Hoarding the Herd: The Convenience of Productive Stocks

• Author: Atle Oglend,Frank Asche,Dengjun Zhang
• Date: 01 July 2015
• DOI: http://doi.org/10.1002/fut.21679
• Published date: 01 July 2015

HOARDING THE HERD:THE CONVENIENCE OF

PRODUCTIVE STOCKS

FRANK ASCHE, ATLE OGLEND* and DENGJUN ZHANG

This paper investigates the convenience yield that emerges in markets with productive stocks.

We isolate the economic fundamentals giving rise to the yield, and show how these map to the

empirical convenience yield measure. A model for price dynamics is derived from an economic

model for optimal stock levels. We show how the price process reduces to a simple non‐linear

first‐order Markov process. The model is estimated for the Norwegian market for farmed salmon

by Generalized Methods of Moments, where stock growth is approximated by sea‐water

temperature. Our estimation result supports the theorized role of stock growth as a convenience

yield component. Our results are relevant for the functioning of futures markets for

commodities such as fish and other animal production where systematic stock growth affects

the term structure. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:679–694, 2015

1. INTRODUCTION

This paper shows that productive storage or stocks lead to the inverted term‐structure

generally associated with a convenience yield. This is an important factor in most forms of

animal production, where stocks are fed and are therefore growing. The convenience yield

depends on both expected growth and price, in addition to the co‐variance between growth

and prices. We demonstrate the empirical relevance of this convenience yield by analyzing the

market for farmed salmon, including the relativity new futures market for salmon.

The convenience yield was first introduced to account for the observation that agents in

commodity markets held stocks even when prices for future delivery where lower than current

prices (Brennan, 1958; Kaldor, 1939; Working, 1948, 1949). The convenience yield can be

defined as an incremental economic benefit of holding stocks outside of the spread between

futures and spot prices, adjusted for the full carrying cost (interest, warehousing, insurance

etc.). Several economic factors have been proposed to account for such an economic benefit.

Deaton and Laroque (1992) suggest that when the commodity is scarce, stocks have an

additional value as insurance against future stock‐outs. The convenience yield is then the

result of the real option value of holding stocks (Heaney, 2002; Litzenberger &

Rabinowitz, 1995; Routledge, Duane, & Chester, 2000). It is also argued that producers

requiring primary commodities as inputs might sit on stocks to avoid costly changes in

production schedules or complete shut downs (Considine & Larson, 2001; Litzenberger &

Rabinowitz, 1995). This will imbue stocks with a convenience yield as derived demand

Frank Asche (Professor), Atle Oglend (Associate Professor), and Dengjun Zhang (Post doc.) are collocated at

the Department of Industrial Economics, University of Stavanger, Stavanger, Norway. We would like to thank

the Norwegian Research Council for financial support.

*Correspondence author, Department of Industrial Economics, University of Stavanger, 4036 Stavanger, Norway.

Tel: þ47‐41‐44‐64‐14, Fax: þ47‐51‐93‐17‐50, e‐mail: atle.oglend@uis.no

Received September 2013; Accepted March 2014

The Journal of Futures Markets, Vol. 35, No. 7, 679–694 (2015)

© 2014 Wiley Periodicals, Inc.

Published online 22 April 2014 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21679

becomes highly inelastic when scarcity increases. These explanations originate from

uncertainty regarding future availability, and the convenience yield is essentially the result

of hoarding behavior, although the behavior can be purely economically motivated. Other

explanations suggest that the convenience yield might be the result of data aggregation issues

(Benirschka & Binkley, 1995; Brennan, Williams, & Wright, 1997; Wright & Williams, 1989).

Here, the observed convenience yield is the result of prices being averaged across different

locations and grades. It is an artifact of the data, whereby transportation costs or quality

differences are not properly accounted for when comparing prices. In an examination of the

United States corn market, Frechete and Fackler (1999) fails to find empirical support for this

hypothesis. In the traditional financial interpretation, which can be tracked back to Keynes

(1930), a backwarded futures market that would give the appearance of a convenience yield is

the result of a necessary risk compensation to holders of futures contracts. In practice, risk

compensation results in a spot price above the futures prices and a generally downward

sloping futures curve. This explanation does not require any marginal economic benefiton

stock‐keeping, but is the result of risk‐averse agents in the futures market.

Looking beyond specific causes, the market effects of the convenience yield are well

known. A high convenience yield is associated with low stocks, price spiking, high price

volatility, and an inverted term structure of futures prices. The hoarding‐like behavior

associated with a convenience yield reduces the market elasticity of demand and leads to

increasing prices as the commodity is effectively removed from the normal flow of the market.

Volatility increases as the inter‐temporal smoothing function of storage is reduced. Since the

convenience yield varies with stock levels, it is endogenous to the market, while

simultaneously affecting the behavior of individual market agents. Hence, the convenience

yield is an indicator of scarcity and future security of supply and plays a relevant informational

role in price discovery.

The exact convenience yield is generally thought of as a latent variable. In empirical

analysis, it is measured by the spread between a futures price and the spot price, adjusted for

carrying costs and the interest rate. If this spread is negative, suggesting an economic loss from

keeping stocks, it is argued that a convenience yield is present. Much work has been done on

investigating the economic significance of this convenience yield and its consistency with

economic theory. Ng and Pirrong (1994) and Nielsen and Schwartz (2004) show that a high

convenience yield is associated with higher spot price volatility. Casassus and Collin‐Dufresne

(2005) find a strong spot price dependence of the convenience yield for crude oil, copper, gold,

and silver. Chiou Wei and Zhu (2006) show that for natural gas the convenience yield is

economically significant, at 3–5% of the spot price on average, and that it varies in a manner

consistent with economic theory. In agricultural markets, Fama and French (1987) show that

the convenience yield has considerable variability, in addition to a seasonality. More recently,

Gorton, Hayashi, and Rouwenhorst, (2013) investigate 31 commodities using futures and

physical inventory data from 1969 to 2006. They find that the convenience yield is decreasing

and non‐linear in inventories. Related to a convenience yield, Peterson and Tomek (2005)

demonstrate how prices of storable crops become increasingly volatile and right‐skewed as one

approaches harvest time. Similarly, Lence and Hayenga (2001) show that a high current spot

price is associated with low stocks and a high convenience yield. The convenience yield is also

recognized as relevant when pricing commodity based contingent claims, such as in the

futures pricing model of Gibson and Schwartz (1990). Although the adjusted basis is the

conventional empirical measure of a convenience yield, it does not by itself provide any insight

into how and what relevant economic fundamentals generate it.

A feature that has not received much attention is that a convenience yield can emerge

when stocks grow in storage—that is, when stocks are productive. If stocks grow, as is typical

in animal production, there is a direct economic benefit from keeping stocks. To allow for

680 Asche, Oglend, and Zhang