CHAP15A

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International Financial Management

P G Apte

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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.

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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

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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.

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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” because FRA 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.

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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

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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

L)] x (DF + 100) x [(B

A x DF x L)-(R = P

L)] x (DF + 100) x [(B

A x DF x R)-(L = P

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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.

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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

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• 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

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• 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

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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

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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)

Trade date Maturity dateFRA start date/settlement date

Fixing date

t=0 t+3m-1 t+3m t+6m

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• 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

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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

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Interest Rate Options

• An interest rate cap consists of a series of call options on interest rate or a portfolio of calls

• A cap protects the borrower from increase in interest rates at each reset date in a medium-to-long term floating rate liability

• An interest rate floor is a series or portfolio of put options on interest rate which protects a lender against fall in interest rate on rate rest dates of a floating rate asset

• An interest rate collar is a combination of a cap and a floor

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Interest Rate Options• A Call option on Interest Rate

– Payoff profile from the call option where the payoff has been reckoned at option expiry.

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Interest Rate Options– 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

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• A Put Option on Interest Rate

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• A Put-Call Parity Relation– A long position in a call option with strike rate

R and a short position in a put with the same strike and same maturity, both on the same underlying index are equivalent to a long position in an FRA at R – If maturity rate is higher than R, long call will be exercised; if lower than R, the sold put will be exercised. Borrowing/lending will take place at R like in an FRA.

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Interest Rate Caps, Floors and Collars

• Interest Rate Caps– A portfolio of call options on interest rate.– Provides protection against rising rates on a floating rate

debt.– Depending upon the evolution of the underlying interest

rate, some of the options in the cap will be exercised while some will lapse.

– Borrowing cost capped at a rate which equals the strike rate plus a margin representing the amortization of the premium paid.

– The effective cost of a floating rate loan plus a long cap will depend upon the evolution of the underlying rate.

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Interest Rate Caps, Floors and Collars• Interest Rate Floors• A portfolio of put options on the underlying rate.• Protection against falling rates on a floating rate

asset.• The return on the asset floored at a rate equal to

the strike rate minus an allowance for amortization of the premium.

• Effective return on a floating rate note plus a long floor depends on the evolution of the underlying rate

V

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Interest Rate Caps, Floors and Collars• An Interest Rate Collar• A long cap with strike R1 plus a short floor with strike

R2 , R2 < R1 is a long collar.• Protection against rising rates, cost of protection reduced

by sacrificing some of the benefit of lower rates. Borrowing cost capped at R1 plus a margin but will not fall below R2 plus a margin. The margin represents annualized cost of the premium for the collar.

• R1 and R2 can be chosen so that the collar is a “zero cost” collar. The premium paid for the cap cancelled by the premium received for the floor. The borrowing cost would vary between a low of R2 and a high of R1.

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Interest Rate Caps, Floors and Collars

Payoff Diagram of a Zero-Cost Collar

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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

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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.

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Options on Interest Rate Futures

Payoff from a Put on Eurodollar Futures

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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

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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

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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

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CHAP15A