6.1 Swaps

6.2 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules

6.3 An Example of a “Plain Vanilla” Interest Rate Swap An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million Next slide illustrates cash flows

Millions of Dollars LIBORFLOATINGFIXEDNet DateRateCash Flow Mar.1, % Sept. 1, %+2.10–2.50–0.40 Mar.1, %+2.40–2.50–0.10 Sept. 1, %+2.65– Mar.1, %+2.75– Sept. 1, %+2.80– Mar.1, %+2.95– Cash Flows to Microsoft (See Table 6.1, page 127)

6.5 Typical Uses of an Interest Rate Swap Converting a liability from –fixed rate to floating rate –floating rate to fixed rate Converting an investment from –fixed rate to floating rate –floating rate to fixed rate

6.6 Intel and Microsoft (MS) Transform a Liability (Figure 6.2, page 128) IntelMS LIBOR 5% LIBOR+0.1% 5.2%

6.7 Financial Institution is Involved (Figure 6.4, page 129) F.I. LIBOR LIBOR+0.1% 4.985% 5.015% 5.2% Intel MS Dealer spread =.03% evenly split

6.8 Intel and Microsoft (MS) Transform an Asset (Figure 6.3, page 128) Intel MS LIBOR 5% LIBOR-0.25% 4.7%

6.9 Financial Institution is Involved (See Figure 6.5, page 129) Intel F.I.MS LIBOR 4.7% 5.015%4.985% LIBOR-0.25% Dealer spread =.03 %

6.10 The Comparative Advantage Argument (Table 6.4, page 132) AAACorp wants to borrow floating BBBCorp wants to borrow fixed FixedFloating AAACorp10.00%6-month LIBOR % BBBCorp11.20%6-month LIBOR %

6.11 The Comparative Advantage Argument AAACorp has absolute advantage in both markets But a comparative advantage in fixed BBBCorp has comparative advantage in floating If AAA borrows fixed, the gain is 1.2% If BBB borrows floating, the gain is reduced by.7% Therefore, we have a net gain of =.5% If the gain is split evenly, we have a gain per party of: G = ( )/2 =.25%

6.12 Swap Design Design the swap so AAA’s borrowing rate equals the comparative disadvantage (CD) rate minus the gain: LIBOR Do the same thing for BBB BBB’s rate with swap: Now, draw the diagram

6.13 The Swap (Figure 6.6, page 132) AAA BBB LIBOR LIBOR+1% 9.95% 10% The floating rate leg should be LIBOR

6.14 Swap Design with FI Adjust swap gain for dealer spread Suppose dealer spread =.04% Then gain: G = ( )/2 =.23% AAA’s rate with swap: LIBOR = LIBOR +.07 BBB’s rate with swap: = 10.97% Draw swap diagram

6.15 The Swap when a Financial Institution is Involved (Figure 6.7, page 133) AAA F.I.BBB 10% LIBOR LIBOR+1% 9.93% 9.97% Check that dealer spread =.04%

6.16 Criticism of the Comparative Advantage Argument The 10.0% and 11.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates The LIBOR+0.3% and LIBOR+1% rates available in the floating rate market are six- month rates BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future

6.17 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

6.18 Swap Valuation Fixed Receive: V swap = V fixed – V floating Fixed Pay: V swap = V floating - V fixed The fixed rate stream is valued as an annuity The floating rate stream is valued by noting that it is worth par immediately after the next payment date

6.19 Floating Rate Perpetuity To create a floating rate perpetuity, invest principal value in 6-month LIBOR At the end of 6-months, remove the interest and reinvest the principal value at the new 6- month LIBOR Therefore, the cost of a floating rate perpetuity is principal value It always sells for its par value immediately after interest payment

6.20 Floating Rate Instrument with Maturity T At the end of T years, floating rate perpetuity is worth the principal value M Therefore, the floating rate instrument is worth: M – Md T Or M - M/(1+y/2) 2T, where is the rate on a zero-coupon bond maturing in T years

6.21 Swap Valuation The floating rate instrument is worth: V floating = M – M/(1+y/2) 2T The fixed rate stream is worth: V fixed = (C/2)(Annuity Factor) So for Fixed Receive Swap: V swap = (C/2)(Annuity Factor) - M +M/(1+y/2) 2T

6.22 Swap Valuation The swap is structured such that initial value is zero to either party Set V swap = 0 Rearrange terms: M=(C/2)(Annuity Factor) + M/(1+y/2) 2T The left-hand side is the present value of a bond at y Since the bond is selling at par, CR = C/M = y For the swap to have zero value the fixed rate must equal the yield to maturity on a par bond The swap rate is the coupon rate on a LIBOR bond that causes it to be worth par

6.23 Example Zero coupon LIBOR curve is 5%, 6%, and 7% for one, two, and three years What is the swap rate on a three year interest rate swap? Assume payments are annual and yields are compounded annually Solve for LIBOR par yield M = CRxM(d 1 + d 2 + d 3 ) + Md 3

6.24 Example Continued Solution:

6.25 Interest Rate Risk Receive Fixed: V swap = V fixed – V floating Pay Fixed: V swap = V floating – V fixed

6.26 An Example of a Currency Swap An agreement to pay 11% on a sterling principal of £10,000,000 & receive 8% on a US$ principal of $15,000,000 every year for 5 years

6.27 Exchange of Principal In an interest rate swap the principal is not exchanged In a currency swap the principal is exchanged at the beginning and the end of the swap

6.28 Three Cash Flow Components t = 0: exchange principal based upon current exchange rates Pay: $15 M Rcv: £ 10 M t = 1, 2, 3, 4, 5: Pay:.11x10 = £1.1 M Rcv:.08x15 = $1.2 M t = 5: Pay: £ 10 M Rcv: $ 15 M

6.29 The Cash Flows (Table 6.6, page 140) Years DollarsPounds $ millions – – – – – £

6.30 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

6.31 Comparative Advantage Arguments for Currency Swaps (Table 6.7, page 141) General Motors wants to borrow AUD Qantas wants to borrow USD USDAUD General Motors 5.0%12.6% Qantas 7.0%13.0%

6.32 Comparative Advantage GM has absolute advantage in both markets But GM has comparative advantage in dollars Qantas has comparative advantage in Australian dollars So GM should borrow dollars and Qantas Australian dollars Then swap cash flows to earn gain from comparative advantage

6.33 Comparative Advantage Gain per party: G = (2 -.4)/2 =.8% GM’s rate with swap: = AUD 11.8% Qantas’ rate with swap: = USD 6.2%

6.34 GM Qantas AUD 11.8% USD 5% AUD 13% USD 5% Qantas Assumes Exchange Rate Risk

6.35 GM Qantas AUD 13.0% USD 5% AUD 13% USD 6.2% GM Assumes Exchange Rate Risk

6.36 FI Assumes Exchange Rate Risk Adjust swap gain for dealer spread Suppose dealer spread =.2% Then gain: Gain per party: G = ( )/2 =.7% GM’s rate with swap: = AUD 11.9% Qantas’ rate with swap: = USD 6.3%

6.37 GM F.I.Q USD 5% AUD11.9% AUD 13% USD 5% USD 6.3% Check that dealer spread =.2% Pay: 13.0 – 11.9 = AUD 1.1% Rcv: 6.3 – 5.0 = USD 1.3% FI Assumes Exchange Rate Risk

6.38 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

6.39 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 Fraps The “fixed for fixed” currency swap in our example consisted of a cash transaction & 5 forward contracts

6.40 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

6.41 Credit Risk A swap is worth zero to a company initially At a future time its value is liable to be either positive or negative The company has credit risk exposure only when its value is positive