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Commodity pricing

A new paper combines two key aspects of commodity pricing: [1] a rational pricing model based on the present value of future convenience yields of physical commodity holdings, and [2] the activity of financial investors in form of rational short-term trading and contrarian trading. Since convenience yields are related to the scarcity of a commodity and the value of inventories for production and consumption they provide the fundamental anchor of prices. The trading aspect reflects the growing “financialization” of commodity markets. The influence of both fundamentals and trading is backed by empirical evidence. One implication is that adjusted spreads between spot and futures prices, which partly indicate unsustainably high or low convenience yields, are valid trading signals.

Bredin, Don and Potì, Valerio and Salvador, Enrique (2018), “Commodity Pricing: Evidence from Rational and Behavioral Models, Michael J. Brennan Irish Finance Working Paper Series Research Paper No. 18-1.

The post ties in with SRSV’s summary lecture on implicit subsidies, particularly the section on commodity futures.
The below are quotes from the paper. Emphasis and cursive text have been added.

The fundamental approach to commodity pricing

“A formal definition of a commodity is that it is a raw material or a primary agricultural resource that can be purchased or sold for production and/or consumption.”

“At the heart of our classical fundamental-based model, which represents the benchmark specification in our study of commodity pricing, lies the rational asset pricing model (RAPM)…The RAPM indicates that commodities are valued based on their cash flows (convenience yield) that are likely to be generated. This model implies fundamentals-based rational pricing of commodities whereas any deviations point towards bubbles or excessive speculation. “

“In…rational present value models…commodity prices are the [discounted sums of] rational expectation of future’ payoffs associated with holding the commodity…The one period-payoff…is defined as the value of the overall benefit that accrues to the holder of a storable physical commodity, rather than the owner of the futures contract… More concretely, it represents the net benefits associated with holding inventory, e.g. maintaining a smooth production process and so avoid any disruption to the flow of goods being produced, net of any storage cost and/or any other cost of carry except funding costs at the risk-free rate… we refer to this benefit as…the convenience yield… In each period, the convenience yield thus defined plays a role analogous to the one played by the one-period net dividend in the rational valuation model of equities…Commodity prices change when there are changes in expected future convenience yields (the ‘payoffs’) and/or changes to the discount factor.”

The expectation of a positive convenience yield is the reason why firms maintain positive stocks of inventory even when the expected capital gain is below the risk-adjusted rate or negative. For many commodities…this expectation is large enough to motivate firms to maintain positive inventory levels even in the presence of expected costs (negative capital gain), in addition to funding and storage costs, of 5% to 10% per month….The literature on the convenience yield explains it as a function of the net cost of storage, through the interaction of supply and demand in the cash market and the storage market…Models… predict that the convenience yield is high (low) during periods of time where inventory levels are at their lowest (highest), e.g. during times of scarcity. Related empirical literature…shows that the convenience yield is mean-reverting.”

The RAPM can thus be interpreted as a reduced form dynamic demand-supply model of commodity prices. It is compatible with an underlying structural model in which the market price of all commodities (e.g. agricultural and energy) is determined by the market expectation of the commodity scarcity, reflected in the balance between current supply and demand, both driven by expectations about the convenience yield.”

“The convenience yield is unobservable but can be estimated via a no-arbitrage relationship between spot prices and futures prices [stipulating that convenience yield is the difference between the spot price increased by a risk-free rate to the futures date and the futures price]…This no-arbitrage relation provides a convenient way to estimate the otherwise unobservable convenience yield.”

“The rational valuation model with constant discount rate implies that changes in the convenience yield are predicted by the errors of the long-run relationship between prices and convenience yield…In the rational valuation model with constant discount rate… the scaled spread… between the commodity price and its steady-state rational valuation…is a sufficient statistic for the predictable change of both prices and convenience yields…The predictable variation in prices can be explained in full also by the futures and spot prices.”

The influence of “financialization”

“A regular commentary during the commodities super cycle of the early to mid-2000s, was the obvious role played by financialization and, by extension, speculators…Rather than as a consumption asset, commodities have hit the headlines as an investment asset. The flow of investors’ funds into commodities since 2000 has been striking.”

“The flood of funds into commodities, via commodity futures, has been referred to as the financialization of commodities. This process represents a structural change in commodity market participation and, combined with the price increase during the super cycle, leads to concerns over the potential role of speculation. Parts of the media and, to some extent, regulators have adopted the view that this process of financialization has been feeding through to physical commodity prices, to such an extent that physical prices are no longer closely tied to their fundamental value. Formal evidence of the increased role of financialization since 2005 has been provided by [various academic studies]…The return correlation between commodities and conventional financial assets (stocks) has turned positive and statistically significant since 2008, after being negative and significant in previous years.”

Rational and contrarian trading

“In order to explain deviations from the classical fundamental-based benchmark model based on the rational asset pricing model (RAPM), we extend it in a behavioral direction… This is the first known evaluation of the RAPM applied to commodities using a formal behavioral perspective.”

“Fundamental based investors with a short-run (one-period) perspective…[can be called] rational speculators. The rational speculators adopt the same information and model as the above long-run rational model, however here the value of the commodity is the discounted present value of the price at which it is expected to be sold in the next period…While expected changes in the convenience yield and rates of return play a role in both the short-run and long-run models, the role of the expected rate of price change (capital gain) is only present (and with a large weight) in the short-run model.”

“We also…consider the case of heterogeneous types of investors. Rather than being driven by rationality, this investor takes a short-run perspectives and takes the exact opposite path (in relation to commodity price changes) to the rational speculator. We refer to this type of investor as a contrarian speculator.”

“The augmentation of the model to include both rational and irrational speculators is particularly relevant given how the commodities super-cycle historically unfolded.”

Empirical evidence

“Our study examines a total of 15 commodities covering agriculture, softs, energy and metals and a sample where possible covers the period from 1959 to 2017…All reported data is for futures prices on the first Wednesday of each month…The proxy for the spot price is the spot futures contract…The proxy for the futures price will then be the next to expire futures contract. Thus the spot and futures prices represent the exact same good and the time intervals between the two delivery dates is known.”

We do find evidence of long-run relationships between prices and fundamentals, consistent with the rational asset pricing model and thus in line with the conclusions of recent empirical studies,”

“The overall fit of the model improves considerably when we simultaneously take account of agents with a long-run focus (fundamentals) and a short-run focus (rational and contrarian speculators). The long-term fundamental based agents…certainly play a role, but not a dominant role relative to speculators and rational speculators in particular.”

“Our results are consistent for all commodities examined and for a range of different specifications.”


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