Policy, Research, and External AffaIr . -WORKING-PAPERS, L International Trade International Economics Department The World Bank Aprl 1991 WPS 653 The Effects of Option-Hedging on the Costs of Domestic Price Stabilization Schemes ¶~~~~~~~~~~~~~~~~~~~~~~ Donald F. Larson and Jonathan Coleman Whether a stabilization fund is hedged or not, it will inevitably generate large amounts of debt. But hedging the fund will make it more likely to survive in the short term. The Policy, Research. and Extemal Affairs Complex ditnobutes PRE Working Papers todissemnate the fGdings ofwok in progess and to rcoumge the exchange of ideas among Bank staff and all othcrs interested in development issues. These papers cmrry the names of the uthors, eflect only their views, and should be used and cited accordingly The findings, mnerpret3tons, and conclusions are the Polly, R0oeah, and Exbrnol Affairs tenationl Trodo WPS 653 Thispaper-aproductofthe International Trade Division, International Economics Departmnent is part of a larger effort in PRE to improve the developing countries' management of commodity price risks. Copies are available free from the-World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Dawn Gustafson, room S7-044, ext6psion 33714 (23 pages, plus 19 pages of annexes). Casual observation leads to the conclusion that Positive net benefits stemming from fund commodity-stabilization funds tend to be short- hedging can occur even when the welfare gains lived. While some funds may have fi ,d to producers and consumers stemming from the becuse of poor management or unwarranted stabilization program are small or nonexistent political interventions, the stochasdc components of commodity prices can generate insurmount- To the extent that international prices follow able difficulties for even the most expert manag- a log-normal random walk, the stochastic cr8 By transferring price risk from domestic component of price variability can become producers and consumers to government-backed overwhelming in relatively large samples of 500 stabiliation funds, these programs generate observations increasing the error associated with welfare benefits that end abruptly when the price expectations and hampering the ability of fumds faiL fund management to determine long-rn "rea- sonable" prices. While hedging techniques are In the context of a price-taking country perhaps more obviously useful when the stochas- sabilizing domestic prices through variable tic component of price is large, similar risk border tariffs, Larson and Coleman annotate the benefits occur under simulations in which prices cirumstances under which fund resources face are deterministic and only international supplies large or unlimited liability and provide a simple contain a random component. strategy of bpging with commodity options to limit fund risk. Using stochastic computer Hedging techniques will not render the fnds simulations, the authors demonstrate that using immortal; they will generate revenue-based risk financial options will generate positive net benefits for governments backing the funds, and welfare gains for the government agencies can generate benefits to producers and consum- backing the funds. These results are quite robust ers by extending the probable lives of the under a nurnber of underlying assumptions. stabilization schemes. Mm PRE Worldng Paper Senes duaPnates the findmgs of wotrk under way in the Bank's Poly Rescrh, md txtnal AffaisComplex. Anobjpctiveof ffsiesei is to getthewe rumdmngs out quickly, even if presntations are ]ess tha fally polished. Mwfndns _ n taim an conluson in the pr do not e_ _tuaiy represent ofrcial Bankc policy, Produced by the PRE Dissemination Center THE EFFECTS OF OPTION-HEDGING ON THE COSTS OF DOMESTIC PRICE STABILIZATION SCHEMES TABLE QF CONTENTS Introduction 1 The Price Band Outcomes and Fund Revenues 2 Welfare Gains and Losses 4 Hedging Fund Risk 9 Model Description: production and the price-band mechanism 11 Simulation Results on Prices and Welfare Changes 13 Simulation Results on Fund Financing 16 Alternative Scenarios 18 Deterministic Price Movements 19 Conclusions 22 Introduction Commodity pnces are notoriously unstable and many countries, both industrial and developing, intervene in commodity markets in order to limit the range of price movements. Sometimes the interventions require international efforts in the form of commodity agreements' which attempt to use the market power of major producers and sometimes consumers to stabilize global prices; other programs are unilateral in nature and are designed to defend prices within national borders. While the mechanisms are varied, a common charactedstic of almost all such programs is their eventual failure. Tbere are multiple reasons for the failure of the various schemes, and some of the reasons are related directly to the form of the stabilization program12; however, a constant stain on any stabilization program is the stochastic component of commodity prices which renders the financial, or in the case of buffer stocks, the physical exhaustion of resources a statistical eventuality. In this paper a simple simulation model is used to derive several results. First, different samples of prices generated by a log-normal random walk can exhibit remarkably different sample-distribution charact cs. Ths is not a new tesult -- see Wright and WilLiams (1990)- but serves to emphasize that, as a pratical matter, stabilization fund managers must treat the future as unchartable even when expectations are rationat tbat Is, even when market agents are fiuly aware of the deterninistic and stochastic components of price movements. Secondly, the simulations demonstrate that price-band stabilization methods, simil!r to those currently used in Clie and Papua New Guinea are fairly neutral in long-term effects, including inefficiency losses, but that single-period income effects can be quite large. In addition, the over-all "risk" benefits coming from reduced price variability tend to be small. Finally, by operating a stabilization scheme, the govermnent transfers the risk of large price movemenls from producers and consumers to the government and tax payers, or more particularly, to the financial or physical assets of some stabilization fund or buffer stocr. The simulations show that simple hedging strategies can greatly reduce the varability of fund revenues and payments. By limiting the extreme payouts from the fund, such hedging can extend the probable life of the stabilization scheme. Hedging does not, however, offer immortlity. These results 'McNicol (1978) documeuts 17 major commodity agreements since the close of World War I. 2S-e Knudsen and Nash (1990) for a description of a wide range of stabilization programs. I ate quite robust across a wide range of assumptions. In addition, the gains-to-bedging results were shown to be independent of the assumption that prices follow a random-walk. In building the simulation model, some very broad assumptions needed to be made about the basic way in which the modeled market was to operate and these basic assumptions are maintained throughout the paper. Included are the assumptions that the country is a price--taker, that expectations are rational, and that the country attempts to limit domestic price movements via a price-band mechanism that draws its financial backing either from general government revenues or from a special buffer fund. The price band outcomes and und revenues Consider a price-taking country which hopes to stabilize domestic prices around some moving average of international prices. For such a country there are nine exhaustive possible states defined by the relationships between border prices, the price-band, and trade flows; the price-band may fall in a range in wbich the county would always be a net exporter, a net importer, or the price band may straddle the point at which domestic supplies equal domestic demand. In addition, the border price may fall above the band, below the band, or within the band. In operating a price-band program, price-risk is transferred from the producers and consumers to the govertment or stab; izton fund. The government fund gains revenues in some of the states and pays out in other states. In four of the rine possible states the stabilization mechanism would produce revenue; in two of the nine states the mechanism woold generate a loss; and in three of the states there would be neither a pay-out nor revenues generated. Figures 1-3 illustrate the three possible states if the country is a perennial expotter of the "stabilized" commodity. In Figure 1, the border price (Pw) falls above the upper limit of the price band. In order to peg domestic prices at the top of the band (Pu), the government would impose an export tax equal to Pw minus Pu. If producers correctly anticipate the prevailing domestic price, Qs will be produced. At the prevailing price of Pu domestic demand will be Qd. Qs minus Qd will be exported generating (Pw-Pu)*(Qs-Qd) in revenues for the government. Figure 2 illustrates the state in which the border price falls below the lower range of the band (PI). In this case, the government must first impose an impon lax equal to (Pl-Pw) to prevent less expensive foreign supplies from filling domestic demand, then subsidize exports (Qs-Qd) by (PI-Pw). The import tax will generate 2 _w supply _upply Pu Pu P1 _ I PV1 __ q pi ~~~IPi - I I Dexnd I I De I I O 09 Od Qs Figure 1: Exporter facing world prie above band. Figure 2: Exporter facing w rld prce below band. no revenues, and the net loss of revenues from the goverment or stabization find would equal (Qs-Qd)*(Pl- Pu Supply N). In Figure 3, the border price falls wiiin the price P - - - - - - - - Pi band; import and expolt taxes are set to zero and fi Imd neither gai nor loses revenue. I ~~~DBaand Figures 46 illusae the three importing states In I Figure 4, the bomder price fills above the price band. The Od 09 goverment must impose an export tax equal to (Pw-Pu) to Figure 3: Exporter facing world pri within band. prevent domestic supplies from Oowing to the more supply ~~~~~~~~~~~~Supply p9 Pu P… Pi De8fI DaePia- and Qs Cd OS Od Flgure 4: Importer facing world price above band. FIgure 5: Importer facing world price below band. 3 profitaile erxpor martke In wPlition, imports (Qd-Qs) supply mdst be subsidizec y (Pw-Pu). In this state the fund loses (Pw-Pu)*(Qd-Qs). Figure 5 illutates the importing case when the border price falls below the price band. The PU - - - - - - - - govenment imposes an import tax equal to (PI-Pw) which Pi - - - -su-nd generates (Qd-Qs)*(PI-Pw) in revenue for the stabilization I fund. Figue 6 shows the state where the border price falls Os Od within the band, generatng neither revenue nor losses8 F. gure 6: Importer fad og world prioe ban ! inally Figure 7 illustntes the case when the price band straddles the point at which domestic supplies equal supply domestic demand. When the border prce falls abo'e the upper range of the price band the country will be a net exporter. To bting the domestic price in line wits the P1 price band (Pu), the govemment must impose an export tax equal to (Pw-Pu) which generates revenues equal to (Pw- Pu)*(Qs-Qd). When the world price (Pw') falls belovw the ad 08 Sd' as price band, the country is a net importer. Tbe government Figure 7: Marginal trader. imposes an import tax equal to (Pl-Pw') and coflects revenue equal to (Pl-Pw')*(Qd'-Qs'). If the price falls witbin the band, the country may either import or eVport, but taiiffs will be set to zero and no revenues will be generated or lost. Welfare gains and losses By intervening in the domestic market the govemment generates welfare transfers between consumers and producers as well as efficiency loses. These transfers occjr for each period the govenmment or fund manager intervenes and may have off-setting effects. In fact, one of the advantages of a price-band mechanism is that the average effect on domesiic prices is neutral-- see Coleman and Larson (1990). In addition, by stabilizing the price 4 component of producer income the program also generates a stabilization benefit which occurs over tbe life of the program. Efficiency losses3 and the monets- transfers between producers, consumers, and the govemment ane readily calculated through changes in the tradtional measures of consumer u 'producer surplus which analyw areas under the demand and supply curves. These measures give a general indicaton of the welfare gains and losses for each period in which the govenmment intervenes.4 Figure 8 illustrates the consumer, producer, and govemment surpluses generated by imposing an export tax on an exported good in order to lower domestic prices. P___d_ Domestic prices fall from the border price of P to P' as the PI government imposes a tax equal to (P-P'). Demand increases from Qd to Qd' and supplies decline from Qs to l Od Od' asos Qs'. The govermnent receives revenues equal to area d; producer surplus drops by an amount equal to the sum of Figure 8: Income transfers and efficency losses under an export tax. areas a,b,c,d, and e; consumer surplus increases by an amount equal to areas a and b, leaving an efficiency loss equal to areas c and e. Generally speaking, consmer surplus is given by: Pt ACS -f D(p, (1) pe where P and P' are the original and altemative prices respectively, and where demand D0p) is a function of price. 3Once expected price replaces price in the supply equation, efficiency losses need not be negative. This result comes from the fact that a price band can accidentally provide a domestic price that is closer to the actual prevailing price than the expected price, generating a positive efficiency gain. 4Only under very strong assumptions do ordinal monetawy measures of consumer surplus correspond to unique measures of consumer welfare. However, for applied work there are few practical altematives. See Just, Hueth, and Schmitz (1982), chapter 5 for a discussion of consumer surplus and applied economic analysis. 5 Producer surplus is similry defined as: APS =fS(p)dp (2) pi The change in govenmment revenues is given by: AGR [S(pQ) - D(p)] P0 - pl. (3) The efficiency loss is defined as: EL = ACS + APS + AGR (4) The way in which income is transferred, or lost to inefficiencies, will vary depending upon the type of govemment intervention and will differ from period to period as the type of intervention needed to deend a price band changes with intemaional price movements. In general, the transfers between producers, consumes, and the Table 1: Producer, consumer, and govenmrent surplus gains and losses under a prce-band stabization scheme. Border priem Trade State Above band Within band Bdow bend Bxxver Conswcr surplus gain neutdal los0 Proder suplus los neutal gan Fund revenue gain nutal loss Marginl trader Consumer suplus gain neutmal loss Producer surplus loss neulral gain Goveranet revenue gain neutral gain Importer Consumer surplus gain neutals loss Producer suplus loss neutral gain Govenment revenue loss neutral gain govemment stabilization fund are likely to be offsetting. Inefficiency losses, however, are not oifset and are a general social cost incurred by operating a price stabilization program. Table I lists the income transfers associated 6 with each of the possible aie states that can occur undet a price-band wbeme. To the exten that producers prefer stable Incomes to unstable incomes, additional benefits aue over the hfe of the stabilization program based on the efficacy ot the program in reducing income variabty by reducing the vadablity of the price component of producer income.5 Newbery and Stglitz (1981) derived a quandfiable measure of the value of the income stabilization achieved based on assumptions conceming the relative risk aversion for producers. Assuming that producers can be teated as a single aggregated agent whose utlity can be represented by a Von-Newman Morgenstem Utility function of income U(Y), average benefits relative to income are defined as: B_ = _y_o - 1R( ,.2 iyiy)2- (5) whete B is the money value of the stabilization benefits; Y0. Y, represent income without and with a stabiiz*ulon progam, respectively, and a bar over a variable represents the variable's mean; where ad2 is the square of the coeffident of varioation for the i,nme Y;, and R is the coefficient of relative risk avesion given by: R _y dU(Y) (6) U'(Y) The first term in (5) is a transfer benefit resulting from any change in the mean level of income, while the tem following the addition sign measures the benefit directly attributable to a reduction in the variance of income resuting from a reduction in the varability of price. Tbe derivation of the benefits formula is given in Annx H. Produce vers fund risk By intervening at the border, a govemmeim operating a price-band scheme commits its own resource to offset a portion of the range of international price movements. Consumers and especially producers gain a risk- benefit because the risks associated with intemational price movements are ttansfred from individuals to the VPotentially, there is a gain to consumers from stable prices-- see Newbery & Stiglitz (1981), chapter 9; however, if consunption substiutes are readily availeale or expenditures on the good are small relative to income, the benefits will be quantitatively small. 7 govemment Genrlly, tis is asswned to produce a not gain in welfare as the govenmnent is assmned to be less averse to the risk associated witl price movements than individual producen. Ths is consistet with one of the few empirical studies of risk aversion. Using games of chance in mral India to measure attitudes toward risk, Binswanoe (1978) concluded that relative disk aversion tended to increase as the ganble increased as a portion of wealth. To the extent that the total resources of the goveumneni are less volatle as a result of price movements relative to producer incomes, a stabilization scheme and the transfer of risk should produce a flow of benefits. Although tt appears trivial to do so, it should be noted that the d(erived benefits -f a sta' ilization scheme flow only if the stabilization scheme remains operational. Mundalk and Larson (1989) have shown that changes in intermational prioes tend to lead to changes in domestic producer prices, despite an ample number of programs designed to mitigate such effects. This result is more general, but consistent with the recognized failure of most intemadonal commodity stabilization schemes. Wright and Williamns (1990) note that stabilizaton schemes "almost never succeed for very long-- and I do not mean long in the Keynesian long run. The founders easily survive the life span of the typical scheme, physically if not financially." The recent defise of two higly-regarded stabilzation schemes, wool in Australia, and programs for cocoa, palm oil, copra, and coffee in Papua New Guinea emphasises the file nature of stabllization programs. And when formerly successfd stiization programs do fail, it is unclear whether the beLefits accumulated during the fumntioning life of the program outweigh the abrupt maiket reactions and the ensuing adverse effects as the mechanism cmmbles.6 Stabilization programs can use discretionary rules to stabilize prices around some expert or legislated notion of the correct long-run prices or can use fixed nrles to define the range in which prices should be defended.7 Unforunately, computer simulations demonstrate that extremely simple prioe movements, such as a log-normal random walk, can lead to exteme price distibutions. Stabilization schemes which tequire the defense of 'Akiyama and Varangis (1989) simulated the long-term eftects of the International Coffee Agreement and concluded that the long-term production and price effects of the agreement were smaU but that the shon-tn effects of the agreement's dissolution were large. 7The Australian Wool Fund is an examr.ple of the fonner and the Papua New Guinea stabilization programs exanples of the latter. 8 unreasonable price levels will fail and fail rapidly, however, there remains a great deal of uncertainty as to whether a "reasonable" price band can ever be defined. For example, Wright and Williams (1990) used computer simulations to demonstrate that a simple autocorrelated price mechanism can generate samples of 50,000 observatlons in which tbere remains a greater than 5% chance of improperly identifying a stationary-meau by more than a standard deviation. Rules can be used to generate a stabilization scheme d4at contains some feed-back and tewefore wme adjustment mechanism. However, as the simulations later demonstrate, the ability of the fund to remain liquid, given a limited borrowing capacity, is primarily a matter of luck. lTis is perbaps the most frequent reason why stabilization schemes fail. At the same time, the following section lays out a strategy of hedging which can greatly reduce the variability of stabilization fund payouts and thereby help the fund manager survive small doses of bad luck. Hedging fund risk Of the nine possible states relating prices and trade which can occur under a price-band measm, only 2 create a liability for a stabilzation fund, while four of the states generate nrvenues (see Table I.) In addition, the liability faced by the fund is limited; however, the limit may be quite large. Conversely, Potential tax re/nue Pu the potential for tax revenue is aot bot Aded. Figure pi I\ otental payout 9 Aliustrates the case for an exporter. Ihe area above the price band and between the supply and demand curves is unbounded above and represents the potential area that the could be used to finae Figure 9: Poenta tax revenue and tand payout. a stabilization fiud via an export tax. The area between the lower range of the price band and the demand and supply curves at PI down to the axis represents the maximum payout from the fund for an exporter. However, the value of this area goes to zero as the lower range of the price band falls. A similar situation exists for the other 9 "liable" state, the case of subsidized imports.8 For the exporter case, the maximum fimd liability has the following characteristics as prices fall: lm,,.(p,-p)[S(p)-D(pv)] , ( where S(pm) = D(pm). Fo. the ces of the importer: llmp,