Riding The Wave

September 01, 2005

INDEX BASICS

A number of broad-based commodity indexes are currently available, each with different rules regarding a host of issues (calculation methodologies, component selection criteria, futures roll periods, etc.). Investors should be aware of these differences before making investment decisions.

When constructing an index, product providers are trying to satisfy two different masters. The first is the desire to compose a basket of components that is "representative" of the market in general-although "re p resentative" can be interpreted differently by the various providers. The second issue is how readily exposure can be gained-the so-called " investability" of the basket. Investability covers issues such as component liquidity, suitable proxies and other operational concerns. Each of the index providers attempts to draw a balance between these demands. The balance that is struck is the source of many of the differences between the various indexes.

In general, the available indexes draw their constituents f rom the accompanying list of commodity sectors and components. These component products offer an acceptable balance between demand re p resentation and liquidity. The RICI is an exception, drawing constituents from a larger pool of commodities, albeit at the anticipated cost of liquidity and operational efficiency.

Figure 5

Sector Components

Energy

Crude Oil, Natural Gas, Heating Oil, Unleaded Gas, etc.

Grain / Agricultural

Soybea ns, Wheat, Corn, Oats, etc.

Industrial Metal

Aluminum, Copper, etc.

Livestock

Cattle, Hogs, etc.

Precious Metal

Gold, Silver, etc.

Softs / Fibers

Coffee, Sugar, Cocoa, Cotton, etc.


Arithmetic Vs. Geometric

One of the most prominent differences between the various indexes currently offere d is in the calculation methodology. This is the actual formula used to compile the individual component prices and compute an index value.

Figure 6

Index

Methodology1

CRB

Geometric

DJ-AIG

Arithmetic

GSCI

Arithmetic

RICI

Arithmetic

SPCI

Geometric

There are some key points to keep in mind when discussing the differences between the geometric and arithmetic index constructs, which can have profound impacts on the actual behavior of the products.

Arithmetic

A three-constituent arithmetic index would be represented by the following formula:

The main details to keep in mind when discussing arithmetic indexes are the following:

  • Constituent dollar weights change as underlying prices move.
  • To replicate the index, a portfolio manager must buy and hold the basket.
  • An arithmetic index will outperform a straight geometric index.

Investors are probably most familiar with arithmetic indexes, as this is the methodology employed by most equity indexes. When a component within an arithmetic index appreciates relative to the other components, its weight within the index increases. A geometrically calculated index would keep the representation of this component constant, holding fewer shares at the higher price.

Geometric

A three constituent geometric index is represented by the following equation:

The main points to keep in minds are:

  • Each component has a fixed dollar weight in the index, and that weight remains constant.
  • In order to maintain the constant dollar weight, a portfolio manager must react to changing constituent prices by continually rebalancing the portfolio by:
  • Buying commodities when prices fall relative to the basket.
  • Selling commodities when prices rise relative to the basket.

A geometric index which includes the returns from the convexity associated with this methodology often outperforms an arithmetic index in oscillating markets.2

In theory, a geometric index rebalances in real time throughout the day, each time a component price changes. In reality, this is not practical for investors. For one thing, futures trade in whole lots-fractional amounts cannot be transacted. Therefore, geometric indexes may establish rules governing when rebalance trades are initiated and how to reinvest any profits generated by this activity.3

Although geometric indexes are not as well known as their arithmetic cousins, there are some notable examples, including the Consumer Price Index, most currency indexe s (such as the USDX) and some equity products (such as the Value Line Composite Index).

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