The final intercommodity spread we will look at is unusual in two respects:

1. The spread is based on the way the index is calculated.

2. The spread is initiated by buying or selling both sides.

The spread involves the US Dollar Index against some of the component currencies. This is a rather complicated spread and cannot be thoroughly analyzed, but we will look at the salient points to show how the spread is done.

The index has two important properties:

1. The USDX is quoted in European terms (foreign currency/US dollar) but settled in US dollars. A given percentage change in one currency will not equal the percentage change in the other currency because the relationship is reciprocal.

The index is inversely proportional to the component currencies. This means the index goes up if the currencies go down and vice versa. Therefore if the German mark drops by a certain amount, the dollar index will rise by a certain amount assuming the other currencies decline or stay the same. A given percentage change in one currency will not necessarily equal the same percentage change in another currency.

For example, assume 1 US dollar = 2 German marks. The European quote is a foreign currency divided by the dollar so a European quote of the dollar and mark would be 2 marks per dollar. The American quote is the dollar divided by the foreign currency so an American quote would be 1/2 dollar per mark.

1. The index is a geometric index. A geometric average will usually increase less and decrease more than the corresponding arith­metic average. Most of us are familiar with arithmetic averages. An arithmetic average is calculated by adding all the prices and dividing by the number of prices. A geometric index is calculated by taking the nth root of the product of the prices.

When on element increases from 2 to 3, note how the geometric average goes up less from 2 to 2.4, whereas the arithmetic average goes up more from 2 to 2.5. When one element decreases from 2 to 1, the geometric average also drops more from 2 to 1.4, whereas the arithmetic average drops from 2 to 1.5. This is a normal property of the averages, but it has important implications in the dollar index versus the component currencies. A portfolio of currencies is an arithmetic average so it should outperform a geometric index.

These factors give the index option like properties similar to a straddle. If a trader buys the index and buys the component currencies, the component currencies will usually outperform the index, no matter what the prices are.

The basis is partly a function of this phenomena so there is a premium inherent in the basis calculation. The basis is partly a function of the volatility of the index and the component currencies. If the basis is too great and volatility too low, then money will be lost in buying the basis spread but made in selling it. If the basis is too low and volatility higher than anticipated, then money will be made in buying the basis spread and lost in selling it.

A trader would buy the dollar index and buy the currencies if the basis were too low for the given volatility. A trader would sell the index and sell the currencies if the basis were too high for the anticipated volatility. Although all ten currencies do not trade on the IMM, a proxy can be developed to simulate some of the currencies. Some of the currencies which are not on the IMM are highly correlated with the mark.

This type of trade can be done as an arbitrage if the cash inter-bank market is used. Most of the trading is still done as a spread, as opposed to a pure arbitrage.