BUS326 Lect 10 Swaps - INTEREST RATE SWAPS AND FRNS REFERENCES Hogan W et ai 2004 Management of Financial Institutions Brisbane Wiley Chapter 15 Lange H

BUS326 Lect 10 Swaps - INTEREST RATE SWAPS AND FRNS...

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Unformatted text preview: INTEREST RATE SWAPS AND FRN’S REFERENCES Hogan, W. et ai ., 2004. Management of Financial Institutions, Brisbane Wiley, Chapter 15. Lange, H. et al., 2007. Financial Institutions Management. Sydney: McGraw Hill, Chapter 20. Marshall, HF. and Kapner. KR. 1993. Understanding Swaps, New York: Wiley, Chapter 7. 1.0 Overview - This topic is primarily concerned with interest rate swaps. These involve the exchange of a sequence of fixed—rate payments that resemble the coupon payments from a bond for a sequence of floating rate payments that resemble the interest payments from a floating rate note. 0 The features of bonds have been covered extensively in previous topics. The features of floating rate instruments however, will be discussed briefly. ° Interest rate swaps are used by banks to hedge exposures to interest rate changes. This may be achieved on a micro level by hedging their exposure to a particular liability, or on a macro level by hedging their total interest rate exposure. - Major international banks may also perform the role of swap dealer by running a “swap book’ by offering both sides of a swap to counterparties. 2.0 Floating Rate Instruments - Floating Rate Bonds and Loans Defined as coupon bonds or loans with payment tied to a market rate of interest such as T»bill rate, LIBOR or bank bill rate (BBR). 0 Characteristics of Floaters (1) Price Stability Consider'a 15% coupon rate bond with 5 years to maturiw fand face (value of $1000 and interest paid anm‘i‘ally. ISOL ‘ 150L 11 150jL 1150i 1 2 3 4 5 If the discount rate is 15% then the price of the bond equals $1000. If the discount rate changes to 10% and the bond is a fixed rate then the price of the bond equals approximately $1 189. If the discount rate changes to 10%, and the bond is a variable rate then the price of the bond equals approximately $1000. The price of a floating rate instrument returns to exactly the par value at the interest rate reset date. The price is therefore equal to the par value discounted at the current market interest rate over the period to the next reset. (2) Duration After reset, the floater's duration will equal the remaining time to reset. Examine two strategies rolling over of T- bills and the alternative of purchasing a floater " Strategy 1: Rolling over T- Bills every 90 days or 0.25 year ._ . $1000 1000(l+r0) 1000(1—11-1) l U. ii 0.25 0.50 Strategy 2: Purchase of a floater L3:1000 1000 (r0)i 1000 (r1:l 0.25 0.50 Since the net cash flows are identical then duration at the beginning of each roll over is 0.25 year. 3.0 Interest Rate Swaps - Features of interest rate swap: - Both parties exchange periodic cashflows based on — notional principal amount - market interest rates - “Plain vanilla’ swap trades a fixed interest rate for a floating interest rate - In practice only net cashflows are paid ° It is useful to review an example of a swap arrangement that was presented in BUSZ44 Treasury Management. 3.1 Example of InterestRate Swap * Suppose two parties, Bill and Ben need to borrow $2 million for four years. Bill is of higher credit standing and borrows at: fixed rate with semi-annual interest payments to exploit his comparative advantage. Ben however uses short—term money market instruments that can be rolled over on a sixw monthly basis. Relative to the form of their incomes, both however have an interest rate exposure as indicated below: F Income Liability Bill Libor + 2% pa. 9.5% p.a. fixed Ben 11.5% p.a. fixed Libor + 0.5% p.a. Weed bank has the following indicative pricing schedule for plain-vanilla interest rate swaps: Maturity Mid-rate 2 years 9. 00% 3 years 9.20% 4 years 9.35% 5 years 9.45% For dealer pays fixedwrate, subtract 10 basis points and for dealer receives fixed, add 10 basis points. Quotes are against 6-month AUD Liborflat. The, following swap arrangement removes the interest rate risk for both Bill and Ben, allowing Bill to earn 1.75% pa. and Ben to earn 1.55% p.21. irrespective of interest rates. Weed Bank would earri.‘0.2% p.a. A This followed because: Bill effectively borrows at: 9.5 ~ 9.25 + libor = libor+~0.25% p.a. Ben effectively borrows at: 1ibor+0.5 + 9.45 — libor = 9.95% pa. - The following example from Hogan (p473) explains the concept of “comparative advantage, and why Bill and Ben may have borrowed at fixed and floating rate respectively in spite .of having income that was respectively floating and fixed rate. Borrowing opportunities, Aqua Ltd and Brown Ltd BBSW BBSW + 50 bps Aqua Ltd Brown Ltd Aqua Ltd advantage over Brown Ltd : 3—year’l‘reasury L ii: W; 3‘YeaFT1'easu1—y .15 : rate plus 48 bps rate plus 53 bps I Barrows ({3} £313st plus 50 pbs ‘ Sorrows (ti) 6'35‘36: Gains to Swaps 'I'Aqua has exploited its comparative advantage in the capital market of SObp o? Split: 23bp to Aqua 22bp to Brown, and pr to the swap dealer eioBrown has taken on the risk that the spread paid over BB SW may change over the 3 years 4.0 Micro Hedging ' North Bank 1n the previous lecture had made loans of $10 million at 10% p. a., payable semi- annually, that mature in 10 years. Suppose that 6- month CDs were used to finance these loans and that they would be rolled over on maturity. Currently, the CD rate is 8% p a., but may increase by 0.5% p. a. over the following 3 months (as before). Assuming there is no other interest rate change over the life of the loans, the present value of North Bank’s interest margin would decrease by: l x 1.0425 + (0.015 x 0.5 x $10 Willi0n)A19,4.25%] — (0.02 x 0.5 >< $10 million)A20=4_00% : $1,021,058 — $1,359,033 m ~£337,975 x [0.02 x 0.5 x $10 million Note that this is similar to the decrease in the value of the $10 million loan arising from the 0.5% p.a. increase in interest rates that was hedged against using futures (the difference is because the loan was discounted at the lending rate). - By entering an interest rate swap to receive 6— month libor and pay fixed rate semiaannually, North Bank would avoid the decrease in net interest margin (aside from differences in changes to 6-month libor compared to changes to 6-month CD rates) and thus a decrease in the value of its equity. Further, the swap hedge has the advantage over the futures hedges-in the previous lecture in that it does not have to be‘v‘Frolled over prior to expiry of the futures contract (every 3 months) with the associated basis risk. " '520 Hedging the Duration Gap ' * Bank’s can use swaps to hedge against changes to interest rates adversely affecting the value of the bank’s equity. Rather than by micro-«hedging each asset and liability mismatch on the balance sheet, it can apply a macrowhedge to the duration gap. - The key to hedging using swaps is to note that a fixed-rate payer is effectively short in a fixed—rate bond, and long in a floating-rate note. Both will change in value as interest rates change, but as the duration of a floatingwrate note is short, being equal to the time until repricing, the change in the value of the swap is approximately equal to the change in the value of the bond. That is: AS W AB ° For a bond: AR 1+ R Where DB is the duration of the fixed rate bond. ABz—DBX XB ° For value of a bank’s equity: L AR .. AE:W(DA —ZDL)~X 1+R XAV ' Hence the: value of a bank’s—"i'equity can be hedged by setting AB S AE . I AR L AR xB=—D —~—D >< 1+R (A A L) 1+R L DB.B : (DA ”EDL).A XA will provide a hedge for the bank’s equity, Where B is the notional value of the swap, and DB is determined as the duration of the bond representing the fixed-rate leg of the swap. If the duration gap is positive, a short position in a bond would be required as a hedge, and therefore the bank would enter the swap as the fixed-rate payer. ~ Consider East Bank in the previous lecture (pl 1): A = $100 million DA = 6.5 years L = $90 million D1, = 2.0 years int = 10% pa. (all maturities) Suppose that a four-year swap in which the fixed—rate payer pays 10% pa. semiwannually against 6—month libor was available.- The duration of the swap would be approximated as 3.39 years. ‘ L 13,13 2(1),, ~2DL).A L29", 3.39X B 2 (6.5 #2,,ng 20)){100 100 B: 470 3.39 B = $138.64 million Thus East Bank would enter a 4-year plain-vanilla interest rate swap with a notional $138.64 million principal, as fixed-rate payer. ° It was calculated in the previous lecture (pl 1) that a l% increase in interest rates would result in a decrease in the value of East Bank’s equity by $4,272,727. 10 The present value of the payment obligation on the fixed-rate leg would decrease from $138,640,000 million to $134,248,900. That is a decrease of $4,391,100. Hence, the decrease in the value of the bank’s equity is approximately offset by the decrease in the value of the bank’s payment obligations under the swap. 0 Note however, that this is an approximation since the change in the value of a swap following an interest rate change should properly take into account the change in the value of the floating rate payments as well. It should also be noted that in this example, the yield curve was assumed to be flat, With a parallel .. shift. This will not normally be the case. ' 6.0 Swap Pricing - ‘Pricing’ a swap refers to the process of determining the interest rate that should be paid on the fixed rate (as a mid—rate) against a floating—rate. For an ‘on— market’ ‘plain vanilla’ configuration swap, the floating rate is set to an indicator rate such as libor or BBSW. The ‘indicative pricing schedule’ in the example in section 1.1 results from swaps with different maturities being priced. ll - Swap dealers must correctly price a swap in order to successfully make both sides (i.e. the ‘dealer pays fixed’ side and the ‘dealer receives fixed” side) of the swap attractive to the counterflparties. Note that it is not necessary to have equal but opposite counter- parties on each swap (as illustrated in the section 1.1 example), but rather, the dealer will offer several swaps on each side (i.e. running a hook) with the aim of them balancing in aggregate. ' The ‘price’ of a swap should not be confused with its ‘value’. At origination, the value of a swap is zero. As interest rates change over time, the value of the swap will take on aiepositive value to one party, and a corresponding negative value to the other. 6.1 Pricing From the Yield Curve °§°Method 1: k «2°Set PV(floating—rate stream) = PV(fixed-rate stream) eieMethod 2: ¢i°Set PV(fixed-rate bond) : par value ' Swap Pricing Example e? Find the fixed rate for a 4~year swap given a zero~ coupon spot yield curve of: Years 1 2 3 1; Spat rate 0.85 0.055 {1% 9.065 ®§°Step 1 ._ Find the zero-«coupon yield curve (given above) 12 a? Step 2 — Calculate implied forward rates Forward rates 1% f1 f2 fa {105 0.06 0.07 8.08 °§°Step 3 — Calculate PV(floating stream) °§° Step 4 - Solve for P which has same PV - Swap Value After the Start Date °§° If the yield curve moves, then the value of the swap .Will charrge fieThe value is computed as PV(fixed — floating) Lei» Based on the new yield curve for the floating leg and for the discount rates ' 9%» Based on. the original interest rate for the fixed leg 6.23 Pricing from Bank Bill Futures Strip $011 3 August we arrange a $100 million notional swap with a 1 year maturity eWe pay fixed and receive BBSW every 3 months el’recise timing of payments will depend on the nearest bill futures contract with a shorter ’stub’ period from origination. to the first payment date .3 Trade. Reset Reset Reset . i . Expiration : date 333 date we date £9112 date 1013 date 319 Q ' and 2nd and 311-} 3 pay date. 1333! date 13 etoAs indicated above, the first payment will be on 10 September, with 3 subsequent payments 3 months apart Implied futures rates for discounting fixed~rate leg of fixed-for—fleating swap 3 Aug. to 19 Sept.M 10 Sept. to 10 Dec. 10 Dec. to 10 March 10 March to 9 June 9 June to 8 Sept. 3 August 10 September 10 December 91 9? 9} September Becember March 10 March Eune 9 June * BBSW spot rate on 3 August (trade date). ** Stub period. - a Calcuiation of the value of a swap 3 August 0.994247 10 September 0.120548 0.994247 10 December 0.249315 0.987907 0.982223 1.224137 1.202376 10 March 0.249315 0.987129 ‘ 0.969581 1.303918 1.264254 9 June 0.249315 0.986861 0.956842 1.331342 1.273884 8 September 0.249315 0.986109 0.943551 1.413863 1.329114 SBM 5.069627 otoAt this point we need to solve for the fixed payment P which gives a present value of 5.069627 P (0.98222 «+~ 0.96958 + 0.95684 + 0.94355) 2 5.069627 F .._., 1.3160 05A fixed payment of 1.3160 per quarter on a notional principal of $100 implies an annual fixed interest rate of: 14 13160 x 363 = 0.0528 100 91 6.3 Swap Credit Exposure °§°Swap participants are subject to counterparty risk as there is no clearing house to guarantee performance #26 Generally, swap users maintain credit lines with their banks to cover this risk °3°Credit exposure from swaps is included in riskwbased capital computations 15 ...
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