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## International Financial Management P G Apte

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**CHAPTER - 15**Management of Interest Exposure, FRAs, Interest Rate Caps and Floors International Financial Management P G Apte P.G.Apte International Financial Management**Introduction**• Interest rate uncertainty poses a worrisome problem for companies which borrow and invest in the international money and capital markets • The last decade of has seen a significant increase in interest rate volatility. • Fluctuations in interest rate affect a firm's cash flows by affecting interest income on financial assets and interest expenses on liabilities • For non-financial firms with floating rate liabilities it poses considerable uncertainty about cost of capital • For financial institutions with large portfolios of debt securities, interest rate movements can imply huge capital gains or losses as well as fluctuations in income. P.G.Apte International Financial Management**The Nature and Measurement of Interest Rate Exposure**• Effective assessment and management of interest rate exposure requires a clear statement of the firm's risk objectives • Primary Objectives • Net interest income • Net equity exposure • Secondary Objectives • Credit exposure • Basis risk • Liquidity risk P.G.Apte International Financial Management**The Nature and Measurement of Interest Rate Exposure**• The most often used device to assess interest rate exposure is Gap Analysis. It focuses on timing mismatches between maturing assets and liabilities. During each time interval the gap is the difference between assets and liabilities which mature during that interval • A more sophisticated approach uses the concept of duration. This attempts to measure the sensitivity of the market value of a debt security to changes in interest rates. A large value of duration implies larger change in the value of a debt instrument for a given change in yield. Suffers from assumption of flat yield curve and parallel movements in yield curve. P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• A Forward Rate Agreement (FRA) is notionally an agreement between two parties in which one of them (the seller of the FRA), contracts to lend to the other (the buyer), a specified amount of funds, in a specific currency, for a specified period starting at a specified future date, at an interest rate fixed at the time of agreement • “Notional” becauseFRA will not normally involve actual lending of the principal but only settlement of interest rate difference. • The underlying loan and FRA are separate contracts generally with separate banks • The seller of FRA essentially agrees to deposit funds at an agreed upon rate with the buyer. P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• Figure below is a schematic diagram of an FRA contracted at t = 0, applicable for the period between t = S and t = L. DS and DL are actual number of days from t=0 to t=S and t=0 to t=L respectively. The period from t=S to t=L is the contract period, t=S is the settlement date and DF is the number of days in the contract period P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• The important thing to note is that there is no exchange of principal amount • One of the following two formulas is used for calculating settlement payment from the seller to the buyer (L>R) or buyer to seller (R>L) • L: Settlement Rate R: Contract Rate A: Notional Principal • DF: No.of Days in FRA period B: Day Count Basis P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• FRAs quotes: 6-9 FRA USD 5.50-6.00 • Bank will guarantee a “deposit rate” of 5.50% for a 3-month deposit starting 6 months from now- Bank buys an FRA; bank will guarantee a lending rate of 6.0% for a 3-month loan starting 6 months from now- Bank sells an FRA. Quotes based on forward rates implied by spot rates • 3-month rate 6 months from today is implied by the 6 and 9 months actual – “spot” rates today • (1+i0,6)180/360 (1+if6,9)90/360 = (1+i0,9)270/360 if6,9 denotes the 6-month forward 3-month rate. FRA quotes will bracket this. P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• Given the spot interest rates for a short and a long maturity, the rate expected to rule for the period between the end of short maturity and the end of long maturity is given by • (1+i0,S)DS/B (1+ifS,L)DF/B = (1+i0,L)DL/B B is the day count basis (360 or 365 days) Interest rates i0,S, i0,L stated as fractions, (not percent) are the spot interest rates at time t = 0 for maturities S and L respectively P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• The (if)S,L computed from above forms the basis for quoting the bid and ask rates in an FRA DS/DL • ifS,L = [(1+i0,L)DL/B/ (1+i0,S)DS/B]B/DF -1 • The rate so calculated will only serve as a benchmark for a FRA quotation and the actual quote will be influenced by demand-supply conditions in the market and the market's expectations P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• Applications of FRAs for borrowers and investors • FRAs, like forward foreign exchange contracts are a conservative way of hedging exposure • The relationship between a FRA and an interest rate futures contract is exactly analogous to that between a forward foreign currency contract and a currency futures contract • Another product similar to a FRA for locking in borrowing cost or the return on investment is known as a "forward-forward" contract P.G.Apte International Financial Management**Forward Rate Agreements (FRAs)**• FRAs were introduced in the Indian money market in 1999 • The benchmark rate may be any domestic money market rate such as t-bill yield or relevant MIBOR (Mumbai Interbank Offered Rate) though the interbank term money market has not yet developed sufficient liquidity • RBI guidelines state that corporates are permitted to do FRAs only to hedge underlying exposures while market maker banks can take on uncovered positions within limits specified by their boards and vetted by RBI P.G.Apte International Financial Management**Example : A Typical FRA Deal**• Bank A sells to Bank B a 3 X 6 FRA at 10% against floating 91 day t-bill rate. Notional principal Rs10 crore • Bank A receives fixed rate (10%) for a 3 month period starting 3 months from trade date • Bank B receives floating rate for the same period. The floating rate would be the 91 day t-bill rate 3 months from trade date • though net amount is due on maturity (6 months from trade date), settlement is done on start date (3 months from trade date) FRA start date/ settlement date Trade date Fixing date Maturity date t=0 t+3m-1 t+3m t+6m P.G.Apte International Financial Management**Bank A & Bank B enter into a 6 X 9 FRA. Bank A pays fixed**rate at 9.50%. Bank B pays floating rate based on 91 day T-bill yield. Additional details • Notional principal = Rs 10 Crore • FRA start & settlement date 10/12/99, Maturity date 10/3/00 • T bill yield on fixing date (say 9/12/99) = 8.50% • Determine cash flow at settlement (assume discount rate as 10.0%) • Working • (a) Interest payable by bank A = 10 Cr * 9.50% * 91/365 = Rs 236,849 • (b) Interest payable by bank B = 10 Cr * 8.50% * 91/365 = Rs 211,918 • (c) Net payable by bank A on maturity date ((a)-(b)) = Rs 24,932 • (d) Discounting (c) to settlement date = (c)/(1+ discount rate*discount period) • = Rs 24,932/(1+10.0%*91/365) = Rs 24,325 • Amount payable on settlement date = Rs 24,325 payable by Bank A P.G.Apte International Financial Management**Interest Rate Options**• A less conservative hedging device for interest rate exposure is interest rate options • A call option on interest rate gives the holder the right to borrow funds for a specified duration at a specified interest rate without an obligation to do so • A put option on interest rate gives the holder the right to invest funds for a specified duration at a specified return without an obligation to do so P.G.Apte International Financial Management**A Call Option on Interest Rate**Consider first a European call option on 6 month LIBOR. The contract specifications are as follows : Time to expiry: 3 months (say 92 days) Underlying Interest Rate: 6 month LIBOR Strike Rate: 9% Face Value: $5 million Premium or Option Value : 50 bp (0.5% of face value) = $25000 The current three and six month LIBORS are 8.60 and 8.75%. respectively. P.G.Apte International Financial Management**A Call Option on Interest Rate**P.G.Apte International Financial Management**Call Option on LIBOR….**• 3 months later 6 month LIBOR 9%. • The option is not exercised. The firm borrows in the market. The payoff is a loss of compounded value of the premium paid three months ago. The present value of the loss (at the time of option expiry) is the premium compounded for three months at the 3 month rate which prevailed at option initiation. In the above example it is • $ 25000[1+0.0860(92/360)] = $25,549.44 • If the loss is to be reckoned at the maturity of the loan, this amount must be further compounded for 6 months at the 6 month LIBOR at the time the option expires. P.G.Apte International Financial Management**2. 3 Call Option on LIBOR…..**3 months later the 6 month LIBOR > 9%. Say 10%. The option is exercised. The option writer has to pay the option buyer an amount which equals the difference in interest on $5 million for 6 months at today's 6 month LIBOR (10%) and the strike rate 9% : (0.10-0.09)5000000(182/360) = $25277.78 This amount would be paid not at the time of exercise of the option but at the maturity of the loan 6 months later. Alternatively, its discounted value using the 6-month LIBOR at option exercise can be paid at the time of exercise : (25277.78)/[1+0.10(182/360)] = $24061.36 P.G.Apte International Financial Management**A Call Option on LIBOR**• The breakeven rate is defined as that value of LIBOR at option expiry at which the borrower would be indifferent between having and not having the call option. It is the value of i which satisfies the following equality • A[1+i(M/360)]=A[1+R(M/360)]+C[1+it,T(T/360)][1+i(M/360)] • A is the underlying principal, R is the strike rate, it,T is the T-day LIBOR at time t when the option is bought, C is the premium paid at time t, and, T and M are number of days to option expiry and maturity of the underlying interest rate P.G.Apte International Financial Management**A Call option on Interest Rate**• Payoff profile from the call option where the payoff has been reckoned at option expiry. P.G.Apte International Financial Management**A Put Option on Interest Rate**Consider an investor who expects to have surplus cash 3 months from now to be invested in a 3-month Eurodeposit. The amount involved is $10 million. The current 3 month rate is 10.50% which the investor considers to be satisfactory. A put option on LIBOR is available with the following features : Maturity : 3 months (91 days) Strike Rate : 10.50% Face Value : $10 million Underlying : 3-month LIBOR. Premium : 25 bp (0.25% of face value) = $ 25000 To hedge the risk, the investor goes long in the put. P.G.Apte International Financial Management**A Put Option on LIBOR**3 Months later if 3-month LIBOR > 10.50%’ option lapses If 3-month LIBOR < 10.50%, say 9%, put holder exercises. Put seller pays the put holder (0.1050-0.09)(10000000)(91/360) = $37916.67 This is paid 3 months later or its discounted value at option exercise: 37916.67/[1+0.09(91/360)] = 37073.25 Breakeven rate A[1+i(M/360)]=A[1+R(M/360)] - P[1+it,T(T/360)][1+i(M/360)] P.G.Apte International Financial Management**Interest Rate Options**• A Put Option on Interest Rate P.G.Apte International Financial Management**An Interest Rate Cap**A corporation has borrowed $50 million on floating rate basis for 3 years. The interest rate reset dates are March 1 and September 1. The spread over LIBOR is 25 bp (0.25%). It is a bullet loan (i.e. repayment of the entire principal is at maturity). It buys a 3-year cap on 6 month LIBOR with the following features: Term : 3 years Underlying : 6 month LIBOR. Reset Dates : March 1, September 1. Strike Rate : 9% Face Value : $50 million Up-Front Fee : 2% of face value or $1 million. The cap is traded on February 27 2000, the settlement date is March 1, 2000. The current level of 6 month LIBOR is 9%. P.G.Apte International Financial Management**Interest Rate Cap….**Rate applicable to the first 6-month period is known, there are five interest rate call options in this cap maturing at six monthly intervals starting six months from March 1. Each option has a strike rate of 9% and face value of $50 million. To determine the effective cost of borrowing with the cap we must assume an interest rate scenario. Measuring time in half-years suppose the 6 month LIBOR at subsequent reset dates moves as follows : Reset Date LIBOR (%) 1/9/00 10.0 1/3/01 9.5 1/9/01 9.5 1/3/02 9.0 1/9/02 8.5 P.G.Apte International Financial Management**A Floating Rate Loan with an Interest Rate Cap**____________________________________________________ Time Cash Flow Amortisation Cash Flow Total t from loan of premium from cap ____________________________________________________ 0 +50000000 --- --- +50000000 1 -2344618.1 -227790.43 --- -2572408.5 2 -2598090.3 -227790.43 +253472.2 -2572408.5 3 -2471354.2 -227790.43 +126736.1 -2572408.5 4 -2471354.2 -227790.43 +126736.1 -2572408.5 5 -2344618.1 -227790.43 --- -2572408.5 6 -52154514 --- --- -52154514 P.G.Apte International Financial Management**Interest Rate Floors**A fund manager is planning to invest $50 million in 5-year FRNs. The notes pay 6 month LIBOR+0.50%, the rate being reset every 6 months. The current 6 month LIBOR is 8.60%. As protection against falling rates the manager decides to buy an interest rate floor with the following features : Term : 5 years Underlying Interest Rate : 6 month LIBOR. Reset Dates : June 1, December 1 Strike Rate: 8% Face Value : $25 million Up-front Fee : 1.5% of the face value or $375000 A portfolio of put options on 6-month LIBOR. Depending on how 6-month LIBOR evolves, some options will lapse, some will be exercised. P.G.Apte International Financial Management**An interest rate Collar is a combination of a cap and a**floor. A corporation wishing to limit its borrowing cost on a floating rate liability might find the premium associated with a cap too expensive. It can reduce this by sacrificing some of the potential gain from low interest rates. It buys a cap and simultaneously sells a floor. The premium received from the sale of the floor would partly or wholly compensate for the premium paid for the cap. In the latter case we have a Zero Cost Collar. Thus suppose the current 6-month LIBOR is 7.50% and the company has a floating rate liability with rate reset every six months indexed to 6-month LIBOR. It might buy a cap with a strike rate of 9% and sell a floor with a strike rate of 7%. Suppose the premiums cancel out. Effectively, its borrowing cost will vary between 7 and 9% (plus of course any spread over LIBOR it must pay). P.G.Apte International Financial Management**Options on Debt Instruments**Options on T-bonds and Notes : Standard calls and puts which entitle the holder to buy/sell the underlying debt instrument at a specified price on or upto a specified date without the obligation to do so. Options on T-bond and Note Futures – Right to establish long/short futures position in the relevant contract. P.G.Apte International Financial Management**OPTIONS ON INTEREST RATE FUTURES.**• Options on interest rate futures contracts are traded on a number of financial exchanges including LIFFE. • The underlying asset is a futures contract such as T-bill or Eurodollar futures. The options are American opitons • The holder of a call has the right to establish a long position in a futures contract while a put holder has the right to establish a short position. • Recall that short term interest rate futures prices are quoted as "points of hundred" i.e. (100-the relevant interest rate in percent). • Thus payoffs from a long call (put) on futures are similar to a long put (call) on the underlying interest rate itself. P.G.Apte International Financial Management**Borrower's hedge : Hedging against a rise in interest rate.**Today is March 1. A corporation is planning to issue 92-day commercial paper with face value $20 million on June 1. To protect itself against a rise in interest rate, it decides to buy a put option on 20 Eurodollar futures contracts. The option has the following features : Type : American put option Underlying : June Eurodollar contracts Expiry date : June 1 (91 days from today) Strike price : 91 Face value : $1 million per contract, $20 million total. Premium : 0.75 bp P.G.Apte International Financial Management**The Current price of June futures is 92. The current 3 month**dollar LIBOR is 8.5%. 3 month CP rate is 9%. The dollar value of the premium is calculated as follows : 0.75 (1/100) (90/360) $1,000,000 = $1875 per contract On June 1, the payoff from each option is : June futures price F Payoff 91 Option lapses, no payoff < 91 [(91-F)(1/100)(90/360)1,000000] Thu Suppose the futures price has fallen to 90. The put holder exercises the option and closes out position. The gain is (0.01)(90/360)(1000000)(20) = $50,000. P.G.Apte International Financial Management**Valuation of Interest Rate Options**• The risk-neutral binomial model can be applied to simple interest rate options • Since caps and floors are portfolios of simple options, they can be valued by simply valuing each of the embedded options separately and adding together the values • Options on interest rates can be treated as options on corresponding debt instruments and approximately valued using the Black-Scholes model. • More accurate valuation requires term structure models P.G.Apte International Financial Management**Options on Interest Rate Futures**• The underlying asset is a futures contract such as T-bill or Eurodollar futures contract • The holder of a call has the right to establish a long position in a futures contract while a put holder has the right to establish a short position • Payoffs from a long call (put) on futures are similar to a long put (call) on the underlying interest rate itself. • E.g. Hedging against a rise in interest rate • Buy a put on an interest rate futures. If rates rise, futures price will fall, put will be in the money. Same as buying a call on the underlying rate. • To hedge against a fall in rates, go long a call on an interest rate futures. P.G.Apte International Financial Management**Options on Interest Rate Futures**Payoff from a Put on Eurodollar Futures P.G.Apte International Financial Management**Options on Interest Rate Futures**• Alternatively, if rates are expected to rise, the firm can write a call option on futures and collect an up-front premium; if rates rise, futures price would fall, call would lapse. Premium income would partly compensate for increased interest cost. • Comparison of a number of alternative strategies for an investor to cope with interest rate risk • The available instruments allow the investor a lot of flexibility in designing a package with the preferred risk-return profile given his views about future movement in rates P.G.Apte International Financial Management**Some Recent Innovations**• An interest rate cap can be designed that provides protection contingent upon the price of some commodity or asset • Average rate or Asian interest rate options have payoffs based on the average value of the underlying index during a specified period • Look-back options give payoffs determined by the most favorable value • In a cumulative option the buyer can obtain protection such that cumulative interest expense over a period does not exceed a specific level P.G.Apte International Financial Management**Summary and Conclusion**• Interest rate volatility is a major source of uncertainty particularly for financial institutions • Use of gap analysis and duration • A single-period interest rate exposure can be hedged using FRAs, interest rate futures, simple interest rate options and options on interest rate futures • Multi-period risk can be managed with interest rate caps and floors • Valuation of interest rate derivatives must take account of the stochastic evolution of the entire term structure and in certain cases, simpler approaches using binomial lattice or modifications of Black-Scholes model may be adequate P.G.Apte International Financial Management

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