Streetwise Professor

James Hamilton and Jing Wu have a new paper on speculation and oil futures pricing (h/t Brian Goff).  The paper is very carefully done and very impressive econometrically.  It presents some provocative results, but IMO the radical simplifying assumptions James and Jing used in order to come up with something that they could estimate cast serious doubts on the results.  I am also sure that the results will be overinterpreted and misinterpreted to advance political agendas, and regret that the authors provide the hook in a few careless statements that should have been heavily qualified, but weren’t.

Here are my initial detailed comments:

1. The paper focuses on risk premia.  Hallelujah!  The price of risk is what speculators are most likely to affect, because most speculative transactions involve a transfer of risk, rather than the commodity.  A very basic point, but one which is all too frequently overlooked.
2. The most provocative result in the paper is a huge discontinuity of their estimate of the risk premium in oil futures  between the pre-2005 period and 2005-2011 (see Fig. 5).  This discontinuity is an artifact of HW’s splitting of the sample.  They motivate the choice of splitting date by observing that the growth in crude oil futures open interest increased dramatically beginning in 2004.  It would be preferable to do some testing for structural breaks and estimate accordingly.
3. More generally, I am very suspicious of such a sharp discontinuity.  I think it is highly likely that it is symptomatic of other changes going on in the market, and the limitations of their model.  (More on the latter below).
4. The model is not complete, even on its own terms.  Although it discusses the role of speculators (“arbitrageurs” in HW) in absorbing risk from hedgers, hedgers are not formally modeled.  This is a huge hole.  Moreover, “investors”–such as those who trade via index funds–are modeled extremely mechanically.  Yes, once they are in the market, index traders tend to trade mechanically, but the allocation of speculative capital between index funds and other investment opportunities is not as mechanical a process as the paper assumes.  Indeed, in the model the index-fund investors’ trading does not depend at all on risk-return tradeoffs.  They are just automatons that flow in and out of the market based on some autoregressive process. This is extremely problematic: index investor capital allocation decisions are presumably the result of an optimization process that reflects their investment opportunity set and the pricing of risk across these opportunities.  (Again, more on this below).
5. Relatedly, since hedgers are not in the model, there is no effect of index investors shocks on hedger behavior.
6. The model of fundamentals is extremely cramped and limiting.  I am no big fan of affine models generally, but even overlooking that, it is definitely the case that more than one (latent) fundamental factor drives spot oil prices.  Thus, the model becomes a two-factor model, with one (fundamental) factor driving the spot price and the “risk neutral” forward curve and the other (index-investor buying) affecting the shape of the forward curve.
7. One cannot generate interesting forward curve dynamics using a one-factor fundamental model.  One cannot generate interesting and realistic inventory-price relations using a one factor model.  As I show in my forthcoming book, at least two fundamental factors are needed to generate reasonable dynamics.  Furthermore, as I also show in the book, the homoskedastic error structure for the fundamentals variable assumed in the HW paper cannot generate price and inventory behavior observed in the real world.
8. Thus, the fundamentals model is almost certainly seriously mis-specified.  I can understand the modeling choice, but it has consequences.  It is my sense that this mis-specification is so severe that it casts serious doubts on the results.
9. In a frictionless world, risk premia for a particular factor are determined by the covariation between that factor and the pricing kernel.  In markets with frictions (as in the Hirshleifer models of the late-80s, early-90s), idiosyncratic risk of the factor may impact risk premia, in addition to the effect of systematic risk (driven by the covariation).  HW is a single market model: the oil market is all there is, and only factors within the oil market affect risk premia.  This is in essence an old-school Keynesian model of the risk premium.  Again, this is highly problematic.  In particular, since the whole movement of financial investors into commodities strengthens the linkage between broader financial markets and commodity markets, ignoring systematic risk (and hence inter-market covariation) is a serious deficiency.
10. It is a stylized fact that correlations between commodity returns and returns on broad equity indices and FX have changed substantially in recent years.  Although some have asserted a connection between index trading and this change in correlation structures, you can tell fundamentals-based stories as well.  For instance, if supply shocks were dominant in pre-2005, but demand shocks (e.g., the growth of China, the financial crisis) were dominant since, one would tend to observe the oil-S&P correlation to change from negative to positive.  As long as you are not in a Keynesian world with each commodity and investment an island with risk borne only by those living on that island, this change in correlations would lead to a change in risk premia.  The change in sign in the risk premium at the end of the sample corresponds to the financial crisis and associated major recession.  During this time demand shocks were clearly driving oil prices, and the correlation between the S&P and crude prices was very high and positive.  Thus, there was more systematic risk 2007 and later, and this would be expected to affect risk premia, but the model precludes this.
11. The omission of systematic risk in a model of risk premia is a serious, and IMO disabling, limitation.  It is particularly odd to ignore this in a paper that examines “financialization” of a commodity market, since financialization involves financial investors adding commodities to broadly diversified portfolios in order to optimize some risk-return trade-off.
12. These issues all affect how one interprets the HW findings.  What if risk premia did in fact change?  This could well reflect more accurate risk pricing due to the integration of commodities into investor opportunity sets.  Risks are going to be priced differently–and more efficiently–if there is more trade between islands.  A reduction in frictions, and an increase in the connections between markets, should lead to better risk pricing.  So finding a change in risk pricing could represent a very salutary development.
13. Indeed, tying some of these threads together, doesn’t “financialization” reflect a normal economic process of equilibrating prices between segmented markets?  Here, the prices are the prices of risk, and the movement of resources (risk) is more abstract than the movement of physical oil between Cushing and the Gulf.  In the latter example, profit seeking traders will drive the difference in prices in the two markets to the cost of transportation between them.  In the case of risk premia, any innovations (which could well include index investing) that reduces the costs of moving resources (risk bearing capacity) between prices will affect the prices in those markets, and tend to equalize them.  Since in the broader financial markets, oil and other commodities are small relative to the broader capital markets, it should be expected that the risk prices of commodities should account for the bulk of the change toward equalization.  It should also be welcomed.
14. To summarize a bit, the crucial questions include: what risks are priced?  Who participates in the market that determines these prices?  and, What are the investment opportunities available to these participants?  I think on every question, the HW paper is on very, very shaky ground.  The one-dimension model of fundamentals is far too restrictive, and the dynamics are far too simplistic.  Crucial players–hedgers–are left out, and others are treated mechanically.  In a paper that attempts to determine the effect of the movement of well-diversified financial investors into commodities, the Keynesian islands approach is inadequate: these investors have extensive investment opportunities that affect their behavior–and the pricing of risk that is the whole subject of the paper.  Mechanical treatment of one group of agents can make sense in some models, as in noise trader microstructure models.  Mechanical treatment of investors actively and aggressively looking for superior risk-return performance is a serious shortcoming in a model of the pricing of this trade-off.
15. I sympathize with James and Jing.   The impressive empirical cleverness required to estimate even this radically simplified model demonstrates just how challenging is the task of understanding the pricing of commodity risk.  I could readily believe that it could be impossible to estimate a richer model that includes fundamentals subject multiple, potentially heteroskedastic shocks, and three classes of optimizing investors with diverse investment opportunities. But the very complexity of the problem should make people very reluctant to make strong statements about the effects of “financialization” on price behavior.
16. In summary, I believe Hamilton-Wu are eminently correct to focus on risk premia as the variable that could be affected by the entry of a new class of market participant, but the daunting nature of that task is evident.  The radical simplification (again, understandable as a practical matter) needed to permit estimation, which involves abstraction from virtually all of the important economic issues makes their conclusions and results highly dubious as a basis for policy.  But there are plenty of fools out there (and let’s be clear, I do not include the authors in that category) who will no doubt rush in where prudent and thoughtful angels fear to tread.
17. For this reason, I wish they would have abstained from statements likely the valediction in their paper: “We suggest that increased participation by financial investors in oil futures markets may have been a factor in changing the nature of risk premia in crude oil futures contracts.”  This kind of suggestion only encourages the fools.  Every link of the chain of reasoning supporting this suggestion is flimsy.  Most importantly, the suggestion rests on a structural break which corresponds roughly with a period of time during which more financial investors participated in commodity markets.  But many other things changed during the same period.  Indeed, Hamilton himself has repeatedly pointed out that this period was one in which there was a virtual cessation in the growth of oil output.  That’s a pretty important fundamental.  Moreover, this was a period in which emerging markets, notably China, began to impact commodity markets dramatically.  Furthermore, most of the period (say 2007-2011), was one of financial an economic upheaval not observed since the 1930s.  That’s a pretty big change too.  Why put all the focus on index investing?  The model certainly doesn’t support that, because (a) all of these other factors are omitted altogether, and (b) even the model of index investing is crude and mechanical.
18. That is, to attribute the change in risk premia estimated from a clearly mis-specified model to a single change among many that occurred during the period of change is highly, yes, speculative, and an extremely tenuous piece of post hoc ergo propter hoc reasoning.

I do not want to close on a negative note.  I admire that Hamilton and Wu have focused on the right issue and have brought impressive econometric skills to the problem.  Improving our understanding of these issues would best be achieved by following the direction James and Jing have pioneered, by incorporating some of the features discussed above.  It will be a hard road, but worth taking.  Hamilton-Wu is a helpful first step along that road, and I hope that people understand it is only that, and that much hard slogging remains.

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A few technical asides:

1. The use of NYMEX data in which time to expiration changes presents some complications to the estimation and interpretation.  It would be worthwhile to look at LME metals data (e.g., copper) because (a) it has also been claimed that financial investors have affected metals pricing, and (b) LME trades constant-maturity contracts that are easier to handle empirically.
2. If the focus is on index investors, who by definition trade in multiple commodities in a mechanical way, it seems that cross-sectional evidence would be quite informative.  For instance, did risk premia change in a way similar to that claimed for oil in other markets that are also part of commodity indices?