INTEREST RATE SWAPS - NYU Stern School of Business

1 INTEREST RATE SWAPSS eptember 19992 INTEREST RATE SWAPSD efinition: Transfer of INTEREST rate streams without transferring underlying FOR FLOATING SWAPSome DefinitionsNotational Principal:The dollar the INTEREST rates apply Period: Period over which the coupon is tradition fixed rate payer has sold swap, floating rate payer has bought fixed for floating pays B 8% pays A six-month T bill rate + 2% three Principal one millionPERIODT-BILL RATE A B 0 4 1 330,00040,000 2 425,00040,000 3 530,00040,000 4 735,00040,000 5 845,00040,000 650,00040,0005 SOME VALUATION PRINCIPALSI gnore risk for momentAlthough principal not traded equivalent to selling afixed for floating bond of one million since this onemillion cancels initiation, both sides must be happy. Thus price offixed and floating must be same. Since floating is atpar, rate on fixed must equal rate on fixed > Duration of floatingTherefore, if rates increase, person receiving floaterbetter off.

2 If rates decline, want to receive no change in yield curve and upward sloping yieldcurve, payer of floating has positive value over itsearly + 1% for for fixed minus 1%.Example:T-bill + 1% ------------> <------------ 10%can be valued asT-bill ------------> <------------ 9%7 GENERAL SWAP spot fixed rate as fixed rate coupon minus anyfloating spread. Discount at spots to get floating is par when reset treat floating as ifbond maturing at reset date and discount cashflows at appropriate spot get present rate on six-month T-bill as of beginning 8% (semi-annual) life 18 principal 100 rates 10, , on floater OF A SWAPS waps can be valued:Difference of two bonds:Let,It follows that:NONot1)2r(1QN1ii)2r(1C B++++++++ ====++++====)()(2r1Q2r1U2B0101++++++++++++====variable onflow cash First Uflow cash Fixed Cagreement swapthe in principal NotationalQ swapthe underlying bondrate floating ofValue Bswapthe underlyingrate fixed ofValue Bswap ofValue V21========================21 BBV ==== ).

3 ().().( fixed Value====++++++++====3055110420525140514 Value variable ).(.========05188104 Value swap = fixed - variable= as futures of futures contract on six-month these floating is pegged to LIBOR(London Interbank Offer Rate)LIBOR has credit risk. Thus it has a spread over T-billrates, usually about 1/2%. Considered an AA , if initial value of swap is to be zero, the fixedrate must also exceed rate on default-free FACTORSIt is evident that a swap is equivalent to an exchange of the fact that SWAPS are carried out between corporateentities, they should display all the features of corporatebonds. However, this is usually not the case. Litzenberger(Journal of Finance, 1992) points out that there are threefeatures of difference between SWAPS and exchange of purecorporate spreads are far less than on corporate bonds,and even governments in most cases.)

4 Swap spreads arearound 5 bps, the lowest in any spreads (the difference between the fixed andfloating leg) do not display the volatile cyclical behaviorof corporate bond quoted swap rates do not reflect credit ratingdifferences between call these "credit risk anomalies."13 RISK AND principal is not swapped, maximum loss much lessthan on , if risky corporation would normally need to pay3% over Treasuries for swap, need to pay much Loss is value of swap at If floating payer is defaulter, then fixed rate payerLosses: if rates increasedGains:if rates : May gain or lose with swap deals have clause that swap is settled if oneparty's credit institutions have subsidiary that in essence insuresagainst FOR rate basis Differential information and restrictions15 MANAGING DURATIONWhy use SWAPS to manage Duration Risk? institutions such as federal agencies arerestricted or disallowed to trade in costs are can be tailored to meet needs where futuresare more ADVANTAGE The average quality spreads between Aaa and Baa in thefixed rate corporate bond market are 50-100 basis points.

5 Spread in the floating rate markets = 50 do such differences in spreads exist? This is becausecredit risk is also a function of time to maturity of a bond. Wehave also seen that SWAPS are less sensitive to credit swap technique is often evidenced when a firm expect itscredit rating to improve. Then it finds that it can obtain well-priced floating rate loans, and hence will prefer to access themin lieu of fixed rate debt. Swapping is a way out. Thefollowing example is an extremely common type of suchfinancial engineering:Why might this make sense?-Comparative advantageFixedFloatingA. 8 Libor + 9 Libor + 2 Lower-A wants floating and B wants fixed17 Example of Lowering Fixed Rate Costs:Baa corporate borrows at floating rate = T-bill + corporate borrows at floating rate = T-bill + .25%Quality spread for five years maturity = corporate borrows at fixed rate = corporate borrows at fixed rate = Differential = swap is depicted in ** Figure 3 **Method:1.

6 Aaa issues bond at Enters into swap with Baa to receive fixed 12% and pay floatingsix-month T-bill Cost of Funds:Aaa: T-bill - (gains = 75 bps)Baa: (gains = 50 bps)Result:Credit Risk Arbitrage (the total gain of 125 bps is equal to thecaptured spread differential)18 Figure 3 Fixed/Floating Rate SwapBaaCorporation12%------------------- > <-------------------T-billAaaCorporatio nT-bill + 1/2%11 1/2%(Floating-rateMarket)(Fixed-rateMark et)In fixed/floating rate swap, the Baa corporation raises funds in afloating-rate market and promises to pay the Aaa corporation a fixed-rate INTEREST , while the Aaa corporation raises funds in a fixed-ratemarket and promises to pay the Baa corporation a SWAPS (floating/floating)MANAGING BASIS RISKB asis risk arises from unequal changes in floating rates in twoseparate markets, , LIBOR vs. CD we used a floating-floating swap to hedge away this :A bank has an asset yielding LIBOR+ , and is funded bya liability at T-bill - A counterparty has floating-ratefunds atLIBOR - Swap:Bank pays floating at LIBOR (6 month), receives T-bill+ (reset weekly).

7 ** See Figure 4 **20 Figure 4 Floating/Floating Rate SwapAsset Yield(LIBOR + 3/4%BankT-bill + 1/2%<<<<------------------------------------------------>>>>LIBORC ounterpartyCDLIBOR Funding(T-bill - 1/4%)(LIBOR - 1/4%)In a floating/floating rate swap, the bank raises funds in the T-bill rate market and promises to pay the counterparty aperiodic INTEREST based upon the LIBOR rate, while thecounterparty raises funds in the LIBOR rate market andpromises to pay the bank a periodic INTEREST based upon the T-bill SWAP (Eliminating Currency Risk)- Exchange fixed for fixed in different Comparative advantage:DollarsPoundsA. 8 10B. 10 11-Note 1% A wishes to borrow in pounds, B in 8 11 Pounds 11 9 1/2 Dollars22 SIGNALLINGThis play is also often called "Synthetic Fixed RateFinancing."This arises in an asymmetric information environment.)

8 Firmshave a better idea of their credit risk levels, and often need acredible way to convey this to the market. This is called"signaling." Signaling must be credible, which basicallymeans that false signals will be punished by the market, henceonly true signals will occur in method is to signal good credit levels by borrowingfloating debt short-term and swapping out to fixed ratefinancing. A firm will only do this when it knows that itsprospects are improving and by going floating it will accessbetter and better rates in the future. The market will alsorecognize this and be willing to offer better rates today itself,provided it is sure that the firm is not bluffing. The firm isstrongly dissuaded from doing so because if next period it isfound that its credit is not improving, the market willdowngrade its credit by more than SWAPS Extendable SwapsEmbedded option to extend maturity -- analogous to anoption on a forward bond.

9 Off-Market SwapsWhen the rates at which the two legs are closed are offmarket. Reason: Usually for rearrangement of incomeflows (tax purposes). Basis SwapsFloating-Floating SWAPS Amortizing SwapsDecreasing principal Step-Up SwapIncreasing principal Deferred SwapForward start Circus SwapCross currency fix-flo