“In conclusion, the present study supports the hypothesis

that the recent oil price run-up, when expressed in

any of the major currencies, has been amplified by speculative

behavior of the type found during a bubble-like

expansion. The underlying positive feedbacks, nucleated

by rumors of rising scarcity, may result from one or several

of the following factors acting together: (1) protective

hedging against future oil price increases and a

weakening dollar whose anticipations amplify hedging in

a positive self-reinforcing loop; (2) search for a new highreturn

investment, following the collapse of real-estate,

the securitization disaster and poor yields of equities,

whose expectations endorsed by a growing pool of hedge,

pension and sovereign funds will transform it in a selffulfilling

prophecy; (3) the recent development since 2006

of deregulated oil future trading, allowing spot oil price

to be actually more and more determined by speculative

future markets [19] and thus more and more decoupled

from genuine supply-demand equilibrium.”

“The declining liquidity of the physical base of the reference crude oil and the narrowness of the spot market have caused many oil-exporting and oil-consuming countries to look for an alternative market to derive the price of the reference crude. The alternative was found in the futures market. When formula pricing was first used in the mid-1980s, the WTI and Brent futures contracts were in their infancy. Since then, the futures market has grown to become not only a market that allows producers and refiners to hedge their risks and speculators to take positions, but is also at the heart of the current oil-pricing regime. Thus, instead of using dated Brent as the basis of pricing crude exports to Europe, several major oil-producing countries such as Saudi Arabia, Kuwait and Iran rely on the IPE Brent Weighted Average (BWAVE).11 The shift to the futures market has been justified by a number of factors. Unlike the spot market, the futures market is highly liquid which makes it less vulnerable to distortions. Another reason is that a futures price is determined by actual transactions in the futures exchange and not on the basis of assessed prices by oil reporting agencies. Furthermore, the timely availability of futures prices, which are continuously updated and disseminated to the public, enhances price transparency.

[11] The BWAVE is the weighted average of all futures price quotations that arise for a given contract of the futures exchange (IPE) during a trading day. The weights are the shares of the relevant volume of transactions on that day. Specifically, this change places the futures market, which is a market for financial contracts, at the heart of the current pricing system.”

Also here is a good example of speculators at work:

]]>Last word (I promise). You have convinced me about the symmetry of the trades. Here is where I made my mistake. When I said that it would never pay to close out the short storage long futures trade, I failed to take into account that when you repurchase the oil, you are also buying back the oil convenience yield as well. So you would be willing to pay a premium over the futures net of holding cost.

Thank you for an enlightening discussion and apologies to Steve for hijacking this thread.

]]>“The spot price will never get that low, because anyone with spare storage can earn a risk-free return by buying spot and selling forward.”

You may be right in part or in whole. I don’t know. But a counterargument exists that contradicts such an inference.

Your point is consistent with the idea that the market is more efficient in arbitraging away potential profit opportunities on the storage convenience trade than on the oil convenience trade. The implication is that realized spread volatility is always skewed; i.e., realized volatility offers trading opportunities in one direction (oil convenience), but not in the other (storage convenience).

If an arbitrage exists that is inverse to the one you’ve described, it would suggest that we can expect similar levels of intensity of both arbitrage and more aggressive volatility trading on either side of the curve. There would be no reason to expect a skew in realized volatility, or to expect volatility trading opportunities for oil convenience yield while not expecting them for storage convenience yield. Conversely, there would be no reason to expect any less dampening of volatility opportunities due to ongoing arbitrage in oil convenience than there would be for storage convenience.

Such an arbitrage does exist on the oil convenience side. You’ve described the arbitrage that seems natural on the storage convenience trade. The strategy over the entire holding period comprises an investment in cash, at the risk free rate, with an option to exit cash into a fully hedged investment in oil, resulting in a risk free return that exceeds the risk free rate. But the inverse arbitrage opportunity exists on the oil convenience side. This consists of a fully hedged investment in oil, at the risk free rate, with an option to capture excess return through arbitrage, and exit oil into risk-free cash.

Assume the investor faces a neutral or fully-arbitraged oil curve at the outset. The curve by definition is in contango, with the forward yield covering interest and storage costs. You’ve alluded to the arbitrage that one might expect to occur immediately if the contango accentuates. The investor buys spot oil and sells futures in order to capture excess forward yield on a risk free basis. He exits cash and move into fully hedged oil.

Now suppose the same investor adopts the inverse strategy at the outset. Since the curve is fully arbitraged, he can buy oil and sell futures immediately and capture the risk free rate of interest. Then, like a volatility trader, he waits for curve volatility. If the curve contango compresses and moves in the direction of backwardization, the investor closes his position at a profit, just like a volatility trader. He exits oil and moves into cash.

The investor captures this excess return when he closes his spot and futures positions. He realizes this gain as the net result of these two components. This net gain translates to the present value of a yield pick-up over the remaining holding period for the combined oil/cash investment. Depending on the degree of movement in the curve, the investor captures profit translatable to excess return over the remaining period, as happens directly in storage convenience arbitrage.

Both types of investment are risk free. The order of cash and oil is merely reversed. In either case, the investor must define a holding period that is determined by the date of the futures contract prospectively used in the oil investment component. This is a parameter that makes holding periods comparable. Then the excess return in either case is defined by the timing of the arbitrage execution (i.e. the remaining time to the end of the holding period) and the amount of spread profit that is captured in the arbitrage. Spread profit in storage arbitrage is inherently amortized over the contract life of the concluding oil investment. Spread profit in oil arbitrage is translatable to an equivalent amortization of excess return over the remaining holding period for cash, as defined by the expiry date of the futures contract used in the front oil investment component. Given the comparable nature of these arbitrages as inverses of each other, there is nothing to suggest that one should have a biased advantage over the other in terms of either their timing or the amount of spread or excess return that is captured. These arbitrage opportunities on either side of the curve are just mini-versions, or buy and hold investment versions, of the more aggressive volatility trading strategies already discussed. There is no reason not to expect such strategies to be operating without bias on both sides of the curve.

]]>Thanks for your extensive post. I have spent some time thinking about it. I feel I have a good handle on the oil convenience yield. You store oil and sell forward hoping for the spread to widen in favor of the spot. You try to sell at the maximum spread and close out the futures position (exercising the option). If the spread moves against you, the worst case is you deliver the oil against the futures position. The cost is the premium you paid for spot over the futures price net of holding costs. So far so good.

Now the other trade: you sell oil and take a long futures position and you earn some interest on your cash position. In this case, exercising the option means buying back spot and closing out the futures position. When does it pay to exercise? It’s not enough for the spread to move in your favor. Unless spot moves below the futures price net of holding costs, you are better off earning interest on your spot sale and taking delivery of the futures position. But, unless storage is full (or you control all of it), the spot price will never get that low, because anyone with spare storage can earn a risk-free return by buying spot and selling forward. Therefore, the option is never exercised and has no value. I think. Sorry for beating a dead horse.

]]>I believe the equations in question are correct:

Interest rate – oil convenience yield = forward yield

Interest rate + storage convenience yield = forward yield

The re-work follows (this is pretty long):

Let:

p = oil spot price

f = oil futures price

i = interest

Then, apart from convenience yield of either type or storage cost of normal type, arbitrage suggests:

f – p = i

i.e.

forward yield = interest (or interest rate when expressed in terms of 1/p)

Oil Convenience Yield

The convenience yield on oil is the expected profit from trades that are expected to benefit from upside volatility in spot oil and the spread (p – f). The trader puts on a position of long spot oil, short oil futures. The short futures position hedges the long spot position against directional downside price risk. In option terms, the trader is long spot volatility, short future delta. The trade is long the spread position (p – f), which is the same as short the spread position (f – p), or short the forward yield.

Since the trader is short the forward yield, he profits if volatility reduces that spread – i.e. if volatility moves the spread marginally in the direction of backwardation.

There are three sources of price impact associated with this trade, all of them driving the spread in the same direction:

a) Marginal backwardation associated with putting on the marginal trade (long spot; short futures)

b) Cumulative marginal backwardation associated with the degree to which the trade is “in the market”

c) Expected future marginal backwardation associated with any individual trader’s proprietary view of the spread, and his expectation that the future spread will moved favourably beyond what is already reflected in market pricing

The degree to which forward yield arbitrage is affected by oil convenience yield at any point in time is an indicator of effect b) above. Oil convenience yield in and of itself reflects the expectation of positive spot price volatility and negative forward yield volatility. It is in the market as the equivalent of the premium on an embedded put option on (f – p); i.e. an embedded call option on (p – f). The cost of the option premium (invested by traders) marginally backwardizes the (f – p) spread, and the trader expects to gain from an extension of that move.

So the new arbitrage, including the effect of oil convenience yield, is:

Forward yield = interest rate – OCY (marginal backwardization effect)

Storage Convenience Yield

The convenience yield on storage is the expected profit from trades that are expected to benefit from downside volatility in spot oil and the spread (p – f). The trader has access to unused storage capacity in order to be able to buy spot oil after it spikes downward. The trader puts on a spread position of short spot oil (i.e. unused storage capacity), long oil futures. The long futures position hedges the short spot position against directional upside price risk. In option terms, the trader is short spot volatility, long future delta. The trade is short the spread position (p – f), which is the same as long the spread position (f – p), or long the forward yield.

Since the trader is long the forward yield, he profits if volatility increases that spread – i.e. if volatility moves the spread marginally in the direction of contango.

There are three sources of price impact associated with this trade, all of them driving the spread in the same direction:

a) Marginal contango associated with putting on the marginal trade (short spot; long futures)

b) Cumulative marginal contango associated with the degree to which the trade is “in the market”

c) Expected future marginal contango associated with any individual trader’s proprietary view of the spread, and his expectation that the future spread will move beyond what is already reflected in market pricing

The degree to which forward yield arbitrage is affected by storage convenience yield at any point in time is an indicator of effect b) above. Storage convenience yield in and of itself reflects the expectation of negative spot price volatility and positive forward yield volatility. It is in the market as the equivalent of an embedded call option premium on (f – p); i.e. an embedded put option premium on (p – f). The cost of the option premium (invested by traders) effects marginal contango on the (f – p) spread, and the trader expects to gain from an extension of that move.

So the new arbitrage, including the effect of storage convenience yield, is:

Forward yield = interest rate + SCY (marginal contango effect)

I think this should answer your first question, which was:

“I believe they imply that if oil convenience yield is positive then storage convenience yield must be negative. I thought both had to be positive?”

Both types of convenience yield are positive, as they represent long option premium investments that are expected to deliver positive returns to the respective trades. But as explained above, an oil convenience trade puts downward pressure on forward yield because it is a bet on marginal backwardization, and a storage convenience trade puts upward pressure on forward yield because it is a bet on marginal contango.

In summary, both of the equations in question appear to be correct:

Interest rate – oil convenience yield = forward yield

Interest rate + storage convenience yield = forward yield

Your second question was:

“Also, conceptually, unless you have a monopoly on storage space in a given market, you should never be able to earn a return on storage from buying spot and selling forward that exceeds the interest rate. So I’m having a problem with the convenience yield on storage argument. Or maybe I’m just confused.”

I haven’t considered this question to the same extent as the first. But I can’t see anything in the conceptual model that constrains positive yield expectation as a function of interest rates. The convenience yield on storage as defined represents the opportunity for strategies that take advantage of downside volatility in the spot oil price (and upside volatility in the forward yield). Those with unused storage have a number of strategy choices. They can employ storage convenience strategies as defined, which involve opportunistic volatility trading – essentially waiting to buy spot on a downside spike and then covering on reversion. A second strategy choice, assuming the forward yield offers an arbitrage opportunity, is simply to buy spot and sell futures, holding that position to the futures date, and locking in arbitrage profit on the oil thus purchased and stored. But it is the activity of those executing the first strategy – i.e. waiting for volatility opportunities while hedging with futures – that can cause this “mispricing” opportunity for those executing the second strategy. The two activities are diametrically opposed in terms of marginal pricing effect. The question is which one is stronger at the margin. Finally, a third strategy is that those with unused storage capacity presumably can ‘rent’ it out, although I have no idea how this market works. Perhaps that’s the activity you refer to when you say such operators shouldn’t be able to earn more than the interest rate. I don’t know.

An additional aspect may be relevant, although I’m not familiar with the economics of storage costs, so I’m guessing here. Suppose there is some fixed cost associated with owning storage capacity, regardless of capacity utilization – something like “owner’s equivalent rent” in residential real estate. And suppose some traders actually rent storage as inferred above when needed. The arbitrage equatio

n might take these types of costs into account. If so, oil or storage convenience costs should then be viewed net of such storage cost. But that just requires tweaking the cost structure of the model a bit.

Finally, I’ll return to my own original question that sparked the discussion on storage convenience yield. Are negative convenience yields possible?

You and Steve responded immediately with the answer that’s taken me several days to work through – which was that a negative oil convenience yield is more easily thought of as positive storage convenience yield. But unused storage is conceptually equivalent to a short spot oil position. Therefore, a negative oil convenience yield can also be thought of intuitively as a short position in oil convenience yield that is associated with a short position in spot oil. This becomes even more intuitive when one considers that a trader with a position in storage convenience yield (i.e. betting on downside oil spot volatility and upside (f – p) volatility) is effectively trading against, or shorting, the view of a trader with a position in oil convenience yield.

]]>See John Mauldin’s presention of a piece by Louis Gave on world-wide inflation trends for circumstantial evidence supporting my story (I think) and also predicting the commodity inflation is about to roll over.

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