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Short-term foreign exchange risk management: Zero net exposure models
OMEGA, The Int. Jl of Mgmt Sci., Vol. 6, No. 3, pp. 249-256
0305-0483/78/0701-0249502.00/0
© Pergamon Press Ltd ~978. Printed in Great Britain
Short-Term Foreign Exchange Risk Management" Zero Net Exposure Models MARTHA
S HOLLIS
University of California, Irvine (Received July 1977; in revised form October 1977)
By balancing the relevant end of period assets and liabilities (i.e. a zero net exposure approach
to foreign exchange risk management) the multinational corporate treasurer can, conservatively, protect against parity fluctuations without requiring exchange rate forecasta. This paper presents two goal programming formulations for short-term money management and evaluates the resulting strategies (via simulation) in terms of their impact on corporate profits. A hypothetical multinational corporation with headquarters in the US and subsidiaries in Canada, West Germany, and the United Kingdom serves as the experimental unit. The results suggest that the zero net exposure approach is no better than a naive 'dart=throwing' approach.
THE RESULTS of short-term money management decisions can be influenced by foreign exchange rate fluctuations. Exchange rate movements can lead to currency gains and losses that are reflected in the corporation's net income statement. To offset this foreign exchange rate risk some analysts have suggested using a zero net exposure approach to short-term money management (that is, the balancing of end-of-period short-term monetary assets and liabilities).. . 1 Prior work on net exposure models has been predominately qualitative in nature and can be characterized by the omission of specific details such as the length of time horizons, how variables are related, and the mathematical form for finding solutions. 2 Qualitative methods, because of their lack of specificity in dealing with the multitude of factors which are of vital importance in the decision-making process, cannot demonZero net exposure is defined herein as the balancing of end-of-period short-term monetary assets and liabilities to avoid rate risks eschewing all types of forward contractual arrangements a n d other hedging instruments. For other definitions of net exposure see Teck [14]. 2 See, for example, the expositions of Eiteman a n d Stonehill [2], Goeltz [5], K o r t h [9], a n d Teck [14]. 249
strate the quantitative impact on profits. This research overcomes some of the deficiencies of prior studies in the international money management process by stating precisely two of the most frequently advocated zero net exposure approaches in the form of mathematical models. Two archtypical models of multinational corporations' (MNCs) organizational control are explored: a centralized single period zero net exposure model (CSP) and a decentralized multiperiod zero net exposure model (DMP). The third model, developed for comparative purposes, represents a naive random selection process (NRS). Each model is used to obtain monthly strategies for a hypothetical US MNC operating during the time period September 1974 through August 1975. The twelve monthly strategies that are obtained from each of the three models are submitted to a simulator that determines what would have happened with respect to before-tax consolidated profits if the transactions had been implemented during this period of volatile exchange rate fluctuations. Profits resulting from simulated implementation are compared using nonparametric inferential statistics. This research should provide
250
Martha S Hollis--Foreign Exchange Risk Management
MNCs with some preliminary guidance regarding their short-term money management decision-making. This paper suggests that there are no significant differences among the profits resulting from the strategies suggested by the two zero net exposure models and a naive random approach. The assumptions of net exposul'e models are detailed in Section I. The mathematical formulations for the centralized single period model, the decentralized multiperiod model, and the naive random strategy are presented in Sections II, III, and IV, respectively. Profit results of the simulated applications are presented and tested in Section V. The final section contains conclusions and areas for future research.
I. N E T E X P O S U R E A S S U M P T I O N S In the CSP and D M P models, to preclude the necessity for forecasting directions of exchange rate movements, the firm is assumed to strive for an ending exposure balance as close to zero as possible in each country of operation. 3 The firm's exposure position is assumed to preclude any willingness to experience exchange rate fluctuations. This study is limited to the essential decision variables of short-term financial management in multinational corporations. These variables, derived from prior work in the theory of financial management, are: investments with duration of less than one calendar year and borrowings with repayment terms less than one calendar year. 4 Short-term investments are included by considering only the most active classification in each country (those similar in risk and liquidity to the US Treasury Discount Bill). Borrowing opportunities will be restricted to commercial banking operations in each country.
3 See Giddy and Dufey [4] for recent work on exchange rate forecasting techniques and their results. 4 Other short-term variables include the management of inventories, accounts payable, and cash m a n a g e m e n t etficiency m o v e m e n t s (such as lock boxes and wire transfers). These are not considered in order to concentrate on purely monetary decisions. Hedging devices are excluded to focus attention on pure net exposure approaches.
Short-term financial decisions are made using a multitude of period lengths. The strategies studies here allow the firm to select alternatives and implement decisions on a monthly basis (based on a total horizon of either one or three periods in the future) over the course of one year. The period of one calendar year is chosen to demonstrate the total results ot short-term transactions which would be summarized on MNC's consolidated annual financial statements. Presently, many firms operating in the international markets consider such decisions on a quarterly basis to coincide with forecasts provided by large commercial banks' multinational money management centers. Given the anticipated increased parity fluctuations, a monthly basis appears to be more advantageous as it affords an opportunity to update information on a more timely basis. It is infeasible to consider a shorter time. period (weekly or daily) due to the lack of available data. The following assumptions are made in order to limit the study of the short-term financial problems to the use of net exposure models: 1. The cash budgets for the subsidiary in each country, for each monthly period, are exogenously determined; 2. The cost (return) and availability of financing and investment opportunities are known, as are the firm's upper limits on such activities; 3. Commissions, transaction costs, and other compensatory charges are not considered; 4. The firm's transactions in various markets are not of significant magnitude to influence the various rates and costs of financial instruments, that is, the firm's operations are independent of the markets' rate determination system. Assumption 2 represents the only departure from the condition that data used to obtain a strategy at any point in time would be available to a decision maker. A decision maker would not know the exact value of future borrowing and investment rates. When such specifications become pertinent to decision making, forecasts will be required.
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II. C E N T R A L I Z E D S I N G L E P E R I O D (CSP) M O D E L The first model represents a centralized single period, ~--'SP, approach to the money management problem. 5 Located in the domestic country (United States) is a cash pooling center serving as a medium for transferring funds among the countries in which the firm has operations. Decision-making is centralized at the domestic corporate headquarters. The framework of a net exposure model precludes any hedging devices, because a series of multiple exposure goals seek to maintain a zero net exposure position in each foreign subsidiary at the end of the single period. If zero net exposure can be achieved, the firm is invulnerable to any exchange rate fluctuation. A feature of the CSP, particularly attractive to firms, is that no spot exchange rate forecasts are required. The firm is viewed as being riskaverse; that is, neither willing to gain nor lose on exchange rate fluctuations relative to the domestic currency. If no exposure prevails, the firm's short-term money management profits are not subject to exchange rate risks. In the CSP model, single-period investments and financings are permitted in each foreign country in addition to the domestic center. Cash requirements are assumed to be known for each period and for each subsidiary. The pooling concept allows transfer of funds from each country through the pool to every other country. Let :
Xjk
= units of foreign currency of country j denominated in US dollars transferred from country j (j = 1,2,3) to cash center pool, k; Xkj = US dollars transferred from pool. k, to foreign country j; lj = units of foreign currency invested in country j; lk = US dollars invested in pool country k; Bj = units of foreign currency borrowed in country j; Bk --US dollars borrowed in pool country k; Oj = deviations over net exposure goal for country j;
-~ F o r a m o r e Hollis [6].
detailed
examination
o f this m o d e l ,
251
Uj = deviations under net exposure goal for country j; R i = required cash budget in country j; Sj = maximum permissible investment in country j; Tj = maximum permissible borrowing in country j; ij = percentage return on investment for duration of one month in country j; ik = percentage return on investment for duration of one month in pool country k; bj = percentage cost of financing for duration of one month in country j; bk = percentage cost of financing for duration of one month in pool country k. The objective is to make the firm's net exposure in each of the foreign subsidiaries as close as possible to zero at the period's end. Using goal programming, the objective can be expressed as the minimization of the sum of the deviations over and under each net exposure goal for each country. The goal programming objective is stated as minimize
: =
~ (Oj + L,'jJ. J 1
The firm is constrained by certain operating restrictions. The first set of constraints requires the amount of funds invested at the beginning of the period plus earned interest (exposed assets) less the amount of funds borrowed at the beginning of the period plus financing expense (exposed liabilities) be equal to zero (plus or minus deviations for each country). This may be stated as (I + ij)l i - (I + hiJB i -
Oj + L:; = 0 : ¥ i.
In other words, the constraint takes into consideration the realization that it may be impossible to obtain a zero net exposure position and allows the firm to be as close as possible to a risk-free cash position. At the beginning of the period, funds transferred from the pool less funds transferred to the pool less investments plus financing must be equal to the required budget for the period. If excess funds exist, the budget has a negative sign. Budget constraints are
see X k i -- Nik -- [ j ~ B i :
R i : ¥ i.
Martha S Hollis--Foreign Exchange Risk Management
252
The third constraint maintains the cash_ III. D E C E N T R A L I Z E D M U L T I P E R I O D pool's balance. The total funds transferred into (DMP) M O D E L the pool less the total funds transferred to subsidiaries operating in foreign countries from The second model, again a net exposurq the pool less investments plus financing in the 'formulation, describes a decentralized multidomestic country must equal zero; or period (DMP) money management system. ~ Each foreign-based subsidiary forrrm/ates anc X~k- ~ X k j - Ik + Bk =0. executes its own strategies, but must operatc j:l j 1 without the use of a centralized cash poolin~ Investments made by the foreign subsidiaries center. A multiperiod decision model provide~ are constrained from above by establishing a strategy decisions for the current period of om maximum permissible investment level. The in- month in addition to strategies for the follow. ing two periods. Only the strategy for the cur. vestment constraints are rent period is implemented. A moving horizot /j___ sj,vr of three periods is considered at the start o Financing opportunities are similarly limited each month, allowing parameters to b~ in each foreign arena by updated with information that would becom~ available at the start of each month. Bj <_ rj, vj. As in the CSP model, cash requirements fol Let the subscript n (n = 1,2 . . . . . 12) rep- the beginning of each period are known ant resent the current application period. Sub- must be satisfied by transactions at the onse~ sequent to the initial application of the model of the period. By expanding the decision hori. (n = 1), the formulation must be modified to zon to several periods, more investment oppor. reflect implemented decision variables from the tunities are considered in each country. Invest. immediately preceding period, n - 1, and cur- ments for durations of one, two, and thre~ rency fluctuations. These modifications affect months may be executed. Borrowings remair only the right-hand sides of the budget con- at one period durations, due to the lack of pubstraints (Rjn) and the cash pool balancing con- fished information which would have beet traint by reflecting the fact that funds invested required for model testing. in the previous period plus earned interest are Operating within a single country, the firrr a source of funds for the current period. In faces no direct exchange rate risk. However addition, these constraints must specify the if the firm is a subsidiary of a corporatior repayment of financing incremented by interest whose financial statements are reported ir expense. All foreign transactions which are another currency, the effects of currency trans. measured in US dollars must reflect previous lations may yield substantial exchange/rate cur. currency value changes. This is accomplished rency losses or gains. Thus, any funds held ir by multiplying the amount of the transaction a foreign subsidiary at the termination of ar by the ratio of the current exchange rate (in accounting period are subject to translatior US dollars per unit of currency j), ejn, to the gains or losses. exchange rate at the beginning of the previous Let: period, e~n-l. The budget constraint is, thus, lij t = units of foreign currency of country j modified by changing the right-hand side to invested in country j's short-terrr money market of maturity R j . - ejn [(1 +ijn-1)ljn-t-(1 + b ~ _ l ) B j n _ l ] ; V j . ejn- 1 (i = 1, 2, 3) months placed in time (t = I, 2. . . . . T); The necessary modification to the cash pool B jr = units of currency of country j obtained constraint is from short-term loans of one period (1 + ikn-1)lkn- 1 r- (1 + b~-l)Bk.-t. in time t; Off = deviations over zero net exposure in country j at the end of period t; I U jr = deviation under zero net exposure in 6 A more detailed exposition of the D M P model is found country j at the end of period t; in Hollis [7].
•
Ome#a, Vol. 6. No. 3
R jr = net cash requirements in country j in time t; Sit = maximum permissible outstanding investments in country j in time t; Tit = maximum permissible borrowings in country j in time t; iij t = percentage investment yield for duration i for purchases in country j in time t; and /~j, = percentage cost of borrowing for one period in country j in time t. For each country the model is applied with the objective of obtaining, as close as possible, zero net exposure at the end of each period. The objective function seeks to minimize the sum of the deviations from each period's net exposure goal and may be expressed as
253
As in the CSP model, formulations after the first application (when n = 1) require updating to include implemented policies that affect operating conditions in later periods. Therefore, when n > 1, changes are needed. First, in the net exposure goal constraints, it must be recognized that investments placed in previous periods will affect the end-of-period exposure. The right-hand side modification of the goal constraint equation is (1 + i i j l . n _ i + , ) I u l . n _ i + ~ ;
The budget constraints are modified by changing R jr to Rit-
~ (1 + i i j l . . - i + t i=t
T
The first set of constraints requires that the end-of-period net exposure be as close as possible to the prescribed goal of zero. That is, the assets maturing at the end of the period less obligations due less variations over the goal plus variations under the goal must equal zero, or ~(1
+ iij.t+l_i)lij.t+l_
i
-- (1 + b j . , _ t ) B j . , _ ~
-
Ojt + Ui, = 0 : Y t .
Budget constraints require that the cash needs of each period be satisfied. Sources of funds are single-period loans obtained within country j and maturing investments. Uses of funds include money market instruments (investments of varying maturities) or repayment of previous loans. The budget constraints are (T+ 1)-t
Bit -
~ i=1
t~l
.
Iij, + ~ (I + l i j . t _ l ) l i i . t _ i 1
1
-- (1 + b j . , _ t ) B i . , _
j = R i t : ~gt.
To more fully describe the operating environment of foreign subsidiary, it is necessary to bound the maximum amount of outstanding investments and borrowings. This may be accomplished by constraints of the form IT*ll-t i=l
Iijt + I 2 j . t - 1
4- lait_ I <-- Sir: ¥ t.
if ,,~
and Bj, <_ Tj, : ~t.
l ) l i ' tj .n- 1+ t - i +(1
minimize z = ~ (0~, + Ujt). t=l
V-l.
i::t+ 1
+bjt.~_t)Bjl.._l:~t.
To maintain an upper limit on total investments, the right-hand side for the investment constraints becomes Sjl - I"jl.n-I
-- I 3 j l . n - I
-- / 3 j l , n - 2
Sj2 - I 3 j l , n _ 1
(when t = 2). and
(when
t = I),
Sj3 (when t = 3). Finally, no changes are required on the maximum borrowing constraint because previously implemented financings with duration of a single period are independent of the present period's decision alternatives. IV. NAIVE R A N D O M STRATEGY (NRS) The final money management strategy (not approximating existing practices) serves as a benchmark with which to compare the strategies obtained from the previous two models. This strategy is a naive random strategy (NRS), in which the net funds requirement for each period is determined by summing the cash requirements for each subsidiary. Next, random numbers are generated and normalised to indicate the proportion of the total funds to be obtained (invested) in each foreign country and in the domestic country. The NRS functions merely as a vehicle to facilitate the profit comparisons resulting from short-term financial practices. Any money management model performing worse than the NRS suggests the futility of that particular approach. If a naive manager can outperform another strategy by
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Martha S Hollis--Foreign Exchange Risk Management
simply generating random numbers, the time and effort consumed in a more complicated approach is egregiously wasted. To apply this unsophisticated strategy the manager first determines the cash needs of the total firm; i.e. ZjRj (where Rj is the net cash requirement exogenously determined for country j at the beginning of the period). If the net figure is positive, financing must be obtained; if negative, investments are placed. If the net figure is zero, no action is taken. After obtaining the net cash position, four random numbers are generated. These numbers are normalized to obtain weighting factors, wj, which when multiplied by total cash needs indicate the amounts of US dollar equivalents to be invested, I t, or borrowed, B j, from each of the j countries (wher e j = 1, 2, 3, 4). Subsequent to the n = 1 (first application period) case, certain modifications are required to ensure repayment of loans or inclusion of matured investments and to incorporate currency value changes measured in US dollars, That is, the net cash needs for the M N C are found by summing the following: j= 1
Rj. -
ejn- I
( 1 + % _ , ) Ij._ ~ +
e jn (1 + b j . _ l ) B j . _ l ejn- 1
1•
where:
Rj, = net cash needs for country j in period n; Ij.-1 = investments placed in the previous period, n - 1, in country j; Bj,_I =financing obtained in country j in n-l; ij,-x = percentage yield from investment in country j placed in period n - 1; bj,_t =percentage cost of financing in country j obtained in period n - 1; ej, = exchange rate in US dollars/unit of currency of country j at the beginning of the current period, n; ej.-1 = exchange rate in US dollars/unit of currency of country j at the beginning of the previous period, n - 1. The coefficients required for updating the NRS are known with certainty. That is, the 7 Exchange controls, of course, could prevent the firm from implementing desired transactions. a No multiple period financing is permitted due to lack of published information.
manager knows borrowing costs or investment yields, and the exchange rate for the previous period. Further, the current exchange rate, ej., is known. In the case of domestic transactions, both ej, and ej._ 1 have values of one (illustrating that US investments and borrowings are not subject to exchange rate fluctuations). V. E X P E R I M E N T A L D E S I G N A N D PROFIT RESULTS This section compares the results that would have been experienced had NRS, CSP and D M P money management strategies been implemented each month during the period September 1974 through August 1975. For each strategy, the associated model (as described in preceding sections) was used to obtain recommended monthly transactions. The transactions were then submitted to a simulator that determined what would have happened had an M N C consistently followed a strategy for twelve consecutive months. It is important to notice that results presented do not represent profits that are predicted by models; rather, the results show the profits that would have been experienced had a decision maker implemented strategies suggested by models. 7 The reported profit performances of alternative strategies are before-tax consolidated profits measured in US dollars. Profits are comprised of gains from short-term investments reduced by costs of short-term financings adjusted for exchange rate changes on net exposed assets. A randomly determined set of cash requirements is established for each foreign subsidiary in each of the twelve months (see Appendix). Cash needs for each period range from -$25,000 to $25,000. Negative and positive signs represent, respectively, cash-rich and cash-poor subsidiaries. In all models, foreign financing is limited to a maximum of $50,000 obtained in each country for a period of thirty days.8 Domestic financing is available only in the centralized models (CSP) with no limits. The short-term rate to prime borrowers is obtained from the
Bimonthly FFO Updater and Forecaster of Interest Rates [1]. For all models, foreign investments are constrained to a maximum of $150,000 per period per country, while no limit is placed on domes-
Omega, Vol. 6, No. 3
tic investment. In t h e multiperiod model (DMP) investment constraints are refined to specify a maximum of $150,000 outstanding per period. 9 Thus, if the maximum investment is placed with a more-than-one period maturity, no other investments may be executed until the investment matures. Short-term investments selected for inclusion are similar with respect to risk and liquidity characteristics of the US Treasury Discount Bill. Yields for the US bills are obtained from Moody's Bond Record [12]; United Kingdom rates are obtained from the Financial Times [3]; and the Canadian rates are obtained from International Financial Statistics [9]. l° The
Monthly Report of the Deutsche Bundesbank [ 11 ] is the source for German call money rates. Monthly before-tax money management profits are calculated from the application of each model on a cash basis for the hypothetical MNC. Profits are defined to be before-tax consolidated gains on investments resulting from interest and revaluations from parity changes (or reductions from devaluation) less financing charges and revaluation changes (or increases from devaluation). Profit results are detailed in Table 1. An inferential test is presented to afford generalizations of the research results. The hypothesis is that the respective applications of the three money management strategies result in no significant differences among monthly before-tax consolidated profits for the period September 1974 to August 1975. The hypothesis is tested using the nonparametric Friedman test for analysis of variance for dependent groups. For each month, the profits resulting from the three strategies are ranked and the ranks are summed. If the null hypothesis is true, the sum of the ranks used should be equivalent for each model. The sum of the ranks used in the Friedman test are, respectively, 26 (NRS), 22 (CMP), and 24 (DMP). The value of the calculated Friedman statistic is 0.7 which would require at least a 0.975 significance level for rejection according to tables 9 The p a r a m e t e r s of this research h a v e been fixed at particular values to prevent u n l i m i t e d recourse to m o n e y m a r kets. 1o G i v e n the u n a v a i l a b i l i t y of the term interest s t r u c t u r e of s h o r t - t e r m C a n d i a n bill rates, it was a s s u m e d t h a t onem o n t h rates were 31}~, a n d t h a t t w o - m o n t h rates were 63% of the t h r e e - m o n t h rates which were r e a d i l y available.
255
TABLE 1. MONTHLY CASH PROFITS (IN US DOLLARS)
Month
NRS
Strategy CSP
DMP
1/75 2/75 3/75 4/75 5/75 6/75 7/75 8/75
341.22 -441.03 -66.82 267.55 -46.60 559.96 - 164.77 -30.35 - 54.86 29.64 424.34 -83.03
274.69 -244.84 -27.53 146.88 210.36 144.32 41.92 -69.13 - 130.50 -47.95 - 105.27 -425.61
0.00 -302.95 - 10.56 35.68 229.17 507.13 767.06 16791 - 254.90 53.82 -442.64 - 1,683.62
Total
735.25
-232.68
-933.90
9/74 11/74 10/74
12/74
found in Lehmann [10]. At generally accepted levels of significance, then, there are no significant differences in the profit 1,zvels of the three models. VI. C O N C L U S I O N S The inferential conclusions reached in this research study are only generalizable to the M N C operating in the countries specified for the sampled period for any series of cash requirements given the set of assumptions invoked. The net exposure models performed no better than a random "dart throwing" approach. This is not surprising in the volatile period of fluctuating exchange rates. Most of the pure net exposure models were developed and reported prior to February 1973 when the flexible exchange system was introduced for most major currencies. Even the extension of a net exposure model into a multiperiod formulation does not yield a viable foreign exchange risk management model. The multiple-period formulation introduces matching exposure problems. Equal dollar assets and liabilities obtained in different periods do not yield net exposure of zero (when considering translation procedures for independently managed subsidiaries) if incremental movements in exchange rates differ. Projected zero net exposure in a currency (measured in the foreign currency with different transaction dates) does not leave the M N C invulnerable to exchange rate fluctuations. Indeed, the naive random approach results in no significant profit differences. Firms currently operating with
256
Martha S Hollis--Foreign Exchange Risk Management
simple net exposure schemes should re-evaluate their management procedures. Strategies resulting from the multitemporal model, DMP, have strong implications for the importance of the length of planning horizons. The closer to time of implementing transactions, the more accurate future strategies approximated the actual transactions. That is, the formulation of planning is better with more current information.ll Use of the threeperiod time horizon (while not rigorously tested in this research) may be better than a longer number of periods. With longer time horizons, additional inaccuracies (forecasts on future parameters) are introduced as well as additional computational burdens incurred. International short-term money management affords many avenues for continued research. Forecasting methods for future spot exchange rates, investment rates, financing rates, and forward contracts need to be explored and validated. Strategies which include all exposed assets and liabilities rather than monetary classifications would be invaluable to the MNC. Sensitivity analysis of the models to the robustness of parameters' values (which were assumed to be fixed at certain levels in this research) needs to be explored. More specifically, simulation methods can be employed to ascertain the effects of profits by varying the range of the randomly determined cash requirements and levels of maximum permissible investments and financing. In conclusion, MNCs which are currently making decisons based on simple zero net exposure methods should re-evaluate their practices. It appears that some degree of exposure may be desirable. ACKNOWLEDGEMENTS The author wishes to thank Dale VorderLandwehr. Roger Eck, and Joe McGuire for their helpful comments on this research.
1 The author wishes to thank the referees for pointing out that there may be a case for time-dependent weightings for DMP deviational goals. For example, the more recent the period, the more costly should be weights employed in the objective function for exposure deviations since only the current period's solution is implemented.
REFERENCES 1. Bimonthly FFO Updater and Forecaster of Interest Rates. Various Issues. Business International Corporation, New York. 2. EITEMAN DK & STONEHILL AI (1973) Multinat. Bus. Fin. Addison-Wesley, Reading, Massachusetts, US. 3. Financial Times. Various Issues. London. 4. GIDDY IH & DULLY G (1975) The Random Behavior of Flexible Exchange Rates: Implications for Forecasting. J Int. Bus. Stud. 6 1-32. 5. GOELTZ GK (1972) Managing Liquid Funds Internationally. Columbia J Wld. Bus. 7 59-65. 6. HOLLIS MS (1976) Illustration of the Behavior of a Single-Period Net Exposure Model. Working paper. University of California, Irvine, US. 7. HOLLIS MS (1976) A Mathematical Multiperiod Decentralized Net Exposure Model. Working paper. University of California, Irvine, US. 8. International Financial Statistics. Various Issues. International Monetary Fund, Washington. 9. KORTH C (1971) Survival Despite Devaluation: Reducing Overseas Exposure. Bus. Horiz. 14 47-52. 10. LEHMANN EL (1975) Nonparametrics: Statistical Methods Based on Ranks. Holden-Day, San Francisco. 11. Monthly Report of the Deutsche Bundesbank. Various Issues. Deutsche Bundesbank, Frankfurt, Germany. 12. Moody's Bond Report. Various Issues. Moody's, New York. 13. TECK A (1970) Financial Planning in Nations with Fluctuating Currencies. Mgmt. Acct. 58 25-28. 14. TECR A (1971) Control Your Exposure to Foreign Exchange. Harv. Bus. Rev. 52 66-75. Ms Martha Hollis, Assistant Professor of Management Science, Graduate School of Administration, University of California, Irvine, CA 92717, USA.
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APPENDIX RANDOMLY GENERATED SUBSIDIARY MONTHLY CASH REQUIREMENTS* (US DOLLARS) Subsidiary Month
United Kingdom
Germany
Canada
9/74 10/74 11/74 12/74 1/75 2/75 3/75 4/75 5/75 6/75 7/75 8/75
- 10,097 12,831 20,632 -20,247 - 11,087 10,600 14,259 13,452 - 20,662 - 19,008 18,062 20,474
- 10,480 22,368 -24,130 19365 - 14,158 - 15,290 15,404 -14,542 12,595 20,665 - 20,335 10,526
- 14,194 24,830 - 18,738 - 17,617 13,602 15,398 - 14,778 23,495 18,059 - 15,053 12,566 17,983
* Negative values represent excess cash.
0305-0483/78/0701-0249502.00/0
© Pergamon Press Ltd ~978. Printed in Great Britain
Short-Term Foreign Exchange Risk Management" Zero Net Exposure Models MARTHA
S HOLLIS
University of California, Irvine (Received July 1977; in revised form October 1977)
By balancing the relevant end of period assets and liabilities (i.e. a zero net exposure approach
to foreign exchange risk management) the multinational corporate treasurer can, conservatively, protect against parity fluctuations without requiring exchange rate forecasta. This paper presents two goal programming formulations for short-term money management and evaluates the resulting strategies (via simulation) in terms of their impact on corporate profits. A hypothetical multinational corporation with headquarters in the US and subsidiaries in Canada, West Germany, and the United Kingdom serves as the experimental unit. The results suggest that the zero net exposure approach is no better than a naive 'dart=throwing' approach.
THE RESULTS of short-term money management decisions can be influenced by foreign exchange rate fluctuations. Exchange rate movements can lead to currency gains and losses that are reflected in the corporation's net income statement. To offset this foreign exchange rate risk some analysts have suggested using a zero net exposure approach to short-term money management (that is, the balancing of end-of-period short-term monetary assets and liabilities).. . 1 Prior work on net exposure models has been predominately qualitative in nature and can be characterized by the omission of specific details such as the length of time horizons, how variables are related, and the mathematical form for finding solutions. 2 Qualitative methods, because of their lack of specificity in dealing with the multitude of factors which are of vital importance in the decision-making process, cannot demonZero net exposure is defined herein as the balancing of end-of-period short-term monetary assets and liabilities to avoid rate risks eschewing all types of forward contractual arrangements a n d other hedging instruments. For other definitions of net exposure see Teck [14]. 2 See, for example, the expositions of Eiteman a n d Stonehill [2], Goeltz [5], K o r t h [9], a n d Teck [14]. 249
strate the quantitative impact on profits. This research overcomes some of the deficiencies of prior studies in the international money management process by stating precisely two of the most frequently advocated zero net exposure approaches in the form of mathematical models. Two archtypical models of multinational corporations' (MNCs) organizational control are explored: a centralized single period zero net exposure model (CSP) and a decentralized multiperiod zero net exposure model (DMP). The third model, developed for comparative purposes, represents a naive random selection process (NRS). Each model is used to obtain monthly strategies for a hypothetical US MNC operating during the time period September 1974 through August 1975. The twelve monthly strategies that are obtained from each of the three models are submitted to a simulator that determines what would have happened with respect to before-tax consolidated profits if the transactions had been implemented during this period of volatile exchange rate fluctuations. Profits resulting from simulated implementation are compared using nonparametric inferential statistics. This research should provide
250
Martha S Hollis--Foreign Exchange Risk Management
MNCs with some preliminary guidance regarding their short-term money management decision-making. This paper suggests that there are no significant differences among the profits resulting from the strategies suggested by the two zero net exposure models and a naive random approach. The assumptions of net exposul'e models are detailed in Section I. The mathematical formulations for the centralized single period model, the decentralized multiperiod model, and the naive random strategy are presented in Sections II, III, and IV, respectively. Profit results of the simulated applications are presented and tested in Section V. The final section contains conclusions and areas for future research.
I. N E T E X P O S U R E A S S U M P T I O N S In the CSP and D M P models, to preclude the necessity for forecasting directions of exchange rate movements, the firm is assumed to strive for an ending exposure balance as close to zero as possible in each country of operation. 3 The firm's exposure position is assumed to preclude any willingness to experience exchange rate fluctuations. This study is limited to the essential decision variables of short-term financial management in multinational corporations. These variables, derived from prior work in the theory of financial management, are: investments with duration of less than one calendar year and borrowings with repayment terms less than one calendar year. 4 Short-term investments are included by considering only the most active classification in each country (those similar in risk and liquidity to the US Treasury Discount Bill). Borrowing opportunities will be restricted to commercial banking operations in each country.
3 See Giddy and Dufey [4] for recent work on exchange rate forecasting techniques and their results. 4 Other short-term variables include the management of inventories, accounts payable, and cash m a n a g e m e n t etficiency m o v e m e n t s (such as lock boxes and wire transfers). These are not considered in order to concentrate on purely monetary decisions. Hedging devices are excluded to focus attention on pure net exposure approaches.
Short-term financial decisions are made using a multitude of period lengths. The strategies studies here allow the firm to select alternatives and implement decisions on a monthly basis (based on a total horizon of either one or three periods in the future) over the course of one year. The period of one calendar year is chosen to demonstrate the total results ot short-term transactions which would be summarized on MNC's consolidated annual financial statements. Presently, many firms operating in the international markets consider such decisions on a quarterly basis to coincide with forecasts provided by large commercial banks' multinational money management centers. Given the anticipated increased parity fluctuations, a monthly basis appears to be more advantageous as it affords an opportunity to update information on a more timely basis. It is infeasible to consider a shorter time. period (weekly or daily) due to the lack of available data. The following assumptions are made in order to limit the study of the short-term financial problems to the use of net exposure models: 1. The cash budgets for the subsidiary in each country, for each monthly period, are exogenously determined; 2. The cost (return) and availability of financing and investment opportunities are known, as are the firm's upper limits on such activities; 3. Commissions, transaction costs, and other compensatory charges are not considered; 4. The firm's transactions in various markets are not of significant magnitude to influence the various rates and costs of financial instruments, that is, the firm's operations are independent of the markets' rate determination system. Assumption 2 represents the only departure from the condition that data used to obtain a strategy at any point in time would be available to a decision maker. A decision maker would not know the exact value of future borrowing and investment rates. When such specifications become pertinent to decision making, forecasts will be required.
Orneqa. Vol. 6. N o , 3
II. C E N T R A L I Z E D S I N G L E P E R I O D (CSP) M O D E L The first model represents a centralized single period, ~--'SP, approach to the money management problem. 5 Located in the domestic country (United States) is a cash pooling center serving as a medium for transferring funds among the countries in which the firm has operations. Decision-making is centralized at the domestic corporate headquarters. The framework of a net exposure model precludes any hedging devices, because a series of multiple exposure goals seek to maintain a zero net exposure position in each foreign subsidiary at the end of the single period. If zero net exposure can be achieved, the firm is invulnerable to any exchange rate fluctuation. A feature of the CSP, particularly attractive to firms, is that no spot exchange rate forecasts are required. The firm is viewed as being riskaverse; that is, neither willing to gain nor lose on exchange rate fluctuations relative to the domestic currency. If no exposure prevails, the firm's short-term money management profits are not subject to exchange rate risks. In the CSP model, single-period investments and financings are permitted in each foreign country in addition to the domestic center. Cash requirements are assumed to be known for each period and for each subsidiary. The pooling concept allows transfer of funds from each country through the pool to every other country. Let :
Xjk
= units of foreign currency of country j denominated in US dollars transferred from country j (j = 1,2,3) to cash center pool, k; Xkj = US dollars transferred from pool. k, to foreign country j; lj = units of foreign currency invested in country j; lk = US dollars invested in pool country k; Bj = units of foreign currency borrowed in country j; Bk --US dollars borrowed in pool country k; Oj = deviations over net exposure goal for country j;
-~ F o r a m o r e Hollis [6].
detailed
examination
o f this m o d e l ,
251
Uj = deviations under net exposure goal for country j; R i = required cash budget in country j; Sj = maximum permissible investment in country j; Tj = maximum permissible borrowing in country j; ij = percentage return on investment for duration of one month in country j; ik = percentage return on investment for duration of one month in pool country k; bj = percentage cost of financing for duration of one month in country j; bk = percentage cost of financing for duration of one month in pool country k. The objective is to make the firm's net exposure in each of the foreign subsidiaries as close as possible to zero at the period's end. Using goal programming, the objective can be expressed as the minimization of the sum of the deviations over and under each net exposure goal for each country. The goal programming objective is stated as minimize
: =
~ (Oj + L,'jJ. J 1
The firm is constrained by certain operating restrictions. The first set of constraints requires the amount of funds invested at the beginning of the period plus earned interest (exposed assets) less the amount of funds borrowed at the beginning of the period plus financing expense (exposed liabilities) be equal to zero (plus or minus deviations for each country). This may be stated as (I + ij)l i - (I + hiJB i -
Oj + L:; = 0 : ¥ i.
In other words, the constraint takes into consideration the realization that it may be impossible to obtain a zero net exposure position and allows the firm to be as close as possible to a risk-free cash position. At the beginning of the period, funds transferred from the pool less funds transferred to the pool less investments plus financing must be equal to the required budget for the period. If excess funds exist, the budget has a negative sign. Budget constraints are
see X k i -- Nik -- [ j ~ B i :
R i : ¥ i.
Martha S Hollis--Foreign Exchange Risk Management
252
The third constraint maintains the cash_ III. D E C E N T R A L I Z E D M U L T I P E R I O D pool's balance. The total funds transferred into (DMP) M O D E L the pool less the total funds transferred to subsidiaries operating in foreign countries from The second model, again a net exposurq the pool less investments plus financing in the 'formulation, describes a decentralized multidomestic country must equal zero; or period (DMP) money management system. ~ Each foreign-based subsidiary forrrm/ates anc X~k- ~ X k j - Ik + Bk =0. executes its own strategies, but must operatc j:l j 1 without the use of a centralized cash poolin~ Investments made by the foreign subsidiaries center. A multiperiod decision model provide~ are constrained from above by establishing a strategy decisions for the current period of om maximum permissible investment level. The in- month in addition to strategies for the follow. ing two periods. Only the strategy for the cur. vestment constraints are rent period is implemented. A moving horizot /j___ sj,vr of three periods is considered at the start o Financing opportunities are similarly limited each month, allowing parameters to b~ in each foreign arena by updated with information that would becom~ available at the start of each month. Bj <_ rj, vj. As in the CSP model, cash requirements fol Let the subscript n (n = 1,2 . . . . . 12) rep- the beginning of each period are known ant resent the current application period. Sub- must be satisfied by transactions at the onse~ sequent to the initial application of the model of the period. By expanding the decision hori. (n = 1), the formulation must be modified to zon to several periods, more investment oppor. reflect implemented decision variables from the tunities are considered in each country. Invest. immediately preceding period, n - 1, and cur- ments for durations of one, two, and thre~ rency fluctuations. These modifications affect months may be executed. Borrowings remair only the right-hand sides of the budget con- at one period durations, due to the lack of pubstraints (Rjn) and the cash pool balancing con- fished information which would have beet traint by reflecting the fact that funds invested required for model testing. in the previous period plus earned interest are Operating within a single country, the firrr a source of funds for the current period. In faces no direct exchange rate risk. However addition, these constraints must specify the if the firm is a subsidiary of a corporatior repayment of financing incremented by interest whose financial statements are reported ir expense. All foreign transactions which are another currency, the effects of currency trans. measured in US dollars must reflect previous lations may yield substantial exchange/rate cur. currency value changes. This is accomplished rency losses or gains. Thus, any funds held ir by multiplying the amount of the transaction a foreign subsidiary at the termination of ar by the ratio of the current exchange rate (in accounting period are subject to translatior US dollars per unit of currency j), ejn, to the gains or losses. exchange rate at the beginning of the previous Let: period, e~n-l. The budget constraint is, thus, lij t = units of foreign currency of country j modified by changing the right-hand side to invested in country j's short-terrr money market of maturity R j . - ejn [(1 +ijn-1)ljn-t-(1 + b ~ _ l ) B j n _ l ] ; V j . ejn- 1 (i = 1, 2, 3) months placed in time (t = I, 2. . . . . T); The necessary modification to the cash pool B jr = units of currency of country j obtained constraint is from short-term loans of one period (1 + ikn-1)lkn- 1 r- (1 + b~-l)Bk.-t. in time t; Off = deviations over zero net exposure in country j at the end of period t; I U jr = deviation under zero net exposure in 6 A more detailed exposition of the D M P model is found country j at the end of period t; in Hollis [7].
•
Ome#a, Vol. 6. No. 3
R jr = net cash requirements in country j in time t; Sit = maximum permissible outstanding investments in country j in time t; Tit = maximum permissible borrowings in country j in time t; iij t = percentage investment yield for duration i for purchases in country j in time t; and /~j, = percentage cost of borrowing for one period in country j in time t. For each country the model is applied with the objective of obtaining, as close as possible, zero net exposure at the end of each period. The objective function seeks to minimize the sum of the deviations from each period's net exposure goal and may be expressed as
253
As in the CSP model, formulations after the first application (when n = 1) require updating to include implemented policies that affect operating conditions in later periods. Therefore, when n > 1, changes are needed. First, in the net exposure goal constraints, it must be recognized that investments placed in previous periods will affect the end-of-period exposure. The right-hand side modification of the goal constraint equation is (1 + i i j l . n _ i + , ) I u l . n _ i + ~ ;
The budget constraints are modified by changing R jr to Rit-
~ (1 + i i j l . . - i + t i=t
T
The first set of constraints requires that the end-of-period net exposure be as close as possible to the prescribed goal of zero. That is, the assets maturing at the end of the period less obligations due less variations over the goal plus variations under the goal must equal zero, or ~(1
+ iij.t+l_i)lij.t+l_
i
-- (1 + b j . , _ t ) B j . , _ ~
-
Ojt + Ui, = 0 : Y t .
Budget constraints require that the cash needs of each period be satisfied. Sources of funds are single-period loans obtained within country j and maturing investments. Uses of funds include money market instruments (investments of varying maturities) or repayment of previous loans. The budget constraints are (T+ 1)-t
Bit -
~ i=1
t~l
.
Iij, + ~ (I + l i j . t _ l ) l i i . t _ i 1
1
-- (1 + b j . , _ t ) B i . , _
j = R i t : ~gt.
To more fully describe the operating environment of foreign subsidiary, it is necessary to bound the maximum amount of outstanding investments and borrowings. This may be accomplished by constraints of the form IT*ll-t i=l
Iijt + I 2 j . t - 1
4- lait_ I <-- Sir: ¥ t.
if ,,~
and Bj, <_ Tj, : ~t.
l ) l i ' tj .n- 1+ t - i +(1
minimize z = ~ (0~, + Ujt). t=l
V-l.
i::t+ 1
+bjt.~_t)Bjl.._l:~t.
To maintain an upper limit on total investments, the right-hand side for the investment constraints becomes Sjl - I"jl.n-I
-- I 3 j l . n - I
-- / 3 j l , n - 2
Sj2 - I 3 j l , n _ 1
(when t = 2). and
(when
t = I),
Sj3 (when t = 3). Finally, no changes are required on the maximum borrowing constraint because previously implemented financings with duration of a single period are independent of the present period's decision alternatives. IV. NAIVE R A N D O M STRATEGY (NRS) The final money management strategy (not approximating existing practices) serves as a benchmark with which to compare the strategies obtained from the previous two models. This strategy is a naive random strategy (NRS), in which the net funds requirement for each period is determined by summing the cash requirements for each subsidiary. Next, random numbers are generated and normalised to indicate the proportion of the total funds to be obtained (invested) in each foreign country and in the domestic country. The NRS functions merely as a vehicle to facilitate the profit comparisons resulting from short-term financial practices. Any money management model performing worse than the NRS suggests the futility of that particular approach. If a naive manager can outperform another strategy by
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Martha S Hollis--Foreign Exchange Risk Management
simply generating random numbers, the time and effort consumed in a more complicated approach is egregiously wasted. To apply this unsophisticated strategy the manager first determines the cash needs of the total firm; i.e. ZjRj (where Rj is the net cash requirement exogenously determined for country j at the beginning of the period). If the net figure is positive, financing must be obtained; if negative, investments are placed. If the net figure is zero, no action is taken. After obtaining the net cash position, four random numbers are generated. These numbers are normalized to obtain weighting factors, wj, which when multiplied by total cash needs indicate the amounts of US dollar equivalents to be invested, I t, or borrowed, B j, from each of the j countries (wher e j = 1, 2, 3, 4). Subsequent to the n = 1 (first application period) case, certain modifications are required to ensure repayment of loans or inclusion of matured investments and to incorporate currency value changes measured in US dollars, That is, the net cash needs for the M N C are found by summing the following: j= 1
Rj. -
ejn- I
( 1 + % _ , ) Ij._ ~ +
e jn (1 + b j . _ l ) B j . _ l ejn- 1
1•
where:
Rj, = net cash needs for country j in period n; Ij.-1 = investments placed in the previous period, n - 1, in country j; Bj,_I =financing obtained in country j in n-l; ij,-x = percentage yield from investment in country j placed in period n - 1; bj,_t =percentage cost of financing in country j obtained in period n - 1; ej, = exchange rate in US dollars/unit of currency of country j at the beginning of the current period, n; ej.-1 = exchange rate in US dollars/unit of currency of country j at the beginning of the previous period, n - 1. The coefficients required for updating the NRS are known with certainty. That is, the 7 Exchange controls, of course, could prevent the firm from implementing desired transactions. a No multiple period financing is permitted due to lack of published information.
manager knows borrowing costs or investment yields, and the exchange rate for the previous period. Further, the current exchange rate, ej., is known. In the case of domestic transactions, both ej, and ej._ 1 have values of one (illustrating that US investments and borrowings are not subject to exchange rate fluctuations). V. E X P E R I M E N T A L D E S I G N A N D PROFIT RESULTS This section compares the results that would have been experienced had NRS, CSP and D M P money management strategies been implemented each month during the period September 1974 through August 1975. For each strategy, the associated model (as described in preceding sections) was used to obtain recommended monthly transactions. The transactions were then submitted to a simulator that determined what would have happened had an M N C consistently followed a strategy for twelve consecutive months. It is important to notice that results presented do not represent profits that are predicted by models; rather, the results show the profits that would have been experienced had a decision maker implemented strategies suggested by models. 7 The reported profit performances of alternative strategies are before-tax consolidated profits measured in US dollars. Profits are comprised of gains from short-term investments reduced by costs of short-term financings adjusted for exchange rate changes on net exposed assets. A randomly determined set of cash requirements is established for each foreign subsidiary in each of the twelve months (see Appendix). Cash needs for each period range from -$25,000 to $25,000. Negative and positive signs represent, respectively, cash-rich and cash-poor subsidiaries. In all models, foreign financing is limited to a maximum of $50,000 obtained in each country for a period of thirty days.8 Domestic financing is available only in the centralized models (CSP) with no limits. The short-term rate to prime borrowers is obtained from the
Bimonthly FFO Updater and Forecaster of Interest Rates [1]. For all models, foreign investments are constrained to a maximum of $150,000 per period per country, while no limit is placed on domes-
Omega, Vol. 6, No. 3
tic investment. In t h e multiperiod model (DMP) investment constraints are refined to specify a maximum of $150,000 outstanding per period. 9 Thus, if the maximum investment is placed with a more-than-one period maturity, no other investments may be executed until the investment matures. Short-term investments selected for inclusion are similar with respect to risk and liquidity characteristics of the US Treasury Discount Bill. Yields for the US bills are obtained from Moody's Bond Record [12]; United Kingdom rates are obtained from the Financial Times [3]; and the Canadian rates are obtained from International Financial Statistics [9]. l° The
Monthly Report of the Deutsche Bundesbank [ 11 ] is the source for German call money rates. Monthly before-tax money management profits are calculated from the application of each model on a cash basis for the hypothetical MNC. Profits are defined to be before-tax consolidated gains on investments resulting from interest and revaluations from parity changes (or reductions from devaluation) less financing charges and revaluation changes (or increases from devaluation). Profit results are detailed in Table 1. An inferential test is presented to afford generalizations of the research results. The hypothesis is that the respective applications of the three money management strategies result in no significant differences among monthly before-tax consolidated profits for the period September 1974 to August 1975. The hypothesis is tested using the nonparametric Friedman test for analysis of variance for dependent groups. For each month, the profits resulting from the three strategies are ranked and the ranks are summed. If the null hypothesis is true, the sum of the ranks used should be equivalent for each model. The sum of the ranks used in the Friedman test are, respectively, 26 (NRS), 22 (CMP), and 24 (DMP). The value of the calculated Friedman statistic is 0.7 which would require at least a 0.975 significance level for rejection according to tables 9 The p a r a m e t e r s of this research h a v e been fixed at particular values to prevent u n l i m i t e d recourse to m o n e y m a r kets. 1o G i v e n the u n a v a i l a b i l i t y of the term interest s t r u c t u r e of s h o r t - t e r m C a n d i a n bill rates, it was a s s u m e d t h a t onem o n t h rates were 31}~, a n d t h a t t w o - m o n t h rates were 63% of the t h r e e - m o n t h rates which were r e a d i l y available.
255
TABLE 1. MONTHLY CASH PROFITS (IN US DOLLARS)
Month
NRS
Strategy CSP
DMP
1/75 2/75 3/75 4/75 5/75 6/75 7/75 8/75
341.22 -441.03 -66.82 267.55 -46.60 559.96 - 164.77 -30.35 - 54.86 29.64 424.34 -83.03
274.69 -244.84 -27.53 146.88 210.36 144.32 41.92 -69.13 - 130.50 -47.95 - 105.27 -425.61
0.00 -302.95 - 10.56 35.68 229.17 507.13 767.06 16791 - 254.90 53.82 -442.64 - 1,683.62
Total
735.25
-232.68
-933.90
9/74 11/74 10/74
12/74
found in Lehmann [10]. At generally accepted levels of significance, then, there are no significant differences in the profit 1,zvels of the three models. VI. C O N C L U S I O N S The inferential conclusions reached in this research study are only generalizable to the M N C operating in the countries specified for the sampled period for any series of cash requirements given the set of assumptions invoked. The net exposure models performed no better than a random "dart throwing" approach. This is not surprising in the volatile period of fluctuating exchange rates. Most of the pure net exposure models were developed and reported prior to February 1973 when the flexible exchange system was introduced for most major currencies. Even the extension of a net exposure model into a multiperiod formulation does not yield a viable foreign exchange risk management model. The multiple-period formulation introduces matching exposure problems. Equal dollar assets and liabilities obtained in different periods do not yield net exposure of zero (when considering translation procedures for independently managed subsidiaries) if incremental movements in exchange rates differ. Projected zero net exposure in a currency (measured in the foreign currency with different transaction dates) does not leave the M N C invulnerable to exchange rate fluctuations. Indeed, the naive random approach results in no significant profit differences. Firms currently operating with
256
Martha S Hollis--Foreign Exchange Risk Management
simple net exposure schemes should re-evaluate their management procedures. Strategies resulting from the multitemporal model, DMP, have strong implications for the importance of the length of planning horizons. The closer to time of implementing transactions, the more accurate future strategies approximated the actual transactions. That is, the formulation of planning is better with more current information.ll Use of the threeperiod time horizon (while not rigorously tested in this research) may be better than a longer number of periods. With longer time horizons, additional inaccuracies (forecasts on future parameters) are introduced as well as additional computational burdens incurred. International short-term money management affords many avenues for continued research. Forecasting methods for future spot exchange rates, investment rates, financing rates, and forward contracts need to be explored and validated. Strategies which include all exposed assets and liabilities rather than monetary classifications would be invaluable to the MNC. Sensitivity analysis of the models to the robustness of parameters' values (which were assumed to be fixed at certain levels in this research) needs to be explored. More specifically, simulation methods can be employed to ascertain the effects of profits by varying the range of the randomly determined cash requirements and levels of maximum permissible investments and financing. In conclusion, MNCs which are currently making decisons based on simple zero net exposure methods should re-evaluate their practices. It appears that some degree of exposure may be desirable. ACKNOWLEDGEMENTS The author wishes to thank Dale VorderLandwehr. Roger Eck, and Joe McGuire for their helpful comments on this research.
1 The author wishes to thank the referees for pointing out that there may be a case for time-dependent weightings for DMP deviational goals. For example, the more recent the period, the more costly should be weights employed in the objective function for exposure deviations since only the current period's solution is implemented.
REFERENCES 1. Bimonthly FFO Updater and Forecaster of Interest Rates. Various Issues. Business International Corporation, New York. 2. EITEMAN DK & STONEHILL AI (1973) Multinat. Bus. Fin. Addison-Wesley, Reading, Massachusetts, US. 3. Financial Times. Various Issues. London. 4. GIDDY IH & DULLY G (1975) The Random Behavior of Flexible Exchange Rates: Implications for Forecasting. J Int. Bus. Stud. 6 1-32. 5. GOELTZ GK (1972) Managing Liquid Funds Internationally. Columbia J Wld. Bus. 7 59-65. 6. HOLLIS MS (1976) Illustration of the Behavior of a Single-Period Net Exposure Model. Working paper. University of California, Irvine, US. 7. HOLLIS MS (1976) A Mathematical Multiperiod Decentralized Net Exposure Model. Working paper. University of California, Irvine, US. 8. International Financial Statistics. Various Issues. International Monetary Fund, Washington. 9. KORTH C (1971) Survival Despite Devaluation: Reducing Overseas Exposure. Bus. Horiz. 14 47-52. 10. LEHMANN EL (1975) Nonparametrics: Statistical Methods Based on Ranks. Holden-Day, San Francisco. 11. Monthly Report of the Deutsche Bundesbank. Various Issues. Deutsche Bundesbank, Frankfurt, Germany. 12. Moody's Bond Report. Various Issues. Moody's, New York. 13. TECK A (1970) Financial Planning in Nations with Fluctuating Currencies. Mgmt. Acct. 58 25-28. 14. TECR A (1971) Control Your Exposure to Foreign Exchange. Harv. Bus. Rev. 52 66-75. Ms Martha Hollis, Assistant Professor of Management Science, Graduate School of Administration, University of California, Irvine, CA 92717, USA.
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APPENDIX RANDOMLY GENERATED SUBSIDIARY MONTHLY CASH REQUIREMENTS* (US DOLLARS) Subsidiary Month
United Kingdom
Germany
Canada
9/74 10/74 11/74 12/74 1/75 2/75 3/75 4/75 5/75 6/75 7/75 8/75
- 10,097 12,831 20,632 -20,247 - 11,087 10,600 14,259 13,452 - 20,662 - 19,008 18,062 20,474
- 10,480 22,368 -24,130 19365 - 14,158 - 15,290 15,404 -14,542 12,595 20,665 - 20,335 10,526
- 14,194 24,830 - 18,738 - 17,617 13,602 15,398 - 14,778 23,495 18,059 - 15,053 12,566 17,983
* Negative values represent excess cash.