One of the oldest living couples, gold and silver, share a resplendent and sometimes checkered past — valued for their rarity, providing coinage for realms both ancient and modern, lending their talents to industrial and scientific uses, adorning humanity as jewelry, and sharing duties as vessels for food and drink. Their personalities are different – gold is staid and somewhat aloof while silver is flamboyant and risk-loving.
During the Nixon administration, France’s President de Gaulle decided to test the convertibility of paper dollars to gold. The relationship between the dollar and gold already had been diluted by a diminished percentage of gold backing, but de Gaulle’s demands sealed the doom of an official linkage to the precious metal. With demands by Congress for spending programs that would have been limited by the amount of gold in the Treasury and by the U.S. appetite for foreign goods and services, the promise of metallic backing for U.S. paper money flew out the window.
The fallback position for the value of the U.S. dollar is restraint in spending by the Federal government, so that the amount of dollars in circulation (paper and electronic) does not exceed the correct balance between the U.S. national economy and the world’s dollar holdings in the opinion of foreign governments and business firms. The futures markets for gold and silver provide an excellent measure of how well the United States currently is protecting the dollar’s value, and the recent struggle in Congress over extending the national debt limit highlights the difficulty of restraint in spending.
Value proposition
From Sept. 1, 2010 to March 1, 2011, the December 2011 gold futures price increased 14.2% from $1,257 per ounce to $1,436. Over the same period, December 2011 silver futures advanced by 77% from $19.53 to $34.57. The variations over this six-month period are shown on "Daily percent changes" (below).
Through September and October the percent changes are relatively small, confined within plus and minus 4%. November experienced much larger volatility, with several days exceeding plus or minus 5%. As we can see, the daily volatility of silver is higher than that of gold, on average.
"Cumulative percent changes" (below) shows the determined increase in December 2011 silver futures vs. gold futures from Sept. 1, 2010 to March 1, 2011. The intermediate peaks and troughs in the price of gold are matched in timing by silver, with some exaggeration especially noted in early November. Declines in silver vs. gold during January 2011 may be related to short sales of silver, while the increase in silver futures in February 2011 may be because of market resistance against short-selling silver. Attempts at manipulation of precious metal prices have been noted through history, although the turmoil in North African nations in early 2011 is probably the major cause of price escalation during January and February.
To see how well the percentage changes in the price of December 2011 silver futures are correlated with the changes in the price of gold futures, a regression analysis of the 123-day period of comparison is shown on "Silver and gold correlation" (below). The results of regression are: slope 1.80, y-intercept 0.0028, and correlation coefficient 0.84. Thus, the straight regression line rises and falls from a zero change in the price of gold futures, with changes in silver futures approximately 80% larger than changes in the gold futures price.
With the volatile price movements occurring near the close of the year 2010 and early 2011, it is interesting to see the price forecasts implied by the options market. The results of option pricing analysis are shown on "Options market forecast" (below). The analysis is based on the December 2011 expiration date for gold and silver futures on March 1, 2011. For both metals, option prices predicted by the regression equation are close to the actual market prices, showing that call price curves describe a parabola between the natural logs of option price/strike price and futures price/strike price. Heights of the call option price curves reflect the expected volatility of silver vs. gold futures, with the time premium of silver at 11.4% vs. 6.7% for gold.
It should be noted that the option pricing model is based on the market’s perception of price variability of the underlying asset. The reason that both upper and lower break-even prices are shown is that the forecast does not indicate a direction of rising or falling prices. It forecasts the price range at expiration — a forecast that the market must make on a continuous basis as a requirement for computing option price curves in which the current futures price is located at the approximate center of an estimated price range. With decreasing time to expiration, the spread between upper and lower breakeven prices will be reduced along with the associated time premiums.
The analysis shows that silver and gold futures prices are a tandem set, with silver price movements oscillating around the gold percent price changes, but with significantly greater variations. It is obvious that price changes of this magnitude are favorable to spread trading between gold and silver futures.
As shown by the high correlation between options market prices and prices predicted by the log-log regression equation, the call and put options related to every strike price have a definite place on the price curve. Completely organized markets, such as the U.S. options market, encourage spread trades and other more complex trades based on continuing predictable relationships between options and their underlying assets.
Silver in backwardation
Near the end of February 2011, an unusual price pattern emerged for silver futures, causing a condition of backwardation with the spot price of silver higher than the futures price. Futures prices for precious metals are generally expected to exceed the cash price. Reasons include the ability to have access to the metal without storage and other costs, and leverage that permits reduced investment of capital.
Backwardation in the silver futures market implies a shortage of silver available for arbitrage that would control the futures-cash price differential. A physical shortage helps to explain the long-lasting effect of this backwardation — days or weeks instead of the usual hours required for arbitragers to smooth the price differences. The possible shortage also helps to explain the rapid increase in the price of December 2011 silver futures vs. the slower increase in the price of gold futures.
The difference between the usual expectation of contango for precious metal futures and the existing backwardation for silver futures is shown in "Moving in opposite directions" (below). This chart shows the cash or spot price of the metals on March 1, with 19 futures contract dates ending at December 2015. For gold futures, the first 14 contracts are slightly above the spot price — then increase by approximately $200 to the 2015 delivery date. Silver futures are approximately equal to the spot price through the first six contracts — then gradually decline by $1.20 through the December 2015 date.
Implied by the contango and backwardation chart is that December 2015 silver futures would be priced higher — perhaps by $2.00 or more — under normal conditions in the silver market. It is interesting to see that the factors that are affecting silver seem to have little or no impact on gold. This suggests the possibility of price manipulation or shortage of supply in the silver market — perhaps in combination.
Through the remainder of 2011, the price action of gold and silver, and the December 2011 futures relationships described above, may show that both metals — particularly silver — currently are undervalued. They are islands of safety in a world of increased risk; however, pricing anomalies add an element of concern.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.
