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Money and Banking

by: Madie Schinner

Money and Banking ECN 135

Madie Schinner
GPA 3.57

Kevin Salyer

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Kevin Salyer
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This 27 page Class Notes was uploaded by Madie Schinner on Tuesday September 8, 2015. The Class Notes belongs to ECN 135 at University of California - Davis taught by Kevin Salyer in Fall. Since its upload, it has received 70 views. For similar materials see /class/191864/ecn-135-university-of-california-davis in Economcs at University of California - Davis.


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Date Created: 09/08/15
Hedging Interest Rate Risk with Financial Futures Some Basic Principles Michael T Belongia and G J Santom39 FOR much of the postwar period stable rates of inflation accompanied by stable levels of interest rates 7 created a comforting economic envimnment for managers of depository institutions Beginning in the mid1970s however more variable interest rate brought about in part by more variable in ation caused a substantial Change in the economic conditions facing depository institutions ffeiing longterm credit at xed rates became riskier as larger and mom frequent unexpected changes in interest rates introduced more variation into the market value of these assets This article describes how variation in interest rates affects the market value of depository institutions The discussion then demonstrates how nancial futures contracts might be used to hedge some of the interest rate risk of a portfolio composed of interestsensitive deposit accounts and loans of unmatched maturities Although some regulatory authorities have denied or strictly regulated the use of futures contracts by de Michael T Belongia is an economist and G J Santoni is a senior economist at the Federal Reserve Bank of St Louis John G Schulte provided research assistance For a general description of events that have introduced or in creased interest rate risk see Carrington and Hertzberg 1984 and Koch et al 7 positery institutions in the belief that futures trading is risky and unduly speculative we argue that the judicious use of futures can reduce the rm39s expo sure to interest rate fluctuationsf DURATION GAP AND INTEREST RATE SK in the midA1970s when large uctuations in interest rates began to occur it became increasingly evident that depository institutions needed some measure of the relative risks associated with various portfolio holdings One approach to the measurement of inter est rate risk is called Duration Gap analysis Dura tion refers to the average life of some group of assets or liabilities Gap refers to the difference between the durations ofan institution39s assets and its liabilities 2Legal restrictions and guidelines on the use of nancial futures by different types of financial institutions are summarized in L0 r 1982 A comparison of statutes on the use of iutures by insurance companies is made in Gottlieb 1984 3For more detailed discussions of duration analysis and its applica tion to financial institution i tfolios see Kaufman 1984 Bierwag Kau man an Toevs 1983Toevs 1983 Santoni 1984 Samuel son 1944 and Hicks 1989 pp tar88 15 FEDERAL RESERVE BANK OF ST LOUIS mm An Example The risk introduced into a portfolio of assets and liabilities of different duration is illustrated in tables 1 an 2 In this example for expositional simplic y the rm39s planned life is assumed to be only one year It has extended a loan with a face value of 81000 to be repaid in a single payment at the end ofthe year at an interest rate of 10 percent The present value of the loan and thus the amount paid out by the rm to the borrower is 590909 To nance this loan the firm borrows 90909 for 90 days at 8 percent interest The two percentagepoint spiead is the tetum earned by 16 OCTOBER 1984 the rm for employing its specialized capital in inter mediating between borrowers and lenders The amount that the rm will owe in three months time is 392675 1 90909l108l 15 which it plans to pay by borrowing this amount for another 90 days Because the rm s pipeeeds from the new loan and its payment of the old loan cancel its net receipts at this time are zero The rm anticipates being able to roll the loan over every 90 days at the same interest rate Consequently at the end of 180 days the rm expects to owe 594476 92675108gt 3 t which it plans to pay with new borrowings At the end of the year the rm FEDERAL RESERVE BANK OF ST LQUlS anticipates having to pay 98182 1 90909 gtlt 108I This amount will be paid out of the 1000 proceeds from its matured asset The rm39s expected net receipt at yearend is 1818 as Shown in panel A of table 1 Panel A of table 2 is a balance sheet summary of the present value of this investment plan The present value of the expected net receipt at yearend is 1653 and is equal to the difference between the present value of the asset 90909 i Sl000110l and the present value of the expected liability 89256 l 3981821110 Both future values are discounted at 10 percent the rms opportunity cost The Effects of Changing interest Rates on Equity This package of assets and liabilities is subject to considerable interest rate risk because the 10 percent interest rate on the rm s loan is fixed for one year while its borrowings must be refunded every 90 days In this example the gap between the durations oftlie OCTOBER 1984 asset and liability is 270 days i 360 90 As a practical matter the asset s longer duration implies that a given change in interest rates will Change the present value of the asset more than it will affect the present value of the liability This difference of course will change the value of the rm s equity Panel B of table 1 shows the effect of an unexpected 200 basispoint rise in interest rates The increase raises the firm s anticipated refunding costs AS a result the amount the rm expects to pay at year end increases to 99542 Net receipts fall to 458 and the present value of the investment plan falls to 409 Panel B ot table 2 presents a balance sheet summary of the effect of the change on the present values of the asset liability and owner equity The increase in interest rates reduces the present values of both the asset and liability but the asset value falls by relatively more because its life is fixed for one year while the liability must be rolled over in 90 days at a higher interest rate The increase in interest rates causes owner equity to fall by 1244 or about 75 percent In contrast had the interest rate declined by 200 basis points the net present value ofthe rm s equity would have risen to 2949 see panel C of table 1 an increase of about 78 percent This extreme volatility in the firm39s equity is due to the mismatch of the durations of the asset and liability that make up the firm39s portfolio Table 3 illustrates this point The only difference between this and ear lier examples is that in table 3 the duration of the liability has been lengthened to match the duration of the asset While a 200 basispoint increase in the interest rate still causes the present value of the portfolio to fall the change w 030 or w 18 percent is much less than before Clearly matching the dura tions of the asset and liabi 39ty exposes the value of the portfolio to much lower interest rate risk COPING W39ITH THE GAP Depository institutions particularly savings and loan associations maintain portfolios of assets and liabilities that are similar to the one shown in the initial example3 That is the duration of their assets The durations of singlepayment financial instruments are equal to the maturities of the instruments ln 0 er cases calculation of duration is not as straightforward See footnote 3 5Savings and loan associations are required to maintain a significant share ol their portfolios in longterm home mortgages in order to obtain federal insurance of deposits See Federal Home Loan Bank Act of 1932 sec 4a 17 FEDERAL RESERVE BANK OF ST LOUIS typically is longer than the duration of their liabilities As a result the market values of these institutions have been particularly sensitive to interest rate fluctua39 tions This along with the recent expeiience of highly variable interest rates has led these institutions to seek out methods to reduce their exposure to interest rate risk Among other things these firms have made greater use of oating rate loans and interest rate swap agieementsr Recent regulatory changes have allowed them to allocate more of their loan portfolios to short term consumer loans In addition a number Ofinstitu tions are using nancial futures to reduce their expo sure to interest rate tiskG ESee Booth Smith and Stolz 1984 While a number of financial firms are employing the futures market it seems that accounting n u t t A OCTOBER 1984 Futures Markets and Risk It may seem odd that the futures market which is generally thought of as being very risky can be used to ieduce risk Futures trading is risky for people who bet on the future price movements of particular commod ities or nancial instruments by taking long or shon positions in futures contracts Such speculative bets on future price movements however are not unique to futures market trading The nature of most types of businesses requires a speculative bet about the future course of a particular price Growing crops for example gives farmers long positions in physical commodities during the growing season These long positions expose the farmer to the risk of price declines declines that can reduce the pro ts from efficient farming the activity that the farmer specializes in Judicious use of the futures market allows the farmer to offset his long position in the commodity by selling futures contracts Since the sale reduces his net holdings of the commodity the farmer39s exposure to the risk offuture price declines is reduced Similarly futures trading presents deposi tory institutions with the opportunity to reduce their exposure to the risk of interest rate changes Futures Contracts A futures contract is an agreement between a seller and a buyer to trade some wellde ned item wheat corn Treasury hillsl at some speci ed future date at a price agreed upon now but paid in the future at the time of delivery The futures price is a prediction about what the price of the item will be at the time of delivery In the case of commodities the price of the good today the spot price on average will be equal to the futures price minus the cost of storage insurance and foregone interest associated with holding the good over the interval of the contract A similar relationship exists between the spot and futures prices of nancial instruments However since the storage and insur ance cost ofholding these instruments is very low the spread between the spot and futures prices is largely me use v rate risk Until recently regulators and accountants feared that Therefore they would not permit a hedge to count as one transac tion with spot gains or losses offsetting futures markets losses or gains instead they required futures losses to be marked to the market while spot gains could be deferred This asymmetric treat ment of gains and losses on the two sides of a hedge distorted earnings estimates and therefore discouraged the use of futures 18 by the interest cost See Morris 1984 for more detail on changes in accounting stan dards Asay et at 1981 provide examples of how former account ing standards discouraged the use of futures by banks and thrift institutions FEDERAL RESERVE BANK OF ST LOUIS The Relationship Between Spot and Futures Markets for Treasury Bills An Illustration In January 1976 the International Monetary Market ltMMi now part of the Chicago Mercantile Exchange CMEI began trading futures contracts in 13 weck I reasuiy billsf The basic contract is for 1 million with contracts maturing once each quarter in the third week of March June September and December Since there are eight contracts outstanding the most distant delivery date varies between 21 and 24 months into the future Panel A of table 4 presents quotations for Treasury bill futures for the trading day of August 7 1984 Panel B of table 4 lists spot quotations for Treasury bills for the same trading day Panel A of table 4 is interpreted as follows Septem ber Treasury hill futures were trading at a discount of 1049 percent on August 7 1984 Any person trading this contract obtained the right to buy sell a Treasury bill the third week in September with a remaining maturity of 13 weeks at a discount rate of 1049 percent A similar statement holds for the other con tracts listed in panel A Panel B lists spot market quotations For example Treasury bills due to mature August 9 1984 traded at a discount of 991 percent lbidl to 979 percent task while those maturing September 20 1984 traded at a discount of995 bid to 991 iaski etc We noted earlier that the spot and futures markets must be closely related and the data in panels A and B can be used to illustrate this point For example on August 7 1984 an investor could purchase a Treasuiy hill due to mature December 20 1984 lie 134 days later If he purchases the bill on the spot market he obtains the asked discount of 1039 percent At this discount rate the price he pays for the bill is 9641 per 100 of face valuequot 7Futures contracts in other types of financial instruments such as GNMA passthrough certi cate contracts 90day CD5 Treasury bonds and Treasury notes also are available at the Chicago Board of Trade 8The information in table 3 is taken from pages 38 and 39 of the August 8 1984 W I Street Journal contain more information than is presented here For our purposes however the additional information is extraneous 59641 2 MOO11039 37 The discount factor is raised to the poweroi134360 371 quot 39 39 lull me discount calculation used in determining actual trading prices but OCTOBER 1984 Alternatively the investor could purchase a futures contract that gives him the tight to buy a 39I reasury hill in September that will mature the third week in December This alternative gives him a discount rate of 1049 percent Buying the Treasury bill in September at this discount would require a payment of 9754 This payment will be made 43 days into the future roughly September 20 and the present value of the payment on August 7 is 9644 Notice that this is very near the amount that the investor would pay 9841 if he were to purchase a Treasury hill on the spot market that matured during the third week of December Of course other alternatives are open to the investor as well He could for example buy a Treasury bill that matured the third week in March on the spot market numerical differences between the two formulas are small See Stigum 1981 for the market s discount formula 9754 1 00 1049 25 9644 9754t0991 2 The interest rate used in the calcula quot L 3 u August 7 for a security maturing on September 20 43 days in the future 19 FEDERAL BESERVE BANK OF ST LOWS The present cost of doing this should be near the present cost of buying a futures contract that allows him to purchase a Treasury bill in December maturing the Ihll d week in March Table 5 uses the data in table 4 to compare the present costs of this and other alternatives In each case the present costs of employ ing the spot vs the futures market are very closequot Because a close relationship between these markets exists the Treasury bill futures market can be used etiectively to hedge inteiest rate risk HEDGING THE GAP The Streams of Receipts and Payments The example in table 1 can be used to illustrate how futures contracts can be applied to hedge the interest rate risk caused by the mismatch in the lives ldura tionsl of the rm s assets and liabilities Considerable confusion appears to exist as to what the rm s hedg ing objective should be and how hedges should be Constructed One possible hedging strategy is to pro tect the equity of the rm in the present value sense from interest rate uctuations Another often cited strategy is to minimize discrepancies between cash ows over time It seems clear however that firm owners will choose a hedge that protects their net wealth present value of the rm39s equity This focus on net wealth is crucial because as the examples show reducing cash ow mismatches to zero does not minimize the exposure of the rm39s equity to interest rate changes Hedging Net Wealth An Example Suppose it is September 15 1984 and the rm initiates the transactions summarized earlier in panel A of table 1 In addition to hedge each of its three refunding requirements the rm sells December March and June futures contracts at 10 percent dis counts The price of each contract is SLOWlilo 3quot A A 5 v mhe differences were large pro table arbitrage opportunities would exist These oi course would vanish quickly as traders took advantage of the situation There is of course the problem that the spot instrument being hedged may not be identical to the futures market instrument It so k L facial that affects the pride of one but not the other This is called basis risk and is ignored in the following examples A flat yield curve is assumed for ease of exposition The examples 39 39 Im N do nand r 395 1 r r or the spread between borrowing and lending rates changes 20 GCYOBER 1984 97645 These contracts obligate the rm to deliver a 13 week Treasury bill with a face value of1000 during the third week of December March and June in exchange for 97645 Panel A of table 6 presents the rm39s expected streams of receipts and payments given the structure of interest rates on September 15 It is identical to panel A of table 1 except that the streams of receipts and payments generated by the futures contract are included The futures contract generates a Certain stream of receipts equal to 97645 in December March and June in exchange for delivery of the 90day Treasury bills The firm must acquire these bills in order to make delivery and on September 15 the expected cost of acquiring each of the Treasury bills is 97645 If interest rates remain unchanged expected and actual costs will be the same so that the actual receipts and payments generated by the futures con tract net out in each period The net ow of receipts is zero until yearend when the rm receives 1818 The present value of this amount is 1653 In panel B interest rates are assumed to rise unex pectedly by 200 basis points immediately following OCTOBER 1984 FEDERAL RESERVE BANK O 8 0123 6 4 L 53 mg 39 g 3 7 h ni M 7gp 391 3 a V z g Q35 N v 7 j 9 A A n 1 s 1 W cm a m m quot M33 f gt 3 3 x 14 e W a g A N X a r a W 3 m 1 ax A A r f4 5 35 9 3 v25 it 1 39a D Q 3 3 f my 3 5 e A w W m FEDERAL RESERVE BANK OF ST LOUIS the rms September 15 transactions As in panel B of table 1 the increase in interest rates raises the rm s refunding cost and reduces the net yearend receipt to 458 In addition however the increase in interest rates reduces the expected cost of acquiring the Trea sury bill to 97207 Since the rm will receive 597645 upon delivery of the Treasury bills the futures con tract will generate a net ow of receipts equal to 5438 in December March and June The present value of this llow added to the present value ot the net receipt at yearend 458 is 1650 which is nearly identical to the present value for the case in which interest rates remained unchanged the small difference is due to rounding errors Panel C illustrates the outcome for a 200 basisvpoint decline in interest rates In this case the futures contract generates negative net receipts for the rm in December March and June The present value of this negative ow added to the present value of the higher positive net receipt at yearend sum to 1652 As the examples show this hedge protects the net wealth of the rm regardless of the direction of the change in interest rates While this hedge protects net wealth front changes in interest rates it does so by allowing net cash receipts to vary Net cash receipts both in amount and timing are considerably different in panels A B and C In panel A net receipts are 1818 at year end while in panel B net receipts are spread out over the year and total only 1772 in panel C the rm has negative net receipts during the year and a large positive net receipt at yearend for a total of 1838 However the present value of the rm is the same in all three cases The Balance Sheet Panel A of table 7 presents the firm39s balance sheet position in terms of present values The futures con tracts are entered as both assets and liabilities leaving equity the same as that shown in panel A of table 2 The futures asset is the present value of the future receipt of a xed amount The futures liability on the other hand is the present value of the expected cost of covering the futures contract given the structure of interest rates on September 15 Panels B and C illus SStrictiy speaking futures contracts entered into by member banks of the Federal Reserve System are treated as balance sheet memo randa items These are reported on Schedule L Commitments and Contingencies of the Call Report Hence for accounting purposes futures contracts do not affect the assets and liabilities of the firm until the contracts are exercised 22 OCTOBER 1984 trate the effect on the present values of the tirm s assets liabilities and equity if immediately following the above transactions interest rates rise unexpecb edly panel B or fall unexpectedly panel C by 200 basis points An unexpected increase in interest rates causes the present value of the loan to fall relative to the present value of the liability By itself this would cause a reduction in the frrm39s equity At the same time however the increase in interest rates generates a positive expected net cash flow from the futures contracts which of course has a positive net present value Other things the same this causes equity to r The net effect of both changes is that equity remains unchanged The reverse occurs if interest rates do Cline by 200 basis points This hedge has eliminated the finn39s exposure to interest rate risk In contrast recall that a 200 basis point change in the interest rate causes the equity of the unhedged rm in table 2 to change by about 75 percent Hedging as a Pro t Center The purpose of hedging is to reduce the variance of a firm owner s wealth In a textbook example of a perfect hedge the gain or loss from a short position in the futures market will offset exactly the compensat ing loss or gain on the spot assets and liabilities held by the rm A hedge is constructed because in the presence of an uncertain future wealth is greater if the institution foregoes a pro t stream that is higher on average it it goes unhedgedl in exchange for a pro t stream that is lower on average by the cost of the hedging operations but more certain Some portfolio managers however lose sight of this fact and assume speculative positions in the futures market with the objective of earning pro ts from the position if interest rates change in their favor While speculative positions in futures or spot instruments can increase earnings they can have the opposite effect as well One potentially significant danger in the use of futures contracts to hedge interest rate risk is that the firm may misunderstand the nature of the hedging function Trading futures for hedging is not intended to generate pro ts from the trading itself Rather its purpose is to establish futures positions so that the owner39s wealth is held constant this will occur if the increase decrease in the value of the firm39s spot holdings of assets and liabilities is offset exactly by the loss igainl in the futures market OCTOBER 1984 FEDERAL RESERVE BANK OF ST LOUES 39s 23 FEDERAL RESERVE BANK OF ST LGUQS SUMMARY Higher and more variable interest rates have in creased the risk faced by nancial institutions associ ated with attracting deposit funds and extending creditThis article presented some simple examples of techniques that can isolate and quantify sources of a nancial institution39s exposure to interest rate risk The discussion also described how nancial futures can be used to reduce this risk A simple hedging example indicated that relatively conservative use of futures markets can have a potentially large impact on reducing risk exposure The use of futures trading is a threat to the longrun performance of a nancial rm only if applied in a manner inconsistent with hedging REFERENCES Asay Michael FL Gisela A Gonzalez and Benjamin Wolko 39 Financi l Futures Bank Portfolio Risk and Account ingquot Journal of Futures Markets Winter 1981 pp 607 18 Bierwag G 0 George G Kaufman and Alden Toevs Bond Portfolio immunization and Stochastic Process Risk Journal of Bank Research Winter 1983 pp 282 91 E u N OCTOBER 984 Booth James R Richard L Smith and Richard W Stolz Use of Interest Rate Futures by Financial Institutions Journal of Bank Research Spring 1984 pp 15 20 Carrington Tim and Daniel Hertzberg Financial Institutions Are Showing the Strain of a Decade of Turmoilquot Wall Street Journal September 5 1984 Federal Home Loan Bank Act of 1932 Public No 304 72 Cong HR 12280 Gay G D and R W Kolb The Management of Interest Rate Riskquot Journal of Portfolio Management Winter 1983 pp 65 70 Gottlieb Paul M New York and Connecticut Permit insurers to se Futures and Options A Comparisonquot icago Mercantile Exchange Market Perspectives MayJune 1984 pp 1 6 Hicks J R Value and Capital Oxford Clarendon Press 1939 Kaufman George G Measuring and Managing interest Rate 39 k A Primer Federa Resewe Bank oi Chicago Economic Perspectives JanuaryFebruary 1984 pp 1amp29 Koch Donald Delores W Steinhauser and Pamela Whigham Financial Futures as a Risk Management Tool for Banks and SampLsquot Federal Reserve Bank of Atlanta Eco nomic Review September 1982 pp 4 14 Kolb R W interest Rate Futures A Comprehensive introduction Robert F Dame inc 1982 Kolb Robert W Stephen G Timme and Gerald D Gay Macro Versus Micro Futures Hedges at Commercial Banksquot Journal of Futures Markets Spring 1984 pp 4754 Managing Interest Rate Risk Interest Rate Swaps Using financial futures to hedge exposure to interest rate risk is useful but there are two main problems 1 There may not be a futures contract that corresponds precisely to spot activity that is being hedged This increases basis risk Example Small credit union s assets loans do not have the same risk characteristics as Treasury securities 2 Futures contracts are only traded out to about 25 years So a manager can not hedge against interest rate risk at long maturities k ANSWER INTEREST RATE SWAPS Managing Interest Rate Risk Interest Rate Swaps Basic interest rate swap Two parties issue debt and make each other s payments Typically one rate is fixed and the other is variable7 ie oating This idea has been extended to currency swaps two parties issue debt denominated in different currencies and then they swap payments Often a financial intermediary plays a role as a swap facilitator Interest Rate Swaps First interest rate swap was between the World Bank and IBM in 1981 Since then the growth in the market has been staggering roughly 50 per year Managing Interest Rate Risk Interest Rate Swaps The Bank for International Settlements reports that interest rate swaps are the largest component of the global OTC derivative market The notional amount outstanding as of December 2006 in OTC interest rate swaps was 2298 trillion up 607 trillion 359 from December 2005 These contracts account for 554 of the entire 415 trillion OTC derivative market However interest rate swaps are not standardized enough to allow them to be traded through a futures exchange like an option or a futures contract k J Managing Interest Rate Risk Interest Rate Swaps A Plain Vanilla the only kind we are interested in Interest Rate Swap IBM and the World Bank have each issued debt for 1000000 IBM s debt is a 5 year note that has a oating rate tied to the London Interbank offered rate LIBOR The rate is 3 LIBOR The World Bank s debt is a fixed rate of 12 also With maturity of 5 years Both parties agree to pay each other s annual interest payments Since the value of these payments is 1M but this is not exchanged this is referred to as the notional principal Also actual payment is the implied difference if LIBOR 10 then WB pays IBM 10000 Fixed 12 World IBM 4 Bank Floating Libor 3 Managing Interest Rate Risk Interest Rate Swaps It is Clear from this example why interest rate swaps would be attractive to depository institutions By engaging in a swap7 a bank or savings and loan can transform its oating rate liabilities into fixed rate liabilities Consequently both FGAP and DGAP can be managed via interest rate swaps But another motivation Comparative Advantage Interest Rate Swaps Comparative Advantage Nobel laureate Paul Samuelson was once challenged by the mathematician Stanislaw Ulam to name me one proposition in all of the social sciences which is both true and non trivial It took Samuelson several years to find the answer Comparative Advantage That it is logically true need not be argued before a mathematician that it is not trivial is attested by the thousands of important and intelligent men who have never been able to grasp the doctrine for themselves or to believe it after it was explained to them k J Comparative Advantage Comparative Advantage It s opportunity costs that matter Take the following example In one day Jed can produce either 1 book or 1 You Tube video In the same time Fiona can produce 2 books and 4 You Tube videos Fiona has absolute advantagebut that is not relevant for trade What is the relative price for each good For Fiona she gives up 4 videos to produce 2 books so the relative price of a book is 13 13 2 Pp F For Jed it is clear that his relative price is simply 13 13 1 Pp J Comparative Advantage Review So Jed has a comparative advantage in book production and Fiona has a comparative advantage in video production What is the relative price of videos Any trading price between 1 and 2 will make both Jed and Fiona better off Suppose the price is 15vb Jed specializes in book productionthen he can now obtain a maximum of 15 videos through trade rather 1 Fiona specializes in books7 she can now obtain a maximum of 83 videos through trade rather than 2 Both are happy Same idea with regard to borrowing Managing Interest Rate Risk Interest Rate Swaps Now consider two firms both can borrow at either a xed or oating rate One will have a comparative advantage at xed rate borrowing and one will have a comparative advantage at oating rate borrowing Specialize in appropriate debt and then swap the payments Acme Corp Widget LLC Difference in Good Credit Poor Credit 003135 Desires Floating Desires Fixed basis points Rate Rate 5year fixed rate 11 125 150 debt Floating rate LIBOR 25 bp LIBOR 50 bp 25 bp debt Acme has a comparative advantage in fixed rate debt Managing Interest Rate Risk Interest Rate Swaps 1 Acme issues fixed rate but pays oating rate of LIBOR to Widget 2 Widget issues oating rate at LIBOR 50bp but pays Swap Rate fixed to Acme LIBOR Acme Widget Swap Rate fixed Issues Fixed Issues Floating At 11 At LIBOR 50bp Managing Interest Rate Risk Interest Rate Swaps What determines the Swap Rate Must lower costs to both parties Acme wants oating rate Allincosts AIC are Fixed Rate Debt issue 11 Floating rate paid in swap L Fixed rate received SR AIC 11 L SR For the swap to be acceptable to Acme AIC39 lt L 025 11L SRltL025 1075ltSR Managing Interest Rate Risk Interest Rate Swaps What determines the Swap Rate Must lower costs to both parties Widget wants fixed rate Allin costs AIC are Floating Rate Debt issue L 050 Fixed rate paid in swap SR Floating rate received L AIC SR 050 For the swap to be acceptable to Acme AIC39 lt 125 SR 050 lt 125 SR lt 12 Managing Interest Rate Risk Interest Rate Swaps Acme s condition SR lt 1075 Widget s condition SR lt 12 So any rate in the range 1075 lt SR lt 12 is acceptable to both parties You have a deal k Managing Interest Rate Risk Interest Rate Swaps Hedging with Interest Rate Swaps You are a manager of a small bank First Bank of Winters that has the following data Assets 2 100 million Net Worth 2 5 million DGAP 172 years One way to eliminate the DGAP is to lengthen the maturity of your liabilities Swap your floating rate liabilities for fixed rate liabilities Acme Bank offers to pay you 1 over the 1 year T Bill rate over the next 10 years in exchange for First Bank paying a 7 fixed payment The Question What should be the value of the swap the notional principal to hedge net worth from interest rate changes Managing Interest Rate Risk Interest Rate Swaps First recall what the DGAP tells us DGAP DA BL And the duration of each term is used to calculate its elasticity with respect to an interest rate change recall liabilities were scaled by assets AA AL ANW Ai AA AL T 7 T DGAP1Z Hence7 the absolute change in net worth will be determined by the factor ANWZAXDGAP So you need to engage in a swap that will change by the same absolute arnount hilallaging Interest Rate Risk Interest Rate Swaps So the first step is to figure out the implied duration of the swap deal The duration of the oating rate component is easy since the TBill is a pure discount bond7 its maturity is equal to the duration So duration 2 1 year The duration of the fixed rate payment is determined by your finance diVision to be 81 years We skip the details So duration of the swap is Dswap 1 81 71 Just as in the earlier discussion of DGAP the absolute change in the value of the swap Will be determined by the factor lswap X Dswap lla11agi11g Interest Rate Risk Interest Rate Swaps Recall we had the following information Assets 2 100 million Net Worth 2 5 million DGAP 172 years And we know D5 71 If interest rate rise7 bank NW falls but the value of the swap increases We want the absolute change to be the same which requires lswap X Dswap A X Which implies VS AgtltI GAP For the numbers given we have V5 W 242771


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