The True Cost of Hedging.
Exhibit 10.6 also shows that the true cost of hedging cannot be calculated in advance because it depends on the future spot rate, which is unknown at the time the forward contract is entered into. In the GE example, the actual cost of hedging can vary from +$210,000 to −$790,000; a plus (+) represents a cost, and a minus (—) represents a negative cost or a gain. In percentage terms, the cost varies from −5.3% to +1.4%.
This example points out the distinction between the traditional method of calculating the cost of a forward contract and the correct method, which measures its opportunity cost. Specifically, the cost of a forward contract is usually measured as its forward discount or premium:
where e0 is the current spot rate (dollar price) of the foreign currency and f1 is the forward rate. In GE’s case, this cost would equal 1.4%.
However, this approach is wrong because the relevant comparison must be between the dollars per unit of foreign currency received with hedging, f1, and the dollars received in the absence of hedging, e1, where e1 is the future (unknown) spot rate on the date of settlement. That is, the real cost of hedging is an opportunity cost. In particular, if the forward contract had not been entered into, the future value of each unit of foreign currency would have been e1 dollars. Thus, the true dollar cost of the forward contract per dollar’s worth of foreign currency sold forward equals
The expected cost (value) of a forward contract depends on whether a risk premium or other source of bias exists. Absent such bias, the expected cost of hedging via a forward contract will be zero. Otherwise, there would be an arbitrage opportunity. Suppose, for example, that management at General Electric believes that despite a one-year forward rate of $1.479, the euro will actually be worth about $1.491 on December 31. Then GE could profit by buying (rather than selling) euros forward for one year at $1.479 and, on December 31, completing the contract by selling euros in the spot market at $1.491. If GE is correct, it will earn $0.012 (1.491 − 1.479) per euro sold forward. On a €10 million forward contract, this profit would amount to $120,000—a substantial reward for a few minutes of work.
The prospect of such rewards would not go unrecognized for long, which explains why, on average, the forward rate appears to be unbiased. Therefore, unless GE or any other company has some special information about the future spot rate that it has good reason to believe is not adequately reflected in the forward rate, it should accept the forward rate’s predictive validity as a working hypothesis and avoid speculative activities. After the fact, of course, the actual cost of a forward contract will turn out to be positive or negative (unless the future spot rate equals the forward rate), but the sign cannot be predicted in advance.
On the other hand, the evidence presented in Chapter 4 points to the possibility of bias in the forward rate at any point in time. The nature of this apparent bias suggests that the selective use of forward contracts in hedging may reduce expected hedging costs, but beware of the peso problem—the possibility that historical returns may be unrepresentative of future returns. The specific cost-minimizing selective hedging policy to take advantage of this bias would depend on whether you are trying to hedge a long or a short position in a currency. The policy is as follows:
• If you are long a currency, hedge (by selling forward) if the currency is at a forward premium; if the currency is at a forward discount, do not hedge.
• If you are short a currency, hedge (by buying forward) if the currency is selling at a forward discount; if the currency is at a forward premium, do not hedge.
As discussed in Section 10.4, however, this selective hedging policy does not come free; it may reduce expected costs but at the expense of higher risk. Absent other considerations, therefore, the impact on shareholder wealth of selective hedging via forward contracts should be minimal, with any expected gains likely to be offset by higher risk.
Money Market Hedge
An alternative to a forward market hedge is to use a money market hedge. A money market hedge involves simultaneous borrowing and lending activities in two different currencies to lock in the dollar value of a future foreign currency cash flow. For example, suppose euro and U.S. dollar interest rates are 7% and 5.5%, respectively. Using a money market hedge, General Electric will borrow €(10/1.07) million = €9.35 million for one year, convert it into $14.02 million in the spot market, and invest the $14.02 million for one year at 5.5%. On December 31, GE will receive 1.055 X $14.02 million = $14.79 million from its dollar investment. GE will then use the proceeds of its euro receivable, collectible on that date, to repay the 1.07 X €9.35 million = €10 million it owes in principal and interest. As Exhibit 10.7 shows, the exchange gain or loss on the borrowing and lending transactions exactly offsets the dollar loss or gain on GE’s euro receivable.
The gain or loss on the money market hedge can be calculated simply by subtracting the cost of repaying the euro debt from the dollar value of the investment. For example, in the case of an end-of-year spot rate of $1.50, the €10 million in principal and interest will cost $15 million to repay. The return on the dollar investment is only $14.79 million, leaving a loss on the money market hedge of $210,000.
We can also view the effects of this transaction with the simple T-account used earlier:
December 31: GE T-Account (Millions)
Account receivable
€10.00
Loan repayment (including interest)
€10.00
Investment return (including interest)
$14.79
As with the forward contract, the euro asset and liability (the loan repayment) cancel each other out, and GE is left with a $14.79 million asset (its investment).
The equality of the net cash flows from the forward market and money market hedges is not coincidental. The interest rates and forward and spot rates were selected so that interest rate parity would hold. In effect, the simultaneous borrowing and lending transactions associated with a money market hedge enable GE to create a “homemade” forward contract. The effective rate on this forward contract will equal the actual forward rate if interest rate parity holds. Otherwise, a covered interest arbitrage opportunity would exist.
In reality, there are transaction costs associated with hedging: the bid-ask spread on the forward contract and the difference between borrowing and lending rates. These transaction costs must be factored in when comparing a forward contract hedge with a money market hedge. The key to making these comparisons, as shown in Chapter 7, is to ensure that the correct bid and ask and borrowing and lending rates are used.