Shadow pricing futures and ETFs

December 15, 2014 05:54 AM

A shadow price is created when any asset’s price changes are influenced by the changes in price of another asset. The influence may be so strong as to completely govern the shadow’s price changes. For example, an exchange-traded fund (ETF) may have its value determined by futures on a single commodity, a situation that permits little independent price movement of the ETF, aside from the price changes of the underlying commodity. 

Other shadow prices may be less controlled by the related asset. Silver traditionally has been linked to gold, and its price tends to shadow gold over the long-term but with wide variations because of the larger volatility of silver vs. gold. Other pairs exhibiting shadow pricing are live cattle and lean hogs, and corn and soybeans. Agricultural commodities are connected by common markets for their products, similar structures of costs and profits, and all are affected by climate as well as shifts in the import/export of them.

Economic competition is one reason for shadow pricing. This is as close-to-home as your local supermarket and as far-reaching as international currency markets. A country may allow its currency to gain value with respect to other currencies, but eventually either will permit or force it to fall to restore economic competitiveness. 

Examples of loose and strong shadow pricing of currencies are shown on “Currency ETF warfare” (below). The Swiss monetary authorities have decreed that the Swiss franc should not be stronger than 1.20 vs. the euro, and thus the franc is trending in an almost perfect shadow of the euro. However, an increasing separation is noted in August 2014 leading into September as the euro declined with respect to the Swiss franc and the Swiss fought back. On Sept. 15 the franc/euro ratio was 1.2105. 

The British pound was permitted to gain in relative value until the need to compete forced a decline to accompany the euro’s drop starting in July 2014. From that point, through the summer and into September, the pound joined the battle, falling almost 8% from July 1 through Sept. 15 compared with the change for the euro and Swiss franc of approximately 6%. As a result of the brawl, the Dec. 2014 dollar index (an innocent bystander, 73% of which is determined by the three currencies) was forced to rise 5.56% between July 1 and Sept. 15.

Forex traders should be able to profit from currency warfare as long as the announced or perceived determination by each central bank to maintain price control is in effect. During this period, normal economic variations in price are temporarily set aside while the battle goes on.

A shadow price may be created by an ETF that is based on the values of more than one commodity. In this case, an artificial “senior asset” price may be computed based on the formula followed by the sponsors of the ETF or ETN (exchange-traded note). An example of this scenario is the agriculture ETN known as COW. The price of COW is determined by the approximate ratio of 61% live cattle futures and 39% lean hog futures. 

The percentages may be used to create the virtual asset (COW’s avatar), COMBO. “COW and COMBO” (below) shows that price changes for COMBO shadow the underlying futures prices contained in COW. Short-term variations due to cattle and lean hogs not being perfectly correlated permit spread trades. COW is at times above or below COMBO in its cumulative percentage price changes, but COW cannot separate from its shadow for long. The two eventually cross paths.

The spread suggested on “COW and COMBO” on March 18, 2014, would have the trader taking a long position in live cattle and lean hogs in approximately a two-to-one ratio, and at the same time selling short an equivalent amount of the ETN COW. A reverse trade is noted for Aug. 21, with a long position in COW and short COMBO. 

Natural shadows

ETFs are, as indicated, natural shadows under their related futures contracts, but what about the options on futures and on ETFs? An ETF whose price is based on a single futures contract should have the same volatility as the futures. Forex futures and ETFs provide good examples of closely coordinated underlying assets and their shadows. 

Other ETFs based on single futures include GLD for gold and SLV for silver. Because silver is more volatile than gold in its futures price variations, it is expected that SLV would be more volatile than GLD in approximately the same relationship shown by the silver and gold futures. When this expectation is not met there may be an opportunity for a profitable spread trade. As shown on “GLD and SLV” (below) there are several potential trades during the period Feb. 4 through Aug. 29, 2014. Like the silver futures contract it represents, SLV moves away from GLD with larger volatility, but inevitably returns. Trades between SLV and GLD have the advantage of being priced and traded similar to stock rather than futures. 

Option opportunities

Options on currency ETFs tend to be priced slightly higher than the comparable options price curves of the underlying futures. “Calls on futures and ETFs” (below) shows calls on euro and Swiss franc futures as well as calls on euro and franc ETFs. Call prices for the ETFs are close to the options on futures but with a difference in height.

Because ETFs have the same volatility as their underlying futures contracts, it should be possible to compute call prices for ETFs based on options pricing formulas developed by regression analysis for calls on futures. The determinants of a call price curve are time to expiration and volatility of the underlying. Once these two requirements are met, an options price curve can be computed based on the given underlying price and a chain of strike prices.

ETF options on the stock price indexes—Dow 30 DIA, S &P 500 SPY, Nasdaq 100 QQQ and Russell 200 IWR—tend to be consistently lower than predicted by the corresponding index futures call price curves. On “ETF variations” (below) the four stock price index ETFs show negative differences from predicted price curves when their underlying index prices and strike prices are used with the pricing formula computed for the corresponding calls on index futures. 

“ETF variations” shows that the silver and gold ETFs, SLV and GLD, have the largest positive difference between the price curves of the ETFs and the prices predicted for each strike price by the price curve of calls on silver and gold futures. In this analysis, when the ETF price increases as a ratio to the strike price, GLD first rises and then falls to a negative difference as the ETF approaches equality with the strike price.

Calls on the three currencies on “ETF variations” are closely grouped and all show positive differences compared with the price curves of the related futures contracts.

The high correlation of the Swiss franc and euro presents a four-way spread possibility. The “Currency ETF warfare” chart (page 27) shows that the two currencies have equal volatilities, courtesy of the Swiss central bank authorities. This means that call options with the same expiration date on the franc and euro futures should have approximately the same options price curves. It also means that options on ETFs, Swiss franc FXF and euro FXE should have approximately the same price curves. Thus there is a four-way equality of options pricing on FXF, FXE, Swiss franc futures and euro futures. If any of the four options price curves shows an overvalued or undervalued call or put option, there are at least three possible spread opportunities.

Paul Cretien is an investment analyst and financial case writer. His e-mail is

About the Author

Paul Cretien is an investment analyst and financial case writer. His e-mail is