How To Understand The Swap Curve

Transcription

1 INSTITUTE OF ECONOMIC STUDIES Faculty of social sciences of Charles University SWAPS Financial Market Instruments (Lecture s Notes No. ) Oldřich Dědek

2 2 A. INTEREST RATE SWAP 1. Basic concepts interest rate swap is a contract in which both parties agree to exchange for a given period two streams of interest rate flows derived form the same notional principal 1 1 Bank A (buyer) 2 Bank B (seller) flow of interest: 1. fixed interest rate paid annually for years from notional principal 10 mil. 2. 6M rate LIBOR paid semi-annually for years from notional principal 10 mil. notes: - swaps are designed with a wide choice of maturities - netting means that only the net balance of cash flow is paid - principal is purely notional (is not exchanged) therefore the swap is so-called off-balance sheet instrument - principal may be fixed or flexible - swaps helps integrate the money and capital markets (interest rates on the both markets are bundled into one product) - naming convention swap buyer is the payer of fixed and the receiver of flexible interest stream swap seller is the payer of flexible and receiver of fixed interest stream - quotation conventions (quoted is swap price of the size of fixed rate) i) bid-ask prices (all-in prices, two-way prices) bid ask, offer swap rate (average) 1 year years

3 ii) mark-up (in percentage points) to the reference bond (swaps may be part of a bond issue) 2 years 21/25 (above the yield over 2Y T-note) years 0/5 (above the yield above Y T-note) swap curve yield curve created from market swap rates (the same concept as the bond yield curve) - over-the-counter product brokers: arrange deals among clients in exchange for commission, they do handle the following payment of interest dealers: act as a counterparty of the deal, the client need not to carry out the credit risk analysis matched books dealers: arrange such swaps which can be hedged in a near future with reverse swaps (techniques of warehousing) market makers: quote two-way prices, willingness to assume more risk basic types of interest rate swap: - coupon swap, fixed-against-floating swap exchange of fixed with floating stream of interest payments - basis swap exchange of two floating streams of interest payments (e.g. M versus 6M LIBOR, M LIBOR versus Treasury, and so on) - (straight, plain vanilla swap conventional swap with simple features (fixed principal, regular payments, immediate start, no option features) 2. Motives for using interest rate swap a) assuming interest rate risk i) speculation on interest rate changes coupon swap: speculation on a change in the level of interest rate A B

4 A: pays fixed and receives floating interest stream, therefore he speculates on interest rate increase B: pays floating and receives foxed interest stream, he speculates on interest rate decline analogy of asset-liability mismatching (gapping): A: issues bond (pays fixed rate) and creates short term deposit (receives floating rate) B: buys bond (receives fixed rate) and takes short term deposit (pays floating rate) basis swap: speculation on a relative change in interest rates 6M A B M A speculates on relative increase of shorter interest rates B speculates on relative increase of longer interest rates ii) transformation of interest rate risk - firm or municipality wants to transform fixed interest rate liability (originated in bond issue) into floating interest rate liability (creation of synthetic variable coupon bond) - underlying motivation may be expected interest rate decline - without swap market a clumsy operation requiring earlier repayment of fixed liability and issuance of floating liability bond issue Firm swap Bank - firm transforms fixed interest rate asset (originated in holding the bond) into floating interest rate asset (speculates on interest rate increase) bond purchase Firm swap Bank

5 5 - government wants to restructure outstanding debt towards higher weight of long-term bonds and lower weight of treasury bills T-bills issue Treasury swap Bank iii) transforming hedged position into a speculative one Bank Counterparty bank transforms hedged position into speculative position in anticipation of interest rate increase (higher received than paid fixed interest) similarly one can transform hedged position (in fixed and flexible rates) into speculative position in anticipation of interest rate decline b) hedging interest rate risk coupon swap: i) hedging the risk of interest rate rise Bond Bank FRN Counterparty examples: financing fixed-rate mortgages through floating rate deposits ii) hedging the risk of interest rate decline Bank Counterparty

6 6 example: financing floating rate mortgages through fixed rate bonds or certificate of deposits basis swap: hedging the mismatch of two floating rates Client Y 6M Bank Y M Client 6M M Counterparty example: bank needs to remove the residual interest rate risk caused by entering into reverse swap c) swap arbitrage i) liability arbitrage a firm has access to cheaper financing in comparison with prevailing swap rate which allows to lower floating rate borrowing cost 9,0 % 8.5 % Borrower Counterparty LIBOR borrowing cost: LIBOR - 50 bp occurrence of arbitrage opportunities: - swap rates do not reflect creditworthiness of individual borrowers but general market conditions (including credit corporate risk) - subsidised financing (i.e. export credits) - differentiated reaction speed of different financial segments to the emergence of new information - supply-demand imbalances, short-term price anomalies

7 7 ii) asset arbitrage 8,5 % LIBOR+75bp Investor Counterparty LIBOR investment return: 9.25 % 8,0 % 8.5 % Investor LIBOR investment return: LIBOR + 50 bp Counterparty occurrence of arbitrage opportunities: holdings of less liquid assets whose higher risk has to be compensated by higher return examples: collateralised mortgage bond (risk of earlier repayment), deeply discounted bond (caused by tax reasons), highly structured securities (held by a limited number of investors), unsuccessful issues (wrong selling price, bad marketing, and so on) iii) new issue arbitrage Fixed rate Floating rate Firm AA Firm A 10 % 12 % LIBOR bp LIBOR bp Difference 200 bp 60 bp firm AA: firm A: - has absolute advantage on both markets - has comparative advantage at fixed rate (equal to 200 bp) - demands borrowing at floating rate (at which it has comparative disadvantage) - has absolute disadvantage on both markets - has comparative advantage at floating rate (equal 60 bp)

8 8 - demands borrowing at fixed rate (at which it has comparative disadvantage) possible swap arrangement: 10.2 % 10 % Firm AA Firm A LIBOR+160 bp LIBOR AA cash flow: revenue 10.2 % expenditure LIBOR + 10 % firm pays LIBOR - 20 bp (without swap it would pay LIBOR bp) gain = 120 bp A cash flow: revenue LIBOR expenditure LIBOR bp % firm pays 11.8 % (without swap it would pay 12 %) gain = 20 bp arbitrage potential = 10 bp = 200 (fixed rate) - 60 (floating rate) distributed as 120 bp firma AA and 20 bp firma A notes: - the arbitrage scheme is the analogy of the Ricardian principle of comparative advantage - firm A may be prohibited to access the bond market, swap is a way of creating the bond synthetically - intermediating role of banks which take over clients credit risk and are paid by sharing a part of the arbitrage profit 10 % AA % LIBOR Banka % LIBOR A LIBOR+160bp sharing of arbitrage potential: 115 bp firm AA + 10 bp bank + 15 bp firm A

9 9 - quantification of arbitrage gains from the swap is conditional on the assumption that participants of the swap will preserve their credit risk during the life of the swap After entering into the swap transaction the worsened rating of firm A increased its borrowing cost at floating rate interest to the level LIBOR bp. New net position of the firm A is LIBOR (LIBOR bp) 10.2 % = % This is more costly position in comparison with the direct borrowing on the fixed market. Borrowing cost of the firm AA at floating rate are unchanged but the firm is exposed to higher credit risk in comparison with direct borrowing at floating rate.. Valuation of swaps swap is the exchange of two cash flows whose present values must be equal if priced fairly value for the swap buyer = PV(float) - PV (fix) value for the swap seller = PV(fix) - PV(float) PV (fix) present value of fixed-coupon bond PV (float) present value of flexible-coupon bond (such as FRN, flooating rate note) a) yield to maturity (YTM) future cash flow is discounted at market swap rate of given maturity PV(fix) = T t= 1 cm (1 + r ) 1 (1 + rt ) = cm r T t T M + (1 + r ) T T T M + (1 + r ) T r T market T-year swap rate, c coupon rate, M principal PV(float) = M (substituting c = r T ) T

10 10 What is the actual value of the 2Y swap which pays fixed rate.5 % (annual compounding) against receiving LIBOR? Notional value of the swap is 100 and the 2Y market swap rate is.6 %.,5,5 100 PV(fix) = ,06 (1 + 0,06) (1 + 0,06) = 101,71 PV(float) = 100 value for the seller = 101, = 1,71 b) bootstrapping cash flow from the fixed leg of the swap is discounted at zero rates see handout BONDS cash flow from the flexible leg of the swap is equal to the notional principal. Warehousing of swaps warehousing of the swap is temporary hedging of interest rate risk until reverse swap position is crated hedged position: Client (seller) fixed LIBOR Swap dealer fixed+spread LIBOR Client (buyer) until matching transaction the swap dealer is exposed to the following interest rate risk: - if he is paying fixed rate and interest rates will decline with the reverse swap the fixed rate obtained will be lower than the fixed rate paid - if he receiving fixed rate and interest rates will increase with the reverse swap the fixed rate obtained will be lower than the fixed rate paid warehousing on the bond market a) swap dealer is the payer of the fixed rate - buying the government bond means obtaining the fixed coupon against paying fixed rate in the swap transaction - financing the purchase of the bond with the repo transaction (alternatively with borrowing on the money market)

11 11 - bond serves as collateral against funds borrowed for paying the purchase of the bond (paying the repo rate, usually overnight rate, due to unknown warehousing period) - technically feasible as a result of simultaneous settlement of all transactions in the end of the business day - the dealer is exposed to the basis risk (repo rate changes each day while LIBOR only after some perid) - if interest rates drop the dealer will get lower fixed rate on the reverse swap but he is partly compensated by capital gain from selling the bond at a higher price Bond market coupon cap. gain/loss Swap dealer fixed LIBOR Client reporate Repo market b) swap dealer is the receiver of the fixed rate - short sale of the bond financed by using the repo market - the owner of the bond is entitled to receive coupons which are paid from the fixed leg of the swap - proceeds from selling the bond are invested on the repo market and used for paying the flexible rate in the swap) warehousing on the futures market - opening long position with long-term interest rate futures position is profitable when interest rates are declining which offsets lower fixed rate of the reverse swap position is loss-making when interest rates are rising but the dealer will obtain higher fixed rate from the reverse swap - opening short position with short-term interest rate futures position is profitable when in interest rates are rising which compensates higher paid flexible rate of the reverse swap

12 12 position is loss-making when interest rates are declining but the dealer will be the payer of lower flexible rate from the reverse swap - the dealer is exposed to basis risk because the underlying bonds of long-term interest rate futures have longer maturities (above 15 years) while maturities of swap contracts may be shorter (up to 10 years), also the time to finding the reverse swap is unknown Long-term int. fut. long Swap dealer fixed LIBOR Client short Short-term int. fut.

13 1 B. FORWARD RATE AGREEMENT 1. Basic concepts forward rate agreement (FRA) is the contract which pays the difference between two interest payments, the first one derived from a fixed rate or FRA rate (determined when the deal is agreed) and the second one from a market reference rate (unknown when the deal is agreed) the value of interest payments depend on the agreed value of notional principal and the length of so called FRA period 6 v 12 FRA, 6 * 12 FRA: 0 6 FRA období 12 beginning of the contract beginning of the FRA period end of the FRA period fixed rate FRA buyer FRA seller reference rate FRA buyer is the payer of fixed rate and the receiver of floating rate FRA seller if the receiver of floating rate and the payer of fixed rate notes: - FRA is an elementary swap with deferred start - reference rate is mostly linked to money market rate like LIBOR - cash payments are made on net basis - interest payments are calculated according the rules of simple interest (in line with money market conventions) - payments occur always in the beginning of the FRA period ( t rp t k p ) cash flow (for the FRA buyer) = M 1+ r t T 60 T 60 M... notional principal, t r p... (p - t)-year reference rate tk p... (p - t)-year fixed rate, T... length of FRA period

14 1 A firm buys 6 v 12 FRA at fixed rate 1 % (which will be paid) and the reference rate LIBOR (which will be obtained). Notional demand is 1 mil. a) After 6 months LIBOR is 15 %. The firm will get from the bank as the counterparty of the contract mil ( ) 902 $ = 180 b) After 6 months LIBOR is 10 %. The firm pays to the bank mil ( ) = 9 79 $ 2. Speculation and hedging trades a) speculation FRA buyer (pay fix, get float) may speculate on interest rate increase (higher received future floating rate) FRA seller (pay float, get fix) may similarly speculate on interest rate decline b) hedging Money market LIBOR + spread Borrower FRA rate LIBOR Bank resulting position: (LIBOR + spread) + (FRA rate LIBOR) = FRA rate + spread. FRA strips FRA strip is a sequence of neighbouring FRA contracts examples: - the sequence ( v 6) & (6 v 9) forms the strip ( v 9) the sequence 2M & (2 v 6) & (6 v 12) forms the strip 12M the absence of arbitrage opportunities requires the validity of interest rate parity which generates prices of FRA contracts with longer-term maturities

15 15 6 examples: 1+ k ) (1 + k ) = (1 + k ) ( ( 1+ 2 r ) (1 + 2k6 ) (1 + 6k12 ) = (1 + r 12 ) Validation interest rate parity for the strip 6M = M & ( v 6) 0 t = 0: - borrowing one unit of principal on money market (at actual market M rate r ) 0 - buying FRA contract v 6 with notional principal (1 + 1 r ) and FRA rate k 6 0 t = : - requirement for repaying the borrowed amount with interest = (1 + 1 r ) 1 0 ( r k6 ) - revenue from the FRA settlement = (1 + 1 r ) 1 1+ r - refinancing the remaining balance with M loan at actual market rate t = 6: - requirement for repaying the due balance with interest which must equal to the 1 0 repaying requirement ( 1 r ) market rate 0 r ( 1+ r ) ( 1+ r ) ( 1+ r ) = = + from 6M loan taken at time in t = 0 at given ( 1+ r ) ( 1+ r ) ( 1+ r ) ( r k6 ) ( 1+ r ) ( 1+ k ) = ( 1+ r ) ( r r k ) r. Hedging FRA contracts using interest rate futurest pay-off from interest rate futures = F0 F = ( 100 F ) (100 F0 ) = r r0 t = interest rate known only when settling the futures contract interest rate known when entering the futures contract pay-off from FRA = (interest rate known only when settling the FRA interest rate known when opening the FRA) discount factor note: FRA buyer profits on interest rate increase while the buyer of futures contract looses on interest rate increase hedging FRA using futures needs to open positions on the same side of both markets t t

16 16 i) pricing and hedging standardised FRA contract standardized FRA is such contract whose basic parameters (such as start of the contract, length of the FRA period) coincide with those of some traded futures contract the two contracts represent in fact two almost identical products therefore the FRA rate should be quoted at the prevailing futures rate Three-month June interest rate futures settled in June 17th is in March 17th offered at price In that day therefore the v 6 FRA will be offered at price 8.25 %. Three-month September interest rate futures settled in September 17th is in March 17th offered at price In that day therefore the 6 v 9 FRA will be offered at price 8.50 %. full hedging condition: ACT 60 ( k LIBOR) 0 m M = n v ( k LIBOR) ACT LIBOR M notional principal of hedged FRA, ACT number of days in the FRA period, n number of futures contract (to be determined), v standardised value of futures contract, m number of months in FRA period, k the common value for the FRA rate and futures settlement rate practical complications: - accuracy of hedging depends on the accuracy of estimating the future value of LIBOR - rounding to the natural number of contract - different quoting conventions for the length of contracts (futures contract use 0 days in a month, FRA contracts take into account actual number of days in a month) How many June ST contracts (short-term interest rate futures with M maturity and nominal value ) is needed to hedge M sterling FRA 1 v with notional principal 10 mil?

17 17 We know that the FRA period covers the time span form 19th June to 19th September (total days is 92) and settlement is against the M LIBOR. The settlement day of hedging futures is 18th June and the settlement rate is also the M LIBOR. The best estimate of LIBOR as of the settlement day is 6.25 %. n = H (1v ) = 20 June = = & The hedged position needs to open 20 June futures contracts. ii) pricing and hedging standardised FRA strip standardised FRA strip is the sequence of neighbouring standardised FRA contracts 17..: A bank sells the v 9 FRA which can be created from standardised FRA contracts v 6 and 6 v 9. These two constituent legs can be therefore priced according the futures prices and hedged by sale of an appropriate number of June and September M interest rate futures. Let H( v 6) = 20 June, H(6 v 9) = 18 Sept 19.6.: The v 9 FRA is settled and all futures positions are closed. This is the summary of received (+) and paid ( ) interest rates: v 9 FRA: + FRA rate actual 6M LIBOR 1 1 = + ( k ) ( r ) 2 9 M June: + actual M LIBOR opening futures rate 1 1 = + ( r ) ( k ) M Sept: + actual futures rate (= M LIBOR expected in months opening futures rate 1 1 = + ( f ) ( k ) the position is hedged due to following parities 1 1 k 6 + r k f 9 6 = & = & Therefore H( v 9) = 20 June + 18 Sept ( 1+ k6 ) ( 1+ 6k9 ) 1 = 2 k ( 1+ r ) ( 1+ f ) 1 = r (standard interest rate parity) (FRA interest rate parity)

18 18 practical complication: - see previous remarks (uncertain future Libor, rounding of number of contracts, different quoting conventions) - FRA interest rate parity uses compounding which cannot be used for futures contracts - terminal day of the FRA strip may not coincide precisely with the settlement day of standardised futures contract iii) pricing and hedging of interpolated (non-standardised) FRA contracts a) interpolation with fixed start FRA contracts k 9 k 8 k 6 v 6 v 8 v 9 FRA maturity 8 6 ( k ) k = k + k 9 6 days in [ v 8] days in [ v 6] days in [ v 9] days in [ v 6] the same interpolating scheme will be used for the number of hedging futures contracts days in [ v 8] days in [ v 6] H ( v 8) = H ( v 6) + ( H ( v 9) H ( v 6)) days in [ v 9] days in [ v 6] What interest rate futures and in which proportion are needed for hedging the v 8 FRA (15 days) if the v 6 FRA (92 days) is offered at 8.25 % and hedged with 10 June futures and at the same time the v 9 FRA (18 days) is offered at 8.6 % and hedged with 10 June and 10 September futures? What will be the offer rate of the above v 8 FRA?

19 k8 = ( ) = 8.9% H ( v 8) = 10 June + (10 June + 10 Sept -10 June) = 10 June + 6,7 Sept = & 10 June + 7 Sept b) interpolation with fixed length FRA contracts 6k 11 5k 10 k 8 v 8 5 v 10 6 v 11 FRA maturity 5 k 10 8 ( k ) = k + k days to [ v 8] days to[ v 6] days to[ v 9] days to[ v 6] the same interpolating scheme will be used for determining the number of hedging futures contracts (the same practical complications) days to [ v 8] days to [ v 6] H (5 v10) = H ( v 8) + ( H (6 v11) H ( v 8)) days to [ v 9] days to [ v 6] basis risk i) hedging strategy may use futures contracts which will not exist at time of hedging (i.e. FRA 5 v 10 settled in August is hedged using June futures) ii) replacement of maturing futures with longer-term maturities is exposed to the risk of non-parallel shift of yield curve (i.e. in case of faster increase of short-term rates the replacement of short June futures with short September futures may cause higher profit from hedging) iii) hedging basis risk assumes that the price change of futures will be equal to the average price change of neighbouring contracts

20 20 In March the 5 v 10 FRA was hedged (the settlement month is August) with selling futures contract in the following composition June + 9 Sept + Dec (therefore in August the June contracts will not exist) How to hedge this basis risk? If se assume that Sept = ½ ( June + Dec) we have June = 6 Sept Dec. Three June futures will be thus replaced at maturity with selling six September futures and buying three December futures. 5. Price links between interest rate swap and FRA strip coupon swap and FRA strip consists in the exchange of same types interest flows (fix versus float) therefore they are eligible for testing arbitrage opportunities (one can compare fixed leg of the swap with synthetically created fixed rate of FRA strip) Following money-market instruments are available: M Libor 12. % (91 days), v 6 FRA 12.1 % (91 days), 6 v 9 FRA 11.8 % (90 days) a 9 v 12 FRA 11. % (90 days). At which price will be quoted one-year coupon swap? 90 ( ) ( ) ( ) ( ) 1+ 1R swap rate = = One-year swap will be offered at 12.5 %.

21 21 C. CURRENCY SWAP 1. Definitions outright forward agreement about future exchange of foreign currency Bank UK Bank US $ forward rate forward swap agreement about today s exchange of foreign currency accompanied with future reverse transaction $ spot rate Bank UK Bank US forward rate $ currency swap contract in which both parties agree to exchange for a given period two interest cash follows derived from principals denominated in different currencies and to exchange respective principals in the beginning and in the end of the contract at given exchange rate $ spot rate Bank UK $ Bank US forward rate $

22 22 - a UK bank pays to a US bank for a given period dollar cash flow based on the underlying value of dollar amount and the dollar rate agreed when the swap was negotiated - a US bank pays to a UK bank for a given period sterling cash flow based on the underlying value of sterling amount and the sterling rate agreed when the swap was negotiated - the exchange of principals need not be the part of the contract (they are notional) types of currency swap: currency swap: exchange of two fixed interest payments (fixed-against-fixed swap) cross-currency swap: exchange of two interest payments from which at leas one is based on floating interest rate - coupon swap (fixed-against-floating): exchange of fixed against floating interest payments - basis swap (floating-against-floating): exchange of two floating interest payments plain vanilla swap: standard non-complicated swap deal (fixed principal, regular payments, immediate start, no option features) 2. Using currency swaps a) hedging exchange rate and taking on interest rate risk firm has a liability denominated in foreign currency (i.e. repays foreign exchange credit) which is covered with revenues in domestic currency - hedging exchange rate risk while speculating on rise of domestic interest rates currency swap Foreigner Firm CZK Counterparty CZK - hedging exchange rate risk while CZKspeculating on drop of domestic interest rates cross-currency coupon swap

23 2 Foreigner Firm CZK Counterparty CZK CZK - hedging exchange rate risk while speculating on drop of domestic and rise of foreign interest rates cross-currency basis swap Foreigner Firm CZK Counterparty CZK CZK rates firm has a variable rate asset denominated in foreign currency (i.e. revenues from purchased bond) whose revenues should finance operational costs denominated in domestic currency - hedging exchange rate risk while speculating on rise of domestic interest cross-currency swap Foreigner Firm CZK Counterparty CZK CZK

24 2 b) new issue arbitrage CHF bank A bank B 6.50 % 7.00 %.00 % 5.25 % difference 50 bp 125 bp bank A (higher rated) has absolute advantage on both markets and comparative advantage on US dollar market bank B (lower rated) has absolute disadvantage on both markets and comparative advantage on Swiss franc market swap deal sill be struck if both banks have borrowing needs on those markets where they have comparative disadvantage possible arrangement: - both banks borrow funds (alternatively issue bonds) on markets where they have comparative disadvantage, values of borrowed amounts reflect agreed exchange rate (i.e. 1.5 CHF/) - banks swap borrowed amounts - banks are exchanging the interest payments according the swap deal - when the swap terminates banks will exchange borrowed amounts according to the previously agreed exchange rate 150m CHF 100m 100m 150m CHF Dollar market % % 7 % CHF Franc Bank A Bank B market 6 % CHF 100m 100m 150m CHF 150m CHF

25 25 position of bank A: pays % + 6 % CHF gets % net interest rate cost 6 % CHF gain 50 bp CHF position of bank B: pays 7 % CHF + % gets 6 % CHF net interest rate cost: % + 1 % CHF gain 125 bp bp CHF conversion of franc basis points into dollar basis points swap page Telerate: 1 bp CHF = 0,92 bp net interest rate cost of band B= % % =,92 % gain = = bp arbitrage potential = 125 bp 50 bp CHF = [ ,92] bp = 79 bp (divided 6 bp for bank A + bp for bank B) notes: - swap makes it possible to separate decisions about the form of financing from managing financial risks (bank A is financed on dollar market and is exposed to the Swiss franc risk) - usually each of the swap contractors has absolute advantage on one of the market (unusual situation for interest rate swaps) - swap may be agreed even in case when counterparties do not have direct access on market with comparative disadvantage (they may make comparisons with some target borrowing costs), the swap is thus the way of creating the issuance of bond synthetically - financial house may act as an intermediator and takes on exchange rate risk, arbitrage profit should be distributed among all three parties to the contract c) asset arbitrage is the strategy for enhancing investment returns i) swapping returns from Swiss franc bond into fixed return of dollar bond (creation of synthetic dollar bond)

26 26 - investor may have comparative advantage on the franc market (20 bp CHF) - investor sells the counterparty bank US dollars, buys CHF and opens swap transaction to exchange franc and dollar interest cash flow - francs are invested into buying the franc denominated bond - opposite flow of principal when swap matures net interest income = 5.5 % % CHF (= 0.18 % ) = 5.68 % CHF CHF Franc market 6.6 % CHF Investor 6. % CHF 5.5 % Bank CHF CHF ii) swapping returns from EUR bond into floating return of US bond EUR EUR Euro market 8. % EUR Investor 8.1 % EUR LIBOR Bank EUR EUR net interest income = LIBOR + 0 bp EUR = LIBOR + 25 bp (after conversion into US rate) arbitrage opportunities may exist as a result of segmentation of international capital markets into currency segments - different borrowing capacity of individual segments (on shallow markets the issuance of a large quantity of bonds may easily saturate demand) - different perceptions of credit risk of borrowers in different currency segments (better knowledge of resident issuers)

27 27 - different national savings rate (influences the availability abundance of cheaper capital) - existence of investment restrictions (foreign exchange controls, precautionary limits on portfolio compositions) - tax reasons d) case studies i) eurokoruna bonds CZK Domestic bank (1) DEM Investor (2) 8 % CZK CZK Issuer DEM CZK CZK () LIBOR DEM - 1 % 8 % CZK () Domestic assets 12 % CZK Swap house DEM LIBOR DEM (5) Forex market 1. Investor buys korunas (sells marks), exchange rate of koruna strengthens 2. Investor buys eurobond from the issuer in exchange for koruna return. Issuer makes a swap deal (coupon cross-currency swap) with swap house. Swap house buys domestic assets (Treasury bills, extension of credit, bank deposit) 5. Swap house refinances itself on forex market

28 28 6. The opposite cash flow when Eurobonds mature summar: - foreign investor gets 8 % CZK - issuer pays LIBOR DEM - 1 % - swap house gets % CZK - 1 % DEM ii) borrowing abroad without influencing the koruna exchange rate Principal Taxes Kč (1) Foreign market Interest Czech government Domestic market () Principal Interest (2) Interest Kč Principal Kč () Principal Interest Swap house Principal Kč Interest Kč 1. Czech government borrows abroad (issues foreign bonds denominated in euro) and then is repaying interest also denominated in euro 2. Swap house arranges currency swap with the Czech government. Swap house invests foreign exchange into foreign assets (avoiding forex conversion shields the koruna from strengthening). Swap house covers its borrowing needs in korunas by borrowing korunas on domestic market summary: - government receives credit and pays interest both denominated in korunas without influencing the koruna exchange rate - potential push on higher domestic interest rates due to higher demand for koruna loans

29 29. Pricing of currency swaps value of swap: net present value of future cash flows (new element is the conversion of cash flaws on common currency) V = NPV(currency A) - NPV(currency B) exchange rate (A/B) What is the value of year currency swap with following features: DEM principal 100 mil. 150 mil. coupon % 10 % Y interest rate 5 % 9 % The contract envisages the exchange of principal amounts at agreed exchange rate 1.5 DEM/ upon maturity of swap. Actual exchange rate is 1.5 DEM/. The swap is priced on base of its underlying yield to maturity. current value of dollar stream ( mil) current value of mark stream ( mil) t= 1 t= t t 100 mil + = mil + = DEM 1.09 = value of swap = (for the recipient of mark stream and the payer of dollar stream)

30 0 C. EQUITY SWAP 1. Equity swap with fixed notional amount equity swap is a contract between two parties consisting in the exchange of two cash flows when: - a bank pays (i.e. semi-annually) investor the yield which is derived from the appreciation of underlying index, if the index drops the inventor pays to the bank - investor pays the bank a variable interest rate (i.e. 6M LIBOR) applied to the same underlying principal (± spread reflecting the creditworthiness of the client) - the money value of exchanged cash flows depends on the agreed notional principal - equity swap is off-balance sheet instrument, principal is notional and does not appear in balance sheet, interest flows are reflected in profit and loss statement - netting of opposite payments - over-the-counter product with individually negotiated parameters Index Investor Bank LIBOR ± spread usage: transformation of money-market investment into diversified stock portfolio (creation of synthetic stock portfolio) initial investment Money market LIBOR Investor index Bank repayment of principal LIBOR ± spread

31 1 advantages: - "buying" diversified portfolio in one transaction (investor does not buy portfolio in reality) - lowering transaction cost in comparison with actual investment into shares (taxes, fees, custody, cash flow management, and other) - simpler techniques of passive management (index tracking), avoiding cost of portfolio rebalancing - circumventing regulatory rules (in company status, supervisory restrictions) - arbitrage against share indexes Cash flow from equity swap with notional value 100 mil GBP. Month FT-SE 100 LIBOR Index payment Interest payment X X 6 (182/65) ( %) (18/65) (-.17 %) (18/66) ( %) (18/66) (+ 2.6 %) Net investor income = = GBP 2. Equity swap with variable notional amount - the aim of the product is to simulate capitalisation of profits and losses on the stock market - the size of notional value is adjusted in line with capital gains and losses in underlying stock index - in combination with the money market the adjusts his position symmetrically with changes in underlying principal (profit from the index appreciation is invested

32 2 into underlying money market instruments, loss from index depreciation is matched by liquidation of money market positions in the same scale) Cash flow from equity index with variable notional amount based on the data from previous example Month Index payment Interest payment Notional amount 0 X X Net investor income = GBP

33 D. CREDIT DERIVATIVES 1. Basic notions forms of credit risk: - default risk means the inability of debtor (issuer of bond, loan taker) to honour fully or partly his or her obligations - downgrading risk means the risk of a lower rating due to declining capacity to generate future earnings for honouring current liabilities - risk of a higher credit spread means the risk of so-called flight to quality during major macroeconomic imbalances (monetary turbulences, worsening of macroeconomic outlook, and others) traditional methods of credit risk management: - credit limits is a quantitative ceiling on credit exposure to individual debtor or to a group of debtor - netting or offsetting mutual receivables and liabilities - collateralisation means hedging the liability with the right of creditor to foreclose some assets in case of default of the debtor - downgrade triggers are provisions to terminate the contract in case the rating of the counterparty declines below some level credit derivative financial instrument which enables to separate credit risk from its host (underlying issuer, underlying asset) and to manage credit risk independently (both for exposing to or hedging credit risk) advantages of credit derivatives: - lower transaction costs in comparison with direct trades (sale of lower-quality bond, foreclosure of collateral, and so on) - non-disruptive links with business clients (client s assets are kept in the balance sheet of the bank)

34 terminology: seller of credit risk = buyer of credit protection buyer of credit risk = seller of credit protection 2. Credit options a) credit level option the pay-off from the security is based on the difference between the price reflecting the credit risk of underlying instrument and the market price of the underlying asset at time of maturity of the option long credit put: V = max CF t ( 0, X ST ), where X = (1 + r + t t s) (discounted to the exercise date of the option) r reference rate, s credit spread (mark-up reflecting credit risk) CF t cash flow form the asset in time t Investor with one-year investment horizon bought 5-year zero coupon bond in nominal value 1000 $ and with credit spread 215 bp over comparable Treasury bond whose yield was at time of the purchase 6.25 %. With purpose of hedging credit risk the investor buys one-year credit put option with exercise spread 225 bp Therefore strike price of the option is 1000 X = 722 $ ( ) =. If the bond price is in one year time (when the option matures) 710 $, investor will exercise the option and gets = 12 $. At bond price 70 $ the option will be become worthless (incurring the loss equal to the paid option premium). b) credit spread option the payoff is derived from the difference between the credit spread at time of option maturity and an underlying spread

35 5 long credit call ( 0,( s ) principal risk factor) V T = x s T spread when option matures, x exercise spread, risk factor = duration + convexity such a construction creates a hedge against the decline in value of underlying bond due to higher credit spread r P ( D + K) = P ) Manager believes that the credit spread of given bond will climb up to 250 bp over Treasury bond during the coming year. He buys credit spread call in notional principal 20 mil $ and exercise spread 178 bp (based on actual spread). Risk factor (bond duration) is determined to be Option premium is 125 bp. In case the manager view proves right the net income form the option will be 20 mil ( ) mil = $.. Credit swap a) credit default swap i) one-off insurance of credit risk Underlying asset Investment Investor Contingent payment Swap counterparty Total return Swap premium structure of payment: - investor (buyer of credit protection) pays swap premium (in several instalments or as a bullet payment) in exchange for contingent liability in case a credit event occurs - investor is recipient of the total return of the asset, therefore eventual depreciation of the (negative total return) is compensated by contingent payment from triggered by credit event credit event: - default in coupon payment, bankruptcy of issuer, debt restructuring, downgrading, general decline of market (rich possibilities in tailoring the contract)

36 6 contingent payment: - financial settlement: agreed fixed cash amount or variable amount dependent on scale of the asset depreciation, fixed date of contingent payment or its determination only after the credit event occurs - physical settlement: sale of the underlying asset for its face value ii) regular exchange of cash flows Underlying asset Investment Total return Investor LIBOR + spread Total return Swap counterparty structure of payment: - investor (buyer of credit protection) passes the counterparty (seller of credit protection) total return of the underlying asset in exchange for agreed interest payments - investor is still the owner of the underlying asset but total return (both positive and negative) belongs to the counterparty - in case of asset s default investor gets agreed interest payment plus compensation for asset depreciation b) total rate of return credit swap (TROR) the investor is not interested in buying credit protection but on the contrary by higher exposure to credit risk (in exchange for higher potential return) Underlying asset Cash Total return Swap counterparty LIBOR + spread Total return Investor Cash LIBOR Money market

37 7 structure of payments: - investor is the recipient of total return from the underlying asset (including capital gains or losses) in exchange for paying regular interest (based on refinancing cost of swap dealer) but is not the owner of the risky asset - swap dealer created hedged position earning fixed spread, the underlying asset is usually bought only after the TROR has been arranged (different arrangement in comparison with credit default swap) motivation for the investor - synthetic (off-balance sheet) ownership of risky asset, i.e. receiving all return of the asset without owning the asset (analogy to leasing) - tailoring maturity of underlying asset (investment horizon of the swap may be shorter than maturity of underlying security) - financial leverage originates from receiving the total return of security without the need to buy the full price of the security A bond with nominal value 100 mil earns 250 bp over LIBOR whose current value is 5.80 %. Non-speculating pension fund who can borrow at LIBOR thus can attain the net yield: 100 (LIBOR ) net yield = LIBOR = = 2.5 % 100 A hedge fund that needs to pay the issuer of TROR the price 5 % from nominal value of underlying asset and the fee LIBOR+100 bp may thus get net yield: 100 (LIBOR LIBOR 0.01) net yield = = 0. = 0 % 5. Credit forward in analogy with classical forward contract the credit forward may pay a) the difference between the future market price of underlying asset and agreed exercise price based on underlying credit risk b) the difference between the future spread of underlying asset and agreed exercise spread pay-off = [credit spread at maturity exercise ] risky factor notional principal

38 8 in contrast to credit option the credit forward puts no ceiling on potential loss, on the other hand it does not require to pay a premium upon opening the contract 5. Credit linked notes (CLN) CLN are securities which combine features of standard bonds and credit derivatives a) bonds with embedded credit derivative i) bond with embedded short credit put option coupon long credit note long note short credit put rating investor believes that the market prices the risk of the underlying bond fairly so the revenue from sold credit options enhance the return of bond (small likelihood of exercising options) in case of downgrading the bond (increase of credit spread) the credit options will be exercised that makes the yield of the bond lower ii) bond with embedded long spread call option construction of pay-off from embedded option protects against depreciation of notional principal while the upside potential is not limited b) arrangement of credit derivatives using special purpose vehicle (SPV) making transactions with credit risk without the explicit need to use credit derivatives

39 9 1. Investor (i.e. pension or mutual fund) makes investment into securities (notes) issued by SPV (subsidiary of swap dealer) especially established for the transaction Investor is not entering into derivative contract but buys securities backed by high-rated investment bank (J. P. Morgan, Chase Manhattan, and others) Investor has access to the total return of risky assets while his initial investment is substantially lower than is the market value of these assets (source of financial leverage) 2. SPV uses the cash from sold notes for the purchase of Treasury notes whose yield is one of the sources yield on SPV credit-linked notes held by investor Treasuries also fulfil the role of collateral in case of asset depreciation (so called first loss position). SPV arranges with the mother company the total return swap whose proceeds form the second part of the yield on SPV notes held by investor. Swap dealer buys the basket of risky assets which perform the role of underlying securities for the total return swap 5. Purchase of risky assets is financed by the loan on money market, these financing cost then shape the level of fees Swap dealer created hedged position which earns a fixed spread being the difference between received fees and paid refinancing interest rate, losses can occur if the depreciation of assets is higher then the value of collateral Treasuries Money market Cash (5) LIBOR Investor Notes (1) Cash SPV Total return () Fees Swap dealer Cash (2) Coupon Cash () Total return Treasuries Risky assets

40 0 c) taking out bad assets form the balance sheet of bank motive: evasion of regulatory requirements on bad loan provisioning (2) Bank SPV (1) () () (5) Bonds 1. Payment for extended guarantee (paying insurance premium) on bad assets - agreed fiction that loans whose loss-making feature is evident will officially default as of a given future date - bank buys a high-quality hedge (approved by auditors) therefore there is no need to create provisions - bank remains the owner of bad loans 2. Contingent payment in case of assets default ( insurance payment ) although in reality the future default is sure thing. Bank uses the obtained cash from insured defaulted assets on buying US Treasury bond and thus receives coupon payments 5. Bond are lent to SPV (some income from lending) as a assurance that the bank will keep paying insurance premiums general features of transaction: - conspicuously negative cash flow for the bank - high sanctions for earlier termination of the contract - SPV is exposed to negligible risks (boiled down to the default of Treasuries)