1. Chapter 24 Advanced Topics in International Finance

2. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-2 The Currency Hedge Ratio The hedge ratio, frequently termed beta ( β ), is the percentage of an individual exposure’s nominal amount covered by a financial instrument such as a forward contract of currency option. Beta is then defined as follows: β = value of currency hedge value of currency exposure

3. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-3 The Currency Hedge Ratio The value of an individual currency position can be expressed as a portfolio of two assets: –A spot asset (the exposure) –A hedge asset (a forward, future, or option) The hedge is constructed so that whatever spot value is lost as a result of adverse exchange rate movements ( Δ spot) is replaced by an equal but opposite change in the value of the hedge asset, the futures position ( Δ futures): Δ position value = Δ spot – Δ futures ≈ 0

4. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-4 The Currency Hedge Ratio The optimal currency hedge can be found by minimizing the terminal (end-of-period) variance of the two asset portfolio. The hedge asset amount as a percentage of the exposure is altered to minimize the terminal portfolio variance.

5. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-5 The Currency Hedge Ratio Sometimes there are no available futures or forward markets for currencies. In these cases the risk manager may substitute a proxy for the underlying currency in a proxy-hedge or a cross-hedge. The cross-hedger would likely go through a simple two-step process to determine the optimal cross- hedge: –First, find the currency futures most highly correlated with the actual currency of exposure –Second, find the optimal hedge ratio using the covariance between the proxy futures and the actual currency as in the previous model

6. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-6 The Currency Hedge Ratio A slightly more sophisticated currency hedging strategy than the traditional one demonstrated in Chapter 6 is called delta hedging. The objective of delta hedging is to construct a position – the combined exposure of the hedging instrument – whose market values (not terminal values) will change in opposite directions with changes in the spot exchange rate; it is the value of the position at all times which is being managed, not the value of the position only at termination.

7. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-7 The Currency Hedge Ratio Returning to the basis position valuation principle introduced at the beginning of this chapter: if the hedge is constructed so that the changes in the spot position and hedge position are equal and opposite in currency value at all times in the life-span of the exposure, it is termed delta-neutral. Δ position value = Δ spot – Δ futures

8. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-8 Financial Engineering and Risk Management Financial engineering has come to mean very different things to different people. We use it here to describe the use of basic financial building blocks (spot positions, forwards, options) to construct positions that provide the user with desired risk and return characteristics. The number of combinations and deviations is indeed infinite.

9. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-9 Financial Engineering and Risk Management The following problem is utilized for the remainder of the chapter: –A US-based firm, Dayton Manufacturing, possesses a long £1,000,000 exposure – an account receivable – to be settled in 90 days –The firm believes that the exchange rate will move in its favor over the 90-day period (the British pound will appreciate versus the US dollar) –Despite having this directional view or currency expectation, the firm wishes downside protection for the event that the pound were to depreciate instead

10. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-10 Financial Engineering and Risk Management Clearly, Dayton could sell the receivable forward at the forward rate, yielding $1,470,000. In addition, Dayton could construct a synthetic forward in which the company would buy a put and sell a call (at the forward rate), again yielding $1,470,000. A firm would undertake this relatively complex position if it altered the strike prices from the forward- ATM (at the money) and was able to make a slight premium (net) on the purchase and sale of the options.

11. 24-11 Exhibit 24.3 Construction of a Synthetic Forward for a Long FX Position US dollar value of A/R (millions) 1.40 End-of-period spot rate (US$/£) 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.421.441.461.501.521.541.481.56 Forward Uncovered Buy a put: $1.47 strike Sell a call: $1.47 strike Instruments Strike RatesPremiumNotional Principal Buy a put Sell a call $1.4700/£ $0.0318/£ £ 1,000,000

12. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-12 Second-Generation Currency Risk Management Products Second-generation risk-management products are constructed from the two basic derivatives used throughout this book; the forward and the option. We will subdivide them into two groups: –The zero-premium option products (which focus on pricing in and around the forward rate) –The exotic option products (which focus on alternative pricing targets)

13. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-13 Second-Generation Currency Risk Management Products The primary “problem” with the use of options for risk management in the eyes of many firms is the up-front premium payment. Although the premium payment is only a portion of the total payoff profile of the hedge, many firms view the expenditure of substantial funds for the purchase of a financial derivative as prohibitively expensive.

14. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-14 Second-Generation Currency Risk Management Products Zero-premium option products are designed to require no out-of-pocket premium payment at the initiation of the hedge. This set of products includes what are most frequently labeled the range forward and the participating forward. Both of these products: –Are priced on the basis of the forward rate –Are constructed to provide a zero-premium payment up front –Allow the hedger to take advantage of expectations of the direction of exchange rate movements

15. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-15 Second-Generation Currency Risk Management Products The basic range forward is constructed by: –Buying a put option with a strike rate below the forward rate, for the full amount of long currency exposure (100% coverage) –Selling a call option with a strike rate above the forward rate, for the full amount of the long currency exposure (100% coverage) The hedger chooses one side of the “range” or spread, normally the downside (put strike rate), which then dictates the strike rate at which the call option will be sold. The call option strike rate must be chosen at an equal distance from the forward rate as the put option strike price from the forward rate.

16. 24-16 Exhibit 24.4 The Range Forward: Hedging a £1,000,000 Long Position US dollar value of A/R (millions) 1.40 End-of-period spot rate (US$/£) 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.421.441.461.501.521.541.481.56 Forward Uncovered Buy a put: $1.45 strike Sell a call: $1.49 strike Instruments Strike RatesPremiumNotional Principal Buy a put Sell a call $1.4500/£ $1.4900/£ $0.0226/£ $0.0231/£ £ 1,000,000 $1.45 strike$1.49 strike

17. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-17 Second-Generation Currency Risk Management Products The participating forward, is an option combination that allows the hedger to take a position that will share in potential upside movements in the exchange rate, while providing option-based downside protection, all at a zero-net premium. The participating forward is constructed in two steps: –Buy a put with a strike price below the forward rate for the full amount of the long exposure (100%) coverage –Sell a call option with a strike price that is the same as the put, for a portion of the total exposure (less than 100% coverage)

18. 24-18 Exhibit 24.5 The Participating Forward: Hedging a £1,000,000 Long Position US dollar value of A/R (millions) 1.40 End-of-period spot rate (US$/£) 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.421.441.461.501.521.541.481.56 Forward Uncovered Instruments Strike RatesPremiumNotional Principal Buy a put Sell a call $1.4500/£ $0.0226/£ $0.0425/£ £ 1,000,000 £ 531,765 $1.45 strike Participating Forward

19. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-19 Exotic Options This second set of instruments offers alternative pricing, timing, or exercise provisions of the product. All of these in some way have altered the valuation principles of the basis option-pricing model; hence the term exotic. These products are therefore products only, and not easily reproducible (though generally possible) by the corporate risk manager.

20. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-20 Exotic Options The knock-out option, differs markedly from previous products covered. The knock-out option is designed to behave like any option, offering downside protection, but to offer only a limited upside range before crossing a previously specified barrier or knock-out level, at which it automatically expires. The automatic expiration of the option would occur only after the exchange rate has moved in the expected direction of the hedger (a favorable movement). In return for giving up the full maturity period coverage, the premium of the option – being a shorter-term option – is smaller.

21. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-21 Exhibit 24.6 The Knock-Out Option: Hedging a £1,000,000 Long Position US dollar value of A/R (millions) 1.40 End-of-period spot rate (US$/£) 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.421.441.461.501.521.541.481.56 Forward Uncovered Instruments Strike RatesPremiumNotional Principal Buy a put $1.4700/£ Barrier: $1.49/£ $0.0103/££ 1,000,000 $1.49 Barrier Put option $1.47 Strike Knock-out option

22. Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-22 Exotic Options In addition, there are more recent second- generation (possibly third generation) currency derivatives: –Average rate option (ARO) –Average strike option (ASO) –Compound option –Chooser option