Comment on “Ex Ante Evidence of BackwardationKontango in

Commodities Futures Markets ”* John F. Wilson

y immediate colleagues and I at the Fed work in the exchange markets M area, and our day-to-day contact with futures issues comprises occasional monitoring of currency futures on the IMM and observing how developments there interact with the larger interbank market. Terminology like “backwarda- tion” and “contango” is therefore not part of our daily parlance, even though it turns out the phenomenon is very much like the subject of a lot of work which has been done on exchange rates. That work centers on the question of whether for- ward exchange rates are unbiased predictors of expected future spot rates. This question has been addressed in numerous empirical studies at the Fed and else- where. Put another way, the question is whether there are verifiable returns to speculation in the exchange markets which might account for the willingness of speculators to take the intertemporal risks involved in providing more liquidity to the exchange markets than would be provided by hedgers alone.

The backwardationlcontango issue in futures markets is on several counts like the “efficient markets” question in the exchange markets. First, both kinds of studies look for empirical evidence of bias in prices of contracts for future de- livery compared with prices realized subsequently (ex post) or those which are presently expected to prevail (ex ante). Second, in both forward and futures mar- kets there are certain intertemporal arbitrage conditions which constrain the rela- tionship between the forwardlfutures price and the currently prevailing spot price for the commodity or currency in question. In the futures markets this condition is that the futures price cannot exceed the sum of the spot price of the commodity plus carrying and convenience costs over the relevant horizon, else arbitragers would buy in the cash market, sell forward, and carry the goods for sure gains. The analog in the exchange markets is the interest-parity condition. Should for- ward rates on major currencies depart by more than a little from international in-

* Presented at the December 1981 meetings of the American Economic Association in Washington, DC.

John F. Wilson is an economist in the Flow of Funds Section in the Division of Research and Statistics at the Board of Governors of the Federal Reserve System in Washington, D C.

The Journal of Futures Markets, Vol. 2, No. 2, 169-173 (1982) 0 1982 by John Wiley & Sons, Inc. CCC 0270-73141821030169-05101.50

terest differentials, there are likewise sure gains to be made via arbitrage. Finally, although it appears that systematic study of backwardationlcontango in the fu- tures markets antedates much of the literature on bias in forward exchange quota- tions, both kinds of work seem to have led to rather inconclusive results. As is evi- dent from the article on which I was asked to comment, neither the Keynes et al. versus Hirschleifer et al. controversy on backwardation and contango nor the comparable disputes in the exchange markets literature have been laid to rest.

Turning specifically to the work of Professors O’Brien and Schwarz, I should say first that I found this article well written, lucid, provocative, and a construc- tive contribution to the backwardationlcontango debate. The authors have ex- ploited a novel methodology, on which I will make further comments shortly, and have come up with an interesting set of results which suggest that the prevailing expectational scenario in the market they examine is one of backwardation. That is, the bulk of their findings, as they relate to the gold market, suggests that there is an ex ante expectation that spot gold prices in the future will be higher than those embodied in the current prices of futures contracts on gold.

Perhaps it would be worth noting now two points about the backwardationlcon- tango and “exchange market efficiency” questions which I think are germane. First, backwardation and contango are two sides of the same coin; each entails a predictive bias, although the directions of the hypothesized bias are opposite. In some markets, particularly those under seasonal or cyclic influences, finding backwardation in some periods would not preclude the possibility of finding con- tango in others. Thus, they are not mutually exclusive. An empirical “finding” of backwardation andlor contango would be equivalent to establishing that there is a risk premium which induces speculative entry into these futures markets. Such a premium could be either positive or negative, depending on expected future spot prices, and its sign would determine whether speculators are tempted to take long or short positions in their commitments. In the subject article, O’Brien and Schwarz predominantly “find” backwardation in the gold futures market, with only occasional evidence of contango. In their analysis the null hypothesis seems to be one versus the other as the alternative. But in a statistical sense perhaps a more meaningful dichotomy is the hypothesis of any risk premium versus none; i.e., futures prices as more-or-less unbiased indicators of expected (or realized) ac- tual future spot prices.

Second, the authors appear to have suggested that looking at backwardationl contango in an ex ante framework is better than using ex post data on the same subject. In fact, most of the earlier studies mentioned in their article do employ ex post spot prices as measures of possible bias in futures prices, and I agree that the ex ante attempt has considerable interest. However, it should be clear that ex ante methods-to get an expected future spot price-cannot really clear up the question as to whether there are actually returns to speculation. Answering that one, to my mind, does seem to require data on realized outcomes. There are vari- ous reasons one might adduce why speculators expect future spot prices to be higher (or lower) than the levels embodied in futures contracts; but if they are wrong then presumably they will lose money or, at least, not make any rather sys- tematically. This implies that existing participants will change their behavior or disappear from the market. Who, then, are the new actors? I suppose it could be argued there is always an elastic supply of new speculators to account for the con- tinuing liquidity of these markets, but at this point the issue would already have

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departed somewhat from actual returns to speculation toward more abstruse ques- tions of expectations formation and how some of the people can be fooled so much of the time. In short, whether backwardationlcontango are verifiable phenomena does seem to depend in good part on expost data, even though I would applaud the attempt to work in the e z ante framework. I do not know what to suggest by way of blending the two, but I do have an impression that part of the story is miss- ing in this article.

To summarize briefly my understanding of the O’Brien-Schwarz procedure, it is basically an application of the model developed by Black-Scholes and extended by Rubinstein, Lee, Rao, Auchmuty, and others in the options-pricing literature, used here to solve (jointly) for expected price variability and the expected future spot price of a commodity. In this case the commodity is gold. Although there is no exchange-traded options market in gold, there is a sort of private, over-the- counter market run by Mocatta Metals, from which gold “options prices” can be obtained. O’Brien and Schwarz have assembled 144 observations on prices during June and July 1981 of options expiring in periods from September through March 1982. There is, of course, an extensive futures market in gold, and by comparing transactions prices there with the implicit expected future spot prices obtained from the modified Black-Scholes model, the authors are able to test statistically whether backwardation or contango obtain. There is no explicit test of a risk pre- mium versus the alternative of unbiased futures prices, but in several cases the au- thors find “neither backwardation nor contango,” and I suppose this could be roughly interpreted as a finding of no predictive bias, again in the ex ante sense.

As we have seen, Table I in the O’Brien-Schwarz article provides summary mea- sures on backwardationlcontango findings for the whole 144 observations, as well as for the June and July subsamples taken separately and for the roughly 18 ob- servations from each subsample which expired in a given month from September through March. With the exception of the July option expiring in October (which showed neither), these first results uniformly indicate backwardation. Tables I1 and I11 partition the data in other ways, the former according to June-July sub- periods when the spot price of gold was fluctuating in different ranges, and the latter according to short-term movements in spot prices on the day before, the day of, and the day after the option quotations. Again, the results predominantly point toward backwardation. However, the authors do not delve into the question of why backwardation should obtain. Why this should be, given our recent history of high and fairly variable interest rates, is not entirely clear to me, but this finding emerges rather persistently, no matter how the O’Brien-Schwarz sample is partitioned.

One of my reservations, expressed a moment ago, is surely the matter of the strictly ex ante framework. In addition, I have three other basic questions, which are more interrogatives than outright criticism.

First is the question of whether gold is really an appropriate subject for such a study. As I understand it, the backwardationlcontango literature has grown up mainly around agricultural goods subject to production cycles and periods of sur- plus and shortage, and for which there is considerable hedging interest. The dom- inant force in most agricultural futures trading comes from hedging desires, with speculators drawn in to provide the “insurance” or bear the risk. Speculators are often thought to be mainly long in the backwardation scenario, and mainly short in the contango situation. None of these patterns apply obviously in the case of gold. Although commercial and industrial uses of gold may be distributed more or

COMMENT ON BACKWARDATIONICONTANGO / 171

less evenly through time, it is not apparent there is any cyclic production pattern, and in any case there is always a large stock of privately held gold in “inventory” relative to foreseeable consumption.

In terms of the drive behind the futures markets, while one cannot discount the role of hedging, I suspect futures trading in gold is dominated by speculators, meaning there is a situation of heterogeneous expectations. Speculators who are long in futures would have ex ante expectations fitting the backwardation pattern, whereas the shorts would have ex ante price expectations conforming to the con- tango pattern. If the O’Brien-Schwarz model is correct, the main implication of their results may be that speculative positions in futures are mostly long and that there is substantial hedging on the short side. If so, why?

My second interrogative concerns the empirical model used to derive the ex- pected future spot prices. The original Black-Scholes model and those of Rubin- stein and Lee-Rao-Auchmuty solve for options prices in terms of a number of variables, including the spot price of the commodity, striking price, time remain- ing to maturity, price “variability,” and rate of return. O’Brien and Schwarz have the series on options prices and solve jointly for variability and expected future spot prices using a nonlinear estimating program and a model derived from the Black-Scholes framework. However, exactly what variables and functional form comprise this derivative model are not indicated in their article, and in looking back through the literature I stumbled somewhat over the fact that the “expected future spot price” is not among the explicit determinants in the predecessor models. Perhaps this term can be derived from the rate-of-return variable, but it was not clear to me how. (I understand that there is a more detailed version of their article in which these steps are made clear, so perhaps this point is not a pro- blem at all. However, I was not able to get quite over this hurdle with the present version, and would suggest that somewhere the exact equation be written out.)

On a related issue, it is of some importance that an options-pricing model un- derlies the present effort. I do not know exactly what kind of “over-the-counter” market Mocatta Metals runs in gold options, but perhaps the pricing of these op- tions is not the kind which would obtain in public exchange trading. Nor was I able to get an idea of whether the options “prices” used in this study reflect any notable volume of transactions or, in short, are or would be “market-related.” The importance of this point is that the Mocatta options prices are crucial to solv- ing for expected future spot prices, and I was left with some doubts as to their reliability.

My third interrogative concerns the results Professors O’Brien and Schwarz have obtained and shown in their three tables. I have already mentioned the ex ante character of these results, and on that point I would only suggest some atten- tion to the ex post relationships. Concerning the overall findings summarized in Table I, the statistical evidence of ex ante backwardation is so pervasive across options and maturities that the strong finding of contango for the October option (at July prices) stands out sharply. Aside from commenting that this result may be associated with the “near-term’’ character of the option, the authors give no par- ticular explanation. If “near-term” is something special, why doesn’t the Septem- ber option (at June prices) also suggest contango?

Results in Tables I1 and I11 tend to show that backwardation is less statistically significant when spot gold prices are low or falling than when they are high or ris- ing. I suppose this finding is the intuitive one, but in some respects the authors’

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description is misleading. They write (p. 163) that “a decline in price expectations appears associated with a decline in the spot price.” Actually, a decline in price expectations is not enough; it must be sufficient to reverse the sign of the dif- ference between it and prices of futures contracts. Obviously, if spot prices of gold decline and futures prices shift downward, merely a decline in expected future prices is not sufficient to turn backwardation into contango; only a dispropor- tionate fall is sufficient. One can imagine small spot price declines without associated large falls in expected future prices, which seems to me still to leave open the question of why evidence for backwardation should weaken under such circumstances.

With regard to the results in Table 111, the smaller sample sizes naturally work to undercut statistical confidence, but I found it interesting that in some of the cases where three or more (of the four) options showed backwardation, gold prices predominantly fell either on the day of dr on the day prior to the observation. I tend to discount the usefulness of price changes on the day after the observation, however, as being essentially beyond the knowledge of market participants.

Finally, despite these caveats, I was pleased to note the authors’ effort to check “the consistency of other Mocatta option prices with the option model,” which suggested the model has a fair degree of reliability and appears to suggest that the Mocatta options prices may be near levels which might prevail if there were exchange trading. To conclude, I hope that my small critiques do not exceed the usual and customary bounds of occasions such as this; and that they may be of some service to the authors in their further work on this interesting topic.

C O M M E N T ON BACKWARDATIONICONTANGO / 1 73