# What is the relationship between US Dollars and Gold Prices?

## Summary

An examination of how Gold prices and the US dollar are related. Gold prices are typically denominated in US dollars and this implies that the exposure gained from buying/selling gold is influenced by changes in the exchange rate for US dollars.

Videos to watch before
1. Why is gold a currency?

## Transcript

In this video we are going to try to answer the question: what is the relationship between the price of gold and the US dollar? The short answer to this question is that the price of gold is inversely related to the US dollar. The long answer involves the following example.

### Setting up an example

Let’s assume that in the world there are only three currencies. We will assume the first currency is the US dollar and the second currency is gold. If you watched our previous video you know the reason that we are treating gold as a currency is because a lot of the people who demand gold in the global markets are people who are looking for a store of value for their money and because people who are investing in gold or buying gold are often comparing it to other currencies. So it makes sense to think of gold as a currency. For the third currency we will group together all the other currencies in the world and treat it as one currency. For example we will group together the Euro, the Japanese Yen, the Thai Baht, the Indian Rupee and so on and just treat it as one currency which we are going to call the “Rest Of the World”.

We are going to assume that the exchange rate between US dollars and gold is such that you can exchange 1 unit of gold for 1,000 US dollars. Typically in the gold market one unit of gold is equal to one ounce so what we are saying is that 1 unit of gold or 1 ounce of gold is equal to 1000 US dollars. That is the exchange rate between US dollars and gold.

We are also going to assume that the exchange rate between US dollars and Rest of the World (ROW) currencies is such that 1 US dollar is equal to 2 ROW currency. This is really just the same as saying that 1 US dollar is worth twice as much as the average rest of the world currency.

Now as you can imagine, there will probably be a large market for exchanging gold to ROW currencies which I am going to draw over here and the question is what should the exchange rate between gold and ROW currency?

The first thing that’s important to realize is that if you’ve defined the exchange rate between Gold/US dollars and US dollars/ROW currency you’ve effectively defined what the exchange rate is between Gold and ROW currencies as you can figure out what that exchange rate is by just solving the other two equations. If you do this you get that 1 unit of Gold is equal to 2000 ROW currency. This is also generally true: if you have defined any too exchange rates in the triangle, you have effectively defined the third.

### Gold prices are linked to the value of US Dollars

But as we’ve already talked about the exchange rate between US dollars and gold is dependent upon the other two exchange rates so if we assume for a second that the exchange rate between Gold and ROW currency is constant that implies that a change in the exchange rate between US dollars and ROW currency will cause a change between US dollars and gold. So let’s assume that the exchange rate between US dollars and ROW now changes such that 1 US dollar = 1 ROW currency. In other words, the value of the US dollar has gone down relative to the rest of the world. What does that mean for this exchange rate between US dollars and gold? Well, we can to solve the two other equations and we can see that the new exchange rate between US Dollars and Gold is such that that 1 unit of goal is equal to 2,000 US dollars. In other words because the US dollar has become weaker or is worth less relative to rest of the world currencies that means that the price of gold in US dollars has gone up.

The opposite is also true. Let us assume that instead 1 US Dollar = 2 ROW currency that 1 US Dollar = 4 ROW currency. This means the value of the US dollar has gone up by a factor of 2 and would imply that the price of gold would be equal to 500 US dollars. So the big picture here is that because gold is denominated in US dollars you are getting exposure to the exchange rate between US Dollars and ROW currency.

### Historical relationships

Now based upon this you might expect historically to see a relationship between Gold prices in US dollars and the exchange rate between US dollars and ROW currency. This is what that chart looks like:

The graph covers the period from 1970 to 2011. The blue line shows the price of gold in US dollars which we’ve been referring to as the exchange rate between US dollars and gold. The pink line shows the value of the US dollar relative to a basket of currencies from the ROW and so when the pink line is going up it means that the value of the dollar is strengthening relative to other currencies and if the pink line is going down it means that the dollar is weakening relative to other currencies. As you can sort of see these two lines tend to the inverses of one another.

### Conclusion

So the big picture here is that when you go out into the market and you buy gold some of the profitability of that investment is simply determined by changes in the exchange rate between the US dollar and ROW currencies. Put in other words when you my gold you are getting inverse US Dollar exposure