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Swaps Finance 298 Analysis of Fixed Income Securities Drake Fin 284 DRAKE UNIVERSITY Drake Introduction Drake University Fin 284 An agreement between two parties to exchange cash flows in the future. The agreement specifies the dates that the cash flows are to be paid and the way that they are to be calculated. A forward contract is an example of a simple swap. With a forward contract, the result is an exchange of cash flows at a single given date in the future. In the case of a swap the cash flows occur at several dates in the future. In other words, you can think of a swap as a portfolio of forward contracts. Drake Mechanics of Swaps Drake University Fin 284 The most common used swap agreement is an exchange of cash flows based upon a fixed and floating rate. Often referred to a “plain vanilla” swap, the agreement consists of one party paying a fixed interest rate on a notional principal amount in exchange for the other party paying a floating rate on the same notional principal amount for a set period of time. In this case the currency of the agreement is the same for both parties. Drake Notional Principal Drake University Fin 284 The term notional principal implies that the principal itself is not exchanged. If it was exchanged at the end of the swap, the exact same cash flows would result. Drake An Example Drake University Fin 284 Company B agrees to pay A 5% per annum on a notional principal of $100 million Company A Agrees to pay B the 6 month LIBOR rate prevailing 6 months prior to each payment date, on $100 million. (generally the floating rate is set at the beginning of the period for which it is to be paid) Drake The Fixed Side Drake University Fin 284 We assume that the exchange of cash flows should occur each six months (using a fixed rate of 5% compounded semi annually). Company B will pay: ($100M)(.025) = $2.5 Million to Firm A each 6 months. Summary of Cash Flows Drake Drake University for Firm B Fin 284 Cash Flow Cash Flow Net Date LIBOR Received Paid Cash Flow 3-1-98 4.2% 9-1-98 4.8% 2.10 2.5 -0.4 3-1-99 5.3% 2.40 2.5 -0.1 9-1-99 5.5% 2.65 2.5 0.15 3-1-00 5.6% 2.75 2.5 0.25 9-1-00 5.9% 2.80 2.5 0.30 3-1-01 6.4% 2.95 2.5 0.45 Drake Swap Diagram Drake University Fin 284 LIBOR Company A Company B 5% Drake Offsetting Spot Position Drake University Fin 284 Assume that A has a commitment to borrow at a fixed rate of 5.2% and that B has a commitment to borrow at a rate of LIBOR + .8% Company A Company B Borrows (pays) 5.2% Borrows (pays) LIBOR+.8% Pays LIBOR Receives LIBOR Receives 5% Pays 5% Net LIBOR+.2% Net 5.8% Drake Swap Diagram Drake University Fin 284 LIBOR 5.2% LIBOR+.8% Company A Company B 5% LIBOR +.2% 5.8% The swap in effect transforms a fixed rate liability or asset to a floating rate liability or asset (and vice versa) for the firms respectively. Drake Role of Intermediary Drake University Fin 284 Usually a financial intermediary works to establish the swap by bring the two parties together. The intermediary then earns .03 to .04% per annum in exchange for arranging the swap. The financial institution is actually entering into two offsetting swap transactions, one with each company. Drake Swap Diagram Drake University Fin 284 LIBOR LIBOR 5.2% LIBOR+.8% Co A FI Co B 4.985% 5.015% A pays LIBOR+.215% B pays 5.815% The FI makes .03% Drake Day Count Conventions Drake University Fin 284 The above example ignored the day count conventions on the short term rates. For example the first floating payment was listed as 2.10. However since it is a money market rate the six month LIBOR should be quoted on an actual /360 basis. Assuming 184 days between payments the actual payment should be 100(0.042)(184/360) = 2.1467 Drake Day Count Conventions II Drake University Fin 284 The fixed side must also be adjusted and as a result the payment may not actually be equal on each payment date. The fixed rate is often based off of a longer maturity instrument and may therefore uses a different day count convention than the LIBOR. If the fixed rate is based off of a treasury note for example, the note is based on a different day convention. Drake Role of the Intermediary Drake University Fin 284 It is unlikely that a financial intermediary will be contacted by parties on both side of a swap at the same time. The intermediary must enter into the swap without the counter party. The intermediary then hedges the interest rate risk using interest rate instruments while waiting for a counter party to emerge. This practice is referred to as warehousing swaps. Drake Why enter into a swap? Drake University Fin 284 The Comparative Advantage Argument Fixed Floating A 10% 6 mo LIBOR+.3 B 11.2% 6 mo LIBOR + 1.0% Difference between fixed rates = 1.2% Difference between floating rates = 0.7% B Has an advantage in the floating rate. Drake Swap Diagram Drake University Fin 284 LIBOR LIBOR 10% LIBOR+1% Co A FI Co B 9.935% 9.965% A pays LIBOR+.065% instead of LIBOR+.3% B pays 10.965% instead of 11.2% The FI makes .03% Drake Spread Differentials Drake University Fin 284 Why do spread differentials exist? Differences in business lines, credit history, asset and liabilities, etc… Drake Valuation of Interest Rate Swaps Drake University Fin 284 After the swap is entered into it can be valued as either: A long position in one bond combined with a short position in another bond or A portfolio of forward rate agreements. Drake Relationship of Swaps to Bonds Drake University Fin 284 In the examples above the same relationship could have been written as Company B lent company A $100 million at the six month LIBOR rate Company A lent company B $100 million at a fixed 5% per annum Drake Bond Valuation Drake University Fin 284 Given the same floating rates as before the cash flow would be the same as in the swap example. The value of the swap would then be the difference between the value of the fixed rate bond and the floating rate bond. Drake Fixed portion Drake University Fin 284 The value of either bond can be found by discounting the cash flows from the bond (as always). The fixed rate value is straight forward it is given as: n B fix keriti Qe rntn i 1 where Q is the notional principal and k is the fixed interest payment Drake Floating rate valuation Drake University Fin 284 The floating rate is based on the fact that it is a series of short term six months loans. Immediately after a payment date Bfl is equal to the notional principal Q. Allowing the time until the next payment to equal t1 r1t1 * r1t1 B fl Qe k e where k* is the known next payment Drake Swap Value Drake University Fin 284 If the financial institution is paying fixed and receiving floating the value of the swap is Vswap = Bfl-Bfix The other party will have a value of Vswap = Bfix-Bfl Drake Example Drake University Fin 284 Pay 6 mo LIBOR & receive 8% 3 mo 10% 9 mo 10.5% 15 mo 11% Bfix = 4e .-1(.25)+4e -.105(.75)+104e -.11(1.25)=98.24M Bfloat = 100e -.1(.25) + 5.1e -.1(.25) =-102.5M -4.27 M Drake A better valuation Drake University Fin 284 Relationship of Swap value to Forward Rte Agreements Since the swap could be valued as a forward rate agreement (FRA) it is also possible to value the swap under the assumption that the forward rates are realized. Drake To do this you would need to: Drake University Fin 284 Calculate the forward rates for each of the LIBOR rates that will determine swap cash flows Calculate swap cash flows using the forward rates for the floating portion on the assumption that the LIBOR rates will equal the forward rates Set the swap value equal to the present value of these cash flows. Drake Swap Rate Drake University Fin 284 This works after you know the fixed rate. When entering into the swap the value of the swap should be 0. This implies that the PV of each of the two series of cash flows is equal. Each party is then willing to exchange the cash flows since they have the same value. The rate that makes the PV equal when used for the fixed payments is the swap rate. Drake Example Drake University Fin 284 Assume that you are considering a swap where the party with the floating rate will pay the three month LIBOR on the $50 Million in principal. The parties will swap quarterly payments each quarter for the next year. Both the fixed and floating rates are to be paid on an actual/360 day basis. Drake First floating payment Drake University Fin 284 Assume that the current 3 month LIBOR rate is 3.80% and that there are 93 days in the first period. The first floating payment would then be 93 .038 50,000,000 490,833.3333 360 Drake Second floating payment Drake University Fin 284 Assume that the three month futures price on the Eurodollar futures is 96.05 implying a forward rate of 100-96.05 = 3.95 Given that there are 91 days in the period. The second floating payment would then be 91 .0395 50,000,000 499,236.1111 360 Drake Example Floating side Drake University Fin 284 Day Futures Fwd Floating Period Count Price Rate Cash flow 91 3.80 1 93 96.05 3.95 490,833.3333 2 91 95.55 4.45 499,236.1111 3 90 95.28 4.72 556,250.0000 4 91 596,555.5555 Drake PV of Floating cash flows Drake University Fin 284 The PV of the floating cash flows is then calculated using the same forward rates. The first cash flow will have a PV of: 490,833.3333 486,061.8263 93 1 .038 360 Drake PV of Floating cash flows Drake University Fin 284 The PV of the floating cash flows is then calculated using the same forward rates. The second cash flow will have a PV of: 499,236.1111 489,495.4412 93 91 1 .038 1 .0395 360 360 Drake Example Floating side Drake University Fin 284 Day Fwd Floating Period PV of Floating CF Count Rate Cash flow 91 3.80 1 93 3.95 490,833.3333 486,061.8263 2 91 4.45 499,236.1111 489,495.4412 3 90 4.72 556,250.0000 539,396.1423 4 91 596,555.5555 525,668.5915 Drake PV of floating Drake University Fin 284 The total PV of the floating cash flows is then the sum of the four PV’s: $2,040,622.0013 Drake Swap rate Drake University Fin 284 The fixed rate is then the rate that using the same procedure will cause the PV of the fixed cash flows to have a PV equal to the same amount. The fixed cash flows are discounted by the same rates as the floating rates. Note: the fixed cash flows are not the same each time due to the changes in the number of days in each period. The resulting rate is 4.1294686 Drake Example: Swap Cash Flows Drake University Fin 284 Day Fwd Floating Period Fixed CF Count Rate Cash flow 91 3.80 1 93 3.95 490,833.3333 533,389.7003 2 91 4.45 499,236.1111 521,918.9541 3 90 4.72 556,250.0000 516,183.5810 4 91 596,555.5555 521,918.9541 Drake Swap Spread Drake University Fin 284 The swap spread would then be the difference between the swap rate and the on the run treasury of the same maturity. Drake Swap valuation revisited Drake University Fin 284 The value of the swap will change over time. After the first payments are made, the futures prices and corresponding interest rates have likely changed. The actual second payment will be based upon the 3 month LIBOR at the end of the first period. Therefore the value of the swap is recalculated. Drake Currency Swaps Drake University Fin 284 The primary purpose of a currency swap is to transform a loan denominated in one currency into a loan denominated in another currency. In a currency swap, a principal must be specified in each currency and the principal amounts are exchanged at the beginning and end of the life of the swap. The principal amounts are approximately equal given the exchange rate at the beginning of the swap. Drake A simple example Drake University Fin 284 Assume that company A pays a fixed rate of 11% in sterling and receives a fixed interest rate of 8% in dollars. Let interest payments be made once a year and the principal amounts be $15 million and L10 Million Company A Dollar Cash Sterling Cash Flow (millions) Flow (millions) 2/1/1999 -15.00 +10.00 2/1/2000 +1.20 -1.10 2/1/2001 +1.20 -1.10 2/1/2002 +1.20 -1.10 2/1/2003 +1.20 -1.10 2/1/2004 +16.20 -11.10 Drake Intuition Drake University Fin 284 Suppose A could issue bonds in the US for 8% interest, the swap allows it to use the 15 million to actually borrow 10million sterling at 11% (A can invest L 10M @ 11% but is afraid that $ will strength it wants US denominated investment) Drake Comparative Advantage Again Drake University Fin 284 The argument for this is very similar to the comparative advantage argument presented earlier for interest rate swaps. It is likely that the domestic firm has an advantage in borrowing in its home country. Example using comparative Drake Drake University advantage Fin 284 Dollars AUD (Australian $) Company A 5% 12.6% Company B 7% 13.0% 2% difference in $US .4% difference in AUD Drake The strategy Drake University Fin 284 Company A borrows dollars at 5% per annum Company B borrows AUD at 13% per annum They enter into a swap Result Since the spread between the two companies is different for each firm there is the ability of each firm to benefit from the swap. We would expect the gain to both parties to be 2 - 0.4 = 1.6% (the differences in the spreads). Drake Swap Diagram Drake University Fin 284 AUD 11.9% AUD 13% 5% AUD 13% Co A FI Co B 5% 6.3% A pays 11.9% AUD instead of 12.6% AUD B pays 6.3% $US instead of 7% $US The FI makes .2% Drake Valuation of Currency Swaps Drake University Fin 284 Using Bond Techniques Assuming there is no default risk the currency swap can be decomposed into a position in two bonds, just like an interest rate swap. In the example above the company is long a sterling bond and short a dollar bond. The value of the swap would then be the value of the two bonds adjusted for the spot exchange rate. Drake Swap valuation Drake University Fin 284 Let S = the spot exchange rate at the beginning of the swap, BF is the present value of the foreign denominated bond and BD is the present value of the domestic bond. Then the value is given as Vswap = SBF – BD The correct discount rate would then depend upon the term structure of interest rates in each country Drake Other swaps Drake University Fin 284 Swaps can be constructed from a large number of underlying assets. Instead of the above examples swaps for floating rates on both sides of the transaction. The principal can vary through out the life of the swap. They can also include options such as the ability to extend the swap or put (cancel the swap). The cash flows could even extend from another asset such as exchanging the dividends and capital gains realized on an equity index for a fixed or floating rate. Drake Beyond Plain Vanilla Swaps Drake University Fin 284 Amortizing Swap -- The notional principal is reduced over time. This decreases the fixed payment. Useful for managing mortgage portfolios and mortgage backed securities. Accreting Swap – The notional principal increases over the life of the swap. Useful in construction finances. For example is the builder draws down an amount of financing each period for a number of periods. Drake Beyond Plain Vanilla Drake University Fin 284 You can combine amortizing and accreting swaps to allow the notional principal to both increase and decrease. Seasonal Swap -- Increase and decrease of notional principal based of f of designated plan Roller Coaster Swap -- notional principal first increases the amortizes to zero. Drake Off Market Swap Drake University Fin 284 The interest rate is set at a rate above market value. For example the fixed rate may pay 9% when the yield curve implies it should pay 8%. The PV of the extra payments is transferred as a one time fee at the beginning of the swap (thus keeping the initial value equal to zero) Forward and Drake Drake University Extension Swaps Fin 284 Forward swap – the payments are agreed to begin at some point in time in the future If the rates are based on the current forward rate there should not be any exchange of principal when the payments begin. Other wise it is an off market swap and some form of compensation is needed Extension Swap – an agreement to extend the current swap (a form of forward swap) Drake Basis Swaps Drake University Fin 284 Both parties pay floating rates based upon different indexes. For example one party may pay the three month LIBOR while the other pays the three month T- Bill. The impact is that while the rates generally move together the spread actually widens and narrows, Therefore the return on the swap is based upon the spread. Drake Yield Curve Swaps Drake University Fin 284 Both parties pay floating but based off of different maturities. Is similar to a basis swap since the effective result is based on the spread between the two rates. A steepening curve thus benefits the payer of the shorter maturity rate. This is utilized by firms with a mismatch of maturities in assets and liabilities (banks for example). It can hedge against changes in the yield curve via the swap. Drake Rate differential (diff) swap Drake University Fin 284 Payments tied to rate indexes in different currencies, but payments are made in only one currency. Drake Corridor Swap Drake University Fin 284 Payments obligation only occur in a given range of rates. For example if the LIBOR rate is between 5 and 7%. The swap is basically a tool based on the uncertainty of rates. Drake Flavored Currency Swaps Drake University Fin 284 The basic currency swap can be modified similar to many of the modifications just discussed. Swaps may also be combined to produce desired outcomes. CIRCUS Swap (Combined interest rate and currency swap). Combines two basic swaps Drake Circus Swap Diagram Drake University Fin 284 LIBOR Company A Company B 5% US$ 6% German Marks Company A Company C LIBOR Drake Circus Swap Diagram Drake University Fin 284 Company B Company A 5% US$ 6% German Marks Company C Drake Swapation Drake University Fin 284 An option on a swap that specifies the tenor, notional principal fixed rate and floating rate Price is usually set a a % of notional principal Receiver Swapation The holder has the right to enter into a swap as the fixed – rate receiver Payer Swapation The holder has the right to enter into a particular swap as the fixed rate payer. Swapation as Drake Drake University call (or put) Options Fin 284 Receiver swapation – similar to a call option on a bond. The owner receives a fixed payment (like a coupon payment) and pays a floating rate (the exercise price) Payer swapation – if exercised the owner is paying a stream similar to the issue of a bond. Drake In-the-Money Swapations Drake University Fin 284 A receiver swapation is in the money if interest rates fall. The owner is paying a lower fixed rate in exchange for the fixed rate specified in the contract. Similarly a payer swapation is generally in the money if interest rates increase since the owner will receive a higher floating rate. Drake When to Exercise Drake University Fin 284 The owner of the receiver swapation should exercise if the fixed rate on the swap underlying the swapation is greater than the market fixed rate on a similar swap. In this case the swap is paying a higher rate than that which is available in the market. A fixed income Drake Drake University swapation example Fin 284 Consider a firm that has issued a corporate bond with a call option at a given date in the future. The firm has paid for the call option by being forced to pay a higher coupon on the bond than on a similar noncallable bond. Assume that the firm has determined that it does not want to call the bond at its first call date at some point in the future. The call option is worthless to the firm, but it should theoretically have value. Capturing the Drake Drake University value of the call Fin 284 The firm can sell a receiver swapation with terms that match the call feature of the bond. The firm would receive for this a premium that is equal to the value of the call option. Drake Example Drake University Fin 284 Assume the firm has previously issued a 9% coupon bond that makes semiannual payments and matures in 7 years with a face value of $150 Million. The bond has a call option for one year from today. Drake Example continued Drake University Fin 284 The firm can sell a European Receiver Swapation with an expiration in one year. The Swapation terms are for semiannual payments at a fixed rate of 9% in exchange for floating payments at LIBOR. The firm receives a premium for the swapation equal to a fixed percentage of the $150 Million notional value (equal to the value of the call option). The firm can keep the premium but has a potential obligation in one year if the counter party exercises the swap. Drake Example Continued Drake University Fin 284 In one year the fixed rate for this swap is 11% The option will expire worthless since the owner can earn a fixed 11% on a similar swap. The firm gets to keep the premium. Drake Example Continued Drake University Fin 284 If in one year the fixed rate of interest on a similar swap is 7% the owner will exercise the swap since it calls for a 9% fixed rate. The firm can call the bond since rates have decreased. It can finance the call by issuing a floating rate note at LIBOR for the term of the swap. The floating rate side of the swap pays for the note and the firm is still paying the original 9% fixed, but it has also received the premium on the swapation Extendible and Cancelable Drake Drake University swaps Fin 284 Similar to extension swaps except extension swaps represent a firm commitment to extend the swap. An extendible swap has the option to extend the agreement. Arranged via a plain vanilla swap an a swapation. Drake Extendible and Cancelable Drake University Fin 284 Extendible pay fixed swap = plain vanilla pay fixed plus payer swapation Extendible Receive-Fixed Swap = plain vanilla receive fixed swap + receiver swapation Cancelable Pay Fixed Swap = plain vanilla pay fixed swap + receiver swapation Cancelable Receive Fixed Swap =plain vanilla receive fixed swap + payable swapation Creating synthetic Drake Drake University securities using swaps Fin 284 The origins of the swap market are based in the debt market. Previously there had been restrictions on the flow of currency. A parallel loan market developed to get around restrictions on the flow of currency from one country to another, Especially restrictions imposed by the Bank of England. Drake The Parallel Loan Market Drake University Fin 284 Consider two firms, one British and one American, each with subsidiaries in both countries. Assume that the free-market value of the pound is L1=$1.60 and the officially required exchange rate is L1=$1.44. Assume the British Firm wants to undertake a project in the US requiring an outlay of $100,000,000. Drake Parallel Loan Market Drake University Fin 284 The cost of the project at the official exchange rate is 100,000,0000/1.44 = L69,444,000 The cost of the project at the free market exchange rate is 100,000,0000/1.60 = L62,500,000 The firm is paying an extra L7,000,000 Drake Parallel Loan Market Drake University Fin 284 The British firm lends L62,500,000 pounds to the US subsidiary operating in England at a floating rate based on LIBOR and The US firm lends $100,000,000 to the British firm at a fixed rate of 7% in the US the official exchange rate is avoided. The result is a basic fixed for floating currency swap. (In this case each loan is separate – default on one loan does not constitute default on the other). Drake Synthetic Fixed Rate Debt Drake University Fin 284 A firm with an existing floating rate debt can easily transform it into a fixed rate debt via an interest rate swap. By receiving floating and paying fixed, the firm nets just a spread on the floating transaction creating a fixed rate debt (the rate paid on the swap plus the spread) Drake Synthetic Floating Rate Debt Drake University Fin 284 Combining a fixed rate debt with a pay floating / receive fixed rate swap easily transforms the fixed rate. Again the fixed rates cancel out (or result in a spread) leaving just a floating rate. Drake Synthetic Callable Debt Drake University Fin 284 Consider a firm with an outstanding fixed rate debt without any call option. It can create a call option. If it had a call option in place it would retire the debt if called. Look at this as creating a new financing need (you need to finance the retirement of the debt.) You want the ability to call the bond but not the obligation to do so. Drake Synthetic Callable Debt Drake University Fin 284 Buying a receiver swapation allows the firm to receive a fixed rate, canceling out its current fixed rate obligation. It will pay a new floating rate as part of the swap (similar to financing the call with new floating rate debt). Drake Synthetic non callable Debt Drake University Fin 284 Basically the earlier example swapations. Drake Synthetic Dual Currency Debt Drake University Fin 284 Dual Currency bond – principal payments are denominated in one currency and coupon payments denominated in another currency. Assume you own a bond that makes its payments in US dollars, but you would prefer the coupon payments to be in another currency with the principal repayment in dollars. A fixed for fixed currency swap would allow this to happen Drake Synthetic Dual Currency Debt Drake University Fin 284 Combine a receive fixed German marks and pay US dollars swap with the bond. The dollars received from the bond are used to pay the dollar commitment on the swap. You then just receive the German Marks. Drake All in Cost Drake University Fin 284 The IRR for a given financing alternative, it includes all costs including administration, flotation , and actual cash flows. The cost is simply the rate that makes the PV of the cash flows equal to the current value of the borrowing. Compare two Drake Drake University alternative proposals Fin 284 A 10 year semiannual 7% coupon bond with a principal of $40 million priced at par A loan of $40 million for 10 years at a floating rate of LIBOR + 30 Bps reset every six months with the current LIBOR rate of 6.5%. Plus a swap transforming the loan to a fixed rate commitment. The swap will require the firm to pay 6.5% fixed and receive floating. Drake All in cost Drake University Fin 284 The bond has a all in cost equal to its yield to maturity, 7% Assuming the firm must pay $400,000 to enter into the swap so it only nest $39,600,000. Today. The net interest rate it pays is 6.8% implying semiannual payments of (.068/2)(40,000,000) = $1,360,000 plus a final payment of 40,000,000. This implies a rate of .034703 every six months or .069406 every year. BF Goodrich and Rabobank Drake Drake University An early swap example* Fin 284 In the early 1980’s BF Goodrich needed to raise new funds, but its credit rating had been downgraded to BBB-. The firm needed $50,000,000 to fund continuing operations. They wanted long term debt in the range of 8 to 10 years and a fixed rate. Treasury rates were at 10.1 % and BF Goodrich anticipated paying approximately 12 to 12.5% * taken from Kolb - Futures Options and Swaps Drake Rabobank Drake University Fin 284 Rabobank was a large Dutch banking organization consisting of more than 1,000 small agricultural banks. The bank was interested in securing floating rate financing on approximately $50,000,000 in the Eurobond market. With a AAA rating Rabobank could issue fixed rate in the Eurobond market for approximately 11% and for a floating rate of LIBOR plus .25% Drake The Intermediary Drake University Fin 284 Salomon Brothers suggested a swap agreement to each party. This would require BF Goodrich to issue the first public debt tied to LIBOR in the United States. Salomon Brothers felt that there would be a market for the debt because of the increase in deposits paying a floating rate due to deregulation. Drake Problems Drake University Fin 284 Rabobank was interested in the deal,but fearful of credit risk. A direct swap would expose it to credit risk. Without an active swap market it was common for swaps to be arranged between the two counter parties. The two finally reached an agreement to use Morgan Guaranty as an intermediary. Drake The agreement Drake University Fin 284 BF Goodrich issued a noncallable 8 year floating rate note with a principal value of $50,000,000 paying the 3 month LIBOR rate plus .5% semiannually. The bond was underwritten by Salomon. Rabobank issued a $50,000,000 non callable 8 year Eurobond with annual payments of 11% Both entered into a swap with Morgan Guaranty Drake The swaps Drake University Fin 284 BF Goodrich promised to pay Morgan Guaranty 5,500,000 each year for eight years (matching the coupon on the Rabobanks debt). Morgan agreed to pay BF Goodrich a semi annual rate tied to the 3 month LIBOR equal to: .5(50,000,000)(3 mo LIBOR-x) x represents an undisclosed discount Rabobank received $5,500,000 each year for 8 years and paid semi annul payments of LIBOR-x Drake The intermediary role Drake University Fin 284 The two swap agreements were independent of each other eliminating the credit risk concerns of Rabobank. Morgan received a one time fee of $125,000 paid by BF Goodrich plus an annual fee of 8 to 37 Bp ($40,000 to $185,000) also paid by BF Goodrich. Drake BF Goodrich Drake University Fin 284 Assuming that the discount from LIBOR was 50 Bp and that the service fee was 22.5 BP (the midpoint of the range). BF Goodrich paid an all in cost of 11.9488 % annually compared to 12 to 12.5% if they had issued the debt on their own. Drake Rabobank’s Position Drake University Fin 284 At the time of financing it would have paid LIBOR plus 25 to 50 Bp. Given that it paid no fees and the fixed rate canceled out it ended up paying LIBOR - x. Drake Securing financing Drake University Fin 284 BF Goodrich was able to secure financing via its use of the swaps market, this is a common use of the market. The example provides a good illustration of the idea of the comparative advantage arguments we discussed earlier. A Second Example of securing Drake Drake University financing* Fin 284 It is possible for swaps to increases accessibility two the debt market Mexcobre (Mexicana de Corbre) is the copper exporting subsidiary of Grupo Mexico. In the late 1980’s it would have had a difficult time borrowing in international credit markets due to concerns or default risk However it was able to borrow $210 million for 38 months from a group of banks led by Paribas * from Managing Financial Risk by Smithson, Smith and Wilford Drake The original loan Drake University Fin 284 The banks lent the firm $210 Million at a fixed rate of 11.48%. The debt replaced borrowing from the Mexican government which had cost the firm 23%. A Belgian company Sogem agreed to buy 4,000 tons of copper per month at the prevailing spot rate from Mexcobre making payments into an escrow account in New York that was used to service the debt with any extra funds returned to Mexcobre. Drake Drake University Fin 284 Quarterly payments of 11.48% Banks interest plus principal Escrow Excess cash $210 if it builds Cash based million up on Spot Price loan 4,000 tons of copper Mexcobre SOGEM per month Drake Swaps Drake University Fin 284 Swaps were added between Paribas and the escrow account to hedge the price risk of copper and between Paribas and the banks to change the banks position to a floating rate Drake Paribas Drake University Fin 284 Fixed Floating $2,000 Spot per ton Price Quarterly payments of 11.48% per ton Banks interest plus principal Escrow Excess cash $210 if it builds Cash per million up ton based loan on Spot Price 4,000 tons of copper Mexcobre SOGEM per month Duration of Interest Drake Drake University Rate Swaps* Fin 284 A plain vanilla swap can be valued as a portfolio of two bonds, therefore the duration of the swap should equal the duration of the bond portfolio. The duration can be either positive or negative depending on the side of the swap * Kolb, Futures Options and Swaps Drake Duration of Swaps Drake University Fin 284 Duration of Receive Fixed Swap = Duration of Underlying coupon bond - Duration of underlying floating Rate Bond >0 Duration of Pay Fixed Swap = Duration of underlying floating Rate Bond - Duration of Underlying coupon bond <0 Drake Example Drake University Fin 284 Consider a swap with a semiannual fixed rate of 7% and a floating rate that resets each six months. The duration of the fixed rate side (assuming a 100 notional principal) is 5.65139 years Duration of Receive Fixed Swap =5.65139-0.5=5.15369 Duration of Pay Fixed Swap =0.5-5.65139=-5.15369 Drake Calculating Duration Drake University Fin 284 Duration of floating rate security is equal to the time between resetting of the rate. Therefore the duration of the swap actually depends upon the duration of the fixed rate side. Receive Fixed rate swaps will then usually lengthen the duration of an existing position while pay fixed swaps will shorten the duration of an existing position. Drake Immunization with Swaps Drake University Fin 284 Swaps can be used to hedge interest rate risk by impacting the duration of the assets and liabilities on the balance sheet. Going to look at a fictional financial services firm FSF Drake Balance Sheet for FSF Drake University Fin 284 Assets Liabilities Cash $7,000,000 6mo money mkt $75,000,000 (avg yield 6%) Marketable Sec $18,000,000 (6 mo mat Yield 7%) Floating Rate Notes $40,000,000 (5 yr mat7.3% yld semi) Amortizing loans $130,467,133 (10 yr avg mat Coupon Bond $24,111,725 semiannual (10 yr semi 6.5% coup 8% avg yield) $25,000,000 par, 7% YTM Total Assets $1555,467,133 Net worth $16,355,408 Total Liab & NW $155,467,133 Drake Basic Duration Drake University Fin 284 $ Weighted Duration N DA w i Da i of Asset Portfolio i 1 Asset i where w i Market Value of All Assets Da i Macaulay Duration of asset i $ Weighted Duration N DL w jDl j of Liability Portfolio j1 Asset j where w j Market Value of All Liabilitie s Dl j Macaulay Duration of Liability j Drake Duration Drake University Fin 284 Assets Liabilities Duration Duration Cash 0.00 6mo money mkt 0.5000 Marketable Sec 0.500 Floating Rate Notes 0.5000 Amortizing loans 4.604562 Coupon Bond 7.453369 Total Duration Total Duration (7,000,000/155,467,133)0.000 (75,000,000/155,467,133)0.500 +(18,000,000/155,467,133)0.500 +(40,000,000/155,467,133)0.500 +(130,467,133/155,467,133)4.605 +(24,111,725/155,467,133)7.45337 3.922013 1.705202 Hedging the Drake Drake University portfolios separately Fin 284 It is easy to use duration to hedge the interest rate risk of the portfolio. The idea is to construct a portfolio with a duration of zero. Let MVi be the market value and Di be the Duration of the assets (A), liabilities (L) or hedge vehicle (H) then MVA(DA)+MVH(DH) = 0 and MVL(DL)+MVH(DH) = 0 Drake Swap notional value Drake University Fin 284 Given the duration of the hedge (a swap) it is then possible to solve for a notional value (or market value) of the swap that would make the portfolio duration zero. Previously we found the duration of a swap: Duration of Receive Fixed Swap =5.65139-0.5=5.15369 Duration of Pay Fixed Swap =0.5-5.65139=-5.15369 Drake Asset Hedge Drake University Fin 284 The asset can then be hedged by solving for the notional value (MVH) of the pay fixed swap MVA(DA)+MVH(DH) = 0 155,467,133(3.922)+(-5.15369)(MVH) =0 MVH=$118,365,451 Drake Liability Hedge Drake University Fin 284 The liabilities can then be hedged by solving for the notional value (MVH) of the receive fixed swap MVL(DL)+MVH(DH) = 0 (-139,111,725)(1.705202)+(5.15369)(MVH) =0 MVH=$46,048,651 Hedging Assets and Drake Drake University Liabilities together Fin 284 The entire balance sheet can be hedged with one interest rate swap by using GAP analysis. Static GAP Analysis Drake Drake University (The repricing model) Fin 284 Repricing GAP The difference between the value of interest sensitive assets and interest sensitive liabilities of a given maturity. Measures the amount of rate sensitive (asset or liability will be repriced to reflect changes in interest rates) assets and liabilities for a given time frame. Drake GAP Analysis Drake University Fin 284 Static GAP-- Goal is to manage interest rate income in the short run (over a given period of time) Measuring Interest rate risk – calculating GAP over a broad range of time intervals provides a better measure of long term interest rate risk. Drake Interest Sensitive GAP Drake University Fin 284 GAP Rate Sensistive Assets - Rate Sensistive Liabilitie s Given the Gap it is easy to investigate the change in the net interest income (NII) of the financial institution. Change in NII (GAP)(Chan ge in Rates) NII (GAP)( R) Drake Example Drake University Fin 284 Over next 6 Months: Rate Sensitive Liabilities = $120 million Rate Sensitive Assets = $100 Million GAP = 100M – 120M = - 20 Million If rate are expected to decline by 1% Change in net interest income = (-20M)(-.01)= $200,000 Drake GAP Analysis Drake University Fin 284 Asset sensitive GAP (Positive GAP) RSA – RSL > 0 If interest rates h NII will h If interest rates i NII will i Liability sensitive GAP (Negative GAP) RSA – RSL < 0 If interest rates h NII will i If interest rates i NII will h Would you expect a commercial bank to be asset or liability sensitive for 6 mos? 5 years? Drake Important things to note: Drake University Fin 284 Assuming book value accounting is used -- only the income statement is impacted, the book value on the balance sheet remains the same. The GAP varies based on the bucket or time frame calculated. It assumes that all rates move together. Drake Steps in Calculating GAP Drake University Fin 284 Select time Interval Develop Interest Rate Forecast Group Assets and Liabilities by the time interval (according to first repricing) Forecast the change in net interest income. Drake Alternative measures of GAP Drake University Fin 284 Cumulative GAP Totals the GAP over a range of of possible maturities (all maturities less than one year for example). Total GAP including all maturities Other useful measures using Drake Drake University GAP Fin 284 Relative Interest sensitivity GAP (GAP ratio) GAP / Bank Size The higher the number the higher the risk that is present Interest Sensitivity Ratio Rate Sensitive Assets Rate Sensitive Liabilitie s 1 Liability Sensitive 1 Asset Sensitive Drake What is “Rate Sensitive” Drake University Fin 284 Any Asset or Liability that matures during the time frame Any principal payment on a loan is rate sensitive if it is to be recorded during the time period Assets or liabilities linked to an index Interest rates applied to outstanding principal changes during the interval Unequal changes in interest Drake Drake University rates Fin 284 So far we have assumed that the change the level of interest rates will be the same for both assets and liabilities. If it isn’t you need to calculate GAP using the respective change. Spread effect – The spread between assets and liabilities may change as rates rise or decrease NII (RSA)( R assets ) - (RSL)( R liabilties) Drake Strengths of GAP Drake University Fin 284 Easy to understand and calculate Allows you to identify specific balance sheet items that are responsible for risk Provides analysis based on different time frames. Drake Weaknesses of Static GAP Drake University Fin 284 Market Value Effects Basic repricing model the changes in market value. The PV of the future cash flows should change as the level of interest rates change. (ignores TVM) Over aggregation Repricing may occur at different times within the bucket (assets may be early and liabilities late within the time frame) Many large banks look at daily buckets. Drake Weaknesses of Static GAP Drake University Fin 284 Runoffs Periodic payment of principal and interest that can be reinvested and is itself rate sensitive. You can include runoff in your measure of rate sensitive assets and rate sensitive liabilities. Note: the amount of runoffs may be sensitive to rate changes also (prepayments on mortgages for example) Drake Weaknesses of GAP Drake University Fin 284 Off Balance Sheet Activities Basic GAP ignores changes in off balance sheet activities that may also be sensitive to changes in the level of interest rates. Ignores changes in the level of demand deposits Drake Basic Duration Gap Drake University Fin 284 Duration Gap $ Weighted Duration $ Weighted Duration Basic DGAP of Asset Portfolio of Libaility Portfolio Basic DGAP DA DL Drake Basic DGAP Drake University Fin 284 If the Basic DGAP is + If Rates h i in the value of assets > i in value of liab Owners equity will decrease If Rate i h in the value of assets > h in value of liab Owners equity will increase Drake Basic DGAP Drake University Fin 284 If the Basic DGAP is (-) If Rates h i in the value of assets < i in value of liab Owners equity will increase If Rate i h in the value of assets < h in value of liab Owners equity will decrease Drake Basic DGAP Drake University Fin 284 Does that imply that if DA = DL the financial institution has hedged its interest rate risk? No, because the $ amount of assets > $ amount of liabilities otherwise the institution would be insolvent. Drake DGAP Drake University Fin 284 Let MVL = market value of liabilities and MVA = market value of assets Then to immunize the balance sheet we can use the following identity: MVL DA DL MVA MVL DGAP DA DL MVA Drake DGAP calculation Drake University Fin 284 MVL DGAP DA DL MVA 139,111,725 DGAP 3.922013 1.705202 155,467,133 2.396201 Drake Hedging with DGAP Drake University Fin 284 The net cash flows represented on the balance sheet have the same properties as a long position in a bond with a duration of 2.396201. We can hedge using our equation from before and the duration of the interest rate swap. Drake Hedging with DGAP Drake University Fin 284 Since the duration of our position is positive we want the duration of the hedge to be negative. This requires the pay fixed swap from before with a notional value equal to MVH below. MVi(Di)+MVH(DH) = 0 $155,467,725(2.396201)+(-5.151369)MVH=0 MVH=$72,316,800 Drake DGAP and owners equity Drake University Fin 284 Let MVE = MVA – MVL We can find MVA & MVL using duration From our definition of duration: Δi ΔP D P Applying the formula (1 i) Δy MVA -DA MVA 1 y Δy MVL -DL MVL 1 y Drake Drake University Fin 284 ΔMVE ΔMVA - ΔMVL Δy Δy -DA MVA - - DL MVL 1 y 1 y Δy -(DA)MVA - (DL)MVL 1 y MVL Δy -(DA) - (DL) 1 y MVA MVA Δy ΔMVE -DGAP MVA 1 y Drake DGAP Analysis Drake University Fin 284 If DGAP is (+) An h in rates will cause MVE to i An i in rates will cause MVE to h If DGAP is (-) An h in rates will cause MVE to h An i in rates will cause MVE to i The closer DGAP is to zero the smaller the potential change in the market value of equity. Drake Weaknesses of DGAP Drake University Fin 284 It is difficult to calculate duration accurately (especially accounting for options) Each CF needs to be discounted at a distinct rate can use the forward rates from treasury spot curve Must continually monitor and adjust duration It is difficult to measure duration for non interest earning assets. Drake More General Problems Drake University Fin 284 Interest rate forecasts are often wrong To be effective management must beat the ability of the market to forecast rates Varying GAP and DGAP can come at the expense of yield Offer a range of products, customers may not prefer the ones that help GAP or DGAP – Need to offer more attractive yields to entice this – decreases profitability. Drake Changing Duration Drake University Fin 284 You can also manipulate the duration of your cash flows. This allows you to lower your interest rate sensitivity instead of eliminating it. Let DG* be the desired duration gap, DG be the current duration gap, DS be the duration of the Swap, and MVH* be the notional value of required for the swap. MVH * Total Assets DG DG DS * Decreasing Duration GAP Drake Drake University to One year Fin 284 MVH * Total Assets D G D G DS * MVH * $155,467,133 1.0 2.396201 5.15369 MVH 42,137,025 * The negative sign just indicate that we need a pay fixed swap (the duration would then be negative making the MV positive)

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