To convert the EUR50,000,000 into USD a month from now, the manufacturer has the following four strategies available:^{[1]}

Strategy 1: Use a spot-currency rate with the prevailing spot rate at the end of 1 month.

Strategy 2: Use a 1-month currency forward to lock in a guaranteed exchange rate 1 month from now.

TABLE 3.14 Pros and Cons Associated with Strategies

Strategies

Pros

Cons

1

No upfront cost

Unlimited downside

Unlimited upside

2

No upfront cost

No upside

No downside

3

No downside

Upfront cost

Upside

Strategy 3: Use a 1-month currency option that is struck at the 1-month forward rate.

Strategy 4: Use a combination of (and variation on) the above-mentioned strategies.

Since strategy 4 is a combination of the first three strategies, I will only discuss the pros and cons associated with the first three strategies, which are summarized in Table 3.14.

To understand the summary in Table 3.14,1 will first discuss strategy Ϊ. In implementing this strategy, the risk to the manufacturer is that a weaker EUR at the end of one month would result in a lesser USD amount after conversion. On the flip side, a stronger EUR would result in more USD, hence there is both an unlimited upside and downside for the manufacturer.

Strategy 2 involves the implementation of at-the-market currency forwards.^{[2]} With this strategy, the manufacturer effectively locks up a guaranteed exchange rate of 1.3098 USD/EUR^{[3]} associated with conversion of EUR50,000,000. As a consequence, the manufacturer does not have any

FIGURE 3.2 Net Impact of Risk-Management Strategies

uncertainty associated with the exchange rate, which results in an opportunity cost (not loss) associated with locking up the rate and forgoing any upside on the exchange-rate movements.^{[4]}

In implementing strategy 3, the manufacturer can partake in favorable gains in EUR at the end of the month while being protected against a weakening EUR. Since this is an option-based strategy, the only setback of this strategy is that the manufacturer has to pay an upfront premium of 0.0196 USD/EUR^{[5]} to be protected against unfavorable movements in the exchange rate. It should be noted that the breakeven in purchasing the option is 1.3098 – 0.0196e0.1(1/12) = 1.2902. This means only if the USD/EUR is less than 1.2902 on its option-maturity date can the manufacturer see some benefit from the purchase of this option after making the appropriate deductions associated with the cost of this protection.

The three strategies discussed above can be graphically represented, as shown in Figure 3.2.

The forward rate is then obtained by observing that X has to satisfy the criteria which results in the expression – using the notation of the currency options example discussed earlier. See Hull (2012).

As can be seen from the Figure 3.3, one difference between the impacts of strategies 2 and 3 on the bottom line is that the latter protects the manufacturer from the weakening of the EUR since the downside risk is limited. Additionally, when the EUR strengthens, the payoff associated with both the strategies are pretty much the same except that strategy 3 pays off slightly lower than strategy 2 (due to the cost of the insurance paid for strategy 2).

Incorporating Views into Strategies

Suppose now that the manufacturer has a view that EUR will weaken in a month's time to 1.2100 USD/EUR or lower. To monetize his view, he could do one of the following:

Strategy 1A: Use a 1-month currency forward to lock in a guaranteed exchange rate of 1.3098 USD/EUR.

Strategy 2A: Use a 1-month currency option that is struck at 1-month forward (1.3098 USD/EUR).

Strategy 3A: Combination of (and variation on) the above-mentioned strategies.

Given how high the forward rate is relative to the view on the potential exchange rate movement, strategy 1A seems to be the logical choice for managing the risks. Having said that, in addition to implementing strategy 1A, the manufacturer can also sell a call on the EUR (or buy a put on EUR) that is struck at 1.2100 USD/EUR to monetize the view that the EUR will further weaken to lower than 1.2100 USD/EUR.

APPENDIX

Finding a Forward Bond Yield

Letting the current time be t and assuming that the bond yield at a future time T can be modeled using a forward bond yield, one can assume that In(FBYT T) is normally distributed with a mean of In and variance of where t = current time T = time in the future FBYt,T – forward bond yield for a bond starting at time T that is computed at time t (that needs to be determined)

Letting the price of the bond at time T be represented by so as to reflect the fact that the bond price at time T is a function of its yield-to-maturity at that time, one can use Taylor's expansion to arrive at (ignoring higher order terms)

where represents the yield corresponding to the forward bond

price

Taking expectations of the right-hand side of the equation with respect tousing the distributional assumption, one gets

Observe now that the expectation of the right-hand side of the equation is also the forward bond price (i.e.,) and is equal to

Thus the above equation simplifies to

which results in FBYt,T (the forward bond yield) being the solution of the equation

[1] In practice one can use more customized options (see Chapter 5) to help with the risk-management program. See Ravindran (1997) for more details on this.

[2] A currency forward is a guaranteed currency bilateral contract in which one party exchanges the floating currency rate on the contract maturity date for a prespecified fixed currency rate on the maturity of the contract. Both parties of the contract are obligated to fulfill their parts of the contract regardless of the strength (or weakness) of the currency rate on the forward maturity date. See Ravindran (1997).

[3] Since a forward exchange rate contract is a bilateral contract that obligates both parties of the transaction, the payoff to one party of the transaction on maturity date is ST – X where T represents the contract maturity date. ST represents the exchange rate at time T. X represents the guaranteed exchange rate (i.e., forward rate) associated with the contract.

[4] An at-market forward is a forward contract that does not cost a counterparty of the contract anything to enter into. The reason for this stems from the fact that the forward rate is chosen based on the market conditions so that it translates to a zero cash-flow exchange up front. In practice, it is possible to transact into a forward contract that is based on an off-market rate (in which case cash is typically exchanged at inception of transaction), as this rate is reflective of a rate that requires an exchange of cash at the inception of the contract.

[5] This can be obtained using the currency option calculator in Table 3.5.

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