Streetwise Professor

In addition to his other sins, John Maynard Keynes sowed confusion in his analysis of commodity forward curves.  He appropriated language from the markets–backwardation and contango–and misused the terms in a way that has left a trail of confusion ever since.

Unfortunately, even the estimable Izabella Kaminska of FTAlphaville has succumbed to this muddle, as has Joelle Miffra at EDHEC.

Here’s the issue.  As used in the markets, “backwardation” describes a situation in which the price for future delivery is below the price for immediate delivery, or more generally, the price for delivery at T’ is below the price for delivery at T<T’  “Contango” is the reverse: prices for nearby delivery are below prices for deferred delivery.  That is, contango and backwardation refer to the relation between traded prices for different delivery dates, where the prices are quoted simultaneously.

That’s not how Keynes used the term.  He used backwardation to refer to a situation in which the expected spot price for a future date is below the current futures price for the contract expiring on that date.  That is, rather than comparing two traded prices for different delivery dates, he compared a traded futures price to the price expected to prevail at a future date.  This difference between a futures price and an expected spot price is a risk premium. The expected spot price is a mathematical construct, and is not observable.

Izabella and Miffra also utilize the basic Keynesian hedging pressure explanation for contango and backwardation.  Here’s Izabella:

The background here is that the long side of the curve in commodities was traditionally always set in backwardation (the opposite of contango, when futures prices are lower than spot). This was because the curve had developed as a financial method for producers to hedge downside risk — meaning most of the risk befell those going long on the opposite side of the trade.

It consequently also meant that those going long demanded compensation for taking that risk — something which was achieved via the backwardation premium at rollover.

However, with the long side increasingly focused on wealth preservation rather than speculation, the risk along the curve has over the last five years or so shifted to the short side — resulting in a contango structure.

Et voila, the most rewarding ‘have your chocolate cake and eat it’ trade in all of history may have become the consequence. For, if you have the means to go physically long the commodity and short the paper, you can quite literally have it all.

You can gather contango yield (which is attractive in a low interest rate environment), whilst also speculating on the appreciation of the underlying price.

This is basically a hedging pressure story a la Keynes.  Hedging pressure and speculation affect risk premia, which doesn’t translate directly into the shape of the visible forward curve.  For instance, you can have a market, like that for an equity forward or a bond forward, that is always at full carry (contango) because the asset is always in positive supply, but for which the risk premium can be of any sign, and can change sign over time, without the shape of the forward curve changing.

Markets can be in backwardation or contango, properly defined, if risk premia are zero, positive or negative.

A little (relatively) simple math.  Consider a commodity or asset that is always in positive net supply (no stockouts).  It has a risk premium of u.  The risk free rate of interest is r.  The current spot price is S.  The forward price, due to traditional arbitrage considerations, is F=(1+r)S: it is in contango.  The expected spot price is E(S)=(1+r+u)S.  If u>0, E(S)>F.  If u<0, E(S)<F.  Neither the sign nor the magnitude of u affect the forward curve.  Arbitrage considerations drive the visible forward curve.  Risk allocation considerations drive the risk premium.

The Keynes explanation is also a little long in the tooth, even as a theory of risk premia.  It implicitly assumes that markets are fragmented, and that speculators do not hold positions across many markets.  Perhaps that was true at one time, but it is certainly not true today (consider hedge funds).  With diversified investors and integrated markets, the risk premium in any commodity is driven by economy-wide risk prices.  For instance, if you believe in CAPM (not that I do, just using this as an illustration), you believe that the beta of the commodity price with respect to the market portfolio drives the risk premium, and hedging pressure matters not a whit.  David Hirschleifer generalized things in the late-80s, with a model where speculators incur fixed costs to participate in a market.  In this case, speculators are not perfectly diversified, and hedging pressure can matter.  But market wide risks matter too.  The more integrated the markets, and the more diversified the commodity players, the less hedging pressure matters in driving the risk premium.  And markets have certainly become more integrated lately, much to the chagrin of some traditionalists.

At best, the Keynes “normal backwardation” story is a useful pedagogical tool that should be used as the start of an examination of the determinants of risk premia in commodities, and certainly not the last word.  It is most useful as a foil, than as a proper explanation.

Contango and backwardation in the visible curves are driven in the first instance by intertemporal allocation considerations.  Storage can be used to allocate a commodity over time.  The forward curve should adjust to give people an incentive to make that allocation optimally.  When future availability is expected to be low, relative to current availability, storage is optimal: forward curves move into contango to provide the incentive to undertake that storage.  If current availability is low relative to what is expected in the future, you would like to bring the commodity from the future to the present.  That’s not possible, so the best we can do is not store.  Backwardation punishes storage, and provides the incentive to consume today rather than carry inventories of a scarce commodity to a future date when it is expected to be less scarce.

Market power can also affect forward curves.  Corners create artificial near-term shortages, leading to backwardation.  The crucial thing is that if the short-term shortage is real, inventories should be low, but artificial shortages are often associated with large inventories.*

If you want to understand the curve, first focus on these intertemporal considerations.  And don’t mix up the visible–the observable forward curve–with the invisible–risk premia.  Keynes did, and has befuddled a lot of people since, and not for the first time and not about only that.

* My 1996 book on manipulation and several of my papers show how manipulation affects the forward curve and forward curve-inventory relations.  Holbrook Working discussed this in detail in the 1930s in his work on the wheat markets.  I have a book forthcoming (draft chapters available online) that is all about the implications of intertemporal resource allocation for the shape of forward curves.