Another Iteration on the Speculation Model

Here's another iteration on the model of oil markets we've been developing. [Update: Paul Krugman comments on the model and provides a simple, continuous time version.]

(I doubt very many of you will have much interest in digging into the details, it's tedious, so the results are summarized at the end).

Here's where it stands. After posting the graphical version of the speculation model, and incorporating Steve Waldman's comments on convenience yields, Paul Krugman noted:

Steve Waldman is right. But we should add that the convenience yield isn’t a fixed number. Actually — I should have realized this earlier — the demand for inventories is like the demand for money. People hold some money for convenience even though money normally yields less than bonds. The amount of money they hold, however, depends on the yield differential. Similarly, the demand for oil inventories should depend negatively on the interest rate minus the contango.

I’ll reformulate my little model to reflect this when I get a chance. ...

And Tyler Cowen remarked:

Mark Thoma has an exhaustive post on convenience yield.  The models used are too piecemeal and they allow "inventories," "convenience yield," and "speculation," to serve as free-floating, not necessarily attached concepts.  The discussion here pays insufficient attention to Holbrook Working, who knew that convenience yield was front and center of the entire analysis, just as "the demand for money" is the centerpiece of the quantity theory. ...

I don't think I will deal sufficiently with Workings discussion for Tyler's taste on this iteration, maybe later, but let me try to incorporate some of the other comments and make convenience yield more "front and center".

The previous version mostly illustrated how the model worked, and used Krugman's model as a baseline for adding in Steve Waldman's suggestion that:

...the future price of a storable commodity is determined by the spot price plus the total cost of storage, defined as foregone interest, plus storage costs, minus ... the convenience yield...

Thus, all that was required was to subtract the convenience yield from the costs specified in Krugman's model, and show how that changed the results.

This model will be quite a bit different than the previous iteration, and, as you can guess from the introduction, I view this as a work in progress. Also, this is a general model of integrating stocks and flows, there may be particulars of oil markets that still need to be incorporated or that I've missed. But it hopefully captures the essence of what we are after.

The model assumes there is a flow demand and flow supply for oil each period. A period could be a day, a week, a month, something like that, I'll use a day just to fix ideas. For example, we might be at a flow equilibrium where we use 100 units of oil each day. Thus, at equilibrium there is a constant flow of oil - we bring in 100 units each day and burn it in our cars, use it to heat our homes, etc. The market is in equilibrium so both the flow demand and flow supplies are 100 at the current spot price.

There are also stock supply and stock demand curves in the model (stock meaning a quantity, not the financial asset sold on Wall Street). For example, suppose a speculator enters the market and wants to purchase 10 units of fuel to store and sell at a later date. The extra demand for fuel that day will increase the spot price. As the spot price goes up, the flow quantity demanded falls, the flow quantity supplied increases, say to 95 and 105 for an excess supply of 10. This 10 units can then be used to augment the speculators stock, as desired.

At this price, then, both markets clear. In the flow market, the price is above equilibrium and there is an excess supply of 10 units, but the extra 10 units are used to increase the existing stock of oil.

Here are the pieces of the model in more detail:

Stock Demand

The stock demand curve has two components, a speculative component, and a service or convenience yield component. The speculative demand, E, depends upon the expected net return from storing oil which, following the lead of others, is assumed to be

[(expected yield per unit) - (cost per unit)] = [((f-p)/p) - (i + c)],

where f is the expected future price, p is the spot price, i is the interest rate, and c is the storage cost. The first term, (f-p)/p, is the expected yield from holding oil and selling it at a future date. As the expected appreciation increases, demand increases. The term i is the opportunity cost of holding the oil, and as i goes up the demand goes down. When the storage costs, c, are higher, demand is lower. Therefore, speculative demand is

E = E[(f-p)/p - (i + c)],

and E is increasing in f, and decreasing in p, i,  and c.

The other term is the convenience yield. Here, I'll take Krugman's suggestion above and model this as depending upon the difference between i and contango

C = C[i-(f-p)/p, c],

that is, it is assumed that the convenience yield depends negatively on the interest rate differential, and also negatively on the storage cost.

Note that all arguments have the same effect on demand as they did in the speculative demand case. That is, as p increases, the expected appreciation falls causing the interest rate differential to increase and this causes C, and hence overall demand for stock balances, to fall. As f increases, the appreciation term increases, the differential falls, and C goes up. Finally, as i and c increase, C falls.

The bottom line, then, is that total stock demand, the sum of speculative demand plus the convenience yield demand, is

D = E + C = D(p, f, i, c) ,

with signs -, +, -, -. [I need to think more about the specification of the arguments of the E and C functions above, but the bottom line assumption about the general form of D in terms of its arguments and their signs seems correct.]

Stock Supply

Stock supply at time t is assumed to be the stock supply at time t-1 plus any additions or subtractions from the stock due to imbalances in the flow market. That is,

S_t = S_t-1 + (s-d),

where s-d is the excess supply in the flow market. For example, if the flow supply is s=100, but the flow demand is only d=90, then the stock today, S_t, will rise above the stock yesterday, S_t-1, by (s-d) = 10.

The connection between the stock supply curve and excess supply or excess demand in the flow market shown in the equation will be important below, so here's how it fits together graphically:

Start at the long-run flow equilibrium shown by Q₀ and p*. At this price, the flow supply and flow demand curves are in balance.

Now let the price rise above p* to p₁.  At p₁, there is excess flow supply as shown by the orange line, and this increases the stock above Q₀ as shown by the corresponding orange line in the stock diagram. If the price increases again to p₂, excess flow supply will go up as shown by the red line, and the stock supply rises to match, again as shown by the corresponding red line in the stock diagram.

For a decrease in the price to p₃, there is excess demand in the flow market as shown by the green line, and the excess demand is met by reducing the stock as indicated by the green line in the stock diagram showing the stock falling below its initial value of  Q₀.

One further point on the mechanics of the model. Suppose the price rises to p₁ as in the diagram increasing the stock supply by the amount indicated by the orange line. Since supply today is supply yesterday plus any additional stock added today from the flow market, i.e. since

S₂ = S₁ + (s-d),

the stock at the beginning of the second period will be higher than in the first period by the amount of the orange line.

This means that at the start of the next period the supply curve will shift out to reflect the higher initial stock:

After the shift, the starting point at the beginning of the second period is p* and Q₁, and the supply curve is S₂.  Any changes in the stock above or below Q₁ must come from excess supply or demand in the flow market, as before. That is, the beginning second period looks just like the diagram above for the first period except that the initial stock is labeled  Q₁, not  Q₀, and the supply curve is S₂ rather than S₁.

Flow Demand

Nothing fancy here, will simply assume

d = d(p), d'<0

Flow Supply

Again, simply

s=s(p), s'>0

We can add more to these functions later as needed. For example, one key question to ask the model is what happens if d, the daily demand for fuel, increases permanently due to higher world demand, and this can be modeled by adding a variable to represent growth in world demand (e.g. world GDP).

We also want to ask the model about speculation, so let's do the graphs for that case next.

Here's a picture of the initial equilibrium:

At the spot price of p*, both the stock market and flow markets are in equilibrium.

Now let f, the expected future price, go up for some reason. The increase in f will increase both the convenience yield and the expected appreciation, and this will shift the stock demand curve out:

After the shift in demand due to the increase in f, and with price still at p*, there is excess stock demand. This excess demand begins to bid the spot price, p, up above p* and as it does excess supply begins appearing in the flow market. As the price gets higher, the excess flow supply, s-d, increases until at some point, p₁ in the diagram, enough excess supply has been created to satisfy the increased stock demand.

Now lets move to the next period. As explained above, because the stock increased from Q₀ to Q₁, the stock supply curve shifts out to start the next period. The shift sets a new round in motion:

The increase in the stock supply causes an excess of stock supply over stock demand at the temporary price of p₁, that drives the spot price down to p₂, and at p_2, the new equilibrium, the excess flow supply just meets the amount needed to clear the stock market.

Again though, since the stock supply went up, there will be a new baseline stock for the next period. One more iteration to fix ideas:

And finally, after enough time, we reach a new long-run equilibrium:

At the new equilibrium, the spot price is the same as its initial value, the amount stored has gone up, and the flow equilibrium is unchanged.

Summarizing, an increase in the expected future price causes

1. a temporary increase in the spot price, but not a permanent increase. When the spot price goes up, some of the daily flow is diverted into storage, and this happens each day that the spot price is above p*. However, after enough time periods have passed, the stock of fuel in storage will be as high as desired, and there's no need or desire to divert any more of the flow into storage. At this point, the spot price returns to where it started, and the flow market will be in balance once again.

2. the amount stored to increase.

In addition,

3. the increase in the expected future price that shifts the stock demand curve isn't driven by a change in the fundamentals in the model, i.e. the change did not shift the S, D, s, or d curves. Thus, if the expected future price returns to its long-run value of p* over time, as it should since nothing fundamental changed, this would all reverse itself. The whole process described above would run backwards.

4. a signature of speculation of the type modeled here is changes in stocks. When the expected future price goes up storage increases, when it goes down, storage decreases.

5. an increase in the spot price over long periods of time is not likely to be a signature of speculation. Speculation can and does drive the price in the short-run, but not the long-run.

Interesting that an increase in speculative demand for oil causes a temporary price spike, but not a permanent one. I missed that before. I guess that's why you build models (and this is a work in progress - more iterations may be needed...).

There are lots of questions we can ask this model, and I probably haven't asked the model the questions Arnold Kling or Tyler Cowen might want to ask of it, but next up: Use the model to show what happens in the short-run and long-run when there is an increase in d, the flow demand, due to an increase in the world demand for oil [Update: see here for details]. I think I can show this is consistent with very little change in inventories, i.e. with little change in stocks, but we shall see. If so, then an increase in flow demand, d, from growth in world demand would be consistent with rising prices and stagnant (or even falling) inventories, while an increase in speculation would show little change in the price and higher inventories. Thus, if we were to observe rising prices and stagnant inventories, that would be consistent with a world demand growth story, but inconsistent with a story that involves an increase in speculative activity to a higher level (though spot prices would rise in the short-run, and a continual infusion of new speculative activity could keep the spot price rising until the increase in speculative activity leveled off).

[In the link in the update at the beginning of the post, Paul Krugman recasts this model in continuous time rather than discrete time.

For example, as he notes, at a point in time with inv=inventories and p = the spot price, let the reduced form equations be p=f(inv, expected future p) and dinv/dt = S(p)-D(p). In this model, as in the model above, the equilibrium price is determined the stock equilibrium and the flows from the commodity market change the stocks over time. It's "basically Bill Branson's 1970-something portfolio balance exchange rate model adapted to commodities." The continuous time formulation is a much simpler framework, both mathematically and graphically.]

Comments

[save_the_rustbelt]

So why are prices up 46% this year?

First guess, collusion.

Second guess, speculation.

I find it unlikely the supply and demand curve has shifted this far in six months.

Your thoughts?

[anne]

Ya' done good.

"One final comment based upon an email from Paul Krugman on this. I probably should have cast this in continuous time rather than discrete time since it's much easier to keep the stocks and flows in alignment."

[ndd]

an increase in flow demand, d, from growth in world demand would be consistent with rising prices and stagnant (or even falling) inventories, while an increase in speculation would show little change in the price and higher inventories.

Per my, er, intellectual "speculation", where does the growth in global Strategic Oil Reserves fit in this model? Are they "higher inventories" or no? Thanks

[halbhh]

Models are fun, and often useful, but we should remember that some systems can work via mechanisms not in models at all. I don't even mean that as a criticism. Rather to remind all that we need to test models with numbers, just like theories are tested in other models of complex systems, like climate modeling, etc.

In this system -- crude oil prices (various) and various fuel prices (each matters and are inter-connecting), I simply asked myself:

Who actually sets an at-the-pump price? And then trace the chain logically.

We know for instance a service station can only add a modest margin to the price from their supplier, and the supplier in turn looks to ____ to set their price. ____ is....yes, the futures market.

So understanding the pricing in the futures market in turn is key.

[hari]

Mark - Thanks for your effort to get to the bottom of oil speculation. Unlike other international commodity trade agreements, OPEC cartel is not regulated. Production, inventory and stocks are difficult to ascertain on a reliable basis, including the fact there are non-OPEC suppliers in the international market. And, I suppose, as long as suppliers/producers operate as a cartel - we'll have problems with their figs. When Opec opened its office in Vienna, I tried to impress on their SG the need for good statistical standards on actual production and supply by country, and stocks art hand and, supply constraints, if any.

Your point (1) adequately covers the fact that futures market, in fact, allocates spot price(s).

Suppose we can (finally) get a model that actually reflects how the crude market allocates price, what assurance do we have that the Cartel is not misleading us on their official inventories/stocks? For example, on basis of production data available from Opec and others, how is Goldman & Sach able to forecast - with certainty - a futures price @ $200/b? DO they have access to *private* data base?

[Nicholas Weaver]

I am NOT an economist: but I really don't like these models at all, simply because I don't think that it reflects reality on the supply/demand curves in the short term:

Demand is notoriously inelastic in the short term.

Supply is highly elastic up to a point, and then it MUST become very inelastic, as "10x the money can't provide hardly any more oil". So IF we are near/at that point of supply constraints, a supply and demand curve like this:

http://www.icsi.berkeley.edu/~nweaver/sdcartoon.gif

would seem to me to be much more realistic, and can explain how increases in demand had a very small increase in price for a long time (D to D') but can have a huge impact today (D' to D''). Likewise, a small decrease in supply...

IF (IF IF IF) the supply/demand curve looks more like what I sketched, you don't need speculators to have the price jump so much so quickly.

[ddt]

wow, thanks mark. you really stepped up to the plate on this one.

The model looks pretty good to me, the only thing I would change is this:

"The other term is the convenience yield. Here, I'll take Krugman's suggestion above and model this as depending upon the difference between i and contango

C = C[i-(f-p)/p, c],

that is, it is assumed that the convenience yield depends negatively on the interest rate differential, and also negatively on the storage cost."

Um, I'm a little fuzzy on this, but I don't think that is quite right. you could have rising convenience yield even with both rising interest rate differential and and rising storage cost even though they cancel each other out in the final determination of whether it is worth while to hold inventory. I'm pretty certain that convenience yield is determined independently of either. I suggest a call option model for determining C.

comments by Steve Waldman from his blog:

Steve Randy Waldman (mail) (www):
anon — I think your intuition about convenience yields and option value is right on. Scanning briefly the academic abstract on convenience yields, there's a lot borrowed from options modeling ideas, and analogies are made to call options. (I like the model in this paper, which is very straightforward, although seems to presume perfect ability to time transactions. -- Approximation for convenience yield in commodity futures pricing, Heaney.)

I also found a recent paper that backs this up through a study on Crude Futures:

The Information Content of the Implied Convenience Yield: Using American Call Option Based Structural Model

Abstract:
This study examines the relationship between volatility and the spread of two commodity futures with different maturities in the NYMEX crude oil market. We find that convenience yield behaves like an American call option, which suggests that the information content of convenience yield is volatility behavior. Our model successfully quantifies the sensitivity of the spread with respect to volatility and provides satisfactory predicting power. For practical applications, we show how to calibrate our model in a trading strategy that can generate significant profit. Our structural framework lays the groundwork for studies on how volatility dynamics are related to commodity fundamentals.

Chen, Te-Feng, Lin, Ming-In and Wang, Kehluh, "The Information Content of the Implied Convenience Yield: Using American Call Option Based Structural Model" (January 2007). Available at SSRN: http://ssrn.com/abstract=957621

so.. I guess the logical question is what the valuation model for an option is, the most common is the Black-Scholes which says that "All the parameters in the model other than the volatility — the time to maturity, the strike, the risk-free rate, and the current underlying price — are unequivocally observable. Furthermore, under normal circumstances the option's theoretical value is a monotonic increasing function of the volatility. This means there is a one-to-one relationship between the option price and the volatility."

In order to determine the volatility you have to get into calculations with The Greeks. (the formula for calculating the option value (similar to convenience yield) is in the top row of the table under 'Black Scholes')

Since the convenience yield has similar properties to an American Call option rather than a European call option, the Binomial Model of options pricing should be used rather than the Black-Scholes model (continuous rather than discrete)

http://en.wikipedia.org/wiki/Binomial_options_model

here's a site with a good summary of options pricing models , as well as a number of calculators based on the models

So it seems that the convenience yield would be best modelled using something very similar to the Binomial Options model. Obviously this would be quite an undertaking, and requires someone with more talents than myself to put together.

[Mark Thoma]

Actually, your question shows why models are useful.

Even if the stock curves are relatively steep (inelastic), because they shift outward, you can still get large changes in inventories. [Krugman makes this point too in his continuous time version - see link at beginning or end of post.]

If you look at the diagram above, the LR outcome shows this best, you will see that what determines the size of the inventory accumulation is the size of the AD shift (not its steepness). Steeper SR curves alter the transitional dynamics, and how the spot price reacts, but not the ultimate outcome in terms of inventory accumulation (since S must intersect the new D curve at p*). The steepness can interact with the size of the shift in some cases, it depends upon which parameters are responsible for the steep slope, but ultimately it's the size of the horizontal demand shift that determines the outcome.

On the strategic reserve, more and more it is functioning like an asset with flows in and out based upon expected future prices and current conditions, so it is starting to behave just like a private sector inventory (it wasn't always that way). But I'd want to dig into it a little more before committing to a particular modeling strategy.

Certainly,however, a decision to increase the amount held would express itself as an increase in the stock demand, i.e. it would have impacts largely as shown above.

ddt - thanks - will think about this. As my hedge on that section indicates, I was worried about that part too.

[Richard H. Serlin]

You seem to be implying that this is a new model. This isn't one of my areas of specialization, and I haven't searched the literature, but I would think all of this would have been modeled well in the literature a long time ago, and you could just use and cite those models, models that I would think would have been debated and settled a long time ago so that there would not be any real debate now. Thus, it surprises my to see this.

[Mark Thoma]

As I note at the end, a la Krugman:

It's "basically Bill Branson's 1970-something portfolio balance exchange rate model adapted to commodities."

So I think it's pretty clear I'm not trying to claim novelty.

The model is new to me - at least in the sense that I sat down yesterday and simply constructed it myself on paper without consulting anything other than thinking through partial adjustment analogies from money demand -money supply models, which didn't help all that much. Turns out it reinvents the wheel (I said this but left it out in an edit), but as I noted, I think I acknowledge that, I even name the primary author of the class of models. And as far as I'm aware, nobody has applied Branson's exchange rate model to commodities - things like getting the convenience yield incorporated correctly are useful, I think.

It was helpful to me to work through it, particularly in thinking about where to take it next, and I thought it would help others to see how it works (it's also a good way to answer questions like those raised about steep supply and demand curves, e.g. see above, I think you had questions along these lines in one of your posts that the model helps to answer). If you know it all already, you should just skip it. But not everyone has this tool in their arsenal already, I didn't (so you are smarter than I am) and a simple link to an old academic paper probably isn't sufficient to elucidate the main points.

Uhm, and finally, there is a real debate right now - that's why I'm presenting the model and the answers it gives, vintage or not.

[anon]

I made several comments on Steve Waldman’s convenience yield post, and have been following the subsequent discussion with great interest, particularly as it begins to integrate with everything else. My comments related mostly to the option idea that seems to be essential to the idea of convenience yield. I’m no option expert, so I’ll proceed with some additional intuition against the backdrop of your analyses and hope that it’s useful. (This adventure is partly inspired by your previous introductory remarks, as there may well be some errors here. BTW – if you and Paul Krugman find this exercise worthwhile, novel or not, I suspect a good portion of your readers should as well.)

Some thoughts:

a) The nature of the “convenience” in question as I understand it is that it allows traders to pursue profit seeking strategies by exploiting pure volatility of expected returns (based on the spread between spot and futures prices) with option related strategies. Steve Waldman describes some of these strategies in his post.

b) The value associated with this convenience is in the form of an up-front capitalized cost that is in effect a subtraction from what would otherwise be the spread between spot and futures prices. This up-front capitalized cost, the “convenience yield” is really an embedded option premium that is de facto extracted from the return that otherwise would have been expected by non-trading hedgers and speculators.

c) “Convenience yield”, as an option premium, is both the cost of entering these trading strategies, and the market’s best determination of the expected risk adjusted profit arising from them. The actual yield to the trader isn’t determined until the option has been exercised or expired. And like any long option strategy, a trader must first earn back his premium expenditure before turning net profits. Traders will eventually realize some gross return on their investment, which will either be equal to, less than, or more than their initial premium investment.

d) Convenience yield has a subtractive effect on the expected speculative/hedging return from holding oil otherwise. Therefore, the total expected return from holding physical oil is the expected holding period return typically sought by hedgers or non-trading holding period speculators/arbitrageurs, plus the convenience yield, which is the value of the option and the corresponding capitalized value of expected returns for volatility traders. This decomposition corresponds conceptually to the sum of a “delta” (linear) return plus a “volatility” (non-linear) return.

e) I had a similar reaction as commenter ddt on the same point. It’s not obvious that the functional arguments for the holding period yield and the convenience yield should be quite the same. Clearly, increased gross spreads, reduced interest rates, and reduced storage costs all operate in favour of the holding period speculator. Convenience yield may be a partial function of interest rates and storage costs as well, similar to holding period yield, but I’m not up to speed on option pricing enough to confirm this. Plus, we’re talking about a spread option, where the sensitivities to these variables may be more complicated than a plain vanilla option.

f) But volatility will be a unique functional argument in the case of convenience yields.

I’m not sure how any of this affects your total stock demand D = E + C. It’s really only a modification to C. And I don’t know right now how the presence of an option component might affect the development of your stock/flow supply/demand analyses. It may well be completely consistent and even reinforce the logic for that matter, but I haven’t though it through.

This is getting sort of messy. I’m hitting send just in case it has some usefulness.

[Richard H. Serlin]

Sorry Mark, I didn't mean to imply you or anyone else was claiming any degree of originality. It's just casually following this, and sometimes just quickly skimming not even all of it, the way that it's been developing starting with Krugman's "tiny theoretical paper", it seemed like there was a lot of creating models with little or no reference to the literature. And something as important as this really should have been hashed out and settled in the literature a long time ago (although I know it doesn't always work this way). So again, please accept my apologies.

[Mark Thoma]

Richard - no problem.

anon - much thanks.

[ddt]

some interesting news from a couple days ago - inventories are actually on the rise:

Energy sector declines on rise in oil inventories

NEW YORK (Thomson Financial) - Energy stocks fell Wednesday as crude oil prices slipped on data that showed inventories rose unexpectedly during the latest week.

The Department of Energy earlier said U.S. crude oil stocks rose by 800,000 barrels last week, more than the 200,000 barrels gain analyst had expected. The rise follows five straight weeks of declining crude stockpiles in the world's largest energy consumer.

The news sent August crude oil futures down $4.00, or 3%, to $132.98..."
http://www.forbes.com/afxnewslimited/feeds/afx/2008/06/25/afx5152566.html

Overall inventories are at 301,800,000 barrels, which is 49,100,000 below last year, so 800,000 barrels isn't a huge increase but it is an unexpected change of the trend. something to keep an eye on I guess.

[ddt]

" hari says...

Suppose we can (finally) get a model that actually reflects how the crude market allocates price, what assurance do we have that the Cartel is not misleading us on their official inventories/stocks? For example, on basis of production data available from Opec and others, how is Goldman & Sach able to forecast - with certainty - a futures price @ $200/b? DO they have access to *private* data base?"

comment hoisted from Steve Waldman's comments:

"Steve Randy Waldman (mail) (www):
Benign — Do you think that what's going on is that people are in fact buying physical, eschewing futures markets but not having their inventories counted by whoever counts inventories? Given your reasoning, this strikes me as the right thing to do. There'd be an opportunity: liquidity constrained producers would avoid selling forward very far for fear of margin calls they'd be unable to meet in uncertain futures markets. Longs who buy outright and unleveraged via futures don't need to fear margin calls (they keep sufficient funds in the bank to meet any margin, synthesizing simple ownership), but they do have to worry about nonfulfillment if they really do think the markets might fail. So, the right play would be oil in a tank purchased from liquidity constrained producers who sell either for cash or forward with fixed collateral, if you think oil is a good bet. Do you think that this is what's going on, old-fashioned buying of physical buy people we cannot see? "

whatever happens with these models, Krugman's original point that there must be inventories for speculation to affect prices still stands. his point about backwardation - not so much. I think that this really just comes down to how confident you are in the official inventory numbers - ie how accurate and complete they are, and whether or not they are being gamed.

SW: "Do you think that this is what's going on, old-fashioned buying of physical buy people we cannot see?"

I strongly suspect that this is the case, but of course I can't prove it. As SW notes, the incentives to do so have all been there. It's what the smartest guys in the room would be doing.

This is one reason that I think politicians getting involved is not bad - a federal investigation/audit of oil storage would reveal a lot, even if it is just limited to US jurisdiction. Hedge funds have been buying dilapidated storage facilities and ag companies to be able to store physical grain for the purpose of speculation (openly declared). It wouldn't be surprising if they were doing the same thing with oil and masking it through some kinds of arcane swap agreements or financing arrangements with the facilities.

If you buy (or make a contract with) a distressed company that stores oil and usually consumes it in the normal course of business, and you somehow secured the use of their tanks for storage, would the oil being stored at the facilities still count in the inventory numbers or would that oil be officially "consumed"? Would that be a viable way to game the system?

[Lafayette]

Interesting intellectual discussion, this, about the economic motives that propel speculation.

Still, I don't think that enough perspective has been given to the mechanics employed. That is, the cost of speculating (i.e., taking risk) is minimal. One does not put down all that much money to take a speculative position on a commodity.

I am wondering therefore if increasing margin requirements on a futures commodity contract would not dampen speculation in that commodity.

It seems to me the same remark was made about the sub-prime mess. But, I acknowledge that I don't know all that well the mechanics of this market.

[halbhh]

Some hypotheses: inventories reported weekly don't tell us as much as we might hope about the real situation since they are managed by folks looking to avoid disadvantages in ways we can't predict easily. For instance, crude oil sellers don't necessarily have to reveal just how much crude they could produce, and may decide its not in their interest to do so. Refiners will try to guess at actual end demand (real actual gasoline sales, etc), and then buy inventory to match their guesses, etc., all of which adds unpredictable complexity.

This has been my understanding for a year or so since I first studied it some. Not to say I know all the complexities of it.

The main thing that causes models to fail is simply that the actual main actors (Saudis, Exxon, etc) can make decisions based on their own expectations contrary to some simple guess they would only try to maximize profits over some reasonably short period like 2 years, etc. etc.

I don't think human deciders are suseptible to modeling. In other words we don't really know what they will do -- our presumptions are more arbritrary than we hope.

But I do appreciate the urge to model and the hopeful pursuit of reducing the unknowns into some reassuring predictability.

[Duke of Moral Hazard]

Stop! Please stop with the models. I have yet to see a model that accurately describes deceit in the real world. Seek out 10 successful commodities brokers (oil preferably) and have them explain this to you. If oil is being hoarded, they will probably have heard a whisper or two about where. If it's not, they will be able to explain how the price of gas goes up without hoarding taking place. This is science too.

[hari]

From a contrarian point of view, what Mark is trying to realize with (his version of *options*) modelling is to provide a reality check on how crude prices are being manipulated, if, in fact, it can be proven.

Let me introduce a *beta coefficient* into his reasoning...

On June 6th Deputy PM of Israel (born in Iran) made it official on (Israeli) IDF trial-run to attack Iranian nuclear facilities ....oil futures spiked 9%, according to Reuters Business...leading to current prices.

Now Iranians have confirmed (as I argued) they'll stop the Strait of Harmuz...oil flow from the Gulf States...the % supply and receipient countries are part of the puzzle, here, because it includes Asian emerging markets.

Geopolitics are part and parcel of this crude futures market, and no model can replicate it, I am afraid, until there is an international commodity agreement on crude supply.

[Aaron Moynahan]

If there are speculators and you want to find them then look to the sea. In the tanker fleet is the place they will be. If they're not there then it ain't happening. Slow steaming and floating storage is where its at if its happening.

[halbhh]

Speculation does not necessarily lead to an inventory buildup!

This point isn't understood yet it appears.

See my previous post for the pieces.

For inventory to build up, refiners and other actual buyers (taking actual delivery) must make errors.

[Aaron Moynahan]

Arbitrage should put a limit on how different the futues price can be from the sport price:

Arbitrage example:

The formula for the futures price is the following:

Futures Price (T) = Sport Price x (1+risk free rate)^T + Future Value(Storage Cost – Convenience Yield)

Given:

Spot price: $135
Futures price: $140
Storage cost for a barrel of oil: $0.07 per day (based on VLCC dayrates)
Borrowing Cost: 7%

You can gain an arbitrage profit using the information above in the following transaction:

Today:

1. Short the futures contract

2. Buy the Oil at $135

3. Borrow $135 @ 7 percent

Net out of pocket cost today: 0

30 days in the future:

1. Settle the short position by delivering the oil and receive $140.

2. Repay the loan for $135.75

3. Pay storage fee of $2.10

Arbitrage Profit: $140-$135.75-$2.10 = $2.90

Now do this for 2.1 million barrels (approximately 1 VLCC) and you have a profit of $6.35 million dollars.

So obviously if you could earn a risk free profit you would do the transaction as many times as possible. In the above example this would mean purchasing crude at spot which would drive up the current spot price and selling futures contracts which would drive them down. If the futures price was under valued you would do a reverse cash and carry transaction by shorting the oil, going long on the futures and investing in a 30 day note. If this strategy made money it would have the reverse effect as above (drive down the spot price and drive up the futures price).

[Aaron Moynahan]

Estimating Crude Storage cost based on VLCC dayrates:

Typical VLCC: 300,000 Metric Tonnes

BBL/Tonne conversion Rate: 7.3

Bbl: 2,190,000

Dayrate for VLCC (floating storage): $150,000

Cost Per Barrel per Day: $150,000 / 2,190,000bbl = 0.068 $/bbl per day.

[Jonathan]

Mark,

One question - it is clear from your 2nd-to-last graph (with 3 red lines) that the stock supply curve does not shift an arbitrary amount with each iteration, but rather shifts exactly an amount such that the two red lines are of equal length. (Or, if you make the process continuous rather than discrete, such that, at the end of the process, the integral of all of the flow rates over time equals the final supply stock differential). This seems to mean to me that this process of returning to the starting price must have a certain speed - it wouldn't work if it were slowed down or sped up. Is this the correct interpretation? Is it true in the real world?

Thanks,
Jonathan

[Jonathan]

Also, I noticed that in the graph under "one further point" the stock supply curve does shift the full amount to return the price to equilibrium, in just one period, which seems inconsistent with the iterations you describe later. Is this just because you compressed all the periods into one in order tp simplify things?