To the gold bugs, a question about the PVE index

Economics Economics Questions
1

Is the Paul Van Eeden (PVE) index a valid construction?

The PVE index somehow combines the currencies of thirty-five of the United States’ largest trading partners into a global price for gold.

Is it valid to compute a weighted sum of currencies to obtain a “global” price? Isn’t this a little like computing the cost of horses by adding barrels of fish and pounds of tobacco?

Furthermore, doesn’t arbitrage ensure that the PVE index would be…less useful? For example, say:

  1. Gold price in America: 500 USD per oz.
  2. Gold price in Switzerland: 1000 CHF per oz.
  3. Exchange rate: USD/CHF = 0.75

An American could buy an ounce of gold for 500 dollars, sell it in Switzerland for 1000 francs, then convert his 1000 francs for 750 dollars. That makes a profit of 250 dollars.

For the record, if the PVE were more-or-less correct, then the current price of gold would be attractive.

2

…about the arbitrage: I assume the opportunity would hasten gold to its correct price thus removing the opportunity.