Gold to Silver Ratio for Equal Valuations

Consider the gold to silver ratio. We will denote this by G/S. This is just the ratio of the spot price of gold to the spot price of silver at a point in time.

We have looked at "natural" and "man-made" G/S ratios. However, what would R be in G/S = R to make the gold and silver valuations equal?

We know that G_valuation = S_spot * R and S_valuation = G_spot / R, and we want to solve G_valuation = S_valuation for R.

Therefore, S_spot * R = G_spot / R

S_spot * R = G_spot

R² = G_spot/S_spot

and finally, R = (G_spot/S_spot)^.5

Using current gold and silver spot prices at the time of writing, we get R = ($1,845/$28.45)^.5 = 8.05.

Using that ratio would make G_valuation = S_valuation = $229.11 / troy oz.

Let's call the (G_spot/S_spot)^.5 ratio R* ("R star"). 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, one possible interpretation of R* is that it gives a maximum valuation for silver, given the current spot price of gold of $1,845, and the current spot price of silver of $28.45.

If R* is smaller than, in this example, 8.05, then the valuation of silver is greater than the valuation of gold, which we're assuming is not allowed. If R* is larger than 8.05, then the valuation of silver is less than the $229.11 calculated above. This is why R* can be interpreted as giving a maximum valuation for silver, and similarly, giving a minimum valuation for gold.

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