OPTIMAL CURRENCY FORWARD MARKET HEDGE RATIOS: HEDGING OR CONCEALED SPECULATION? Anthony F. Herbst Peggy E. Swanson
Finance literature in recent years has contained numerous papers dealing with the issue of optimal hedging ratios. The traditional approach to hedging with futures contracts had been to use a 1:l ratio of futures to spot positions. The more recent portfolio methodology determines the optimal hedge ratio by regressing the cash price, cash price change, or logarithm of cash price relative on the corresponding futures price, change, or logarithm. This procedure, following Johnson , Stein [lo], and Ederington , finds the minimum variance hedge ratio, which is the regression slope term, generally to be other than l:l, depending on whether the spot:futures/forward relationship is one of positive or negative carrying costs. Swanson and Caples [ll] and Herbst, Kare, and Caples  extend the portfolio methodology by using a Box-Jenkins autoregressive, integrated moving average procedure (ARIMA) to explicitly incorporate the effects of serial correlation. This extension yields optimal hedge ratios for major currencies which are lower than those found in the earlier portfolio studies, enlarging the difference in magnitude between traditional and portfolio determined optimal hedging ratios. Most of the studies have focused on risk reduction relating to interest rates and physical commodities. For example, Ederington  and Franckle (31 analyzed T-Bill futures while French  studied spot copper and silver prices in the United States and forward prices in England. More recently, Toevs and Jacob  reevaluated estimation techniques for calculating hedge ratios for interest rate risk and concluded that simple duration-based hedges can dominate regressionbased hedges. Their work thus questions the validity of the portfolio methodology. Less work has been done on foreign currency futures. Cornell and Reinganum [l] compared hedging in the forward and futures market for foreign currencies, and Hill and Schneeweis  attempted to measure hedging effectiveness for five major currencies using the foreign currency futures market. Park Anthony F. Herbst Professor of Finance, The University of Texas at El Paso, El Paso, TX 79968; Peggy E. Swanson Professor of Finance, The University of Texas at Arlington, P.O. Box 19125, Arlington, TX 76019. Global Finance Journal, ISSN: 1044-0283
Copyright o 1991 by JAI Press, Inc. All rights of reproduction in any form reserved.
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and Chen  compared futures prices and forward prices for six physical commodities and four foreign currencies and concluded that differences between the two prices could be attributed to the daily settling up procedure in the futures markets. This paper addresses the issue of whether or not the popular minimum variance approach is appropriate in determining optimal hedging strategies when using the forward foreign exchange market.
Long before the existence of foreign currency futures markets, forward foreign exchange markets had provided a hedging mechanism for those acquiring assets or incurring liabilities denominated in foreign currencies. Little formal study of hedging strategies existed during that time. The general consensus was simply that hedging reduced foreign exchange risk and the choice of whether or not to hedge depended upon expected future spot exchange rates and risk preferences of the participants. The modeling of hedging strategies only began when foreign currency futures markets became prominent. Then, the theory devised for futures market hedging was simply applied to forward market hedging. Recognizing that hedging principles in the two markets should be similar, the different characteristics of the two markets were frequently ignored. Not only are there differences between futures and forward contracts in general, interbank forward contracts in foreign exchange (the largest forward market) differ from foreign currency forward contracts which are traded on organized exchanges. The bulk of forward foreign exchange contracts are entered into by a bank and its client or by two banks. Thus, the forward market discussed in this paper will be called the interbank market to distinguish it from the limited forward foreign currency contract market conducted on exchanges. A major difference between futures and forwards is found in the customized size and delivery dates of the interbank forward contract. Also, the futures contract hedger has much greater liquidity because of the opportunity to reverse a position by an offsetting purchase or sale of the futures position. With a forward hedge, a position normally can be closed out only by entering into another forward contract which reverses the long/short position and whose maturity corresponds to the original contract. In addition, the value of the futures contract approaches the spot price of the currency as the contract approaches maturity. The value of the forward contract does not change; delivery will be made at the pre-specified exchange rate, which may be closer to or further from the actual spot rate at maturity than when the agreement was negotiated. Another difference between hedging in the two markets is the cost of establishing the hedge. Although no money is paid or received for the forward contract at its inception, the market maker (commercial bank holding the opposite side of the contract) for the forward contract will want assurance that the buyer or seller has the ability to deliver. This assurance may be provided by
Optimal Currency Forward Market Hedge Ratios
reputation only, but more frequently results in reducing a line of credit, requiring a minimum level of deposits, and so forth. Other than origination costs and opportunity cost on margin requirements, the transactions costs in the futures market is a round-turn commission of a token amount per contract in relation to the size of a contract.1 Besides commissions, the hedger using futures has an opportunity cost on the margin deposit although this may be reduced/eliminated by the deposit of Treasury bills or other Treasury securities with comparable maturities. A last difference relates to daily marking-to-market (settling up) required for futures contracts. Interbank forward contracts have no comparable daily cash flow aspect. It is reasonable to assume that the objectives of those hedging with futures are the same as those using interbank forward contracts: to reduce or eliminate the foreign exchange exposure resulting from a future receivable or payable denominated in a foreign currency. The opportunity cost of the hedge, however, can not be known until maturity, when the actual spot rate at that time is revealed. Ignoring setup costs, transactions costs, and limitations on matching amounts and maturities in the futures markets, the optimal hedge ratio, based on the standard minimum variance approach, should diverge in the two markets only in relation to the divergence of the differences between forward and futures rates or the differences in characteristics of the two markets.
Virtually all recent studies of hedging in the currency futures and forward markets have determined that the optimal hedge ratio is not 1:l. If the optimal hedge ratio differs from 1:l in the futures market, the ratio should be similar in the forward market because of arbitrage opportunities. In the terminology of Toevs and Jacob , the nature of the hedge will determine whether it is strong form (hedger knows exact time of risk exposure and amount) or weak form (time span of exposure or amount not known precisely), and consequently the ability to hedge precisely. An exporter or importer who incurs payables or receivables for future delivery which are denominated in a foreign currency has three alternatives: (1) try to exactly hedge the exposure and eliminate foreign exchange risk, (2) hedge less than all the exposure and reduce foreign exchange risk, or (3) not hedge and take a speculative (open) foreign currency position for the full amount of the payable or receivable.2 Option (1) is the traditional 1:l hedge while option (2) yields a partial hedge together with a speculative position. The appropriateness and likely effectiveness will depend on whether the hedge is strong form or weak form. Is a portfolio approach appropriate for analyzing optimal hedge ratios given these circumstances? For alternative (l), it may be incorrect to view the expected foreign currency denominated receivable or payable and the forward contract as two different assets in a portfolio; they should be viewed instead as one asset which may be held in two forms: (1) unhedged, with an uncertain domestic currency future value, or (2) hedged, with a certain domestic currency future
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value. Once the forward contract is entered into, the trader has relinquished his right to the cash position in the foreign currency because delivery must be made or taken on the contract. From this perspective there is no portfolio, only a choice of the form in which to hold one asset, and a different methodology would be required to determine optimal hedging strategy. For alternative (2), the hedger can select from a combination of certain and uncertain domestic currency value outcomes. This invokes Tobin’s  separation theorem that the portions of a portfolio to be allocated to riskless and risky assets can be determined independently of the portfolio allocation among risky assets. There is, however, only one risky asset (one expected return) in this hedging decision. Choosing between the expected spot rate and the current forward rate for only one currency does not provide a portfolio of risky assets. The covariances of the expected rates on aIZcurrencies in which the exporter/importer has receivables/payables would constitute the relevant portfolio. Thus, on a bilateral exchange rate basis, there is really no portfolio problem. On a bilateral basis, the only relevant variable is the expected future spot rate for one currency and, while variances of spot and forward rates may measure the perceived riskiness for that currency, they do not do so in a portfolio sense. Thus, the assumptions of homogeneous expectations and market portfolio have no logic in this context. The forward contract the exporter/importer is considering is not an asset/liability until he enters into the contract. He creates this type asset by choice and there is no market portfolio where expected returns will guarantee that all assets are held. There is no set quantity of these assets, and other participants in the forward market, such as interest rate arbitrageurs, have an entirely different view of an equilibrium price. The value of a mean-variance optimal hedge ratio derived from standard portfolio theory is questionable for several additional reasons. The variances, computed on interperiod (between agreement date and delivery date) values do not represent meaningful measurements in forward market hedging. In order for the forward contract holder to take advantage of interperiod values he must be willing and able to continuously change his long/short position, which would entail entering into other forward contracts with matching maturities. The participant would incur multiple transactions costs in order to hold differing speculative positions during the period. The above implies that the holding period analyzed must be less than the time to maturity of the forward contract. In reality, the hedger is concerned with his choice today and the final outcome at the date of the payable or receivable. In standard applications of hedging strategies, the hedger makes his decision on the agreement date and the hedge is lifted only at maturity. The variability of interperiod values may provide a risk measure for an open position, but it does not represent an attainable set of choices. Further, portfolio adjustments in the usual sense are not available in forward contracts-the forward contract (if purchased) cannot be sold because no secondary market exists. One might argue that the appropriate assets for a portfolio are the original forward contract price and prices of shorter maturity contracts which would be available to reverse the original position. The hedger, however, really does not have these opportunities to reverse his position. If he
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enters into a 90-day forward contract today, then prices relevant for a minimum variance hedge ratio are only those contracts with maturity dates identical to the original forward contract, like one would find in futures contracts. Even in the case of futures contracts the date of delivery is exact only for those with short positions because it is they who decide the precise day the currency will be delivered within the allowable time window. Unfortunately, quoted or market rates for such contracts do not exist in the forward market but instead must be negotiated on a case-by-case basis. Thus, in the use of regression coefficients as et al. portfolio minimum risk hedge ratios, the Johnson, Stein, Ederington, approach ignores the fact that a hedger is interested in lifting the hedge not daily, but only at the end of the cash position risk exposure. The minimum variance hedge ratio-whether based on levels, changes, or logarithmsimplicitly assumes daily lifting of the hedge in a way analogous to calculating returns on a portfolio. But, in practice, what matters to the hedger is on the day the hedge is placed and on the day it is lifted, not what happens every day along the way. In other words, it is the cumulative effect of the daily changes that matters, not the unrealizable day-to-day results. Another issue relates to the fact that the distributions of spot and forward exchange rates for major currencies are not normal but instead are leptokurtic. Thus, even if the portfolio model variance minimization problem could otherwise be applied correctly, the regression optimal hedge ratio (the slope coefficient when spot rates are regressed on forward rates) would be biased. This issue has not been addressed in the hedging literature, and the use of an appropriate distribution function would be expected to produce different hedge ratios than those currently presented in the literature. A final point which has been overlooked is that in developing minimum variance hedge ratios using the portfolio approach, one really has a problem in constrained optimization. In futures markets, the constraints are that (1) cash and futures prices must converge at contract maturity, and (2) futures normally cannot differ from cash prices except by the amount of carrying costs. In the interbank forward market, no secondary market exists so there are no interperiod prices. These constraints are not relevant in dealing with common stocks in a two-stock portfolio. For simplicity, and following the logic of previous forward market hedging studies, the exporter/importer is assumed to (1) enter into a forward contract at the time the receivable/payable is acquired or incurred, or (2) not enter into a forward contract. He is thus choosing between a certain outcome and an uncertain outcome, but only as both relate to one asset/liability.
III. SPOT AND FORWARD
Assume the hedger’s base currency is the U.S. dollar, and that he will either have to make delivery in a foreign currency at a point t = N days ahead or take delivery of a foreign currency at the same date ahead. A hedger who has to make delivery is considered to be short the cash currency, so he will be long the
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corresponding forward currency. At maturity he will take delivery on the forward contract and surrender the proceeds against his open cash position, thus closing out both. A hedger who has to take delivery of foreign currency, but wanting dollars, will be considered long the spot currency, and he will have a short position in the forward market. At contract maturity he will accept the foreign currency and surrender it for dollars on the forward contract, thus closing out both. These are termed 20ng hedgers, and short hedgers, based on their forward foreign currency contract positions. Any hedge less than 1:l requires the purchase or sale of foreign currency at the spot price in existence at t = N. The difference between the exposure and the hedge represents a speculative position, although the speculation was not intentionally undertaken. How should the optimal hedging strategy be determined? Should it be determined using a portfolio model and regressing the forward rate or price on the spot rate? No, because that procedure averages the spot-forward relationship over time, and the relevant relationship is that at f = N, because that is when the hedge will be lifted. This implies a strong form hedge, or a close approximation to strong form. However, even for weak form currency hedges, the principles apply because of the inability of hedgers to modify the hedge between t = 0 and t = N.
IV. THE HEDGING
For simplicity, assume an importer and an exporter who elect to hedge foreign exchange exposure and thus have long and short forward positions, respectively. Let E = Expectations operator S = Spot exchange rate expressed as units of domestic currency per unit of foreign currency such that X = SY F = Forward exchange rate expressed as units of domestic currency per unit of foreign currency N = Due date for receivable/payable A = Ask price for spot and forward foreign exchange R = Positive risk premium a hedger is willing to pay per foreign currency unit to eliminate foreign exchange risk
Case 1 Importer with a net payable position would be expected to hedge only if
in the foreign currency.
Wku) > %A - R
The expected gain/loss per foreign currency unit from the long position in the forward market measured in base currency units is given by
Optimal Currency Forward Market Hedge Ratios
E(T) = The opportunity
is given by -
The primary purpose of hedging is to reduce/eliminate foreign exchange risk. Whether or not to hedge will thus depend heavily on R, the premium the hedger is willing to pay: &T/~SN,A> 0, EhldF,,A < 0, ck/aR > 0.
Case 2 Exporter with a net receivable position would be expected to hedge only if
where B = bid price. The expected gain/loss from the long position forward market in home currency units is given by IT
(4) in the
and &T/d&s > 0, &r/as,a < 0, an/aR > 0. Thus, changes in the future spot rate and in the forward rate impact the gain from hedging (as measured by both expected gain and by opportunity gain, the latter of which is not known until maturity) in opposite directions in the two cases. What is the portfolio theory logic that the covariances and variances of the spot and forward rates could affect the behavior of the participants with payables and receivables in the same direction, much less by the same amount? In other words, what is the meaning of the regression slope coefficient for these two categories of hedgers? The hedging strategies must be different for the two types of forward market participants. In markets with positive actual or implied carrying costs, short hedgers gain the basis (forward price or futures price less the spot price at t = 0) while long hedgers lose the basis over time.
V. CONCLUSIONS How does one determine optimal hedging strategies for importers and exporters in the interbank forward foreign exchange market? Minimum variance hedge ratios have little meaning in this context. The importer or exporter does not have the opportunity to select from a set of exchange rates but instead must confine his hedging to currencies in which transactions are to be made. The question of whether or not to hedge one particular currency exposure is not a portfolio question. Another framework for optimal hedging strategy is required. Because there are no portfolio benefits to be derived in the hedging process, the
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traditional 1:l hedge ratio appears to be more appropriate than the more current regression determined ratio which is generally other than l:l, especially for a strong form hedging situation. If a ratio of other than 1:l is believed to be an optimal hedging strategy, then hedging entails speculation. Speculation is undertaken to make profit even if limited to a long hedger trying to capture his basis loss and can apply to all currencies for which a forward market exists, while hedging is undertaken to reduce risk, but is confined to those currencies in which a foreign exchange exposure exists. Conceptually, the risk-return tradeoff framework cannot be applied to both forward market speculation and hedging simultaneously.
NOTES 1. A round-turn commission generally ranges from $50 to $100, depending on the firm handling the transactions and the rate that is negotiated. This is very small in comparison to the size of currency futures contracts, a fraction of one percent. The commission is paid when the contract is offset, not at the beginning. 2. For an importer or exporter who has payables and receivables denominated in the same currency, only the net exposed position is relevant.
B., and M. Reinganum, “Forward and Futures Prices: Evidence from the Foreign Exchange Markets,” @~naZ of Finance, 36:1035-1045 (December 1981). 121Ederington, Louis H., “The Hedging Performance of the New Futures Markets,” Journal of Finance, 34:157-170 (March 1979). [31 Franckle, C., “The Hedging Performance of the New Futures Market: Comment,” Journal of Finance, 35:1273-1279 (December 1980). “A Comparison of Futures and Forward Prices,” @~naZ of French, K.R., 141 Financial Economics, 12:311-342 (December 1983). [51 Herbst, Anthony F., Dilip D. Kare, and Stephen C. Caples, “Hedging Effectiveness and Minimum Risk Hedge Ratios in the Presence of Autocorrelation: Foreign Currency Futures,” The Journal of Futures Markets, 9:185-197 (June 1989). PI Hill, Joanne, and Thomas Schneeweis, “The Hedging Effectiveness of Foreign Currency Futures,” Journal of FinanciuZ Research, 5:94-104 (Spring 1982). [71 Johnson, Leland L., “The Theory of Hedging and Speculation in Commodity Futures,” Review of Economic Studies, 271139-151 (1960). Myers, Robert J., and Stanley R. Thompson, “Generalized Optimal Hedge PI American Journal of Agricultural Economics, 71:858-868 Ratio Estimation,” (November 1989). 191 Park, Hun Y., and Andrew H. Chen, “Differences between Futures and
Optimal Currency ForwardMarket Hedge Ratios
Forward Prices: A Further Investigation of the Marking-to-Market Effects,” Journal of Futures Markets, 5:77-88 (Spring 1985). Determination of Spot and Futures [lo] Stein, Jerome, “The Simultaneous Prices,” American Economic Review, 51:1012-1025 (December 1961). [ll] Swanson, Peggy E., and Stephen C. Caples, “Hedging Foreign Exchange Risk Using Forward Foreign Exchange Markets: An Extension,” Journal of International Business Studies, 18:75-82 (Spring 1987).  Tobin, James, “The Theory of Portfolio Selection,” in The Theory of Interest Rates, Macmillan: London, pp. 3-51 (1965).  Toevs, Alden L., and David I’. Jacob, “Futures and Alternative Hedge Ratio Methodologies,” ~ournu2of Portfolio Management, 12:60-70 (Spring 1986).