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.
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). Two Methods of FX Quotation
Examples of Two Quotation Methods • For Canadian firm. • Direct quote on greenback, US$: C$1.053 • Indirect quote on greenback US$: US$0.95 • 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 US$1million ECF(C$) S(C$/US)
Exporter’s Risk Exposure • Worried about depreciation in FX. • Forward hedge: Sell FX forward. Arrange now to sell 3 months hence at price determined now, F (the forward rate). • Option hedge: Buy right to sell FX, a put option on the FX.
Sell Forward Hedge • Commit now to sell U$ 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 Contract Cash Flow S(C$/U$) F(C$/U$)
Hedge with Forward Contract Hedged Cash Flow F x U$1million S(C$/U$)
Hedge with Put Option • Put option is the right, not obligation like forward contract, to sell U$ 1 million 3 months hence at an exercise or strike price of X(C$/U$). • P, put premium, price paid now for option. • Put contract cash flow = X – S if S<X; 0 otherwise.
Hedge with Put Option Hedged Cash Flow S X
Which is better? Sell forward or Buy put? B = breakeven point S<B, sell forward better S>B, buy put better B S
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 = $1 exp(.06 x .5) • Default assumption: All interest (inflation, appreciation) rates are annual.
Canadian Importer Problem • Has U$ 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 Exposed Cash Flow S -U$ 5 M
Buy U$ Forward: Contract Cash Flow U$5M S F
Buy Call on U$: Contract Cash Flow U$5M S X
Hedged Cash Flows X B S Call Hedge Forward Hedge -F x U$5M
Buy forward versus buy call Contract Cash Flows B S
B, breakeven FX rate between call and buy forward hedges • B = forward rate - FV of call option premium • FV (future value) uses the hedger’s borrowing rate. • S<B call option better ex-post. • S>B buy forward better ex-post.
Calculation of B • Canadian firm with U$ 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
Significance of B = C$1.247 • If futureS > 1.247 better to buy forward ex-post. • If futureS < 1.247 better to buy call ex-post. • Define Pr( ) = probability of the event ( ). • If Pr(futureS>1.247) > Pr(futureS<1.247), better to buy forward, rather than buy call, ex-ante. • Principle: The better ex-ante hedge is that which maximizes the probability of choosing the correct hedge ex-post.
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. Forward vs. Option Hedges: Fundamental Trade-off
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.
Basic problem with writing options as a hedge • Viable if there is no significant adverse move in FX rate. • FX receivable: viable if FX rate does not drop significantly. • FX payable: viable is FX rate does not rise significantly. • The original exposure remains albeit cushioned by the receipt of premium income.
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.
F defines a critical value of X • Another application of Lego set, option collars, and graphical reasoning. • If X = F, C (call premium) = P (put premium). • If X< F, C > P. • If X> F, C < P.
Salomon’s Range Forward • Another application of Lego set. • See Transactions Exposure Cases: Salomon Contract to Aid in Hedging Currency Exposure. • Buying a Range Forward is an option collar where a call, with X = upper limit of range, is purchased and a put, with X = lower limit of range, is written.
Salomon’s Range Forward (specific numbers) • F = 1/DM 2.58 = U$0.3876 • Range Upper limit, U= 1/DM2.50 = U$0.40 • Range Lower limit, L = 1/DM2.65 = U$0.3774 • If S(U$/DM) > U$0.40, US client buys DM at U$0.40. • If S < U$0.3774, US client buys DM at U$0.3774. • If U$0.3774 < S <U$0.40, US buys DM at S.
Salomon’s Range Forward Contract Cash Flow L=$0.3774 U=$0.4 S
Salomon’s Range Forward FX Liability Hedged Cash Flow L U S
Futures Contract Traded anonymously on an exchange. “Marking to market” – there are daily cash flow experienced. Assume: futures rate = forward rate. Forward Contract Deal directly with bank. No cash flows until maturity Empirical result: For FX, futures rate = forward rate on average. 2 alternative ways of committing to buy (sell) FX in future
Conditional (contingent) exposure • Whether or not you are exposed to the contractually specified FX depends on someone else’s decision. • Situation where an option should be used, not a forward. • Examples: cross-border merger, bidding on a foreign construction contract, selling with a dual currency price list.
Telus Case • Dual currency prices: C$1,682 or Bh32,799. • Customer decides on currency. • Hedging the time span between sale and customer’s currency decision must be with a put option, not sell forward. • Defined implied spot rate, S* = C$0.051= C$1,682/Bh32,799.
Telus’ Risk Exposure C$1,682 S(C$/Bh) C$0.051
Effect of dual currency prices • Client chooses to pay currency adjusted amount. • As if the following were true: Telus demands payment in C$’s but gives client a put option on Bh. • Since Telus issues a put option to the client, it must buy the same option to hedge.
Danger in hedging conditional exposure with a forward • Problem if Telus were to sell Bh forward: Telus may not receive Bh’s. • Client will choose to pay in C$’s if the Bh appreciates beyond C$0.051. • If Bh appreciates, Telus must satisfy the forward contract by buying the appreciated Bh on the spot market.
Telus’ hedged diagram if sell forward at F = C$0.051 C$1,682 Telus faces unlimited losses C$0.051
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 C, P = Call and Put premiums R = domestic risk-free rate
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.