principal The Cash Flows (Table 6.7, page 149) In an interest rate swap the principal is not exchanged In a currency swap the principal is exchanged at the beginning and at the end of the swap Dollars Pounds $ Year millions Typical Uses of a Currency Swap Conversion from a liability in one currency to a liability in another currency Conversion from an investment in one currency to an investment in another currency 6.35 Comparative Advantage Arguments for Currency Swaps (Table 6.9, page 150) General Motors wants to borrow AUD Qantas wants to borrow USD USD AUD General Motors 5.0% 12.6% Qantas 7.0% 13.0% 6.36

7 Valuation of Currency Swaps Like interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contracts Swaps & Forwards A swap can be regarded as a convenient way of packaging forward contracts The plain vanilla interest rate swap in our example consisted of 6 FRAs The fixed for fixed currency swap in our example consisted of a cash transaction & 5 forward contracts Swaps & Forwards (continued) The value of the swap is the sum of the values of the forward contracts underlying the swap Swaps are normally at the money initially This means that it costs nothing to enter into a swap It does not mean that each forward contract underlying a swap is at the money initially 6.39 Credit derivatives Three main types: Credit default swaps Total return swaps Credit spread options Two aspects to credit risk The risk of default ( default risk ) Uncertainty about recovered amount in event of default ( Spread risk ) Key contrast between the three derivatives is proportion of Default risk spread risk that is covered Credit default swap Only default risk covered Investor buying credit protection pays the provider to guarantee payment in the event that an investment defaults Provides a lump sum or periodic payments in the event of default Does not cover changes in spreads if no default occurs

8 Total return swap Both default and spread risks (generally) Credit spread options Written on total spread (capital loss/gain + interest) This changes with changes in» Recovery rates» Probability of default 6.43 Example: Total return swap Suppose a bank lends $1m to an A- rated company ( A ) at 12% pa. It does this by buying A s bonds to the value of $1m The bank then purchases a total return swap: Paying to the counterparty (A) a fixed amount pa. F (12%) Representing» the annualised cost of the loan repayments» admin costs of the loan Any change in the market value of the loan Receiving from the counterparty The bank s returns to the swap: Bank payments= F + B / B Bankreceipts = Example suppose that the loan falls in value by 7% F is fixed at 12% pa Then Bank pays counterparty A in the swap 12 % 7% = 5% If is 11% then bank s net position is 5 % + 11% = 6% On average the bank expects at least to break even on the transaction I.e. get at least the change in the market value of the loan, net The bank s net receipt of 6% to some extent compensates for the fall in the market value of the loan (7%)

9 Credit Risk Case study questions A swap is worth zero to the parties initially Expected returns should equal cost Competitive market conditions/arbitrage At a future time its value is liable to be either positive or negative What is a credit derivative? Describe the credit default swap what variants of this transaction are possible? How would you set the y basis points number (the default premium under the swap)? What risks exist in the transaction? Which do you think is of the most concern? Are there any alternative structures you can think of?