Let’s look at gold prices and see how its relationship with different currencies behaves and interacts.
The WTI does not have a very good connection to the Japanese Yen and Australian Dollars. However, gold prices have a more stable and solid connection to these currencies than the WTI does.
In fact, the average correlation for the Yen is +0.35. Whereas, the average correlation for the Australian Dollar is +0.51.
Gold prices are correlate to Australian Dollars. In the world Australia is one of the biggest gold producers. Therefore, any considerable change in the price of this commodity will heavily influence the currency oscillation.
Furthermore, there is a fairly good relationship with the Japanese Yen. This is due to the fact that gold is often used as a hedging tool. (Just like the Asian currency).
Therefore the standard deviation and co-variance are going to move symmetrically.