INTEREST RATE SWAPS September 1999 INTEREST RATE SWAPS Definition Transfer of interest rate streams without transferring underlying debt 2 FIXED FOR FLOATING SWAP Some Definitions Notational Principal The dollar the interest rates apply to Reset Period Period over which the coupon is fixed By tradition fixed rate payer has sold swap floating rate payer has bought swap 3 Example fixed for floating swap 1 A pays B 8 fixed 2 B pays A six month T bill rate 2 floating 3 Time three years 4 Notational Principal one million PERIOD 0 1 2 3 4 5 6 T BILL RATE 4 3 4 5 7 8 4 A B 30 000 25 000 30 000 35 000 45 000 50 000 40 000 40 000 40 000 40 000 40 000 40 000 SOME VALUATION PRINCIPALS Ignore risk for moment Although principal not traded equivalent to selling a fixed for floating bond of one million since this one million cancels out At initiation both sides must be happy Thus price of fixed and floating must be same Since floating is at par rate on fixed must equal rate on three year Treasury Duration fixed Duration of floating Therefore if rates increase person receiving floater better off If rates decline want to receive fixed If no change in yield curve and upward sloping yield curve payer of floating has positive value over its early life 5 Equivalent Swap 1 2 T bill 1 for fixed T bill for fixed minus 1 Example T bill 1 10 can be valued as T bill 9 6 GENERAL SWAP VALUATION 1 Obtain spot rates 2 Treat fixed rate as fixed rate coupon minus any floating spread Discount at spots to get present value 3 Since floating is par when reset treat floating as if bond maturing at reset date and discount cash flows at appropriate spot get present value 7 Example 1 Pay rate on six month T bill as of beginning of period 2 Receive 8 semi annual fixed 3 Remaining life 18 months 4 Notational principal 100 million 5 Spot rates 10 10 5 11 6 Rate on floater 4 88 8 VALUE OF A SWAP Swaps can be valued Difference of two bonds Let V Value of swap B1 Value of fixed rate underlying the swap B2 Value of floating rate bond underlying the swap Q Notational principal in the swap agreement C Fixed cash flow U First cash flow on variable It follows that V B1 B2 N C Q B1 i 1 1 rot i 1 rON N 2 2 Q U B2 r01 r01 1 1 2 2 9 4 4 104 Value fixed 1 05 1 0525 2 1 055 3 95 99 104 88 Value variable 99 89 1 05 Value swap fixed variable 3 90 View as futures contracts Series of futures contract on six month LIBOR Value these contracts 10 LIBOR Usually floating is pegged to LIBOR London Interbank Offer Rate LIBOR has credit risk Thus it has a spread over T bill rates usually about 1 2 Considered an AA risk Therefore if initial value of swap is to be zero the fixed rate must also exceed rate on default free Treasuries 11 INSTITUTIONAL FACTORS It is evident that a swap is equivalent to an exchange of bonds Given the fact that swaps are carried out between corporate entities they should display all the features of corporate bonds However this is usually not the case Litzenberger Journal of Finance 1992 points out that there are three features of difference between swaps and exchange of pure corporate bonds 1 Bid Ask spreads are far less than on corporate bonds and even governments in most cases Swap spreads are around 5 bps the lowest in any market 2 Swap spreads the difference between the fixed and floating leg do not display the volatile cyclical behavior of corporate bond spreads 3 The quoted swap rates do not reflect credit rating differences between counterparties We call these credit risk anomalies 12 RISK AND SWAPS 1 Since principal is not swapped maximum loss much less than on bond 2 Therefore if risky corporation would normally need to pay 3 over Treasuries for swap need to pay much less 3 Loss is value of swap at default 4 If floating payer is defaulter then fixed rate payer Losses if rates increased Gains if rates decreased 5 Note May gain or lose with default 6 Many swap deals have clause that swap is settled if one party s credit downgraded 7 Many institutions have subsidiary that in essence insures against default 13 MOTIVATIONS FOR SWAP 1 Adjust duration 2 Overcome restrictions 3 Interest rate bets 4 Managing basis risk 5 Comparative advantage a Arbitrage b Differential information and restrictions 14 MANAGING DURATION Why use swaps to manage Duration Risk 1 Many institutions such as federal agencies are restricted or disallowed to trade in futures 2 Swap costs are low 3 Swaps can be tailored to meet needs where futures are more standardized 15 COMPARATIVE ADVANTAGE The average quality spreads between Aaa and Baa in the fixed rate corporate bond market are 50 100 basis points Spread in the floating rate markets 50 bps Why do such differences in spreads exist This is because credit risk is also a function of time to maturity of a bond We have also seen that swaps are less sensitive to credit risk aspects This swap technique is often evidenced when a firm expect its credit rating to improve Then it finds that it can obtain wellpriced floating rate loans and hence will prefer to access them in lieu of fixed rate debt Swapping is a way out The following example is an extremely common type of such financial engineering Why might this make sense Comparative advantage A B Fixed 8 9 Floating Libor 1 5 Libor 2 A wants floating and B wants fixed 16 Lower Example of Lowering Fixed Rate Costs Baa corporate borrows at floating rate T bill 0 5 Aaa corporate borrows at floating rate T bill 25 Quality spread for five years maturity 1 5 Baa corporate borrows at fixed rate 13 0 Aaa corporate borrows at fixed rate 11 5 Spread Differential 1 25 The swap is depicted in Figure 3 Method 1 Aaa issues bond at 11 5 2 Enters into swap with Baa to receive fixed 12 and pay floating six month T bill rate Net Cost of Funds Aaa T bill 0 5 gains 75 bps Baa 12 5 gains 50 bps Result Credit Risk Arbitrage the total gain of 125 bps is equal to the captured spread differential 17 Figure 3 Fixed Floating Rate Swap Baa Corporation 12 T bill Aaa Corporation T bill 1 2 11 1 2 Floating rate Market Fixed rate Market In fixed floating rate swap the Baa corporation raises funds in a floating rate market and promises to pay the Aaa corporation a fixedrate interest while the Aaa corporation raises funds in a fixed rate market and promises to pay the Baa corporation a floating rate interest 18 OTHER SWAPS floating floating MANAGING BASIS RISK Basis risk arises from unequal …