commodity storage under backwardation: does the working...
TRANSCRIPT
Commodity Storage underBackwardation: Does the Working
Curve Still Work?
Kishore Joseph, Scott H. Irwin, and Philip Garcia∗
Abstract
We investigate storage in the presence of backwardation and the exis-tence of the Working curve for CBOT corn, soybeans, and wheat mar-kets and the KCBT wheat market using 1990-2010 data. Two mea-sures of the spread–the futures-spot and futures-futures–are matchedwith stock data from delivery locations for the first Friday of the de-livery period. To account for quality differences in the futures-spotspreads, maximum spreads are measured based on the lowest spot bidand highest futures price for the day. Storage in the presence of back-wardation is pervasive both in terms of the percent of observations andthe magnitude of the stockholdings. These findings are supported bythe negligible holdings of delivery certificates during backwardations.
Key words: Backwardation, deliverable stocks, convenience yield,non-convergence, futures markets
JEL codes: G13, Q11, Q13
∗Kishore Joseph is a doctoral student, Scott H. Irwin is the Laurence J. NortonChair of Agricultural Marketing, and Philip Garcia is the Thomas A. HieronymusDistinguished Chair in Futures Markets, in the Department of Agricultural andConsumer Economics at University of Illinois Urbana-Champaign.
Commodity Storage under Backwardation: Does the Working CurveStill Work?
Introduction
Storage is a key aspect in many agricultural commodity markets due to sea-sonal production and geographically dispersed supply and demand locations.The storage function is closely aligned with the resource allocation role playedby futures markets, enabling market agents to decide what, when and whereto store. Typically, the futures price for a storable commodity for any deliverymonth is equal to the current spot price plus the cost of storage, includingphysical warehousing costs, interest charges and a possible risk premium.When the difference between contemporaneous spot and futures prices isgreater than the cost of storage, the market signal is to store. However, inven-tories have been observed when the spread between the current spot and thenext to expire futures contract is negative. This apparent paradox–storageunder negative carrying charges or backwardation–has been a controversialissue among commodity users, analysts, and researchers because it appearsto contradict intertemporal arbitrage conditions.1
Kaldor (1939) was the first to offer an explanation, termed “convenienceyield,” for the apparent paradox. The basic idea is that holders of the physi-cal commodity receive benefits which are not available from holding a futurescontract. For instance, processors and merchandisers might receive benefitsfrom holding stocks to accomplish their operational activities. Based on in-vestigation of the wheat market in Chicago, Working (1933, 1948), developedthe “Working curve” to describe the systematic relationship between storageand the difference between contemporaneous spot and futures prices. Thisrelationship is positively sloped and displays positive storage under inversecarrying charges (see figure 1, panel A). Working (1949) later used the no-tion of convenience yield as a key component of the Supply of Storage Theoryto explain the structure of the Working curve. In effect, negative carryingcharges are attributed to convenience yield, i.e., the benefit accruing to own-ers of commodity stocks.
Convenience yields are typically motivated as embedded option valuesarising from the physical storage of stocks. One form of this optionalityarises when stock levels are low and may be generated from transaction costs
1Throughout the paper we use backwardation and negative carry interchangeably.
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(real cost of communication, transport, and searching) associated with sourc-ing the commodity (Telser 1958) or from the possibility that inventories couldbe driven to their lower bound leading to stock outs (Routledge, Seppi andSpatt 2000). For instance, having grains in store allows processors and mer-chandisers to accomplish operational activities that require immediate accessto grain. In addition, a negative optionality may also arise from the oppor-tunity cost of filling binspace with competing commodities when the stocklevels are large (Paul 1970), i.e., holding corn in store may reduce opportu-nities to take advantage of merchandising opportunities in soybeans.
The concept of convenience yield is embedded in many models of commod-ity price relationships. Pindyck (1993, 2001) uses the present value model ofrational commodity pricing to study the interaction between the cash mar-ket and the market for storage, and to identify how these markets respond tochanges in consumption, production and price volatility. He views the priceof storage as the flow of benefits to inventory holders from a marginal unit ofinventory, which he termed the marginal convenience yield. More recently,Peterson and Tomek (2005) use convenience yields estimated in a nonlinearrational expectations model to simulate corn spot and futures prices. Theuse of convenience yield as a component of the carrying cost is based on theobservation that stocks have always been positive for U.S. crops, and hence,backwardations do not depend on aggregate stock-outs as assumed in theclassical rational expectations storage models.
Working’s argument that negative carrying charges are the result of con-venience yield has been challenged by several researchers, including Wrightand Williams (1989), Benirschka and Binkley (1995), and Brennan, Williams,and Wright (1997). They argue that the Working curve is illusionary andan artifact of data aggregation and mismeasurement. Specifically, stocks ofcommodities are aggregated across locations and grades for market reportingpurposes which may not accurately reflect market conditions. Wright andWilliams (1989) point to the case of corn in Iowa and corn in Louisiana;or certified and uncertified stocks of coffee as examples of such commercialaggregation. They contend that, once stocks and prices are measured for theappropriate location and grade, evidence of stocks being held during back-wardations should disappear. The Supply of Storage relationship identifiedby Working should become more like the letter “L” rotated ninety degreesclockwise (see figure 1, panel B).
In the wake of this work, the aggregation argument has been investigated
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by several researchers. Frechette and Fackler (1999) examine the corn mar-ket and find that backwardations are influenced more by the aggregate levelof stocks than their location, contradicting the claim that location of stocksexplains backwardation. Yoon and Brorsen (2002) compare nearby futuresprice spreads with the contemporaneous costs-of-carry and find more frequentinstances of backwardation towards the end of the crop year when commodi-ties are scarce. They argue the decision to store during backwardations byprocessors and livestock producers is consistent with the theory of price ofstorage. Klumpp, Brorsen and Anderson (2007) take a different approach andcompare differences in storage returns between disaggregate (elevator) andaggregate (USDA) data for wheat markets at elevators in southern centraland northern regions of Oklahoma. Finding little difference in the returns,they contend that their results do not support the conclusion that storage ata loss is due to data aggregation. Franken, Garcia, and Irwin (2009), examinethe spatial aggregation argument for the storage-at-loss paradox using weeklyregional and elevator prices for corn and soybeans in Illinois. Their findingssuggest limited aggregation effects, and identify backwardations inconsistentwith spatial aggregation explanations for storage at a loss.
Two recent analyses have examined indirectly the existence of conve-nience yields in agricultural commodities. Sorenson (2002) uses a Kalmanfilter framework to estimate implied net convenience yields in corn, soybeans,and wheat futures spreads. Subsequently, he identifies a negative relation-ship between convenience yields and stocks amid strong seasonal interactions.While the convexity of the convenience yield-stock relationship was difficultto identify in corn and wheat, the Working curve pattern clearly emergedin soybeans. More recently, Carbonez, Nguyen, and Sercu (2012) indirectlymodel convenience yield in corn, soybean, and wheat using a cost-adjustedbasis measure employing concurrent spot and futures prices. They find a neg-ative relationship between their measure of convenience yield and deliverablestocks using a framework that accounts for the time to maturity and harvesteffects. While both studies generally support the existence of the Workingcurve, the findings do not directly address aggregation concerns raised byWright and Williams (1989) and others, and may be complicated by econo-metric issues. Sorenson’s analysis does not consider aggregation questions ashe uses an average futures price spread and aggregate U.S. quarterly stocks.Carbonez, Nguyen, and Sercu (2012) use more detailed inventory data, buttheir spot prices are an aggregate or an average of reported prices in a some-
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what heterogeneous region of Illinois. Further, both studies do not considerpotential endogeneity in statistical analysis that may exist between their in-direct convenience yield measure and the levels of stocks.
Carter and Giha (2007) examine Working’s arguments from another per-spective–by reassessing the Working curve using his original data. Theyargue that the literature has inadequately addressed the question of whetherthe Working curve is a “realistic stylized fact.” If the Working curve is valid,then explanations must be found to explain why stocks are held under back-wardation. If not valid, then convenience yield and its extensions used inmodeling commodity markets are in question and other stylized facts mustbe used to reflect market behavior. Using data from 1921-1932, they examinestocks only for Chicago to minimize potential spatial aggregation problemsand are careful to avoid errors due to aggregating different wheat grades.They find that wheat stocks were carried under backwardation in a single lo-cation, lending support to the shape of the original Working curve and castingdoubt on aggregation arguments. Carter and Giha’s findings are clear withrespect to Working’s original data. However, a question emerges: Can evi-dence and implications developed with data on one market from the 1920sand 1930s be generalized to current commodity markets? Given the presenceof backwardations in prices and central role that storage plays in many com-modity models, the subject warrants further attention (Carter 1999; Garciaand Leuthold 2004; Franken, Garcia, and Irwin 2009).
This paper offers new empirical evidence on holding stocks in the pres-ence of backwardation with recent spot and futures prices and stock data forChicago Board of Trade (CBOT) corn, soybeans, and wheat and Kansas CityBoard of Trade (KCBT) wheat. Weekly stock data for the four commoditiesat deliverable locations are available for 1990-2010, which provides an exten-sive data set for testing storage under backwardation. The focus of the Carterand Giha (2007) study was on the price spreads towards the end of the cropyear, i.e., September-July wheat spreads calculated each Friday during themonth of July. In contrast, our study examines all price spreads to explicitlyestablish the relationship between the spread magnitude and stock holdingbehavior throughout the crop year. We also contribute to existing literatureby examining the proportion of stocks held in backwardation relative to theaverage stock size within the delivery period. This overlooked dimension ofthe evidence may help clarify what amounts to “substantial” stock holdingfor a particular market under negative carry.
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Previous researchers (e.g., Working 1948; Gray and Peck 1981) have oftenused a conventional measure of the spread, futures less spot to study the tem-poral price structure of commodities. Since the difference between specifiedcash prices and the next-to-expire futures price may include a quality or alocational differential, a maximum futures and spot spread (the difference be-tween the low spot bid and the high futures price of the day) is used to reducethe likelihood that observed relationships are influenced by those differences.In addition, a futures only spread measure i.e., the difference between thenearby futures prices and the next-to-expire futures prices (Working 1948;Telser 1958; Thompson 1986; Yoon and Brorsen 2002) is used as a robustnesscheck. Weekly deliverable stock data on the first Friday of the delivery periodare then plotted against standardized one month spreads that are calculatedon the same day. Finally, these findings are contrasted with the stockhold-ing behavior for a pure financial instrument–shipping certificates that havebeen used as the delivery instrument for CBOT corn and soybean futurescontracts since March 2000.
Data and empirical procedures
The primary objective of the study is to ascertain whether stocks certified fordelivery on futures contracts at delivery locations are held in backwardation.This is similar to the objective of Working’s (1933, 1948) original studiesand Carter and Giha’s (2007) more recent study. Our methods are directand include simple tests on inventory (certified stock data from delivery lo-cations on the first Friday of delivery periods) matched against the price ofstorage (spreads calculated relative to the next nearby futures contract) andrecording positive storage at substantial magnitudes during negative carry.2
In other words, we assess the hypothesis that deliverable stocks exhibit theSupply of Storage behavior as defined by Working (figure 1, panel A), underprecise definitions of grade, location, and price.
The traditional method to calculate the spread is to measure the differ-ence between contemporary spot and futures prices. However, commoditiescertified for delivery can be of different grades which are deliverable at apremium or discount to the par grade.3 In addition, spot prices from the de-
2When stock data are not available on the first Friday of the delivery period, the closestobservation within the delivery period is used.
3See Irwin et. al. (2011) for a detailed review of the delivery process for U.S. grain
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livery territory can vary even within smaller distances causing average pricesused in previous studies to be less representative of actual trades. In orderto address these issues, we follow a conservative approach similar to Carterand Giha (2007) by calculating the largest possible spread of the day. Forany given nearby contract this maximum spread is calculated as the high fu-tures price of the day adjusted by location-specific discount/premiums for thenext-to-expire futures contract minus the lowest spot bid for the par deliver-able grade at the deliverable location. If the maximum futures-spot spreadfor the par deliverable grade is negative, the spread for all other bids for thedeliverable grade at that location should also be negative. For example, ifthe futures contract for delivery in two months is priced at 700 cents/bu.and the current spot prices (low bids of the day) for deliverable grades, no.2 soft red winter wheat (par deliverable grade) and no. 1 hard red winterwheat are 710 cents/bu. and 715 cents/bu. respectively, the use of the low-est bid for the par deliverable grade ensures that the maximum spread of-10 cents/bu. (700 cents minus 710 cents) encompasses all the other spreadsthat are backwardated.4
The conventional method to calculate the spread assumes convergence ofcash and futures prices for the contract in the delivery period (at expiration)or treats the nearby futures price for the current contract in the delivery pe-riod synonymous with the current spot price. Recent studies on CBOT corn,soybean and wheat futures markets (Irwin et. al. 2011; Garcia, Irwin, andSmith 2012), indicate that spot and futures prices do not always converge asexpected, with the spot being below futures prices. Suppose the term spreadbetween current and next-to-expire futures price is capped by the exchangedetermined storage rate and the price of physical storage exceeds this cap,then the delivery location basis (futures less spot price) compensates by re-maining positive during delivery (Garcia, Irwin, and Smith 2012). Hence,the futures-spot spread remains unbiased even during non-convergence.
However, the futures-spot spread can make the identification of the Work-ing curve somewhat difficult because we are using a maximum spread. As aresult, the spread between the nearby and the next nearby futures contracton the first Friday of the delivery period that corresponds to the weekly stock
futures markets.4This is true for CBOT corn, soybean, wheat, and KCBT wheat spreads as the de-
liverable stocks studied are mostly par deliverable grade or a grade/class higher that aredeliverable for a premium.
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data is also examined. The term spread as measured from the futures-futuresmeasure provides a downward-biased estimate of the expected returns fromstorage when the storage rates in the contract specification are less than themarket price of storage (Garcia, Irwin, and Smith 2012). Nonetheless, thisdownward bias in the futures-futures spread occurs when stocks are largeand does not affect the price of storage during backwardations when stocksare in short supply. In addition, the futures-futures spread is based only onfutures prices and measures the incentive to hold inventory independent ofquality and location considerations making it a useful alternative to assesssensitivity in the measurement of stocks held during backwardations.
The study uses data for the 1990-2010 periods for CBOT corn, soybean,and wheat futures prices, KCBT wheat futures prices, with daily spot bidsat delivery locations. Futures prices are from barchart.com. The spot bids atdelivery locations (Chicago, Toledo/Maumee, Illinois River North of Peoria,and Kansas City) are from the Agricultural Marketing Service archives ofthe U.S. Department of Agriculture. These spot bids are from the point ofdelivery and are mostly U.S. no. 2 yellow corn, U.S. no. 2 soft red winterwheat for CBOT wheat, and U.S. no. 2 hard red winter wheat for KCBTwheat. For soybeans, the spot prices are for U.S. no. 1 yellow soybean andwe adjust the spread by adding CBOT determined premiums to the high ofthe day futures price for the deferred futures contract, which reflects U.S. no.2 yellow soybeans. Since our data includes 1, 2, or 3 month price spreads,which correspond to the temporal structure of futures contracts, both spreadmeasures are normalized by the number of months between the nearby andnext-to-expire futures.
Both the CBOT and KCBT collect stock data at warehouses declared reg-ular for delivery and compile them for self-reporting purposes. The weeklystock of grain reports classify stocks as deliverable grades, non-deliverablegrades/ungraded and CCC (Commodity Credit Corporation) stocks at ware-houses declared regular for delivery. The stocks are from delivery regionsspecified by the exchanges where firms regular for delivery have storage fa-cilities and/or shipping stations. Stock data are compiled every Friday andreleased on the second business day of the next week. Following Wright andWilliams (1989), we use deliverable stocks which meet exchange quality re-quirements for futures delivery and correspond most closely to the actualmarket prices. The stock data, compiled from the archives of CBOT andKCBT weekly reports, provide a unique opportunity for testing storage un-
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der backwardation.5
Shifting commercial activity over time, e.g., increased flows to port des-tinations, have forced the CBOT to close some of its traditional deliverylocations and set up new delivery locations closer to the regular commercialgrain flow (Irwin et. al. 2011). Previous research (Working 1948, 1949; Grayand Peck 1981; Carter and Giha 2007; Carbonez, Nguyen, and Sercu 2012)has often used Chicago as the location to study backwardations. Commercialflows of grain through Chicago have been reduced sharply in recent decades,marking the decline of Chicago as a terminal grain market. Nonetheless,Chicago continues to be a par delivery location for CBOT corn, soybean,and wheat for the 1990-2010 periods and is included. The CBOT undertookmajor changes in the delivery system by closing the Toledo/Maumee deliv-ery location and opening new delivery points starting with the March 2000corn and January soybean contracts. The new locations are along the Illi-nois River north of Peoria (Lockport-Seneca, Ottawa-Chillecothe, and CreveCoeur-Pekin); locations that had become major trans-shipment points forboth corn and soybeans. The cheapest-to-deliver location for corn and soy-beans during the 1990’s tended to be Toledo/Maumee with Northern Illi-nois River regions becoming the cheapest-to-deliver post-2000. In order toreflect inventory from cheapest-to-deliver locations with significant commer-cial grain flows over time, stocks from Toledo/Maumee delivery regions andNorthern Illinois River delivery regions are concatenated and reported as asingle delivery point–Toledo/Maumee-Northern Illinois (TOL/MA-NI). TheToledo/Maumee delivery location has tended to be the cheapest-to-deliverlocation for the CBOT wheat contract throughout the sample period (1990through 2010) and this location is used for CBOT wheat. KCBT wheatstocks are also examined from 1990 through 2010 at its cheapest-to-deliverlocation–Kansas City–to study backwardations in another market that hasnot been subject to changes in location and delivery requirements.6
Results
Tables 1 through 3 provide a summary of the number of spreads studied,
5We also performed the analysis using total stocks including CCC and non-deliverableinventory with little change in the findings.
6The results from other delivery locations across commodities excluding the river de-livery points for CBOT wheat and KCBT wheat are available upon request.
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number of spreads with negative carry, percent of spreads that are backwar-dated, the magnitude of the stocks (mean) held under backwardation, andthe proportion (percent) of stocks held under backwardation relative to over-all average stocks for that period. The results are reported separately forthe futures-spot (F-S) spread (i.e., the difference between the contemporarylow spot bid and the high futures price) and the futures-futures (F-F) spread(i.e., the difference between prices of expiring and next-to-expire contracts)by commodity, location, and contract. The spreads are ordered, startingwith the most consistent new-crop spread in the data. Finally, stocks andcorresponding spreads based on the F-S and F-F measures are plotted bycommodity and location (figures 2 through 5). Note that it may be difficultto identify the exact shape of the Working curve from the F-S spread. Byconstruction, the F-S spread is a maximum spread which may require marketinversions of larger magnitude and frequency as observed in CBOT soybeansand KCBT wheat, for the exact shape of the Working curve to emerge.
Corn
For both spread measures in table 1, the highest proportion of backwarda-tions occur late in the crop year in July, which is primarily a reflection of thedifferences between old and new crop prices (Yoon and Brorsen 2002). Theparticularly large number of backwardations in the July-September spreads(35% at Toledo/Maumee-Northern Illinois and 20% at Chicago for the F-Sspread, and 40% for the F-F spread) facilitates the assessment of positivestock holding behavior in inverted markets. Deliverable stocks for corn arenon-zero for all dates the spreads and stocks are matched. The percentage oftotal observations exhibiting positive storage under backwardation are com-parable for the F-S spread at Toledo/Maumee-Northern Illinois (14.7%) andthe F-F measure (18.6%), and is small for Chicago (8.8%).
The magnitude of the stocks (mean) carried under backwardation late inthe crop year is large in Toledo/Maumee-Northern Illinois and is non-trivial inthe Chicago relative to the average stocks that are held at those locations. Forexample, the average stock holding in July for the inverted July-Septemberspreads is 4 million bu. for the F-S spread in Toledo/Maumee-Northern Illi-nois and 4.1 million bu. for the F-F spread, which is nearly 93% of theaverage stock holdings (4.3 million bu.) at that location. Substantial deliv-erable stocks close to 1.5 million bu. (approximately 40.6% of total average)
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are held in July when the July-September F-S spreads are inverted, even atChicago which is not the major delivery location for corn. The F-S spreadsat both delivery regions, (figure 2 (Toledo/Maumee-Northern Illinois region(panel A), Chicago (panel B)) show an upward slope in the spreads making itsomewhat difficult to identify the Working curve. However, the F-F spreadsin figure 2 (Toledo/Maumee-Northern Illinois region (panel C), Chicago re-gion (panel D)) provide strong evidence in support of the Working curve.7
Soybeans
Similar to corn, the new crop for soybeans is most often the November con-tract. The transition from old to new crop is evident from the higher frequen-cies of negative carry in the spreads late in the crop year i.e. the July-August,August-September, and September-November spreads for both spread mea-sures (table 2). The July-August spreads in particular indicates a higherfrequency of backwardations (20% of the F-S spreads at Toledo/Maumee-Northern Illinois, 25% of F-S spreads at Chicago, and 60% of the F-F spreads)among all spreads, again, facilitating assessment of stock holding duringbackwardations. There are no observations with zero stocks when the soy-bean spreads are matched against inventory. For the F-S spread, 9.1% atToledo/Maumee-Northern Illinois and 9.8% at Chicago exhibited positivestock holding under backwardation, while for the F-F spread 30.8% have asimilar pattern. In general, the frequency of backwardations for soybeans(30.8%) is found to be much higher than for corn (18.6%) for the F-F spreadmeasure.
The magnitude (mean) of the soybean stocks held under backwardationis substantially high for both spread measures in Toledo/Maumee-NorthernIllinois and Chicago. The stock holdings for the backwardated July-Augustspreads using the F-S spread measure is above 1 million bu. at both deliverylocations studied, and amounts to 43% of overall average at Toledo/Maumee-Northern Illinois and 30.3% of overall average at Chicago. For the July-August F-F spreads, the average stock holdings during backwardation is 1.8
7The July-September spread for 1996 is one of the most extreme old crop/new cropinverses in recent times, at -64.25 cents/bu./mo. for the F-F spread, -59.5 cents/bu./mo.at Chicago, and -58.5cents/bu./mo. at Toledo/Maumee (Northern Illinois) on 7/5/1996.While we include this spread in the tables for corn, it is excluded while generating figure2 for corn as it distorts the visual appearance of the Working curve.
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million bu. in Toledo/Maumee-Northern Illinois which is close to 76% of theaverage stocks held at that location for that spread horizon. Large stockholdings for soybeans continue to exist despite the higher levels of the nega-tive carry in soybeans compared to corn. The shape of the Working curve isalso clearly evident at both Toledo/Maumee-Northern Illinois and Chicagolocations regardless of the spread measure used. Plots for soybean (figure 3)at Toledo/Maumee-Northern Illinois (panel A, panel C), and Chicago (panelB, panel D) continue to provide strong evidence of stockholdings under back-wardation and support the Working curve.8
Wheat (CBOT)
The March-May and May-July spreads for CBOT wheat exhibit backwar-dations more frequently, coinciding with U.S. soft red winter wheat harvestsin mid-May through mid-July. In contrast to corn and soybeans, the July-September spreads for CBOT wheat indicate only limited evidence of back-wardation for both spread measures. Backwardations in the December-Marchspreads are sparsely observed in the conservative F-S spreads at both loca-tions, whereas they are quite prominent (25%) for the F-F spread measure.Deliverable stocks for CBOT wheat remain positive for all the dates thatspreads are matched against inventory. In table 3, 28.6% of the March-MayF-F spreads and 19% of the May-July F-F spreads exhibited positive storageunder negative carry. Similar patterns of storage are also visible at Chicagofor the March-May and May-July F-S spreads that are backwardated. InToledo/Maumee and Chicago, the percentage of total observations showingstorage under backwardation are 3.9% and 6.9% for the F-S spread, and16.7% for the F-F spread.
Average stock size at Toledo/Maumee in March when F-S March-Mayspreads are inverted is 2.5 million bu. and close to 14% of average stocksheld at that location during the March-May spread horizon. Stock size inChicago during backwardations are found to be negligible when compared
8Soybean prices on 3/7/2008 dropped from news that China reportedly flooded itsdomestic markets with soybean oil to control rising prices. Since the March-May F-Fspread for soybeans measured on 3/7/2008 at 33.88 cents/bu./mo. is considerably higherthan other observed spreads during the period, we use the spread from the previous day(3/6/2008) in our study. For consistency, the March-May spread for the F-S measure isalso calculated on 3/6/2008.
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to the average stocks size held at Chicago. Nearly 8.8 million bu. of de-liverable wheat is carried in March at Toledo/Maumee during the invertedMarch-May F-F spread which amounts to almost 50.3% of average stocksheld at that location. We find only one incidence of backwardation amongthe July-September spreads using the F-F measure for CBOT wheat with anaverage 2.3 million bu. (17.7% of overall average) stored in Toledo/Maumee.Substantial quantities of wheat are also held early in the crop season inToledo/Maumee when the December-March spreads are inverted, with aver-age stock sizes of 5.7 million bu. (28.8% of overall average) for the F-S spread,and 8.5 million bu. (43.3% of overall average) for the F-F spread. For CBOTwheat, evidence of stocks being held under inverse carrying charges can beobserved in figure 4, for Toledo/Maumee (panel A, panel C) and Chicago(panel B, panel D) regions. In both these markets, we observe strong signsin support of the Working curve in the F-F spread.
Wheat (KCBT)
Backwardations are observed more frequently in KCBT wheat than in CBOTwheat (table 3). Hard red winter wheat is the largest wheat crop in U.S.,planted in the fall and harvested in the following summer. Similar to CBOTwheat, the March-May and May-July spreads for KCBT wheat show higherincidence of backwardations reflecting the shift from old to new crop. Incontrast to CBOT wheat, the July-September, September-December, andDecember-March spreads for KCBT wheat also indicate higher incidenceof backwardations for both measures of the spread. Deliverable stocks forKCBT wheat are non-zero for all dates the spreads and stocks are matched.Regardless of the spread measure, more than 38% of the observations exhibitpositive storage under backwardation. Similar to corn and soybeans, back-wardations in KCBT wheat are not concentrated in the old/crop new cropspreads.
Nearly half of all March-May, May-July, and December-March spreads arebackwardated with average storage in excess of 4 million bu. for both spreadmeasures, reaching an average 11 million bu. for the inverted F-S spreads.The stock holdings during backwardations are also substantial when com-pared to the average stocks held at Kansas City and is consistent across allspread horizons and spread measures. For example, the average stock hold-ings in March during inverted March-May spreads is 9.4 million bu. for the
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F-S spread, and 7.8 million bu. for the F-F spread, both amounting to nearly70% of the average stock holdings at Kansas City. The evidence for positivestockholding under backwardation, and the Working curve appears to beoverwhelming for Kansas City spreads in figure 5 (panel A, panel B). KansasCity is predominantly a milling center, whereas Chicago and Toledo/Maumeeare traditional trans-shipment points (Gray and Peck 1981). Consequently,higher convenience yields may accrue at Kansas City where commodities aremore likely to be stored for milling and processing operations.
Validating convenience yield in the Working curve
This section provides additional evidence for the convenience yield explana-tion of the Working curve, made possible by the particular nature of theshipping certificate in use for delivery of CBOT corn and soybeans sinceMarch 2000. Prior to March 2000 for corn and soybeans and July 2008 forCBOT wheat, the delivery instrument for CBOT was a warehouse receipt(Irwin et. al. 2011). The delivery instrument for KCBT has always been awarehouse receipt. A warehouse receipt conveys title to the grain held understorage in a designated warehouse facility which is same as the deliverablegrain physically held at the warehouse facility. In contrast, the shipping cer-tificate is in essence a “Call on Demand” instrument which does not requirethe regular (elevator) to hold grain at the warehouse facility, but have it read-ily available when called upon in the time frame specified by the exchange.In short, the shipping certificate is a pure financial instrument that breaksthe direct link between the delivery instrument and the physical grain stock.
The longs who receive shipping certificates from the shorts during the de-livery process are not required to cancel the certificates for shipment and mayhold them indefinitely by paying the CBOT specified storage rates. Hence,shipping certificates will remain outstanding if the price spread between thecurrent and next-to-expire futures contract exceeds the cost of owning thedelivery instrument (Irwin et. al. 2011).9 The situation is quite differentduring backwardations where the spread is already inverted. Shipping cer-tificates are traded in the secondary market and sell for not less than thehigher nearby futures price (Aulerich, Fishe, and Harris 2011). In the con-
9The possible benefits that may accrue to owners of shipping certificates have beenoutlined in articles by Irwin et. al. (2011), Garcia, Irwin, and Smith (2012), Aulerich,Fishe, and Harris (2011).
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text of a backwardation it would not be rational for a market agent to holda tradable financial instrument incurring storage costs when it can be pur-chased at a lower price in the near future. Since, it is hard to argue thatother benefits to holding shipping certificates exist in negative carry marketsand because pure financial instruments lack convenience yields, ideally noshipping certificates should be held during backwardations, with the Supplyof Storage for certificates resembling the rotated “L” presented in figure 1(panel B).
Total corn and soybean deliverable stocks are plotted against the futures-futures spread, and compared with pure financial instruments–shipping cer-tificates that are exactly identical to deliverable stocks except for the typeof instrument considered. The hypothesis for this model is that Supply ofStorage for physical stocks with convenience yields should follow a convex“Working curve”pattern, whereas pure financial instruments such as shippingcertificates that lack convenience yield should resemble the letter “L” rotatedninety degrees clockwise (figure 1). We use the futures-futures backwarda-tions as our measure of price of storage which is independent of price, grade,and location considerations. The total outstanding shipping certificates forCBOT corn and soybeans are obtained from the Delivery Certificates underRegistration (DCUR) report by the Registrar at the CBOT. The data periodspans from the March 2000 delivery through May 2010 delivery for corn, andJanuary 2000 delivery through May 2010 delivery for soybeans. We use out-standing shipping certificates for corn and soybeans issued from all deliverylocations, and available stock data from all active delivery locations for cornand soybeans beginning in 2000. Data for shipping certificates by location(delivery zone) are sparse and could not be matched consistently with cur-rent deliverable stocks and are hence not reported. For wheat, the shippingcertificate data is relevant only for the shorter July 2008-May 2010 periodwhich is insufficient for meaningful interpretation and are not reported. Afew observations had to be dropped from the corn and soybean plots due tolack of shipping certificate data which has minimal effect on the qualitativeaspects of our study.
Outstanding shipping certificates and total deliverable stocks from all ac-tive delivery locations are plotted against corn and soybean F-F spreads (fig-ure 6). While backwardations are sparse for corn (panel A) during the periodof study, inverted spreads are frequent in soybeans (panel B). As expected,when the spreads turn to a more positive carry, the number of outstanding
14
shipping certificates held increases for both CBOT corn and soybeans. Forthe two backwardated observations in corn (panel A), the magnitude of de-liverable stocks is much higher compared to shipping certificates, revealingthe convenience yield inherent exclusively from physical stock holdings. Forsoybeans (panel B), the number of shipping certificates being held is mini-mal compared to the total deliverable stocks and in many instances closerto zero when the spreads are in negative carry. The hypothesized rotated“L” holding pattern for shipping certificates, while not perfect, can be easilydistinguished from the convex “Working curve” for total deliverable stocks inthe plot for soybeans. Market participants tend to hold corn and soybeandeliverable stocks under storage as opposed to shipping certificates, reflectingthe convenience yield that accrues exclusively to the holder of the physicalstocks and thus validating the convenience yield explanation of the Workingcurve.
Conclusion
We investigate storage in the presence of backwardation and the existenceof the Working curve for CBOT corn, soybeans, and wheat markets and theKCBT wheat market using recent 1990-2010 data. Under precise definitionsof grade, location, and price, deliverable stocks are examined at delivery lo-cations for CBOT corn, soybeans, and wheat and KCBT wheat. We employtwo measures of the spread–the difference between the contemporary lowspot bid and the high futures price (F-S) spreads and the difference betweenprices of expiring and next-to-expire contracts (F-F). Both spreads are calcu-lated relative to the next nearby futures contract, standardized to one monthspreads, and matched with closest weekly deliverable stock information avail-able at the delivery locations for the contracts.
We find that storage under backwardation is pervasive both in terms of thepercent of observations that exhibited storage at a loss, and the magnitudeof the stockholdings for those observations. We trace this storage behaviorto indirect yields earned from holding physical stocks in a competitive mar-ket by individual firms (agents) with more or less similar cost structure andstorage technology. The futures-futures spreads often provide the strongestevidence of storage under backwardation, except for the KCBT wheat marketand CBOT soybean market where substantial evidence is provided by bothmeasures. We find that stocks decline monotonically as the spread falls, but
15
remain positive as the spread falls below zero. Notice that our definition ofbackwardation ignores storage and interest costs i.e., the spreads that arebackwardated are only a subset of the spreads with magnitude less than thefull cost-of-carry. Hence, the incidence of storage at loss (spreads with mag-nitude lower than the full cost-of-carry) is much higher than the incidence ofnegative carry (inverted markets) across all commodities and locations.
While we observe the Working curve for all commodities at all locationsin the futures-futures plots, the upward slope in the conservative futures-spot plots makes the identification of the exact shape of the Working curvesomewhat difficult. The most convincing evidence for the existence of con-venience yield is revealed in the magnitude of stockholdings under backwar-dation in Kansas City (where wheat is likely stored for milling and pro-cessing) and in the plot for shipping certificates and deliverable stocks forsoybeans. We graphically demonstrate that market agents tend not to holdshipping certificates (pure financial instruments lacking convenience yield)in inverted markets while the convenience yields inherent to physical stocksfacilitates continuous stock holding at the same delivery points. In sum, ourresults clearly support Working’s (1933, 1948) original analysis and Carterand Giha’s (2007) more recent re-assessment. Using examples from a numberof important agricultural markets in modern times we substantiate that theWorking curve does indeed still work.
16
References
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Benirschka, M. and J. Binkley. 1995. “Optimal Storage and Marketingover Space and Time.” American Journal of Agricultural Economics77:512-24.
Brennan, D.C., J.C. Williams, and B.D. Wright. 1997. “ConvenienceYield without Convenience: A Spatial-Temporal Interpretation ofStorage under Backwardation.” Economic Journal 107:1009-22.
Brennan, M.J. 1958. “The Supply of Storage.” American Economic Re-view 47:50-72.
Carbonez, A.E., V.T.T. Nguyen, and P. Sercu. 2012. “Remodeling theWorking-Kaldor curve: The Roles of Scarcity, Time to Maturity,and Time to Harvest.” European Review of Agricultural Economics39(3):459-487.
Carter, C.A. 1999. “Commodity Futures Markets.”Australian Journal ofAgricultural and Resource Economics 43(2):209-247.
Carter, C.A. and C.L.R. Giha. 2007. “The Working Curve and Commod-ity Storage under Backwardation.” American Journal of AgriculturalEconomics 89(4):864-872.
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Garcia, P. and R.M. Leuthold. 2004. “A Selected Review of Agricul-tural Commodity Futures and Options Markets.”European Review ofAgricultural Economics 31(3):235-272.
Garcia, P., S.H. Irwin, and A.D. Smith. 2012. “Futures Market Fail-ure.” Working paper. Department of Agricultural and Consumer Eco-nomics, University of Illinois at Urbana-Champaign.
Gray, R.W. and A.E. Peck. 1981. “The Chicago Wheat Futures Market:Recent Problems in Historical Perspective.” Food Research InstituteStudies XVIII(1):89-115.
Hicks, J. 1939. Value and Capital. Oxford University Press.
17
Irwin, S.H., P. Garcia, D.L. Good, and E.L. Kunda. 2011. “Spreads andNon-Convergence in CBOT Corn, Soybean, and Wheat Futures: AreIndex Funds to Blame?” Applied Economic Perspectives and Policy33:116-42.
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Sorensen, C. 2002. “Modeling Seasonality in Agricultural CommodityFutures.” Journal of Futures Markets 22(5):393-426.
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Working, H. 1933. “Price Relations between July and September WheatFutures at Chicago since 1885.” Wheat Studies of the Food ResearchInstitute 9(6):187-238.
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18
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19
Table
1.
Seaso
nal
back
ward
ati
ons
and
stock
hold
ing
inth
eco
rnm
ark
et,
1990-2
010
Sp
read
mea
sure
Mon
ths
No.
Ob
s.S<
0&
I>0
%S<
0&
I>0
(1)
Avg.
I.(2
)A
vg.
I.(1
)as
aS<
0&
I>0
%of
(2)
F-S
Dec
-Mar
201
59,
244
8,33
711
0.9
TO
L/M
A-N
IM
ar-M
ay21
14.
822
,496
8,56
126
2.8
May
-Ju
l21
29.
56,
593
6,96
894
.6Ju
l-S
ep20
735
4,01
44,
291
93.6
Sep
-Dec
204
201,
630
2,37
068
.8A
ll10
215
14.7
5,30
36,
138
86.4
F-S
Dec
-Mar
200
0–
5,79
1–
CH
Mar
-May
211
4.8
4,90
06,
500
75.4
May
-Ju
l21
29.
52,
804
4,81
158
.3Ju
l-S
ep20
420
1,49
73,
689
40.6
Sep
-Dec
202
1024
01,
926
12.5
All
102
98.
81,
886
4,56
541
.3
F-F
Dec
-Mar
201
59,
244
8,33
711
0.9
Mar
-May
212
9.5
13,4
888,
561
157.
6M
ay-J
ul
213
14.3
5,84
46,
968
83.9
Ju
l-S
ep20
840
4,14
24,
291
96.5
Sep
-Dec
205
252,
326
2,37
098
.2A
ll10
219
18.6
5,18
56,
138
84.5
Not
es:
Inven
tory
(I)–
(cor
nd
eliv
erable
stock
s(1
,000
bu.)
wit
hin
the
del
iver
yp
erio
d).
Spre
ad
s(S
)–fu
ture
s-fu
ture
s(F
-F),
and
futu
res-
spot
(F-S
)C
hic
ago
(CH
)sp
reads
are
for
Marc
h1990
thro
ugh
May
2010
contr
act
s.F
-ST
OL
/M
A-N
Isp
read
s
are
for
Tol
edo/
Mau
mee
from
Mar
ch1990
thro
ugh
Dec
emb
er1999
contr
act
san
dN
ort
her
nIl
linois
Riv
erfr
om
Marc
h2000
thro
ugh
May
2010
contr
acts
.W
euse
TO
L/M
A-N
Ist
ock
sfo
rth
eF
-Fsp
read
as
itis
the
most
act
ive
del
iver
ylo
cati
on.
20
Table
2.
Seaso
nal
back
ward
ati
ons
and
stock
hold
ing
inth
eso
yb
ean
mark
et,
1990-2
010
Sp
read
mea
sure
Mon
ths
No.
Ob
s.S<
0&
I>0
%S<
0&
I>0
(1)
Avg.
I.(2
)A
vg.
I.(1
)as
aS<
0&
I>0
%of
(2)
F-S
Nov
-Jan
200
0–
4,74
1–
TO
L/M
A-N
IJan
-Mar
211
4.8
1,01
03,
895
25.9
Mar
-May
211
4.8
593
3,32
517
.8M
ay-J
ul
211
4.8
866
3,32
226
.1Ju
l-A
ug
204
201,
028
2,39
343
Aug-
Sep
203
1568
51,
611
42.5
Sep
-Nov
203
1535
01,
014
34.5
All
143
139.
174
52,
913
25.6
F-S
Nov
-Jan
200
0–
5,80
5–
CH
Jan
-Mar
210
0–
5,51
0–
Mar
-May
210
0–
5,26
1–
May
-Ju
l21
14.
84,
625
5,16
689
.5Ju
l-A
ug
205
251,
440
4,74
930
.3A
ug-
Sep
203
1589
54,
140
21.6
Sep
-Nov
205
2528
13,
019
9.3
All
143
149.
81,
137
4,81
823
.6
F-F
Nov
-Jan
201
51,
183
4,74
125
Jan
-Mar
212
9.5
1,20
63,
895
31M
ar-M
ay21
29.
564
83,
325
19.5
May
-Ju
l21
628
.62,
941
3,32
288
.5Ju
l-A
ug
2012
601,
833
2,39
376
.6A
ug-
Sep
2011
551,
226
1,61
176
.1Sep
-Nov
2010
5057
11,
014
56.3
All
143
4430
.81,
448
2,91
349
.7
Not
es:
Inve
nto
ry(I
)–(s
oyb
ean
del
iver
able
stock
s(1
,000
bu.)
wit
hin
the
del
iver
yp
erio
d).
Sp
read
(S)–
futu
res-
futu
res
(F-
F),
and
futu
res-
spot
(F-S
)C
hic
ago
(CH
)sp
reads
are
for
Janu
ary
1990
thro
ugh
May
2010
contr
act
s.F
-ST
OL
/M
A-N
I
spre
ads
are
for
Tol
edo/
Mau
mee
from
January
1990
thro
ugh
Nov
emb
er1999
contr
act
sand
Nort
her
nIl
linois
Riv
erfr
om
Jan
uar
y20
00th
rough
May
2010
contr
act
s.W
eu
seT
OL
/M
A-N
Ist
ock
sfo
rth
eF
-Fsp
read
as
itis
the
most
act
ive
del
iv-
ery
loca
tion
.
21
Table
3.
Seaso
nal
back
ward
ati
ons
and
stock
hold
ing
inth
ew
heat
mark
ets
,1990-2
010
Mar
ket
Spre
adm
easu
reM
onth
sN
o.O
bs.
S<
0&
I>0
%S<
0&
I>0
(1)
Avg.
I.(2
)A
vg.
I.(1
)as
a)
S<
0&
I>0
%of
(2)
CB
OT
F-S
Jul-
Sep
200
0–
12,8
88–
TO
L/M
AS
ep-D
ec20
00
–20
,786
–D
ec-M
ar20
15
5,67
419
,670
28.8
Mar
-May
211
4.76
2,51
717
,550
14.3
May
-Ju
l21
29.
5271
114
,600
4.9
All
102
43.
922,
403
17,0
7914.1
F-S
Ju
l-Sep
200
0–
2,34
4–
CH
Sep
-Dec
200
0–
4,27
6–
Dec
-Mar
200
0–
3,86
8–
Mar
-May
214
19.0
569
03,
443
20
May
-Ju
l21
314
.29
412,
728
1.5
All
102
76.
8641
23,
327
12.4
F-F
Jul-
Sep
201
52,
278
12,8
8817.7
Sep
-Dec
201
56,
615
20,7
8631.8
Dec
-Mar
205
258,
515
19,6
7043.3
Mar
-May
216
28.5
78,
820
17,5
5050.3
May
-Ju
l21
419
.05
1,17
314
,600
8A
ll10
217
16.6
76,
416
17,0
7937.6
KC
BT
F-S
Jul-
Sep
207
357,
547
8,65
587.2
KC
Sep
-Dec
206
3011
,061
15,1
1873.2
Dec
-Mar
209
4510
,883
13,2
6682
Mar
-May
219
42.8
69,
400
11,0
0485.4
May
-Ju
l21
942
.86
5,76
18,
719
66.1
All
102
4039
.22
8,84
011
,323
78.1
F-F
Jul-
Sep
206
304,
808
8,65
555.5
Sep
-Dec
204
209,
964
15,1
1865.9
Dec
-Mar
209
459,
879
13,2
6674.5
Mar
-May
2110
47.6
27,
802
11,0
0470.9
May
-Ju
l21
1047
.62
4,33
88,
719
49.8
All
102
3938
.24
7,15
411
,323
63.2
Not
es:
Inven
tory
(I)–
(whea
tdel
iver
ab
lest
ock
s(1
,000
bu.)
wit
hin
the
del
iver
yp
erio
d).
Spre
ad
(S)–
futu
res-
futu
res
(F-F
),fu
ture
s-
spot
(F-S
)C
hic
ago
(CH
),F
-ST
oled
o(T
OL
),an
dF
-SK
ansa
sC
ity
(KC
)sp
read
sare
for
Marc
h1990
thro
ugh
May
2010
contr
act
s.
We
use
TO
L/M
Ast
ock
sfo
rth
eF
-Fsp
read
inC
BO
Tw
hea
tas
itis
the
most
act
ive
del
iver
ylo
cati
on
.
22
Fig
ure
1.
Th
eSupply
of
Sto
rage
−505Price of storage
010
020
0In
vent
ory
Pan
el A
. The
Wor
king
cur
ve
−505Price of storage
010
020
0In
vent
ory
Pan
el B
. Alte
rnat
ive
supp
ly o
f sto
rage
rel
atio
nshi
p
23
Fig
ure
2.
Corn
pri
cesp
read
san
ddelivera
ble
stock
s,1990-2
010
−100102030
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
0025
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el A
. TO
L/M
A−
NI (
F−
S)
−100102030
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
0025
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el B
. Chi
cago
(F
−S
)
−10−50510
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
0025
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el C
. TO
L/M
A−
NI (
F−
F)
−10−50510
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
0025
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el D
. Chi
cago
(F
−F
)
Not
es:
TO
L/M
A-N
Ist
ands
for
Tol
edo/
Mau
mee
-Nort
her
nIl
lin
ois
,F
-Sd
enote
futu
res-
spot
and
F-F
den
ote
futu
res-
futu
res
spre
ad.
24
Fig
ure
3.
Soyb
ean
pri
cesp
read
san
ddelivera
ble
stock
s,1990-2
010
−100−50050100
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el A
. TO
L/M
A−
NI (
F−
S)
−100−50050100
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
00
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el B
. Chi
cago
(F
−S
)
−150−100−50050
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el C
. TO
L/M
A−
NI (
F−
F)
−150−100−50050
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
00
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el D
. Chi
cago
(F
−F
)
Not
es:
TO
L/M
A-N
Ist
ands
for
Tol
edo/
Mau
mee
-Nort
her
nIl
lin
ois
,F
-Sd
enote
futu
res-
spot
and
F-F
den
ote
futu
res-
futu
res
spre
ad.
25
Fig
ure
4.
Wheat
pri
cesp
read
san
ddelivera
ble
stock
s(C
BO
T),
1990-2
010
−50050100
Spread (Cents/bu./mo.)
010
,000
20,0
0030
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el A
. TO
L/M
A (
F−
S)
−50050100
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el B
. Chi
cago
(F
−S
)
−30−20−10010
Spread (Cents/bu./mo.)
010
,000
20,0
0030
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el C
. TO
L/M
A (
F−
F)
−30−20−10010
Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el D
. Chi
cago
(F
−F
)
Not
es:
TO
L/M
Ast
ands
for
Tol
edo/
Mau
mee
,F
-Sden
ote
futu
res-
spot
and
F-F
den
ote
futu
res-
futu
res
spre
ad
.
26
Fig
ure
5.
Wheat
pri
cesp
read
san
ddelivera
ble
stock
s(K
CB
T),
1990-2
010
−2002040Spread (Cents/bu./mo.)
010
,000
20,0
0030
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el A
. Kan
sas
City
(F
−S
)
−20−10010Spread (Cents/bu./mo.)
010
,000
20,0
0030
,000
Del
iver
able
sto
cks
(1,0
00 b
u.)
Pan
el B
. Kan
sas
City
(F
−F
)
Not
es:
F-S
den
ote
futu
res-
spot
and
F-F
den
ote
futu
res-
futu
res
spre
ad
.
27
Fig
ure
6.
Supply
of
stora
ge
for
delivera
ble
stock
sand
ship
pin
gce
rtifi
cate
s,1990-2
010
−10−50510Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
00
Tot
al d
eliv
erab
le s
tock
s (1
,000
bu.
)O
utst
andi
ng s
hipp
ing
cert
ifica
tes
(1,0
00 b
u.)
Pan
el A
. Cor
n
−150−100−50050Spread (Cents/bu./mo.)
05,
000
10,0
0015
,000
20,0
0025
,000
Tot
al d
eliv
erab
le s
tock
s (1
,000
bu.
)O
utst
andi
ng s
hipp
ing
cert
ifica
tes
(1,0
00 b
u.)
Pan
el B
. Soy
bean
s
Not
es:
Dat
afo
rdel
iver
able
stock
san
dsh
ippin
gce
rtifi
cate
sare
from
Marc
h2000
thro
ugh
May
2010
for
corn
,and
from
January
2000
thro
ugh
May
2010
for
Soy
bea
ns.
28