Building a Better Gold / Silver Ratio

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Includes: FXF, GLD, SLV
by: Hard Assets Investor

By Charles Armstrong

Commodity traders love spreads. Not only do spreads (intra- or intercommodity) provide guidance for entry and exit points in our trades, they also make a lot of sense. When comparing different types of commodities, it's a straightforward mental leap to understand that a barrel of oil is worth so many mmBTUs of natural gas, or that a bushel of corn is worth about 1 1/2 bushels of oats, and so on. Furthermore, these spreads tend to be easy to derive; all you need is a few years' worth of data and an Excel spreadsheet, and voila, you've calculated your spreads.

No such spread is followed with as much zeal as the gold/silver ratio. We've talked about this ratio before in some depth, but suffice to say, over the past 100-plus years, the gold/silver spread per ounce has remained relatively constant at 30:1—meaning one ounce of gold can buy 30 ounces of silver. However, over the last 12 years or so, that spread has widened to about 60-to-1. William Jennings Bryan would not be pleased.

Now, many traders closely track where the spreads are on any given day; that is, if you think the 60-to-1 spread of recent years is accurate and stable, you want to know when the spread moves significantly away from that, and play accordingly. Be it 70-to-1, 30-to-1, etc., you can always play the spread by shorting one metal and going long the other.

However, if you're like me, it's not the spread that's the most interesting part of this picture, it's what causes the spread to move one way or the other.

Correlations Between Gold, Silver And The U.S. Dollar

Since they're both the precious metals investors tend to flock to as "safe haven" assets, gold and silver prices are highly correlated. Over the last five years, more than 75 percent of the change in value of gold can be explained by the change in value of silver. There appear to be two partially unique trend lines, but in general, when the price of silver goes up, so too does gold's:

GC vs. SI

Gold also has a high negative correlation to the U.S. dollar; as we've covered before, when the dollar improves, gold's appeal as a safe haven diminishes. But what's interesting is that even though gold and the dollar are highly correlated, and gold and silver are highly correlated, silver and the dollar, in fact, do not have as strong a correlation.

Over the past five years, the "R squared"—the degree to which fluctuations in silver prices can be attributed to changes in U.S. dollar value—is only about 0.5983, or about 60 percent. (One quick note: When gauging the greenback's value, I prefer the USD/CHF exchange rate because it provides an actual currency value relative to the U.S. dollar, rather than arbitrary weightings from an index. Also, the swissie is relatively stable, compared with other currencies.):

SI vs. USD

So why does silver have a weaker correlation to the dollar than gold? It comes back to silver's dual nature as both investment metal and industrial powerhouse. Gold may have plenty of appeal as a store of value or an inflation hedge, but it has few real-world industrial applications—unlike silver, which is used in everything from mirrors to solder to antimicrobial agents. Therefore, silver's allure as a "safe haven" asset only drives some of its demand—the metal is also driven by the fate of the broader stock market.

So if we know that silver makes an excellent predictor for gold prices, the US Dollar makes a good predictor for gold prices, and the U.S. dollar makes a comparatively worse predictor for silver prices, then we can use a tool that provides a more informative look than just a simple spread: the multivariate model.

Building A Gold-Silver-Dollar Model

In fact, this model, which allows us to examine all three factors simultaneously, works so well precisely because the silver/dollar ratio is significantly less correlated than the others. If the correlation between the dollar and silver prices were as high or higher than the gold/dollar ratio, a multivariate model would be confounded by co-linearity.

Unfortunately, a multivariate model requires three-dimensional graphing capabilities, which I simply don't have at my disposal, but the following matrix plot should give a good idea of the whole system all at once:

GC vs. SI vs. USD

So plugging in the continuous front-month prices for gold and silver, as well as the closing value of USD/CHF from January 2005 through March 2010 into my statistical analysis package, I end up with the following result:

Gold = 1592.070 + (31.365 * SilverPrices) + (-1070.328 * USD/CHF)

R_Squared = .8489

Let's go over the terms one by one. That first number (1592.070), or "alpha," essentially tells us how much gold would be worth if silver were free and the USD/CHF exchange rate were zero. (Since there never has been nor ever will be such a situation, it's better to think of the alpha as a simple constant.)

The two coefficients before the predictors, or the "betas," represent the amount gold prices would change if that predictor—and that predictor alone—changed by a factor of one. Therefore, if silver prices increase by $1, while the Swiss franc exchange rate stays the same, gold prices should go up by $31.365. (Note how close that is to the historical gold/silver ratio of 30:1.)

So why is the beta coefficient for the USD/CHF exchange rate so high? It comes back to the miniscule movements in currency fluctuations. In the forex markets, a currency moving 6 cents indicates a huge move, and so, according to this model, it makes sense that a change in the value of the Swiss franc by a full dollar would result in a gold prices moving $1,070.328 in the opposite direction.

That's not to say that this is some magic formula that can predict the way gold, silver or the dollar can and will trade in the future. Rather, it's a description of the assets' historical relationships to each other. And as you can see, using the multivariate model allows us to pick up nearly 10 percent improvement on R_squared for our pure gold/silver or silver/dollar spreads.

How To Play The Gold-Silver-Dollar Spread

As of writing, with silver trading around $18.00/oz and the USD/CHF exchange rate hovering around 1.06, our model suggests that historically, we would've seen a point prediction of about $1022/oz for the price of gold. But with gold currently trading at over $1150/oz, gold prices are well above expected historical levels when silver and the USD/CHF were where they are today.

Now, this doesn't necessarily mean that gold is trading at an inflated price and is overdue for a huge crash. All it means is that gold is currently trading higher than it normally would have over the past five years, when silver and the dollar were at their current levels. Specifically because this is a multivariate system, the meaning of our result is ambiguous: It could mean, for example, that either of the two predictors have lost some of their effectiveness, or that the system is moving into a new relative spread. Remember that all this model is doing is examining historical relationships and, in this case, pinpointing deviations from said relationship.

Still, our model does offer some helpful insight for investors. If you put stock in the historical data and interpret the results to mean gold is indeed overpriced relative to where silver and the dollar are, you'd want to sell gold, while buying silver and foreign currency with U.S. dollars. Since gold and silver move together, and gold and the dollar move apart (inverse correlation) there's an added measure of safety built in, as broad swings in precious metals would cause a net sideways move in those two commodities.

The most direct way to get into these markets would be with futures contracts pegged to gold, silver and one of the major U.S. dollar crosses (like the USD/CHF). In fact, depending upon where you have a futures account, you may be able to get relaxed margin requirements for taking a spread position.

But if you're not interested in the futures market, or simply want to keep things in the ETF universe, you could also short a physical gold fund like the SPDR Gold Trust (NYSE Arca: GLD), while also going long a silver fund (like the iShares Silver Trust ETF (NYSE Arca: SLV) and also buying (or selling, depending on the side) one of the CurrencyShares ETFs. In the case of our above example, you'd have to short their CHF/USD fund, the CurrencyShares Swiss Franc Trust (NYSE: FXF), to achieve the effect of buying a USD/CHF position.

One important thing to keep in mind is that the number generated from this model is truly just a point prediction; if one looks back historically at the price of gold compared to these other factors, it certainly deviates, very often and very severely, from whatever its point prediction might be. Even though these historical spreads look to have very strong correlations, there's no rule saying that must or will continue for any amount of time. Always do your research before entering into any position, especially one as potentially volatile as this.

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