Real-time Inflation Indicator (per annum): 7.6% 

Friday was a good day for gold bulls. A $43, or 6%, uptick in the yellow metal's price translated into a 14% bonanza for holders of the PowerShares DB Double Long Gold ETN (NYSEArca: DGP). Meanwhile, crude oil prices remained essentially flat. The last trade in the PowerShares DB Double Short Oil ETN (NYSEArca: DTO) was a 3% downtick.

On Friday morning, we began our examination of these two exchange-traded notes as means to trade the gold/oil ratio last week in "Gold Vs. Oil: Gold Winning."

Gold/Oil Ratio

DTO is new. It was launched in June at a price pretty much in line with the then-current level of DGP. Spread traders have long known that to get the desired effect out of a ratio trade, adjustments must be made for disparate prices and volatilities. Price adjustments are pretty straightforward. A trader simply divides the price of one entity by the other. Back in June, the DTO finished up its first trading day at $24.40 when DGP was at $20.75. If you were trading the gold/oil ratio - that is, you expected gold to outperform oil - you could have bought DGP notes in a 1-to-1 ratio with DTO notes (the actual ratio would have been 1.18-to-1, but unless you were investing in size, 1-to-1 would have been ballpark perfect.

Now, about volatility. Volatility is really a measure of price variance over time. The rate at which investment vehicles fluctuate can vary significantly, and that differential can throw ratio trades off-kilter. Back in June, of course, there was no trading track record for DTO, so you'd be forgiven if you assumed the volatilities of the two instruments would be equal. And, as it turns out, you'd have been spot-on in your belief. In fact, DGP and DTO have been equally volatile since June.

So how would you know? Take the standard deviation of each note's daily price changes and adjust it for a 252-day trading year. If that sounds like a daunting task, you can enlist the aid of your Excel spreadsheet to figure it out for you with the argument:

=STDEV(first daily % change : last daily % change)*SQRT(252)

Using Excel, you'd find that DTO and DGP have both clocked an implied 84% annualized volatility since June. Well, about 84%; DTO comes in at 84.46% and DGP's at 84.75%.

While the ETNs' volatilities are congruent, their prices have changed a lot since June. DTO's ballooned to the $103 level while DGP's slipped to $15.40. Trading the gold/oil ratio with the ETNs will now have to compensate for this lopsided pricing by overweighting DGP.

For every DTO note bought now, 11 DGP notes will have to be acquired. The ratio's based upon this little bit of algebra:

V₁P₁/ V₂P₂ = (103.86 x .84446)/(15.40 x .8475) = 11.06

So now you know. Happy trading!