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# Gold and Silver Spread Arbitrage

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Looking for a way to play Gold and Silver? A quick look at the historical spreads between gold and silver may help you make an educated dicision in your arbitrage.

Let's take a look:

Using Bloomberg's HRA (Historical Regression) function, we can easily find the historical correlation between gold and silver. By using the SILV and GOLDS commodity indices, we can get data much further back than we could if we used the GLD and the SLV.

Using a weekly value correlation going back to 1990, we see a tight correlation and a regression line that looks something like this:

It may be a little hard to read, but as you can see, the data points hug pretty close to the regression line over a period of 20 years, giving us a relatively solid R2 coeficcient of .92. I doubt you can see it, but the box in the upper-left hand portion of the graph tells us the linear equation for the correlation- y=.018x.

If you are lost, or have no idea what I'm talking about, I'll explain it a bit more simply: What this all basically means is that we have about 92% confidence that when gold goes up \$1, silver will go up somewhere in the range of 1.8 cents. Or, to make it more manageable, when we use the GLD and the SLV, we can say that when the GLD goes up \$1, the SLV goes up somewhere around \$0.18. This is because the GLD is basically the price of gold divided by 10.

Another way of looking at this would be to say that in order to hedge your GLD position, you would have to sell 5.5555 SLV to achieve a hedged position. We calculate this by dividing 1 by the hedge ratio (.18), which gives us 5.555. What this means is that if SLV moves 18 cents for every dollar that the GLD moves, then if you sold 5.55 of the SLV, against one GLD, the \$1 gain in gold would be cancelled out by the \$1 loss (.18 x 5.55) in your short SLV position.

Now. Onward to the spread.

When I talk about the spread, I am talking how far out of correlation the two securities are. Here's how we calculate the spread:

The spread = (GLD*Hedge Ratio) - SLV

If silver went up exactly 1.8 cents EVERY SINGLE TIME that gold went up \$1, then there would be no spread; GLD*.18 - SLV would always equal zero. However, if one day silver went up 2 cents versus gold's \$1, there would be a negative spread. Inversely, if gold decided to go up \$2 one day, and silver still only went up 1.8 cents, there would be a positive spread.

(A note: we have to view the spread in terms of which security we are buying and which we are selling. If we are long gold, short silver, then in essence, we are long the gold/silver spread, or we could say we are short the silver spread. If gold goes up more than silver, the spread between gold and silver goes up.
If we are long silver, short gold, then when silver rises more relative to gold, the spread goes up. We would be considered long the silver spread, or short the gold spread. It's all relative to your position.)

Going back to the regression chart from earlier, you can see that the last few data points, located at the top-right end of the regression line, are all above the line. This means that the relative price of silver has risen more than the relative price of gold recently. If we pull up a chart of the spread, calculated as we discussed earlier, you can see that the spread has gone negative, meaning that silver has outperformed gold recently.

You can see from the charts and the bell curve at the bottom right that not only has the spread gone extremely negative, it is the lowest it's been in the last 20 years. Investors looking for an arbitrage would do well to buy the gold.silver spread at these levels...if they think that it's just a minor fluctuation in the spread.

But what if it's not just a short term fluctuation in the spread? What if the correlation between gold and silver has inherently shifted? Anyone working with correlations has to ask this question when spreads and correlations start behaving irregularly. It's not uncommon for correlations to break.

Unfortunately, when working with correlations, only time can tell. Do you invest in the spread, hoping that it is a short term fluctuation, or do you assume that the long-standing relationship between gold and silver have changed?

That's up to you.