# How does the value of an asset (valued in two different currencies) change when the exchange rate changes?

Suppose an asset is traded on two different exchanges in different countries having different currencies. In an ideal world without transaction costs, tariffs, taxes or delivery costs etc, the price of the asset in the two markets, in equilibrium, should be equal after applying the exchange rate. If not, there would be a arbitrage opportunity. That is, one could make a risk free profit by buying the asset from the relative cheaper market (putting upward pressures on prices) and selling it back to the relatively more expensive market (putting downward pressure on prices) until the asset was priced equally-relative to the exchange rate in the two markets.

My question is this, let's assume we begin in this equilibrium situation. Now suppose that overnight the exchange rate experiences a drastic change. What will be the new equilibrium value of the asset in the two exchanges?

For concreteness, suppose that the "asset" is gold. Suppose that the markets are the US and the UK with the initial exchange rate, r=0.6 £/\$. Initially the gold per ounce is worth A=\$1200 dollars in the US and B=rA pounds in the UK. Then suddenly overnight the exchange rate changes to s, where s<< r. It is clear that eventually the asset will reach a new equilibrium value, say, \$x dollars in the US and s*x pounds in the UK. What is x?

Applying the above arbitrage reasoning, immediately after the change in exchange rate, the product will be still worth \$A dollars in the US and B=rA pounds in the UK. So if fast enough one could take sA pounds and convert them into \$A dollars, then buy the gold from the US market and then sell it in the UK for £rA, receiving a risk free profit £(r-s)A. Clearly, if the markets were roughly the same size then this would put supply-demand pressures on both markets, so that the product value would rise in the US and fall in the UK. But by how much? What factors are important in order to work this out? Is the relative size of the two markets, the order book size, important in this calculation? I'm assuming that the markets are efficient in the sense that the price discovery that is due to the change in exchange rate is very fast.

• Can someone enlighten me on why this question is being downvoted? I really thought hard about it before asking, and put time into presenting the question in a way which I thought was accessible and coherent. – Jase Uknow Aug 5 '14 at 11:28
• Perhaps because the question appears to be more like an academic or theoretical question about finance and economics than a practical issue of personal finance. – Chris W. Rea Aug 5 '14 at 12:28
• OK, so I'm in the wrong place. Thanks, good to know. Is there another stack exchange more suitable to theoretical questions like this? – Jase Uknow Aug 5 '14 at 12:31
• Not at the moment. – Chris W. Rea Aug 5 '14 at 14:48

Gold is traded on the London stock exchange (LSE) and the New York stock exchange (NYSE) under various separate asset tickers, mainly denominated in sterling and US dollars respectively. These stocks will reflect FX changes very quickly. If you sold LSE gold and foreign exchanged your sterling to dollars to buy NYSE gold you would almost certainly lose on the spreads upon selling, FX'ing and re-buying.

In short, the same asset doesn't exist in multiple currencies. It may have the same International Securities Identification Number (ISIN), but it can trade with different Stock Exchange Daily Official List (SEDOL) identifiers, reflecting different currencies and/or exchanges, each carrying a different price at any one time.

• So gold on the LSE is different to gold on the NYSE? Is this a standard way to define an asset? I thought it was the same asset, i.e. gold, but its value changed depending on where it was traded. In any case, I don't think you've completely answered my question. You are right costs often prevent the arbitrage op. But I was trying to understand in an idealised world. In any case, even with these costs, if overnight one currency collapses then arbitrage ops would exist i.e., above the spread. Wouldn't this put supply-demand pressures on both "assets" as you say. – Jase Uknow Aug 5 '14 at 8:01
• There are a number of ways to buy gold. Most common is to invest in a gold fund, see What are Gold Funds?. You can buy physical gold bullion, but that incurs additional costs, ref. How to Buy Gold Bullion. If you are investing in gold funds each fund is technically a different asset, although it provides exposure to the same underlying commodity, broadly speaking. – Chris Degnen Aug 5 '14 at 8:14
• Yes, of course but I think this is getting off topic. Gold is just an example. – Jase Uknow Aug 5 '14 at 8:25
• There may well be arbitrage opportunity if a currency suddenly collapses, but automated trades will close the gap very quickly. The side issue is that you can not buy gold or oil funds or shares on one exchange and sell them on another. The positions have to be closed on each exchange, so the arbitrage opportunity would have to be large to cover the costs. – Chris Degnen Aug 5 '14 at 8:33
• Hi Chris, I've now posted an answer to this see below. My answer was a "negative answer" in that I claim you just can't calculate x. However, what you're saying about automated trades is now making me second think it. If algorithmic trading operates so fast, then shouldn't it be possible to determine "x" just by looking at the order book and reading off the price where the two prices would match at the new exchange rate after all the buy/sells (of equal volume) have been executed? – Jase Uknow Aug 5 '14 at 10:02

The value of the asset doesn't change just because of the exchange rate change. If a thing (valued in USD) costs USD \$1 and USD \$1 = CAN \$1 (so the thing is also valued CAN \$1) today and tomorrow CAN \$1 worth USD \$0.5 - the thing will continue being worth USD \$1. If the thing is valued in CAN \$, after the exchange rate change, the thing will be worth USD \$2, but will still be valued CAN \$1.

What you're talking about is price quotes, not value. Price quotes will very quickly reach the value, since any deviation will be used by the traders to make profits on arbitrage. And algo-traders will make it happen much quicker than you can even notice the arbitrage existence.

• You're tying "value" of the asset to a particular currency, then adjusting to the other currency. This makes sense for a product which is made in a particular country, say US. It will cost the manufacturer \$1, regardless of how US-CAN exchange rate changes (assuming they have no operations/suppliers from Canada). But what about when the market decides the price. I thought gold was illustrative. Chris Degnen further clarified that this can be traded on LSE and NYSE. You say, price quotes reach the value. What then is the "value" of gold? Its value on the LSE? Or its value on the NYSE? – Jase Uknow Aug 5 '14 at 8:17

It depends on the asset and the magnitude of the exchange rate change relative to the inflation rate.

If it is a production asset, the prices can be expected to change relative to the changes in exchange rate regardless of magnitude, ceteris paribus.

If it is a consumption asset, the prices of those assets will change with the net of the exchange rate change and inflation rate, but it can be a slow process since all of the possessions of the country becoming relatively poorer cannot immediately be shipped out and the need to exchange wants for goods will be resisted as long as possible.

If there is a very sudden and large collapse in the exchange rate then because algorithmic trades will operate very fast it is possible to determine “x” immediately after the change in exchange rate. All you need to know is the order book. You also need to assume that the algorithmic bot operates faster than all other market participants so that the order book doesn’t change except for those trades executed by the bot. The temporarily cheaper price in the weakened currency market will rise and the temporarily dearer price in the strengthened currency market will fall until the prices are related by the new exchange rate. This price is determined by the condition that the total volume of buys in the cheaper market is equal to the total volume of sells in the dearer market.

Suppose initially gold is worth \$1200 on NYSE or £720 on LSE. Then suppose the exchange rate falls from r=0.6 £/\$ to s=0.4 £/\$.

To illustrate the answer lets assume that before the currency collapse the order book for gold on the LSE and NYSE looks like:

GOLD-NYSE

Sell (100 @ \$1310)
Sell (100 @ \$1300) <———
Sell (100 @ \$1280)
Sell (200 @ \$1260)
Sell (300 @ \$1220)
Sell (100 @ \$1200)
—————————

GOLD-LSE

Sell (100 @ £750)
Sell (100 @ £740)
—————————