Foreign Exchange Exposure

• Cash flows of firm, ergo its market value, are affected by changes in the value of foreign currency, FX.

• Transactions Exposure – Explicit contractual amount denominated in FX.

• Operating Exposure – No contract exists yet FX exposure is present.

Two Methods of FX Quotation

• Direct Quotation• Number of home

(domestic, reference) currency units per unit of FX.

• Direct quote is inverse of indirect quote.

• Assumed in this course (intuitive).

• Indirect Quotation• Number of FX units

per unit of home (domestic, reference) currency.

• Indirect quote is inverse of direct quote.

• Not employed in this course (less intuitive).

Examples of Two Quotation Methods

• For Canadian firm.

• Direct quote on greenback, US$: C$1.35

• Indirect quote on greenback US$: US$0.74

• If FX appreciates (rises in value), the direct quote rises and the indirect quote falls.

• If FX depreciates (drops in value), the direct quote drops and the indirect quote rises.

Transactions Exposure

• First part of this four part course.

• Exporter - receives a contractually set amount of FX in future.

• Importer – pays a contractually set amount of FX in the future.

• Measure of FX exposure – the amount of FX involved.

Exporter’s Transactions Exposure

• Canadian beef exporter will receive US$1 million 3 months from now.

• S = direct quote on the greenback, i.e. C$/US$, 3 months hence. (Note: / means per.) S is plotted on horizontal axis.

• Exposed cash flow (ECF) = S x US$ 1 million. ECF is plotted on vertical axis.

Exporter’s Risk Profile

S(C$/US)

ECF(C$) US$1million

Exporter’s Risk Exposure

• Worried about depreciation in FX.

• Forward hedge: Sell FX forward. Arrange now to sell 3 months hence at price determined now, F (the forward rate).

• Option hedge: Buy right to sell FX, a put option on the FX.

Sell Forward Hedge

• Commit now to sell U$ 1 million 3 months from now at forward price, F, determined now.

• Price paid for Forward Contract = zero.

• Sell forward contract cash flow = (F – S) x U$ 1 million where S is the spot rate 3 months hence.

Sell Forward Contract

S(C$/U$)

Contract Cash Flow

F(C$/US)

Hedge with Forward Contract

S(C$/U$)

F x U$1million

Hedged Cash Flow

Hedge with Put Option

• Put option is the right, not obligation like forward contract, to sell U$ 1 million 3 months hence at an exercise or strike price of X(C$/US).

• P, put premium, price paid now for option.

• Put contract cash flow = X – S if S<X; 0 otherwise.

Put Contract Cash Flow

SX

Hedge with Put Option

SX

Hedged Cash Flow

Which is better? Sell forward or Buy put?

S

B

B = breakeven point

S<B, sell forward better

S>B, buy put better

Determination of B, breakeven FX Rate

• B is point of indifference between sell forward and buy put as hedges.

• S<B Forward is better ex-post• S>B Put is better ex-post• B = Forward rate + Future Value of Put

Premium; where interest rate is hedger’s borrowing rate.

• B = F + FV(P).

Hedging a U$ Receivable

• Canadian firm with U$ receivable due 6 months hence

• F (6 month forward rate) = C$ 1.35

• X (exercise price) = C$1.32

• P (put premium per U$) = C$0.05

• Borrowing rate = 6% quoted APR

• B (breakeven) = C$1.4015

3 Different Interest Rate Quotes

• Borrow $1 for 6 months at 6%:

• APR, annual percentage rate, FV = $1.03 = $1 (1 + .06/2 )

• EAR, effective annual rate, FV = $1.02956 = $1 (1 + .06)^.5

• CC, continuously compounded, FV = $1.03045 = $1 exp(.06 x .5)

Canadian Importer Problem

• Has U$ 5 M payable due 6 months hence.

• Two possible hedges: buy U$ forward or buy call on U$.

• Buy forward: Arrange now to buy U$5M 6 months from now at a rate set now, F.

• Buy call on U$ 5 M with exercise price X.

FX Payable

• Worried about the FX appreciating

S

-U$ 5 M

Exposed Cash Flow

Buy U$ Forward: Contract Cash Flow

F

U$5M

S

Buy Call on U$: Contract Cash Flow

X S

U$5M

Hedged Cash Flows

S

Forward Hedge-F x U$5M

B

Call Hedge

X

B, breakeven FX rate between call and buy forward hedges

• B = forward rate - FV of call option premium

• FV (future value) uses the hedger’s borrowing rate.

• S<B call option better ex-post.

• S>B buy forward better ex-post.

Buy forward versus buy call

B

S

Contract Cash Flows

Calculation of B

• Canadian firm with U$ 5 M payable due 6 months hence.

• F = C$1.35 ( 6 month forward rate)

• X = C$1.32 (exercise price of call)

• C = C$0.10 (call premium per U$)

• Borrowing rate = 6% quoted CC

• B = C$1.247

Forward vs. Option Hedges: Fundamental Trade-off

• Forward – no up-front outlay (at inception value of forward = 0) but potential opportunity cost later.

• Option – up-front outlay (option premium) but no opportunity cost later, ignoring option premium.

Option hedge vs. Forward hedge vs. Remain exposed

• Hedge FX liability.

• Ex-post analysis: S > F, buy forward is best; S < F, remain exposed is best.

• Option hedge is never best ex-post.

• Option hedge is an intermediate tactic, between extremes of buy forward and remain exposed.

Option hedge vs. Forward hedge vs. Remain exposed

F

Remain exposed

Writing options as hedges

• Zero sum game between buyer and writer.

• Writer’s diagram is mirror image of buyer’s about X-axis.

• Writer receives premium income.

• Write call to hedge a receivable, I.e., covered call writing.

• Write put to hedge a payable.

A Lego set for FX hedging

• Six basic building blocks available for more complex hedges.

• Buy or sell forward.

• Buy or write a call.

• Buy or write a put.

Application of Lego set

• Option collar is an option portfolio comprised of long (short) call and short (long) put. Maturities are common but exercise prices may differ.

• What if there is a common exercise price = F, the forward rate pertaining to the common maturity of the options?

• Value of option collar must = zero.• Option collar replicates forward contract.

Option collar (buy call, sell put; common X = F) or Buy Forward

F S

Linkage between forward and options

• Forward contract is an option collar.

• Buy forward = buy call, sell put with X = F.

• Sell forward = sell call, buy put with X = F.

• Value of option collar = 0.

• What if X not = F?

• Put-Call-Forward Parity Theorem

Put Call Forward Parity (graph)

X F S

Put Call Forward Parity

C, P = Call and Put premiums

R = domestic risk-free rate

)()( XFePC RT

Put-Call Forward Parity Example

• 1-year contracts on sterling, PS.

• F = C$2.50; X = C$2.40; T = 1 year

• R (riskless Canadian rate) 5% quoted CC

• Via equation, C-P = C$0.095

• If P = C$0.05 then C = C$0.145.

• If C = C$0.20 then P = C$0.105.

FX Bid-Ask Spread

• Bank is willing to buy FX at Bid.• Bank is willing to sell at (is asking) Ask.• Terms adopt bank’s perspective.• Hedging firm must buy FX at higher Ask

and sell FX at low Bid.• Buying one currency means selling the

other currency. Implies: Bid in one currency is the Ask of the other currency.

Interest Rate Parity Theorem

• Based on financial arbitrage.

• Assume 1 year period.

• Domestic investment/financing: (1+RD).

• Forward hedged foreign investment/financing: (1+RF)(F/S).

• Equality must hold.

Interest Rate Parity: Formulas

F

DT

TRRT

T

F

DT

TR

TR

S

FRsAPR

eS

FRsCC

R

R

S

FRsEAR

FD

1

1:

:

1

1:

0

0

0

Interest Rate Parity: Intuition

• IRP: a statement about what holds in equilibrium.• A high interest rate currency, FX, trades at a

forward discount. Why? Otherwise, if it traded at a forward premium it would be an attractive investment for everyone.

• A low interest rate currency trades at a forward premium. Why? Otherwise, if it traded at a forward discount it would be an attractive financing venue for everyone.

Interest Rate Parity: Numerical Example

• Current spot rate on greenback = C$1.35

• 2-year forward rate on greenback = C$1.41 (this is usually the unknown)

• R canadian = 7% CC

• R u.s. = 5% CC

• Greenback trades at a forward premium because it is the low interest rate currency.

Interest Rate Parity: How many variables?

• How many variables do you see?

• In reality, 8 not 4!

• Domestic borrowing, deposit rates.

• Foreign borrowing, deposit rates.

• Bid, ask spread on spot.

• Bid, ask spread on forward.

Money market hedging

• Application of interest rate parity theorem.

• Synthesize a forward contract with 3 transactions: buy (sell) FX in spot; borrow(lend) in domestic currency; lend(borrow) in FX.

• Why? May be able to enhance cash flows compared with outright forward contract.

Enhance cash flows?

• If have an FX liability, may be able to buy FX at a lower rate than F, I.e., decrease outlays.

• If have an FX receivable, may be able to sell FX at higher rate than F, I.e. increase inflows.

• FX liability: Borrow domestic, buy FX spot, invest foreign synthesizes buy outright forward.

• FX receivable: Borrow foreign, sell FX spot, invest domestic synthesizes sell outright forward.

MMH: 2 complementary interpretations

• Create an offsetting FX cash flow: if FX receivable, create FX outflow; if FX payable, create FX inflow.

• Advance FX transaction date: instead of forward transaction, perform spot transaction now.

Money market hedge: numerical example

• Canadian firm will receive U$1M 6 months from now.

• S bid = C$1.38; F bid (6 months) = C$1.39.

• U$ borrowing rate = 8% APR

• Canadian deposit rate = 10% APR

• If use outright forward will receive C$1.39 6 months hence. Can you enhance this?

Is a money market hedge better?

• Borrow U$1M/1.04 = U$0.9615M• Sell U$’s in spot, receive C$1.3269M• Invest C$’s at C$ deposit rate, receive after

6 months C$1.3269M x 1.05 = C$1.3933M• Payoff U$ loan U$0.9615 x 1.04 = U$1M

with projected receivable. Note: U$ loan principal designed to achieve this.

• Money market hedge superior by C$3,300.

Money market hedge: FX liability

• Canadian firm has a liability of PS(sterling)1M due a year hence.

• F ask (1 year) = C$2.40; S ask = C$2.30.

• Canadian borrowing rate=7% APR or EAR

• UK deposit rate=4% APR or EAR

• Which is better? Buy outright forward or construct a money market hedge?

Buy forward or MMH?

• If buy PS forward (outright), pay C$2.4M a year hence.

• If construct money market hedge, pay synthesized forward rate, FMMH = C$2.37 per PS or C$2.37M a year hence.

• Save C$30,000 by constructing MMH.• MMH steps: borrow C$, buy PS spot, invest

PS.

MMH transactions: FX liability

• Now: Borrow (2.3)PS1M/1.04=C$2.21M• Buy PS spot C$2.21/2.3=PS.96M• Invest PS at 4%• After 1 year: Close out PS deposit, obtain

PS.96(1.04)=PS1M; this is used to meet liability.

• Pay off C$ loan, i.e., C$2.21M(1.07) = C$2.37M = PS1M(FMMH)

Option collar as synthetic forward

• Same exercise price for both put and call.• Buy put & sell call synthesizes sell forward.• Sell put & buy call synthesizes buy forward.• Foc = synthetic forward rate• Apply buy low & sell high rule.• Hedge FX receivable: higher is better.• Hedge FX payable: lower is better.

Forward rate synthesized with option collar

C, P = call, put premiums with common X.

FV = future value using domestic rate borrowing (if initial cash flow negative) or deposit (if initial cash flow positive).

)( PCFVXFoc

FV calculation

• Initial CF < 0, use borrowing rate• Initial CF > 0, use deposit rate• Rationale: Same logic that applies to the use of

WACC in investment appraisal (vide: course prerequisite)

• Notwithstanding that, in a specific year, may have abundant unused bank-borrowing capacity to finance project, must use WACC

• Calculation procedures applied as long-term policy

Sell outright forward or option collar?

• Canadian with U$1M receivable due 6 months hence.

• Canadian deposit rate = 7% APR

• 6-month forward rate on U$ = C$1.39

• X=C$1.37: Per U$ P = C$0.09, C = C$0.14

• Foc=C$1.42 ergo rather than sell outright forward, Foc it!

Option collar transactions now

• Buy put, -C$0.09M

• Sell call, C$0.14M

• Invest initial net cash flow of C$0.05M in bank account, -C$0.05M

• Note: If initial net cash flow is < 0, must finance it. Ergo, use borrowing rate.

Option collar cash flows after 6 months

• Receive exercise price, C$1.37M, for sure either exercise put or the call gets exercised against you (Canadian firm).

• Deliver U$1M with projected receipt

• Close out bank account, receive C$0.05Mx(1.035) = C$0.05175M

• Net CF = C$1.42M > Foutright = C$1.39M

Hedging Protocol

• Determine best forward hedge: outright, MMH, or OC.

• Put your best forward forward.

• Compare best forward hedge with option, I.e., calculate B = breakeven rate.

• Example case: ¡Yo quiero Taco Bell!