Streetwise Professor

I have a relatively simple way to filter out serious research on commodity prices from the not-so-serious. If you rely on “convenience yield” I will not take you seriously. Alas, based on this filter, the bulk of commodities research is unserious.

For the uninitiated (consider yourself lucky!), convenience yield is an attempt to explain that commodity futures prices are typically at less than “full carry”, i.e., that futures prices are below the spot price plus the cost of carrying inventory (financing plus physical storage costs). Furthermore, convenience yield is invoked to explain the fact that departures from full carry vary systematically with (some measure of) inventories, with big departures associated with small inventories.

These are empirical regularities, and convenience yield is invoked to explain them. The idea dates from Kaldor (1939), who was attempting to explain Working’s earlier (1934) empirical findings from the CBOT wheat market.

The intuition is simple. With true assets (e.g., bonds, stock, currencies), the futures price is depressed by the income (“yield”) on the asset (e.g, the dividend on a stock). So, to explain the depression in commodity futures prices below full-carry values, Kaldor said: stocks “have a yield, qua stocks, by enabling the producer to lay hands on them the moment they are wanted and thus saving the cost and trouble of ordering frequent deliveries, of waiting for deliveries.”

Problem solved!

The problem is not solved, because there are no real microfoundations here. Kaldor merely waved his hands, and analogized a departure from full carry in commodity markets to the depression in the prices of futures on assets caused by the income on these assets.

The problem is that, as Stephen Ross pointed out around 30 years ago in a paper on the Metallgesellschaft episode, commodities are not true assets. True assets are always in positive net supply. Commodities–and in particular commodities at the delivery point of a futures contract–are not always in positive net supply: sometimes there are “stockouts” when all inventories at a particular location are consumed. As Bob Lucas taught me years ago, commodity inventories in positive supply at all times is inefficient, as this would imply that a commodity is produced but never consumed. So stockouts are inevitable in competitive commodity markets.

Thus, the real cause of below-full-carry futures prices is that the zero inventory constraint is periodically binding.

So how to explain positive inventories and less-than-full-carry futures prices? There are two basic explanations: aggregation in space, and aggregation in time.

The best exposition of the former is Brennan, Wright, and Williams, (1997). Working off of earlier theoretical research by Wright and Williams, this article shows that including inventories held outside a delivery point (where spreads are used to measure carry) is misleading. When a delivery point is at an inverse/backwardation/less than full carry while inventories are positive at other locations, it is because the inverse (which measures the benefit of immediate delivery and consumption in the market where the inverse is measured) is smaller than the cost of moving inventories from where they are held to the delivery point.

With respect to the latter, the rigorous theory of storage based on optimal intertemporal allocation subject to a non-negative inventory constraint implies that if inventories at the delivery point are positive, the futures price for delivery on the next day will be at full carry. However, most departures from full carry are typically measured using futures prices for many delivery days if not months into the future. (For example, Working analyzed the May-July and July-September spreads.) These deferred delivery contracts can be below full carry when the one-day price is at full carry if there is a positive probability of a stockout prior to the expiration of the futures contract used to measure the spread.

This explains the Working Supply of Storage relationship even when one uses stocks in the delivery market as the independent variable. The smaller the inventory, the more likely a stockout prior to expiration of the futures contract used to calculate the spread, and hence the bigger the inverse.

This was all discussed thoroughly in my book.

In sum, convenience yield is a fudge factor, justified with hand waving. The attempts to provide microfoundations, such as invoking inventories as a factor of production, as in Ramey (1989), have farcical implications (which I ridicule in my book).

The Working supply of storage curve is an empirical regularity. Convenience yield is not the explanation for this regularity. The real theory of storage, which is based on the non-negative inventory constraint, is.

I plead guilty to using convenience yield in some of my earlier research, in particular my fairly widely cited paper with Victor Ng on industrial metals. By way of justification, I would say that (a) I was a young academic that needed to present our research in a way that conformed with the conventional wisdom (which alas did, as it still does, rely on convenience yield, as illustrated by a slightly earlier paper by Fama and French) (ah the price of publish or perish) , and (b) we also invoked the more rigorous theory of storage.

But I have seen the light: indeed, I saw the light years ago. Academics working in commodities now should also have a Come to Jesus moment, and swear off the concept of convenience yield. At least if you want to be a serious researcher committed to analysis grounded in firm microfoundations–which “convenience yield” is decidedly not.