Michael K. Adjemian, Philip Garcia, Scott Irwin, 

and Aaron Smith

Non-Convergence in Domestic 

Commodity Futures Markets: Causes, 

Consequences, and Remedies

Economic

Research

Service

Economic 

Information

Bulletin

Number 115

August 2013

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Adjemian, Michael K., Philip Garcia, Scott Irwin, and Aaron Smith. 

Non-Convergence in Domestic Commodity Futures Markets: Causes, 

Consequences, and Remedies, EIB-115. U.S. Department of Agriculture, 

Economic Research Service, August 2013.

Cover photo credit: Shutterstock.
United States Department of Agriculture

Economic 

Research 

Service

Economic

Information

Bulletin

Number 115

August 2013

Abstract

During most of 2005-10, the price of expiring U.S. corn, soybeans, and wheat futures 

contracts settled much higher than corresponding delivery market cash prices. Because 

futures contracts at expiration are commonly thought to be equivalent to cash grain, this 

commodity price non-convergence appeared inconsistent with the law of one price. In 

addition, sustained non-convergence concerns market participants, exchanges, and policymakers because it can make hedging less effective, send confusing signals to the market, 

threaten the viability of a contract, and ultimately lead to a misallocation of agricultural 

resources. This report summarizes prominent theories that have been offered to explain 

non-convergence, including a new model that explains how the structure of a competitive delivery market can generate a positive expiring basis. The data support this delivery 

market theory over alternative explanations. Finally, we discuss various policy levers that 

have been offered to address non-convergence, as well as their likely impacts. 

Keywords: commodity futures, index funds, grains, non-convergence, price discovery, 

risk management, speculation, storage

Acknowledgments

The authors thank the following reviewers: Linwood Hoffman, Mark Jekanowski, 

Steve MacDonald, and Danny Pick, U.S. Department of Agriculture, Economic 

Research Service; Irene Xiarchos, USDA, Offi ce of the Chief Economist; Roger Cryan, 

USDA Agricultural Marketing Service; Randy Fortenberry, Professor of Agricultural 

Economics, Washington State University; Robert Myers, Professor of Agricultural 

Economics, Michigan State University; and anonymous reviewers. Thanks to Priscilla 

Smith and Curtia Taylor of ERS for editorial and design assistance.

Michael K. Adjemian, Philip Garcia, Scott Irwin, 

and Aaron Smith

Non-Convergence in Domestic 

Commodity Futures Markets: Causes, 

Consequences, and Remedies
ii

Non-Convergence in Domestic Commodity Futures Markets: Causes, Consequences, and Remedies, EIB-115

Economic Research Service/USDA

About the Authors

Michael K. Adjemian is an economist at the U.S. Department of Agriculture, Economic Research 

Service (ERS). Philip Garcia is the T.A. Hieronymus Distinguished Chair in Futures Markets and 

Director of the Offi ce for Futures and Options Research in the Department of Agricultural and 

Consumer Economics, University of Illinois at Urbana-Champaign. Scott H. Irwin is the Laurence 

J. Norton Professor of Agricultural Marketing in the Department of Agricultural and Consumer 

Economics, University of Illinois at Urbana-Champaign. Aaron Smith is an Associate Professor in 

the Department of Agricultural and Resource Economics at the University of California, Davis. 
iii

Non-Convergence in Domestic Commodity Futures Markets: Causes, Consequences, and Remedies, EIB-115

Economic Research Service/USDA

Contents

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

The Role of Futures Markets Under Non-Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

The Delivery Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

Why Did Contracts Fail To Converge? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Delivery Market Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Alternative Explanations for Non-Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Implications of Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Policy Options To Improve Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Change the Delivery Instrument Storage Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Force Load-Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

Change the Futures Contract Terms To Require Cash Settlement . . . . . . . . . . . . . . . . . . . .22

Make Delivery Easier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

Tighten Speculative Position Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
www.ers.usda.gov

What Is the Issue?

From 2005 to 2010, many corn, soybean, and wheat futures contracts repeatedly expired at prices 

much higher than corresponding delivery market cash prices. In principle, these futures contracts 

can be exchanged for the physical commodity at expiration, so their prices should converge with 

the price of the underlying cash commodity. This sustained period of non-convergence, as well as 

its magnitude, was unprecedented in domestic commodity markets. This was a cause of concern 

for many market participants, policymakers, and economists, who worried that those convergence 

failures signaled a weakening of the traditional price discovery and risk management roles of 

these futures markets, and ultimately, a less effi cient allocation of agricultural resources.

What Did the Study Find?

Market observers offered several explanations for the non-convergence puzzle, but none was 

tested rigorously and shown to explain the problem. One theory is that “excessive speculation” by 

nontraditional fi nancial fi rms, like Commodity Index Traders (CITs), overpowered the ability of 

arbitrageurs to balance derivative and cash prices, leading to non-convergence in wheat markets. 

While it is true that CIT trading increased substantially during the time when non-convergence 

became a problem, this theory suffers from several theoretical limitations. For example, if 

purchasing behavior by these fi rms drove up the derivative price relative to the cash price, their 

equally sizable selling behavior before contract expiration should serve to force those prices 

together, leading to convergence. To maintain portfolio exposure, CITs enter one contract and 

then roll to the next, buying at fi rst and holding it until it almost expires, then selling it to buy the 

next expiration. 

In another account, production and trade patterns for these commodities shifted away from longestablished delivery markets, limiting the ability of fi rms to arbitrage away the price difference 

between the two markets by engaging in the delivery process. On the other hand, the commercial 

fl ow for wheat in particular has bypassed these delivery markets for decades, so this theory does 

not adequately explain convergence problems observed since 2005.

United States Department of Agriculture

A report summary from the Economic Research Service August 2013

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of economic research and 

analysis from the U.S. 

Department of Agriculture, 

providing timely information on economic and policy 

issues related to agriculture, 

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rural America.

Find the full report at 

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publications/eib-economic-informationbulletin/eib-115.aspx

Michael K. Adjemian, Philip Garcia, Scott Irwin, 

and Aaron Smith

Non-Convergence in Domestic 

Commodity Futures Markets: Causes, 

Consequences, and Remedies
We conclude that recent convergence failures in grain markets are attributable to inconsistent storage rates for 

the physical commodity and its derivative, a delivery instrument. Specifi cally, the exchange-set storage rate of 

the delivery instrument was too low relative to the true price of storage. The resulting wedge between the costs 

of holding delivery instruments and storing physical grain led to an expansion of the delivery month basis, 

preventing convergence even in a competitive market. The available empirical evidence fi ts this storage rate argument: inventories, which drive the wedge, are the most important factor in explaining the change in the expiring 

basis. In contrast, no empirical support was found for the CIT theory: trading activities by these fi rms are not 

found to affect the change in the basis over time, at any acceptable level of statistical signifi cance. 

How Was the Study Conducted?

This report summarizes the basic theory of how the storage-rate problem caused expiring futures to diverge from 

cash prices and shows how the wedge explains the large magnitudes of recent non-convergence. We also discuss 

prominent alternative explanations for non-convergence and show why they are not supported theoretically or 

empirically. Based on these fi ndings, we discuss the likely impact of various proposed policy options on the prospect of achieving convergence in grain and soybean markets.

www.ers.usda.gov
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Non-Convergence in Domestic Commodity Futures Markets: Causes, Consequences, and Remedies, EIB-115

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Introduction

A futures contract represents the obligation to trade a standardized quantity and quality of a given 

commodity at a specifi ed future period for an agreed-upon price. Commodities such as grains and 

oilseeds are traded in many locations across the United States, so futures exchanges have designated certain markets as delivery markets, identifying those areas where the liquidation of futures 

contracts by delivery is allowed. A cash price is the price for immediate exchange between buyer 

and seller, so the price of a futures contract, or the futures price, is generally conceived of as representing the expected cash price of the commodity in the delivery market, during the specifi ed 

delivery period.1 Convergence implies that these prices draw together when the futures contract 

expires.

Under non-convergence, however, the price of the expiring futures contract does not equilibrate 

with the cash market price in the delivery period. For example, on July 1, 2008, the price for a July 

2008 Chicago Board of Trade (CBOT) wheat futures contract closed at $8.50 per bushel. Even 

though that contract was eligible for immediate physical delivery, the going cash price in the Toledo, 

Ohio, delivery market was only $7.18 per bushel. An expiring basis of $1.32 is much larger than the 

normally observed range of 6 to 8 cents per bushel often attributed to delivery market frictions associated with the cost of load-out (Irwin et al., 2008; Kunda, 2010). During 2005 to 2010, U.S. corn, 

soybeans, and wheat markets failed to converge at these unprecedented levels for a sustained period, 

as shown in fi gure 1. From 1986 to 2005, the average expiring basis at the cash markets in the chart 

was 1.8 cents, 1.8 cents, 10.8 cents, and -1.5 cents, for CBOT corn, soybeans, and wheat, and Kansas 

City Board of Trade (KCBT) wheat, respectively. From 2005 to 2010, the average expiring basis at 

these same locations and markets was 18.2 cents, 20.3 cents, 49.2 cents, and 32.8 cents.

Because an expiring futures contract should be equivalent to cash market grain, non-convergence 

appears to be inconsistent with the law of one price and, therefore, to present an arbitrage opportunity. During 2005-10, the expiring futures price often exceeded the cash price for these commodities, so riskless profi ts apparently could be achieved by acquiring grain at low cash market prices 

1Notably, Keynes (1930) and Hicks (1939) argued that hedgers compensated speculators for providing them with risk 

management services; in a market with short hedgers, for example, the futures price would understate the expected future 

cash price. As the market converged (and the futures price increased relative to the expected cash price), the speculator 

would earn a premium for shielding the hedger from price risk. However, the empirical evidence for this risk premium 

in agricultural futures markets is weak (Chang, 1985; Fishe and Smith, 2011; Frank and Garcia, 2009; Hartzmark, 1987; 

and Hartzmark, 1991). 

Michael K. Adjemian, Philip Garcia, Scott Irwin, 

and Aaron Smith

Non-Convergence in Domestic Commodity 

Futures Markets: Causes, Consequences, 

and Remedies
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Economic Research Service/USDA

and delivering it at high prices through short futures market positions in the expiring contract. 

Done simultaneously, this trading strategy would place downward pressure on the futures price, and 

upward pressure on the cash price, until the two converged (Hieronymus, 1977). However, starting 

in late 2005, as more and more expirations failed to achieve convergence between futures and cash 

prices, some observers began to worry that recent changes in the structure of the market weakened 

the capacity for arbitrage and that the contract was “broken” and unable to fulfi ll its traditional role.

Figure 1

Futures price at expiration minus cash price, 1986-20131

1

City in parentheses is cash price location. Toledo ceased to be a delivery location for corn and soybeans in 1999, so we switch to the Illinois 

River North of Peoria at that time. 

CBOT = Chicago Board of Trade. KCBT = Kansas City Board of Trade.

Source: Garcia, Irwin, and Smith, 2011; and USDA, Agricultural Marketing Service.

Panel A

CBOT corn (Toledo, 86-99; IL River North, 00-12)

Panel B

CBOT soybeans (Toledo, 86-99; IL River North, 00-12)

Panel C

CBOT wheat (Toledo)

Panel D

KCBT wheat (Kansas City)

-25

0

25

50

75

100

1986 1990 1994 1998 2002 2006 2010 2010

Cents/bushel Cents/bushel

Cents/bushel Cents/bushel

-25

0

25

50

75

100

1986 1990 1994 1998 2002 2006

-25

0

25

50

75

100

125

150

175

200

1986 1990 1994 1998 2002 2006 2010

-25

25

50

75

100

125

150

175

200

0

1986 1990 1994 1998 2002 2006 2010
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Non-Convergence in Domestic Commodity Futures Markets: Causes, Consequences, and Remedies, EIB-115

Economic Research Service/USDA

Figure 2

Daily open interest, 1998-2010 

Note: The figure represents the end-of-day outstanding contracts for the nearby series in each market, rolled over 30 calendar days prior to 

contract expiration. 

CBOT = Chicago Board of Trade. KCBT = Kansas City Board of Trade.

Source: Chicago Mercantile Exchange Group (CME) and Kansas City Board of Trade. 

Open interest (number of contracts)

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

CBOT corn CBOT soybeans

CBOT wheat KCBT wheat
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The Role of Futures Markets Under Non-Convergence

Futures markets provide several important economic functions for agricultural commodities: price 

discovery, the opportunity for risk management, and the transmission of storage signals via the term 

spread. Unpredictable convergence undermines confi dence in the market’s ability to perform each 

of these functions and can lead to signifi cant economic damage. When the market fails to converge, 

a commodity’s expiring futures price lies somewhere above or below its corresponding price in the 

cash market. As a result, non-convergence implies that prices discovered in a futures market are an 

inaccurate representation of expected cash market prices in the expiration month. 

If convergence failure is further characterized by futures and cash price series that bear an unpredictable relationship, the risk management benefi ts of hedging may be compromised. As an example, 

consider a short futures hedge, which involves a long cash position—say for a producer who expects 

to reap a harvest—and a short position in the futures market. This sort of strategy is designed to 

reduce risk exposure by compensating cash market losses (when cash prices fall) with short futures 

position gains (when futures prices fall). Now consider a “normal” market (i.e., a market in which 

the futures price exceeds the cash price by an amount equal to the price of storing the commodity 

from now until the futures contract expires). In this case, the market has set the futures price to 

equal the expected cash price at expiration and it is expecting the cash price to increase at a rate 

equal to the price of storage so that convergence occurs at expiration. In the interim, news may enter 

the market—say about the size of the harvest—and shift prices. In a converging market, such news 

affects the cash and futures prices equally (holding constant the price of storage). For each dollar 

lost by a lower expected cash price, the hedger gains an offsetting dollar on his futures position.

In a non-converging market, the hedger is still protected from price risk as long as the futures and 

cash prices trend one-for-one in the same direction. Cash market gains and losses are exactly offset 

by futures market gains and losses. Under this scenario, cash and futures prices do not converge 

to each other, but they converge to a predictable basis. On the other hand, if the basis at expiration 

exhibits random fl uctuations, then a hedger is not insulated from price risk. Because the utility of 

hedging depends on predictable basis relationships, novel or unpredictable basis phenomena can 

make hedging much less attractive.

Persistent non-convergence that suffi ciently degrades hedging effectiveness threatens the viability 

of a futures market, since its hedgers lose interest in trading (Irwin et al., 2011; Peck and Williams, 

1991; Working, 1953; Working, 1970). Moreover, unhedged merchandisers and producers face 

substantial price risks and welfare losses that jeopardize the conventional operation of the food 

production, marketing, and consumption chain. Of course, non-convergence need not threaten 

hedging effectiveness as long as its degree is predictable and participants are well-informed. When 

non-convergence is erratic, the timing of the placing and lifting of hedges will impact hedges’ 

profi tability, making hedging risky. It is useful to note that the unprecedented level of recent corn, 

soybean, and wheat market non-convergence has not affected the level of futures trading noticeably. 

Compared to the previous 5-year period, fi gure 2 shows that the average amount of contracts held 

by traders in each market increased by about a factor of two in 2005-10. At the same time, trading 

volume for commercial traders, who engage in hedging, also increased substantially.2

2See the Commodity Futures Trading Commission (CFTC) website for a graphical depiction of historical trading 

volume by trader type in the CBOT markets, at http://www.cftc.gov/OCE/WEB/index.htm.
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The Delivery Process

For many agricultural commodities, such as corn, soybeans, and wheat, terms of futures contracts are 

satisfi ed through a process that is closely related to physical delivery but does not require the movement 

of any grain.3 As the contract nears expiration, the short side of a futures contract initiates the delivery 

sequence by choosing to make delivery rather than offset its position and notifi es the exchange accordingly. See fi gure 3 for an explanation of the contract termination choices available to a short trader. The 

exchange then informs the oldest outstanding long position holder of the responsibility to take delivery 

from the short. The futures contract is terminated when the short provides the long with delivery 

instruments in return for payment. Delivery instruments for KCBT wheat are warehouse receipts, 

which give the holder title to actual grain in storage at a storage facility. Shipping certifi cates are used 

in CBOT markets; these represent for the holder the right, but not the obligation, to demand load-out 

of the commodity from a particular shipping station. Shipping certifi cates also give the short more 

fl exibility in the delivery process because they do not represent physical grain in a regular warehouse, 

which takes up storage space that they might otherwise use. Instead, shipping certifi cates represent a 

commitment to provide grain when the certifi cate is canceled. 

Delivery instruments provide the holder with access to grain, are transferrable, and do not require 

load-out within a specifi ed timeframe, so long as the holder pays a storage fee. Importantly, the 

maximum fee for holding a delivery instrument is set by the exchange. This fee, which is assessed 

daily, is paid to the regular-for-delivery warehouse, or “regular fi rm,” that originated the delivery 

instrument. In return, the regular fi rm is responsible for presenting the grain to the holder, once loadout is requested. Regular fi rms regulate the delivery process: only they are able to create original 

delivery instruments. Before initiating delivery, other short position holders must acquire either new 

instruments from regular fi rms or existing instruments from other parties. 

Typically, few deliveries are executed because trading the commodity through the delivery process 

is more expensive than offsetting the futures position and transacting directly with a trading 

partner. Grain and soybean futures markets are better suited to facilitate risk management and price 

discovery than to serve as a vehicle for exchange of physical title. In fact, extensive deliveries are a 

sign that a contract is out of balance, meaning that the delivery terms favor one side of the market 

or the other; contract design problems that encourage substantial deliveries cause futures markets 

to fail (Hieronymus, 1977). In the extreme case, favored traders may attempt to use market power 

during the delivery period to artifi cially alter the price of the futures contract and make sizable 

profi ts (Pirrong, 1993; Pirrong, 2001). When the contract is in balance and the market works properly, short and long position holders usually prefer to offset their futures positions. In doing so, both 

sides avoid the costs associated with the delivery process (e.g., placing grain in and out of storage, 

weights and grading fees, storage fees, interest costs, and the opportunity cost of backing the 

delivery instruments). 

The price difference between futures contracts with different delivery dates is commonly referred 

to as the term spread or “carry.” In a well-functioning market, this difference represents the return 

to physically storing the commodity between those dates. To market observers, that return is also 

3CBOT and KCBT rulebooks explain the delivery processes for grains in detail and can be found at www.cmegroup.

com/rulebook/CBOT and http://www.kcbt.com/rule_book_kcbt.html, respectively. Futures contracts for many other 

commodities require immediate load-out or are settled in cash at a benchmark cash market price; as a result, convergence 

in these markets is assured. 
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Economic Research Service/USDA

known as the price of storage. Working (1949) and Brennan (1958) showed that the price of storage 

is determined by the storage market equilibrium, which occurs at the intersection of the demand 

and supply of storage. Assuming a fi xed supply of storage, a large harvest produces large inventories 

and high demand for storage services, which in turn increases the price of storage. In contrast, the 

storage fee for delivery instruments is written into futures contracts and set by the exchange; it does 

not necessarily represent the price of storage. 

Figure 3

Contract termination for a short trader

NOTE: In the figure, nodes represent decision points, F is a futures price, P is a cash price, C is the expected number of 

months until cancelation of the delivery instrument, S is the monthly cost of physical storage, D is the price of the delivery 

instrument, and R is the contract storage rate on that instrument. For simplicity, the time value of money is not considered 

(i.e., the real interest rate is zero).

Make delivery

Regular trading 

period (t=0...T)

Notice period 

(t=T+n for n=0...N)

Delivery period (t=T+N+e, for e=0...E; 

T+N+E = contract expiration day)

Short a futures contract 

at time 0 for Price F0

Offset by taking a long futures 

contract at time t. Profit = Ft - F0

Offset by taking a long 

futures contract at time t. 

Profit = Ft - F0

Purchase a delivery instrument 

for Dt

 and provide it to the taker. 

Profit = F0

 - Dt

Short is not a regular firm. 

Purchase a delivery instrument 

for Dt

 and provide it to the taker. 

Profit = F0

 - Dt

Short is a regular firm:

Notify exchange of intent 

to make delivery

Issue a delivery 

instrument, and 

provide it to the 

taker. Purchase 

and store cash 

grain for price Pt

to cover the 

instrument. 

Profit = F0

 + 

C*(R-S) - Pt
7

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Economic Research Service/USDA

Because term spreads provide, in Working’s words, a “direct measure of the return to storing the 

commodity,” market participants use them as a guide to time their purchase or sales decisions. But, 

because futures contracts convert to delivery instruments upon expiration, the term spread cannot 

exceed full carry, the point at which it refl ects the total cost of holding the delivery instrument over 

time, including fi nancing costs.4 When the cost of holding delivery instruments understates the cost 

of storing grain, the term spread understates the price of physical storage. One effect is that uninformed participants may misinterpret the resulting term spread, triggering a potential misallocation 

of resources by storing less than the optimal amount of grain. 

4Otherwise, an arbitrageur could earn a riskless profi t by purchasing a delivery instrument, shorting a futures contract, 

storing the instrument, and then delivering it at contract expiration.
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Why Did Contracts Fail To Converge?

This section begins by summarizing the work of Garcia, Irwin, and Smith (2011) (referred to as 

GIS, from here), who attribute non-convergence to the institutional structure of the delivery market.5

Next, alternative explanations for non-convergence are described. Finally, we share important results 

of GIS’ empirical tests, which support the delivery market explanation for non-convergence. 

Delivery Market Design

GIS shows how non-convergence can arise through the interaction of rational, competitive market 

participants. If the “wedge,” or the price of physical storage minus the cost of holding a delivery 

instrument, is positive, the cost of holding delivery instruments is cheaper than storing grain physically. However, both represent the same amount of future grain. A fi rm that is short and makes 

delivery on a futures contract will not earn a large enough storage fee from the delivery instrument 

as compensation for the cost of storing the grain that backs the instrument. Such a fi rm therefore 

seeks compensation by issuing the delivery instruments at a high price relative to the price of cash 

grain. Recall that the price of a futures contract represents the market value of the delivery instrument at contract expiration, which can differ from the cash market grain price. As a result, fi rms 

are only willing to make futures market deliveries if the expiring futures price exceeds the price of 

cash grain by an amount suffi cient to compensate them for the artifi cially low storage fees they will 

receive on their outstanding instruments, for as long as the grain is expected to remain in storage.6

To see formally why non-convergence works this way, imagine a market with two types of traders. 

Regular fi rms can store grain and can satisfy the short side of expiring futures contracts by making 

delivery, originating transferable delivery instruments that entitle the holder to a claim on grain that 

can be exchanged at any time, in return for the immediate-delivery futures price. Financial fi rms 

cannot store grain or issue delivery instruments, but they may settle the long side of an expiring 

futures contract by taking delivery, accomplished by paying the futures price for immediate delivery 

and accepting the delivery instrument. Financial fi rms can hold the delivery instrument indefi nitely, 

so long as they pay an exchange-set storage fee to the regular fi rm. Regular fi rms and fi nancial 

fi rms face borrowing costs, although the latter’s may be lower due to possible advantages in capital 

markets. To describe the causes of non-convergence in the simplest possible terms, GIS specifi es 

that one rational representative fi rm of each type interacts over two trading periods, and both fi rms 

operate competitively and have identical information. The two fi rms trade in cash, futures, and 

delivery markets in the fi rst time period, and futures and cash prices converge in the second period.7

Regular fi rms choose among three commodity storage options: (1) holding unhedged physical grain 

until sale at the period 2 cash price; (2) hedging grain by entering the short side of a futures contract 

for delivery in the following period; or (3) making delivery on a futures contract in period 1 by 

issuing a delivery instrument to the fi nancial fi rm and repurchasing the delivery instrument in period 

2. Given the expectation of convergence in period 2, the absence of arbitrage using options 1 and 2 

5Others, such as Heath (2009) and Aulerich et al. (2011), have also attributed non-convergence to market design issues. 

We focus on Garcia, Irwin, and Smith (2011) because it is the most complete explanation of the problem.

6See fi gure 4 (and its explanation on page 10) for a graphical representation of how the wedge generates non-convergence in a competitive market.

7In addition to introducing a more complete version of the two-period model that we describe, GIS expand it to an 

infi nite horizon that does not arbitrarily impose convergence at some future date.
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equates the futures price for later delivery to the period 1 cash price plus the total cost of physically 

storing the commodity. In effect, option 3 is equivalent to storing grain in the delivery market: when 

the fi nancial fi rm delivers the instrument back in period 2, the regular fi rm converts it into grain for 

sale in the cash market. 

If the storage fee is set low enough, the return to option 3 becomes attractive to the fi nancial 

fi rm, which will demand as many delivery instruments as the regular fi rm is willing to offer.8 By 

taking delivery, the fi nancial fi rm pays the futures price for immediate delivery and the storage 

fee in period 1, but earns the futures price for later delivery, discounted by its capital cost, once it 

redelivers the instrument back to the regular fi rm in the following period.9 This strategy remains 

attractive to the fi nancial fi rm as long as the deferred futures price exceeds the price for immediate 

delivery by enough to cover the storage fee and capital costs. Because it behaves competitively, the 

fi nancial fi rm would bid down the term spread until it reaches full carry, which removes the opportunity for making excess profi ts. From the perspective of the fi nancial fi rm, a term spread at full 

carry represents equilibrium.

The supply of delivery instruments is determined by the regular fi rm. If the expiring futures price 

plus the storage fee is larger than the cost of issuing delivery instruments plus the discounted futures 

price for later delivery, the regular fi rm will choose to make delivery on futures contracts, issuing 

delivery instruments and storing grain in the delivery market. From the regular fi rm’s perspective, 

this option partially subsidizes the storage costs for its grain, which never even needs to leave the 

warehouse. Furthermore, by issuing these delivery instruments, the regular fi rm effectively gains 

access to credit at the rate available to the fi nancial fi rm.

Non-convergence occurs when the storage fee is set too low. For example, say a large harvest leads 

to relatively plentiful inventories and therefore creates a high demand for storage space. This high 

demand forces the physical price of storage to exceed the cost of holding delivery instruments 

thereby creating a positive wedge. At the competitive market equilibrium, the wedge generates 

convergence failure because it creates a demand for delivery instruments that would increase the 

unconstrained futures term spread beyond the level of full carry. But because the term spread is 

capped at full carry, it understates the true price of physical grain storage. As both cash grain and 

the delivery instrument represent the same amount of period 2 grain, their present price must differ 

by the difference of the storage costs over the interim (i.e., the expiring futures price must rise above 

the current cash price to compensate the regular fi rm for receiving too low a storage fee on the 

delivery instruments it issues). 

In effect, the wedge creates a non-convergence by decoupling the expiring futures contract from 

the cash grain market, since the delivery instruments will not be converted to grain until the second 

period. The low storage fee leads expiring futures contracts to instead refl ect the price of issuing 

delivery instruments—the price of period 2 grain rather than period 1 grain. GIS shows also that the 

8In the model, the demand for delivery instruments is perfectly elastic. In a market with warehouse receipts, such as 

the KCBT, the number of delivery instruments is capped at the amount that accounts for all the space in regular-for-delivery warehouses. For corn and soybeans, the Chicago Mercantile Exchange Group (CME) limits the amount of shipping 

certifi cates that each regular fi rm may issue based on its throughput and net worth; the exchange adds a storage capacity 

requirement for wheat contracts. In 2009, the CME placed limits on the number of shipping certifi cates a fi nancial fi rm 

may hold. See www.cmegroup.com/rulebook/fi les/CBOT_RA0903-1.pdf. 

9Aulerich, Fishe, and Harris describe the embedded real option that non-convergence assigns to delivery instruments 

(2011). 
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magnitude of convergence failure increases as the fi nancial fi rm’s borrowing costs become cheaper 

relative to the regular fi rm, since that reduces the value of full carry and expands the wedge.

Figure 4 is a graphical depiction of a simplifi ed version of the model. In each panel, the fi rst fi gure 

represents the storage market. The second shows the cash market (C) prices over three or four time 

periods along with futures (Fi

) delivered in each intervening time period (t

i

). Each time period, the 

cash price increases by an amount equal to the price of physical storage. This increase compensates the owners of the commodity for the cost of storage. We construct the fi gures so that all prices 

converge in the fi nal period for every panel in the chart. 

Panel A depicts a market in which the price of storage is positive but not as large as the delivery 

instrument storage rate (Pbar). The term spread is large enough to compensate for the price of storage 

(PI

), and the market converges at all periods. Convergence is represented by the gray and orange 

dashed lines (futures prices on two contracts) converging to the green dashed line (cash price). In 

panel B, a large harvest at t

0 leads to an excess commodity supply that drives the demand for storage 

services higher (to DII) and increases the market price of storage (to PII) and thus causes cash prices 

to increase at a higher rate. Because the delivery instrument storage rate (Pbar) is suffi ciently high, 

the term spread (the difference between F2 and F1) is able to expand suffi ciently to express the 

market price of storage, and futures and cash prices still converge. 

In Panel C, the maximum storage rate on the delivery instrument is set too low, so the wedge is 

positive. This wedge is not expected to persist after t

2, so the futures price converges to cash in t2

(the dashed orange line converges to the green spot price line). Between t

1 and t2, the term spread is 

capped at Pbar to prevent arbitrage on delivery instruments. The term spread cannot expand to the 

price of grain storage (PII), so it understates the true price of storage. Therefore, the price of delivery 

instruments at t

1, F1, must rise above the current cash price, C, to compensate the regular fi rm for 

the low storage rate it earns by issuing delivery instruments. Now, F1 is “decoupled” from the cash 

price—the futures contract for delivery in t

1 no longer represents the expected cash price at t1, but 

instead, the expected price of the delivery instrument at expiry: the cash price plus w.

In panel C, the wedge expires after period 1; panel D shows how the magnitude of non-convergence increases as the expected life of the wedge rises (now, through period 2). Once again, the 

no-arbitrage condition caps the term spread between all futures prices at Pbar, so it cannot expand 

to refl ect PII. Now, F2 does not converge with the cash price, but instead realizes the cash price at t

2

plus w. And when F1 delivers at t

1, the expiring basis is even larger than it is in Panel C—now 2w—

refl ecting the fact that the wedge is expected to last over two periods from t

0 to t2. 

On the other hand, if the wedge is not positive, the grain market converges. For example, if an unexpectedly small harvest drives the price of physical storage below the level required for the fi nancial fi rm to demand delivery instruments, any delivery instruments issued would immediately be 

converted to grain (i.e., load-out would occur). Without a positive wedge, the term spread refl ects 

the price of physical storage, and the expiring futures price is able to adjust to the current cash price. 

The basis for the expiring futures contract is zero, so the market converges. A negative wedge generates a term spread that is lower than full carry, and the market likewise converges (see panels A and 

B in fi gure 4).

In addition to inventory levels, the model predicts that other variables can affect convergence. An 

increase in the maximum delivery instrument storage rate lowers the demand for delivery instruments, reducing the disparity between futures and cash prices, as does a higher borrowing cost for 

fi nancial fi rms. Likewise, the expiring basis is reduced if the regular fi rm faces smaller physical
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Figure 4

Non-convergence is caused by the wedge

Panel A: Convergence when the demand for inventories is normal

C, Cash price

at ti

F1, Futures for delivery

at t1

F2, Futures for delivery

at t2

F3, Futures for delivery

at t3

S

D I

P I

P II

D II

S

P grain P storage

Inventory t time 0 t 1 t 2

P I

P I

Inventory t time 0 t 1 t 2

P bar

P bar

P II

P II

Panel B: Convergence when the demand for storage increases, and the delivery instrument storage rate is high enough

—continued
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Figure 4

Non-convergence is caused by the wedge, continued

Note: PI and PII represent the price of storage under demand levels DI and DII; storage supply is given by S. Pbar is the maximum storage rate 

on the delivery instrument. C is the cash market price; Fi is the futures contract price for delivery at ti for i=1,2,3. The wedge is represented by 

w. A positive wedge signifies non-convergence. For simplicity, the chart assumes no time value of money.

Panel C: Non-convergence at t1 when the demand for inventories increases and the delivery instrument storage rate is too low

Inventory

Panel D: The magnitude of non-convergence at t1 increases when the wedge is expected to last for a longer period of time

P II

P bar

w

D II

S

Inventory

P bar

w

t time 0 t 1 t 2

P II

P bar

w

t time 0 t 1 t 2 t 3

D

II

S

P II

P II

w

2w

PII

PII

PII

Pbar

Pbar
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How Non-Convergence Occurs in a Competitive Market

1. The market price of physical storage is high (e.g., a large harvest generates a high demand 

for storage). In fi gure 4, panel C, demand increases to DII.

2. The exchange-set futures contract storage fee is too low, leading to a “wedge” between the 

price of storage and the cost of holding delivery instruments (w in fi gure 4). 

3. The wedge makes the physical storage of grain unattractive to the regular fi rm, who instead 

seeks to issue a delivery instrument for a high price—effectively store grain in the delivery 

market—earning the return from issuing delivery instruments (the expiring futures price 

plus the storage fee).

4. With a low storage fee, taking delivery becomes appealing for the fi nancial fi rm, which 

demands as many delivery instruments as the regular fi rm will issue as long as the term 

spread is suffi cient to compensate it for the storage fee plus its borrowing costs (full carry).

5. The equilibrium futures term spread is capped at full carry (Pbar in fi gure 4), which is lower 

than the true price of physical storage (PII in fi gure 4).

6. Because the cash grain and the delivery instrument represent the same amount of future 

grain, their present price must differ by the present value of their storage costs over the 

interim, so the futures price fails to converge to the cash price. In fi gure 4, panel C, F1>C at 

t

1. In panel D, the expiring futures price exceeds the cash price at both t1 and t2. 

A Small Wedge Can Generate a Large Degree of Non-Convergence

(a) Delivery instrument storage rate/month 5 cents 5 cents 5 cents

(b) Market price of storage/month 10 cents 10 cents 10 cents 

(c) Wedge/month = maximum[(b) – (a), 0] 5 cents 5 cents 5 cents

(d) Expected length of time that wedge > 0 6 months 12 months 24 months

(e) Basis at expiration = (c) x (d) 30 cents 60 cents $1.20

Note: For simplicity, the calculation in (e) does not account for the time value of money.

The Wedge Drives the Basis and the Futures Term Spread

Non-convergence: Wedge > 0 ⇒ Basis > 0 and Spread = Full Carry

Convergence: Wedge = 0 ⇒ Basis = 0 and Spread = Full Carry

Convergence: Wedge < 0 ⇒ Basis = 0 and Spread < Full Carry
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storage costs or capital costs, since those costs shift the supply of storage curve to the right. 

Providing the regular fi rm with monopoly power in grain storage raises the expected price of storage 

and expands the wedge, although the latter is still determined by the difference between the price of 

physically storing grain and the cost of holding delivery instruments.

Extending this framework to a multiple-period model, GIS shows that the expiring basis in any period 

becomes the present value of the expected stream of future wedges for as long as they are predicted to 

remain positive (see panel D in fi gure 4). The basis must be large enough to compensate the regular 

fi rm for the too-low storage rate for as long as the fi nancial fi rm is projected to hold the instrument. 

Consequently, even a relatively small wedge can generate a large degree of non-convergence if it is 

expected to persist long enough, accounting for the remarkably wide basis observed during recent 

non-convergence episodes. For example, a wedge of just 5 cents per month that is expected to persist 

for 2 years implies a basis of about $1.20 (see box, “A Small Wedge Can Generate a Large Degree of 

Non-Convergence,” p. 13).

Alternative Explanations for Non-Convergence

One theory is that large long positions held by passive commodity index traders (CITs) led to a 

breakdown between the Chicago futures market and the cash market for wheat (United States 

Senate Permanent Subcommittee on Investigations, 2009). This theory is part of a larger movement 

that argues fi rms who trade futures in large volume but do not have a directional interest in the 

underlying commodity price bias derivatives prices away from their fundamental level (Masters, 

2011; Soros, 2008; UNCTAD, 2011). CITs sell fi nancial instruments like index swaps and facilitate 

the sale of exchange-traded notes and exchange-traded funds to customers who seek investment 

exposure to commodity prices. To offset their risk, CITs purchase long positions in commodity 

futures contracts. Because they tend to hold these positions for a relatively long period of time and 

roll them over from one contract expiration to the next, CITs are said to trade “passively” and are 

referred to by observers as “passive longs.” Several of these fi rms have applied for and received 

“hedge exemptions” from normal speculative position limits, as they trade commodity futures 

contracts to manage the risks associated with fi nancial investment portfolios. Since the early 2000s, 

CITs have rapidly increased their presence in commodity futures markets; from 2003 to 2008, the 

value of these traders’ holdings increased by a factor of 10. Likewise, Irwin and Sanders (2011) show 

that the share of corn, soybeans, and wheat open interest held by CITs increased signifi cantly over 

the same time period. Notably, the rise of CIT trading coincides with the convergence problems 

observed in the futures markets for these commodities.

According to this theory, CIT trading activity constituted a major new source of demand for long 

commodity futures contracts, unrelated to underlying market fundamentals. By entering a large 

amount of long futures contracts, CITs boosted the “demand” for these contracts without increasing 

the demand for the underlying physical commodity. As a result, CITs infl ated a speculative bubble, 

driving the price of these contracts higher than the cash market price and increasing the futures 

term spreads above the level justifi ed by a rational market. The resulting price differentials distorted 

traditional storage signals, leading commodity holders to store grain for profi t rather than imposing 

convergence by arbitraging the difference between futures and cash prices. 

However, the speculative bubble theory suffers from numerous limitations. First, the idea that 

CIT traders’ order fl ows can even consistently impact futures prices relies on important assumptions that are not necessarily consistent with the way that these fi rms are known to operate (Irwin 

and Sanders, 2011). Moreover, many empirical studies have failed to fi nd evidence of a causal link 
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between CIT trading and futures prices or term spreads (Buyuksahin and Harris, 2011; Irwin and 

Sanders, 2011; Stoll and Whaley, 2010), and those few that suggest such a relationship suffer from 

important weaknesses (Fattouh, Kilian, and Mahaveda, 2012; Irwin and Sanders, 2001). The bubble 

theory also fails a logical test with respect to convergence: if CIT behavior widens term spreads to 

the degree that grain elevators choose to “hoard” the commodity and take it off the market, then its 

cash price should increase as current available supply falls. At the same time, the tendency of CITs 

to roll their positions should (according to this theory) put downward pressure on expiring futures 

prices. These two forces should act to force the cash and expiring futures prices together, shrinking 

the delivery month basis and generating convergence.

Another explanation for non-convergence is that changes in commodity production patterns and 

transportation logistics rendered traditional delivery points out of the commercial fl ow of the 

commodity (Irwin et al., 2011). According to this hypothesis, regular warehouses were “out of position” in relation to commodity production and trade. As a result, they found it too expensive to draw 

a suffi cient amount of the commodity to arbitrage the basis and effect convergence by initiating 

enough deliveries. In practice, this theory is most applicable to the CBOT soft red wheat (SRW) 

contract. When the CBOT was established in the mid-19th century, Chicago was the most important 

cash grain market in the United States. Over time, as the production and marketing channels for 

the commodities shifted away from the Great Lakes region, the original delivery markets became 

less commercially important. In 2000, CBOT revised the delivery points for corn and soybeans to 

better represent the commercial fl ow of the commodity. CBOT maintained the traditional delivery 

points for wheat, however, until 2009 when persistently small commercial activity at these locations prompted a concern that deliverable supplies were “out of position.” At that time, CBOT added 

Northwest Ohio, Ohio, and Mississippi River barge shipping stations to the established delivery 

locations for soft red wheat: Chicago (Illinois), Toledo (Ohio), and St. Louis (Missouri). Irwin et al. 

point out that because these structural problems existed before the recent episode, it is unclear how 

this theory explains recent non-convergence problems (2011). 

Empirical Evidence

The best available test of the competing non-convergence theories is performed in GIS, which estimates an econometric model of the KCBT wheat, and CBOT corn, soybean, and wheat markets. 

Using relevant futures and cash market prices, the expiring basis series for these markets is calculated over the last two decades.10 The authors approximate the wedge using the change in the basis, 

and test which variables explain the series. Given a constant storage fee, the delivery market design 

theory predicts that the wedge increases with aggregate inventories at deliverable locations; an unexpectedly good harvest that produces a temporarily negative price shock can induce non-convergence 

as deliverable inventories ramp up. Besides inventories, important variables to include in the econometric model to explain the wedge include credit spreads and the delivery instrument storage rate. 

To account for the possibility that fi nancial fi rms generated a speculative bubble that overpowered 

the ability of arbitrageurs to impose convergence, the “net long” open interest held by commodity 

index traders, or the number of long minus short contracts, is included as an explanatory variable.

10For soybeans and corn, the authors use cash prices from Toledo until 1999 and the Illinois River thereafter; for 

CBOT and KCBT wheat, they use cash prices from Toledo and Kansas City, respectively. Corn and soybean prices from 

the Chicago market produce similar results.
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Confi rming the delivery market design theory’s predictions, inventories are the most important factor 

in explaining the change in the expiring basis and prove to be highly economically signifi cant.11 The 

authors estimate that the CBOT wheat market wedge expanded by over 2.6 cents per month, given the 

doubling in deliverable stocks from 2004 to 2008. That expansion represents 60 percent of the value 

of the CBOT contract storage fee, which was 4.5 cents per month at the time. As expected, the wedge 

is highly seasonal for all commodities: it is largest near the harvest and falls as the marketing year 

progresses and inventories draw down. Coeffi cients on other variables are not signifi cant, although they 

generally exhibit the expected signs. Conspicuously, the data do not support the index trader/speculative bubble theory. Commodity index trader positions are not found to affect the change in the basis 

over time: the coeffi cient on their open interest is not at all signifi cant in explaining the change in the 

basis over time, and the sign is not consistent across commodities. 

In addition to the econometric results, GIS provides compelling graphical evidence to support the 

contention that non-convergence is an unintentional product of delivery market structure. In fi gure 5, 

the authors show an example of how non-convergence is closely tied to the wedge, which drives the 

accumulation of inventories in the delivery market.12 For those market episodes in panel A where 

inventories surge suffi ciently, the price of physical storage rises above the storage fee in panel B, 

and non-convergence occurs in panel C. Figure 6 shows that the expiring basis value implied by the 

model (estimated using two different techniques) matches the observed magnitude of non-convergence very closely for all commodities except CBOT soybeans, although the model captures the 

incidence of the latter quite well. This result validates the model prediction that even a small wedge 

can generate a high degree of non-convergence.

Implications of Empirical Evidence

Recent episodes of non-convergence are explained well by competitive, rational participants acting 

within the structure of existing delivery markets. Furthermore, the data show that the expiring basis 

is a good approximation of the present value of the sum of future positive wedges. Appealing to 

alternative explanations, like irrational speculative bubbles or limits to arbitrage, is not necessary to 

explain the incidence or magnitude of non-convergence. What’s more, the alternative theories lack 

empirical support.

Traditionally, the futures term spread has been interpreted as the return to storing the commodity 

(Working, 1949). However, the delivery market design theory shows that a wedge caps the futures 

term spread below the true price of storage. As a result, when the market fails to converge, the 

futures term spread represents only the downward biased return to storage. In GIS’s model, both 

participant fi rms are equally informed, so there are no negative welfare effects associated with nonconvergence. But if some participants in the market are not as well informed and they use the term 

spread to guide physical storage decisions, they may store less than is optimal under non-convergence, leading to an ineffi cient allocation of agricultural resources. Similarly, if farmers interpret the 

magnitude of non-convergence as an indication of the direction of future cash grain prices—rather 

than as an artifact of the difference in asset storage costs—then they may plant more acres to the 

crop than is optimal. 

11GIS uses an instrumental variables technique to verify that inventories drive the wedge and not the other way around.

12CBOT wheat at Toledo is used as an example. 
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Figure 5

Elements of non-convergence in Chicago Board of Trade (CBOT) wheat, 1986-2010

Panel A: Wheat inventory in Toledo

Million bushels

Panel B: Prices of storage

Delivery instrument storage rate Price of physical storage

Panel C: Toledo spot and expiring futures prices

Cents per bushel

Cents per bushel per month

Expiring futures price Toledo spot price

Non-convergence

NOTE: Panel A shows total wheat inventory in deliverable locations in Toledo, OH. Panel B decomposes the wedge. Panel C shows data for 

the CBOT wheat futures contract and the Toledo delivery location on the first day of delivery on each contract from 1986 to 2010.

Source: Garcia, Irwin, and Smith, 2011. 

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

0

5

10

15

20

25

30

35

40

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

-30

-20

-10

0

10

20

30

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

0

200

400

600

800

1,000
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Figure 6

Actual basis versus model predictions: 1986-2010

NOTE: This figure shows the difference between actual cash and futures prices (the basis) on the first day of the delivery month alongside 

Garcia, Irwin, and Smith’s predictions from their perfect foresight model, using two different methods. 

CBOT = Chicago Board of Trade. KCBT = Kansas City Board of Trade.

Source: Garcia, Irwin, and Smith, 2011.

Panel A

CBOT corn (Toledo, 86-99; IL River North, 00-10)

Panel B

CBOT soybeans (Toledo, 86-99; IL River North, 00-10)

Panel C

CBOT wheat (Toledo)

Panel D

KCBT wheat (Kansas City)

Cents/bushel Cents/bushel

Cents/bushel Cents/bushel

-25

0

25

50

75

100

1986 1990 1994 1998 2002 2006 2010

-25

0

25

50

75

100

1986 1990 1994 1998 2002 2006 2010

-25

0

25

50

75

100

125

150

175

200

1986 1990 1994 1998 2002 2006 2010

Basis Model Prediction I

-25

0

25

50

75

100

125

150

175

200

1986 1990 1994 1998 2002 2006 2010

Model Prediction II
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Policy Options To Improve Convergence

Exchanges and policymakers have a strong interest in preserving confi dence in futures markets, 

which is undermined when convergence becomes unpredictable. Several general solutions have 

been proposed to address the non-convergence problem in order to maintain the market’s ability to 

perform its economic functions (Irwin et al., 2008). We describe and evaluate these below, based on 

the model and empirical evidence discussed in this report; fi gure 7 summarizes the options along 

with their potential benefi ts and costs.

Change the Delivery Instrument Storage Rate

Under the delivery market design theory, non-convergence is caused by a positive wedge between 

the price of storage and the cost of holding delivery instruments. Therefore, the exchange can 

drive the wedge to zero and impose convergence by increasing the storage fee to a level that makes 

holding delivery instruments unattractive. This can be done by setting a fi xed rate so high that it will 

not permit a wedge even when the demand for storage—and thus the price of storage—is very high, 

or by creating a variable storage rate that changes based on market conditions. 

To address the problem of non-convergence, in 2009 the Chicago Mercantile Exchange Group 

(CME) replaced its previously fi xed CBOT wheat shipping certifi cate storage rate with a new 

Variable Storage Rate (VSR) system (Seamon, 2009). The CBOT wheat VSR makes storing delivery 

instruments more expensive when the market nears full carry, but decreases storage rates as the term 

spread narrows. Under the VSR, the per bushel cost of holding delivery instruments for a month 

increases by about 3 cents if the expired nearby term spread averaged more than 80 percent of the 

full carry value, does not change if the expired spread average between 50 and 80 percent of full 

carry, and decreases by around 3 cents if that spread averaged below 50 percent of full carry, until 

it reaches a fl oor of 1 cent per bushel, per month. Since its introduction, the VSR has increased the 

storage rate for CBOT wheat and restored convergence to that market. 

Because the VSR aligns the storage fee with the price of storage, it effectively eliminates the wedge 

in a non-converging market over time. Although it operates incrementally and shifts the storage fee 

based on lagged observations, a variable storage rate limits the degree to which the price of storage 

can depart from the cost of holding delivery instruments in a converging market. In this way, even if 

non-convergence between cash and futures prices is still theoretically possible, the VSR ensures that 

it will be small in size and short-lived, since rational traders know that the cost of holding delivery 

instruments will quickly adjust to correct a wedge. Another advantage of the VSR, besides the fact 

that it is shown to work in practice, is that it maintains the traditional delivery process, helping 

prevent price manipulation like corners (Pirrong, 1993; Pirrong, 2001). 

One disadvantage of the VSR is that its complicated method of calculation makes it prone to misinterpretation. Although they acknowledge the VSR has achieved price convergence, some traders 

still fi nd the CBOT wheat VSR to be controversial. These participants have expressed a concern 

that higher storage fees established by the VSR will cause regular fi rms to choose to hoard wheat by 

issuing shipping certifi cates and earning storage fees, rather than transacting grain as part of their 

normal operations (Stebbins, 2011). To make this theory work, a long-side trader is required, one 

who is willing to purchase these shipping certifi cates and hold them for a long time, paying very 

high storage rates. In addition, holding SRW wheat off the market in this way would boost its cash 

prices relative to other grains whose futures markets do not employ the VSR. In fact, the opposite 
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Figure 7

Policy options to improve grain market convergence

How to do it What the policy would do Potential benefi ts Potential costs

Increase 

the delivery 

instrument 

storage rate

Increase the 

maximum storage 

fee for delivery 

instruments using 

a (i) fi xed rate or (ii) 

variable storage rate 

system.

A fi xed-rate (FR) regime 

would set a relatively 

high rate, to be reviewed 

periodically, while a 

variable storage rate 

system would adjust the 

storage rate in response to 

market conditions. Holding 

instruments would become 

unattractive.

The cost of holding 

delivery instruments 

would more accurately 

refl ect the cost of 

physically storing 

grain. If successful, the 

futures contract price 

would not diverge from 

the underlying price 

of grain in the cash 

market.

The method used to 

update the variable 

rate could be overly 

complicated. A high FR 

is transparent and easily 

understood, but the 

exchange would need 

to review it regularly 

to ensure it meets (or 

exceeds) the price of 

physical storage.

Force load-out Change exchange 

rules to prohibit fi rms 

from holding delivery 

instruments beyond a 

specifi ed period.

Traders who hold futures 

contracts until expiry 

would be required to 

load-out. The delivery 

process would require the 

physical transfer of grain; 

instruments could no 

longer be held indefi nitely. 

The price of futures 

contracts would more 

accurately refl ect the 

price of grain in the 

cash market.

Erodes existing delivery 

system protections against 

market manipulation. 

When some fi rms 

are required to take a 

particular action (in this 

case, to load out), other 

fi rms may be able to 

exploit this requirement 

by charging excessive 

loading and transportation 

fees.

Make the futures 

contract cash 

settled

Create a benchmark 

cash price index 

for the commodity. 

Change the terms of 

the futures contract 

so that its value at 

expiration equals the 

price of the index on 

that day.

Traders who hold futures 

contracts until expiry would 

exchange payments based 

on the value of the cash 

index.

The price of the 

expiring futures 

contract will always 

converge to the value 

of the cash index, by 

construction.

Removes existing delivery 

system protections against 

market manipulation. 

Devising the appropriate 

benchmark cash price 

index can be diffi cult.

Make the delivery 

process easier

Increase the amount 

of warehouse space 

available for physical 

deliveries, expand 

the allowable delivery 

territory, and/or 

reduce existing limits 

on issuing delivery 

instruments.

Encourage greater 

participation in the delivery 

process: more futures 

contracts would be settled 

using delivery instruments.

Fewer restrictions allow 

more traders to balance 

cash and futures prices 

through arbitrage 

(assuming the existing 

structure prevents 

these trades right now).

Scant evidence to support 

the claim that the existing 

number of deliveries is too 

low, or that more/easier 

deliveries will generate 

convergence. Does not 

address incentive to hold 

delivery instruments.

Crack down on 

speculators

Apply speculative 

position limits to 

commodity index 

traders (CITs). Phase 

out existing hedging 

exemptions that have 

been awarded to 

these fi rms.

Limiting the trading 

capacity of CITs reduces 

their presence in futures 

markets, on an individual 

basis. It's possible that the 

current aggregate CIT interest could be split among 

many new, smaller traders, 

although they would lose 

existing economies of 

scale.

Position limits are 

intended to prevent 

market concentration, 

manipulation, and 

“excessive speculation,” 

although this term is 

not well-defi ned, and 

empirical evidence of 

their benefi ts is sparse.

Market design problems 

are not addressed. Further, limiting CIT positions 

can decrease liquidity, 

making risk management 

efforts more expensive. 

Also, these changes could 

lead CITs to trade in the 

cash markets, directly affecting grain prices.
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has occurred with respect to corn (Gillam, 2011). Another drawback to the VSR is that it incorporates some uncertainty into futures prices, and the spreads between them, since the delivery instrument storage rate can be updated in real time. Therefore, prices for deferred delivery contracts are 

less reliable, and the spreads between them are a less reliable indicator for storage signals than they 

would be under a fi xed storage rate.

Like the VSR, a high fi xed storage rate would maintain the traditional delivery process. A fi xedrate system is currently used in the CBOT corn, soybeans, and KCBT wheat markets.13 Because 

it is fi xed, this type of storage rate is more transparent than the VSR, is more easily understood 

by traders, does not add extra uncertainty about futures spreads, and is even less likely to offer 

incentives for manipulation at contract expiry. To set an appropriate fi xed rate, the exchange could 

consider the market price of physical storage over the last decade and choose a level at or just above 

its peak. Until recently, exchanges maintained fi xed delivery instrument storage rates for long 

periods of time.14

It is important to note that, whatever storage rate system is employed, the exchange only sets the 

maximum storage rate for delivery instruments—individual regular fi rms are free to charge a lower 

rate. In a competitive market, a high contract storage rate maximum wouldn’t bind under normal 

conditions, so a regular fi rm would charge a delivery instrument storage rate in line with the physical 

price of storage. One drawback is that this maximum rate could act as a magnet for delivery instrument storage rates among regular fi rms: as a price ceiling, it may serve as a signal for regular fi rms 

to collude and charge higher storage rates (Knittel and Stango, 2003). The possibility for this type of 

collusion has always existed, but we know of no instances of it occurring. Moreover, the potential for 

onfarm storage and for small elevators to undercut fi rms by charging artifi cially high storage rates 

makes such collusion unlikely to occur. 

Force Load-Out

Strictly limiting the life of the delivery instrument, say to the end of the delivery month, ensures 

that the long side will load-out soon after taking delivery. By eliminating the ability to hold delivery 

instruments, forcing load-out compels expiring futures prices to refl ect those in the cash market, 

guaranteeing convergence. This solution would produce a similar result as a high fi xed storage rate 

on delivery instruments, with the additional complication that individual fi rms would not be allowed 

to charge a lower rate (everybody has to load-out). One advantage to arranging storage rates this 

way is that an unusually large demand for storage services cannot cause futures and cash prices to 

diverge, which could happen if the maximum fi xed rate is not suffi ciently high. 

However, forcing load-out makes manipulation more attractive to short traders with monopoly power 

in the delivery market. Traders holding short positions wish to lower the price of the expiring futures 

contract and widen the term spread. If a trader is large enough, it can accomplish this objective by 

exercising market power to temporarily increase the deliverable supply of the commodity (Pirrong, 

1993) or increase the costs associated with loading-out. Under the delivery instrument system, long 

13Although the Kansas City wheat market allows for a seasonal rate premium, it is classifi ed as a fi xed-rate system 

because all rates are set a priori—under the VSR, rates respond to market conditions.

14Current rates for corn and soybeans were updated in 2008, but aside from a brief period from 2000-2001, have remained unchanged for decades; prior to the introduction of the VSR, the storage rate for CME wheat remained effectively 

unchanged dating back to the early 1980s. Before moving to a seasonal system in 2011, storage rates for KCBT wheat 

delivery instruments were frozen for just as long. 
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traders have the fl exibility to wait and load-out under more favorable cash market conditions, counteracting the market power of large short traders. On the other hand, a forced load-out scheme would 

prevent longs from using the delivery process to accumulate delivery instruments. Still, forcing loadout represents more change to the existing contract than aligning storage rates, and it also fails to 

preserve the current delivery instrument system, making price manipulation more likely.

Change the Futures Contract Terms To Require Cash Settlement

As opposed to settlement by physical delivery, under cash settlement, an expiring futures contract 

is terminated by a payment exchange between long and short, based on the fi nal settlement price. 

Rules for obtaining this price are determined by the exchange and are written into the futures 

contract terms. For example, the Minneapolis Grain Exchange (MGEX) lists cash-settled futures 

contracts for soft red winter wheat, hard red winter wheat, corn, and soybeans. These contracts are 

all settled to an average of the national cash price bids for the commodity during the delivery month, 

as calculated by the Data Transmission Network (DTN), so convergence always occurs by defi nition. 

Although they were introduced in December 2004, practically no trading occurs on any of the cashsettled MGEX contracts.15

Likewise, making CBOT corn, soybean, and wheat contracts cash settled would ensure convergence 

to an index of cash prices. However, because they are storable, abandoning the longstanding physical 

delivery process for these commodities leaves them more susceptible to manipulation by large long 

traders (Pirrong, 2001). Under physical delivery, an exchange can and typically does offer short 

traders a variety of delivery options in terms of grade and location, which reduces the attractiveness 

to the long traders of forcing excessive deliveries. On the other hand, large long traders can more 

easily increase the price of a cash-settled contract by purchasing the appropriate varieties of the 

commodity in the cash market based on the formula used to calculate the settlement index. 

Arguably, cash settlement is well suited to trading termination for many futures contracts, most 

notably the Standard & Poor’s 500 index but also for livestock contracts like lean hogs. An important feature of the indices that these contracts settle to, though, is that the prices of the underlying 

assets that comprise them are publicly reported. Prices for stocks in the S&P 500 index are available 

to the latest second, while livestock cash markets are subject to mandatory price reporting requirements. Conversely, grain and oilseed markets do not report their cash prices publicly. As a result, 

cash settlement for corn, soybeans, and wheat contracts would probably be tied to cash price bids 

(the method used by the related index contracts on the MGEX). Compared to actual cash prices, 

bids are far more easily manipulated, since they do not represent the execution of an actual transaction between buyer and seller. Finally, changing the contract terms to require cash settlement represents a more drastic change to the existing grain and oilseed contracts than aligning the storage rates 

for the physical commodity and the delivery instrument.

Make Delivery Easier

If limits to arbitrage inhibit convergence, enhancing the capacity of the delivery market should help 

arbitrageurs engage in the type of trading that will force expiring futures and cash prices together. 

This could be accomplished by increasing the amount of regular-for-delivery warehouse space at 

existing locations, expanding the allowable delivery territory, or increasing the maximum number 

15See www.mgex.com/download.html.
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of delivery instruments a regular fi rm may issue. In 2009, CME added three delivery points to its 

SRW wheat contract, which better represented primary production and marketing areas for the 

commodity (Seamon, 2010). But GIS shows that although high delivery costs on their own may 

affect the number of delivery instruments the regular fi rm is willing to issue, they will not affect the 

basis, and therefore not improve convergence. Reducing the cost of issuing delivery instruments by, 

for example, expanding the regular-for-delivery warehouse space or adding deliverable territories 

encourages the regular fi rm to simply issue additional instruments until the marginal cost of delivery 

increases back to its previous level. 

Tighten Speculative Position Limits

One way to address “excessive speculation” by CITs is to place limits on their trading ability. 

Speculative limits have been used in agricultural futures markets for decades: those traders who do 

not have a commercial interest in the underlying commodity ordinarily face caps on the number of 

positions they may hold.16 Until recently, CITs were regularly awarded exemptions from these limits.

Besides the fact that evidence for the benefi ts of position limits is scarce, the speculative bubble/

index trader theory suffers from theoretical weaknesses (as described on pp. 14-15). Furthermore, 

the empirical evidence shows that CIT positions do not correlate with basis changes in the corn, 

soybeans, and wheat markets. That is, the data do not support the contention that speculative activities by CITs caused convergence problems. For all these reasons, imposing position limits on index 

traders is unlikely to improve convergence. Indeed, doing so may actually generate other unintended, negative consequences with respect to risk transfer and price discovery (Pirrong, 2010).

16For a legislative history of position limits in futures markets, see: www.cftc.gov/PressRoom/SpeechesTestimony/

berkovitzstatement072809
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Conclusion

From 2005 to 2010, sustained, unprecedented non-convergence levels in domestic corn, soybean, 

and wheat futures markets led many observers to wonder if the traditional price-discovery and 

risk-management functions of these markets had weakened. Popular explanations for the nonconvergence problem involved constraints to arbitrage (whether or not they were caused by an irrational speculative bubble) or delivery markets that no longer regulated the commercial fl ow of the 

commodity. However, convergence failures in grain and soybean markets are most likely an unintended result of the delivery market structure for these commodities. Specifi cally, the storage rate of 

the delivery instrument was set too low relative to the true price of storage: the wedge between the 

costs of holding delivery instruments and storing physical grain caused non-convergence. 

GIS shows theoretically and empirically that recent episodes of non-convergence are well explained 

by competitive, rational participants acting within the structure of existing delivery markets. 

Predictions from their competitive model match the incidence and magnitude of non-convergence 

very well. Alternative claims like irrational speculative bubbles lack both theoretical and empirical 

support as an explanation for recent convergence problems. Therefore, tightening the enforcement 

of speculative position limits would likely not improve convergence and could produce unintended 

consequences that negatively impact the ability of futures markets to discover prices and transfer 

risk effi ciently. 

Because non-convergence confuses traditional storage signals, it may lead to welfare losses among 

less informed market participants, so futures exchanges and policymakers have an interest in 

preventing future episodes. Changing the futures contract terms to align the storage rates in the 

physical and delivery instrument markets, via either a variable storage rate or a high maximum fi xed 

rate, represents less change to the existing contract than forcing load-out or switching to cash settlement. Maintaining the storage rate system also preserves the traditional delivery process along with 

its built-in protection against manipulation. The fi xed rate has worked well until recently and has an 

additional advantage of being easier to understand than a variable storage rate.
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