From the November 01, 2005 issue of Futures Magazine • Subscribe!

Will the real price please stand up?

Studies that examine the returns of futures-based investments often ignore unique aspects of these markets. Speculative futures positions exist amid many contracts with different expirations and prices. At the same time, prices, not returns, are usually mentioned in the context of inflation, economic growth, revenues of producers or expense of consumers, historical perspective, currency levels, hedging, etc.

Discussions of oil prices and currencies in the media are typical. Often, charts are used to deliver the message, but because of the simultaneous existence of multiple contracts, commodity price charts can create misconceptions. Such illusions affect the public’s perception and can affect traders’ judgment. The reason is the term structure of simultaneous futures prices, but with an understanding of this structure, traders can see prices more clearly.

Countless charting software tools are available today, from free access Web sites to institutional products. In many commercial charting tools, two types of price charts for commodities are available. The first broadly used type of charts is of individual contract prices for a given commodity on, say, a daily scale. These typically are the open-high-low-close charts, with numerous modifications. As an example, “Daily breakdown” (below) shows prices of an August 2005 feeder cattle contract. Similar open-high-low-close charts are also broadly available for equities.

See chart 1 below

In many cases, however, the life span of an individual contract is not long. For a person interested in the long-term price movements of any commodity, other chart types provide a more extensive historical perspective (see “History lesson,” below). Similar historical graphs are widely used in the media. Visual appeal, simplicity and clarity of such charts are the reasons for their proliferation. The problem is that many traders may forget that these price streams are fictional. That’s because these long term charts must be constructed from the actual prices contained in the individual futures contract months, where actual trading takes place.

Despite the clarity of visual presentation, the charting algorithms that are used to create these historical charts may create illusions that affect trader and money managers’ judgment calls.

See chart 2 below

Historical Charts

Usually, charts of historical commodity prices are constructed by referencing the front-month futures contract. Prices of the front month contracts are considered representative for the commodity in general. For many software programs, when one front-month futures contract expires, prices for the next contract, which is now the front-month, are simply added onto the existing price stream. The idea of creating one, long-term price series seems to be borrowed from the stock market, where there is only one tradable instrument.

The difficulty is that with futures, the historical charts “glue” the prices from different contract months together and depict them in continuous fashion. There are two problems with such chart presentations. The first problem relates to liquidity. Once in a while, front-month prices for practically every commodity experiences extra volatility, especially near expiration. Such extra volatility patterns of the front-month prices may be caused, for example, by short/long squeezes or option-related activities. Looking at a chart with squeezed price patterns creates a visual aberration of extra volatility, though the rest of the contracts, which may have most of the open interest, are usually traded at substantially lower volatility than the front-month expiring contract.

Also, the most active trading usually occurs in the contract with the highest open interest. In the context of money manager or hedge fund trading, prices of thinly traded front-month expiring contracts with small and decreasing open interest and wider bid-ask spreads may barely be considered as a characteristic for a given commodity. As a result, prices of actively traded contracts with the highest open interest are more suitable to be considered representative, especially in the context of professional trading activity.

A typical structure of open interest fits perfectly into that. A contract comes into existence, its open interest rises, it becomes a front-month contract and then it expires. This pattern of change of open interest is typical and is observed by practically all commodities. In most of cases, the front-month contract will be the one with the highest open interest except near expiration. In cases where it’s not, the trader must be careful.

A more serious conceptual problem with the merging of front-month contract prices relates to their tradability. To understand the tradability problem, consider the prices of all future contracts for soybeans leading into 2005 (see “Phantom profit,” below).

See chart 3 below

Daily price settlements of the individual contracts are shown by different colors in the chart. If the open interest of the contract is the highest among all other contracts, the prices of the contract are shown in black. These lines can be considered representative for soybean futures. However, the black lines are not continuous. When the contract approaches expiration, its open interest shrinks and open interest of the other contract grows. Therefore, one black line ends and the next line begins.

For instance, the green line represents prices of the July 2004 soybeans contract. Near its expiration, the black line switches to the November 2004 contract. The green line, after being black, shows the prices of the July 2004 soybeans contract until its expiration. Roughly, the black line in “Phantom profit” corresponds to the front-month chart in “History lesson.” Both charts closely correspond to the spot prices.

To highlight the tradability problem, consider the profits of a trader with a short position in the July 2004 contract. On June 17, 2004, the open interest of the November 2004 contract becomes the largest and the trader decides to roll his short position. The trader buys back the July contract and shorts either the November (violet line) or September (blue line) contract.

The trader shorts the next contract at a much lower price than the July contract price. As a result, estimation of a trader’s profit based on a chart with front-month prices are inaccurate. Without an actual rolling process, “History lesson” creates an impression that there was a large drop in soybean prices in June. Hence, an attempt to evaluate the gains of the short position from such a chart may easily overestimate profits by 100% or more.

Existence of such charts, without consideration of actual cash positions, rollover price gaps and spreads between contract structure, may create visual and psychological illusions of trends, breakouts, gaps, etc. Coupled with moving averages, such charts bury the actual mechanics of trading, price difference between different contracts and the difference between physical and futures markets.

It should be clear that rollover gaps have a direct relation to the relative prices of future prices. Popular fixes to this problem tend to focus on these rollover gaps. Attention is paid to the creation of continuous adjusted price time series. Such price series are further used in technical analysis.

While adjusted price series provides adequate basis for estimation of profits and losses, it is not suitable for making trading decisions, especially when some techniques can actually result in negative prices.

Gold standard

Long term chart constructions can lead to psychologically comforting, but incorrect, conclusions. Rigorous analysis of profits and losses may present a substantially different picture than intuition based on historical charts. For example, consider prices of gold in the last five years. “Gold bugs or gold duds?” (below) depicts the difference. The first chart is a standard snapshot of gold prices.

See chart 4 below

The second chart shows the entire history for all gold futures contracts traded. The impression given on the first chart is that gold moved from about $280 dollars per oz. in 2001 to about $430 by the beginning of 2005. This observation seems to support the common idea that gold appreciation is about the same size as U.S. dollar drop vs., say, the euro. Most traders, however, want the benefits of the futures market and use of leverage. And, remarkably for futures, the profit/loss picture is quite different, especially for the long-term investors. Note that in the second gold chart, the black lines are below all of the colored lines: future prices of highest open-interest contracts are lower than the prices of deferred contracts. Such a situation is known as contango.

As a result, each time a trader rolled over his long position during those five years (2000-05), he would buy a gold futures contract at a higher price than he would sell the previous contract. Analysis shows these rollover price gaps would eliminate 30% to 40% of the long-term gains of a long gold position. After this analysis, gold may not be an attractive hedge anymore.

Alternatively, if there is a real or perceived shortage of a commodity, its front-month prices would rise to reflect the shortage and would be higher than prices of more deferred contracts. This situation is called backwardation. The backwardation/contango situations are critical for the proper analysis of profits and losses. Both gold and oil have gone up in price in the last four years. But cash gains of long futures crude oil positions are substantially higher than charts would imply. For gold, gains are substantially lower.

Therefore, front-month charts, adjusted or not, may be informative for a person dealing with a cash business, but for the money manager and hedge fund operator, who deals with profits/losses of futures positions rather than with cash businesses, such charts may send a distorted message.

Spreads, cash-oriented

For commodities such as crude oil and natural gas there are 10 or more different futures contracts traded simultaneously. Some of those commodities exhibit long-term price trends related to structural economic dynamics, and some of the future positions in those commodities are intended for holding through a substantial period of time with many rollovers. There is a clear need to derive quantitative, convenient, robust, easily computable, intuitively clear, cash-oriented measures for the rollover gaps. Note that such estimations would also quantify the “intensity” of contango/backwardation patterns and measure price spreads between different contracts.

To derive such estimators we must consider that return targets of investments are higher than the risk free rate. It seems logical to suggest that such estimators be cash-oriented and should provide an averaged and annualized value of the rollover gaps.

As a result of these requirements, we can suggest estimators of the rollover gaps. At each moment of time (t), sort all N-traded futures contracts in ascending order of time to expiration. The first contract is the front-month contract. Let (k) denote the contract with the highest open interest.

In many cases, k=1. Therefore, N-k is the amount of the deferred-month contracts expiring after the highest-open-interest contract. Let F(k)t be the “settlement” price of the highest-open-interest contract. So, for F(j)t, the relationships j=k+1,...,N are the prices of deferred contracts, and T(kj) is the annualized difference between expirations of the k and j period contracts.

An annualized price spread between the highest open interest and the j period deferred contract is, therefore, |F(k)t-F(j)t|/T(kj). Then, the annualized averaged absolute R(t) and relative P(t) rollover gaps are defined as:

The value of R(t) measures price gaps and what is gained or lost at rollovers. At the same time, it estimates the averaged annual price spread between highest-open interest, and deferred-months contracts. It also quantifies the strength of contango/backwardation patterns. The value of P(t) gives a relative value of rollover price gaps compared to the highest open interest futures price.

Large and positive R(t) or P(t) values mean a strong contango pattern. Each time, for a long position, the trader will have to pay a higher price than the previous contract. Negative R(t) or P(t) values mean a backwardation pattern. For a long position, the trader would buy a contract at a lower price than the expiring contract.

For most commodities, R(t) and P(t) show interesting long-term mean reverting properties. In the context of backwardation, R(t) or P(t) may be regarded as a quantitative measure of the market sentiment, especially when at extremes.

The direct merging of front-month prices for commodity futures is used in many available software platforms for the construction of historic price charts. Such price series are not tradable. Use of charts for estimation of profits/losses of futures positions for commodities may generate gross errors. Such charts also may create visual impressions of large price moves and possible trends and affect traders’ judgment. Adequate evaluation of potential profit/losses for long-term futures positions with many rollovers requires an estimation of rollover price gaps, which in turn, possess additional interesting features and may be used as a gauge of market sentiment.

It is plausible that the next generation of financial software will provide traders with simultaneous charts of future prices for many expirations and for a measure similar to R(t) or P(t)? Such tools will allow traders to make more informed decisions.

Igor L. Kliakhandler is an associate professor in the Department of Mathematical Sciences

at Michigan Technological University and a managing member of North Trading LLC.


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