From the September 01, 2009 issue of Futures Magazine • Subscribe!

Currencies, eurodollars, silver and gold: Not your average relationship

Over the past few years, the relationship between gold and silver has expanded to include a large number of additional financial instruments, among them eurodollars and the U.S. dollar index. These additional markets expand this partnership into new territory and offer several new angles for analyzing the direction of prices.

“The Partners” shows December 2009 gold and silver futures prices, eurodollar rates and the U.S. dollar index from March 2 through July 8, 2009. These charts indicate that the junior partners of eurodollars and the dollar index do not always agree with their precious metals elders. From the middle of April to the first of June, there is almost total disagreement as gold and silver prices climbed, while eurodollar rates and the dollar index declined.

Eurodollar rates and the dollar index would certainly protest their description as a negative influence in the relationship because a decline in either usually accompanies increases in gold and silver prices. Lower interest rates, represented by falling eurodollar rates, allow gold and silver to be held with lower storage costs. A falling dollar value tends to lift all commodities and make gold and silver relatively more expensive. Thus, the charts for eurodollar rates and the U.S. dollar index indicate support for gold and silver. From June 2 to July 8, the dollar index was low and stable, while December eurodollar futures showed low rates at the beginning and end of the period.


Between the senior partners of this ancient relationship, there is some disagreement as to the balance of power. Through the centuries, the ratio of value between gold and silver has varied and as “Ratio of gold to silver” shows, the comparative value of gold to silver increased from 68.6 to 74.5 from March 2 through April 30, 2009, then the ratio declined to 66.5 by the middle of June. Reasons for the decline in the gold-to-silver price ratio include the larger volatility of the price of silver relative to gold and the extra boost given to silver by the decline in interest rates. From June 2 to July 8, gold returned to the level of 70 times silver as both metals fell in price while the higher volatility of silver carried it down relative to gold.

Although the price of gold holds an advantage of approximately 70 times the price of silver, the two partners show a high degree of correlation in their variations over time. “Precious correlation” contains a short-term history of their relationship, from March 5 through July 8, 2009.

The short-term comparison of gold and silver combines two averaging processes to enable the resulting data to vary around the standard ratio of 1.00. Original prices are averaged over 90 days from March 2 through July 8. Each day’s price is computed as a ratio to the 90-day average. To eliminate minor variations, the first ratio is divided by a four-day moving average of ratios to the 90-day average. The final results are referred to as “ratios to moving average.”

The variations of silver and gold indicate that silver is more volatile than gold, with ratios to moving average that reach higher peaks and fall to lower troughs than those of gold. Only one gold ratio rises above 1.02, compared to nine for silver. None of the gold ratios fall below 0.96, compared to four for silver. Along with its higher volatility, silver is still a long-term partner, with ratios to moving average that consistently return to the standard of 1.00 and pass by gold on the way to the other short-term extreme.

Comparative volatilities of gold and silver may be measured by an option pricing method such as the LLP model or Black-Scholes. On July 8, 2009, the LLP method computed the heights of December 2009 call price curves for gold and silver as percentages of the current futures price. For gold, this volatility measure was 5.88%, while silver was higher at 8.66%.

According to the LLP model, the market consensus of the possible price spreads at expiration in December 2009 is $1,020 to $808 for gold and $15.25 to $10.70 for silver. The price spreads equal 23% of the current futures price for gold vs. 35% for silver. The volatility measures confirm that silver will continue to vary more strongly than gold, while the two remain committed to their historical partnership.

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