# Gold to Silver Ratio Musings

**3/2/16**

In the online precious metals blogosphere, a lot of people say stuff like

"*The historical ratio of gold to silver is 15. Therefore, if the current price
of gold is $1,250, then the price of silver should be $1,250/15 = $88.33*".

This thinking is flawed.

First, history is not guaranteed to repeat itself. Second, markets determine price. Well, maybe a mix of markets alongside the actual underlying fundamentals. And last, their bias makes them believe/hope that it is silver to go up, and not gold to go down, to keep the gold to silver ratio at 15. They bought and are therefore cheerleading silver or maybe they even have a realized or unrealized loss on silver they are trying to recoup.

Here's an example. Say the current market price of gold is $1,250 and the current market price of silver is $14.75. They believe that silver's price "should" be $1,250/15 = $88.33. However, why isn't it that gold should be 15*$14.75 = $221.25 ? Note that $1,250/$88.33 = 15 and also that $221.25/$14.75 = 15. That is, either way, the gold to silver ratio is 15.

Ok, yes, I do believe an increase in the price of silver is more likely in the long run (but who knows in the short run)
than a decrease in the price of gold. But still, just appealing to a ratio, __any__ ratio, as if that
__determines__ the future, does not make much sense.

Moreover, the so-called historical ratio of gold to silver is an estimate in the first place. While the majority of people say the ratio is 15 or 16, I have seen some people using other values.

As an intellectual exercise, what is the ratio for the *predicted* silver and gold prices to be equal?

We know that G_{pred} = S_{spot} * Ratio and S_{pred} = G_{spot} / Ratio,
and we want to solve G_{pred} = S_{pred} for Ratio.

S_{spot} * Ratio = G_{spot} / Ratio

S_{spot} * Ratio^2 = G_{spot}

Ratio^2 = G_{spot}/S_{spot}

Ratio = (G_{spot}/S_{spot})^.5

Using current spot prices, we get

Ratio = ($1,250/$14.75)^.5 = 9.21

Using that ratio would make G_{pred} = S_{pred} = $135.78

Let's call the ratio (G_{spot}/S_{spot})^.5 "R star", or R*. What is one possible interpretation of R*?
If you believe that ratios determine the future and that the price of silver can never be higher than the price of gold,
an interpretation of R* is that it gives a prediction on what the maximum price of silver can be, given the current price
of gold of $1,250, and the current price of silver of $14.75.

If R* is smaller than, in this example, 9.21, then the price of silver is greater than the price of gold, which we're assuming is not allowed. If R* is larger than 9.21, then the price of silver is less than the $135.78 calculated above. This is why R* gives a predicted maximum on the price of silver.

I can say 100% confidently that the ratio and the spot prices will fluctuate. You're welcome.

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