# Which currency is cheaper for another currency?

Suppose that I want to buy something in GBP (pounds). How do I determine whether which costs less: CAD (Canadian Dollars) or HKD (Hong Kong Dollars) or USD, all three of which I possess?

First, would I compare CAD vs HKD? http://www.xe.com/currencycharts/?from=CAD&to=HKD&view=1Y shows that CAD has depreciated against HKD. Secondly, because CAD is worth less compared to USD, would I then compare CAD vs USD?

• Perhaps this question would be better posed as pertaining to purchasing power parity. Then it would be a question of which country it is cheapest to buy a specific good, but seemingly more along the lines of what you are interested in. Take an equal amount of money (using the exchange rates) and where do you get the best deal? This of course depends on WHAT you want to buy (e.g. I'm assuming it's cheaper to buy rice in Hong Kong than in Great Britain). Commented Sep 4, 2014 at 20:22
• @farrenthorpe that would be a good question, but it is not this question. Commented Sep 5, 2014 at 1:35
• @farrenthorpe sometimes there are things available exclusively in one currency. I have to buy JPY to buy things from Amazon Japan, and those things are not available anywhere else. P.S: please don't ask what they are Commented Sep 5, 2014 at 4:18

It will cost the same no matter what currency you use, unless you have access to a deal with a currency exchange that gives you an especially favourable conversion rate for a particular currency.

If the current exchange rates are US\$1.70 to the £, CA\$1.80 to the £ and HK\$12.50 to the £, then £1, US\$1.70, CA\$1.80 and HK\$12.50 are just four different ways of writing the same amount of money. So whether you pay in US\$, CA\$ or HK\$ it's the same amount of money that you're paying.

• Would you please explain why 'it will cost the same'? Will you please to respond in your answer, and not as a comment?
– user10763
Commented Sep 4, 2014 at 16:49
• @LePressentiment because if there is an imbalance that makes, say, US\$ be cheaper when bought with CA\$, people can buy CA\$ and then use it to buy US\$ and literally obtain more money by doing virtually nothing. This will devalue US\$ very, very quickly. Thus the balance in conversion rate. Of course, this does not take into account currency exchange rates Commented Sep 5, 2014 at 4:21
• I noticed a possible typo only now; please tell me if my edit is wrong.
– user10763
Commented Mar 9, 2016 at 19:01

As others have pointed out, the theoretical prices in each exchange rate are identical.

However, the cost to you may vary. You need to work out the "opportunity cost" of using each of the three currencies, because you lose money every time you convert between two currencies.

Let's supposed for example that you live in Canada and earn and spend CAD there, but also happen to have some HKD. To keep this simple I'll ignore the USD, but you can apply the same reasoning to that.

If you're not planning on visiting Hong Kong for a while, then your holdings of HKD are just gathering dust, so your choices are to convert them to CAD and make the GBP purchase in CAD, or to spend the HKD directly on the GBP purchase. Probably the first option will end up costing you more in conversion fees than the second, but you need to look at the precise costs to verify this.

If you are planning on visiting Hong Kong soon and will need the HKD, then the choices are somewhat different. You can either spend CAD on the GBP purchase, or you can spend the HKD on the GBP purchase and then soon convert some CAD into more HKD for your trip. In this case the first option will probably end up costing you less in conversion fees.

At any instant, three currencies will have exchange rates so if I know the rate between A and B, and B to C, the A to C rate is easily calculated. You need X pounds, so at that moment, you are subject to the exchange rate right then. It's not a deal or bargain, although it may look better in hindsight if the currencies move after some time has passed. But if a currency is going to depreciate, and you have the foresight to know such things, you'd already be wealthy and not visiting here.

International exchange rates are arbitraged. If I exchange A for B for C and then back to A again, I'll end up with the same amount ex trade fees. Assume this isn't the case. Clearly if I'd gain, someone else loses and I'd make millions by rapidly exchanging. Now assume that I'd lose money on that route. That must be because the reverse route, A->C->B->A gains money. (Again, assuming no fees)

So in this case you'd just look at fees. (And as Ganesh points out, that may include future fees)

• During the early days of crypto-currency (2011-2012) I actually made a fair amount of money using a bot I developed to do just this. Fees were VERY small on some exchanges and if you had a smart enough bot, you could search for currency trading pairs that were undervalued. The A->B->C->A approach to currency profiting is likely possible with international fiat currencies, however this is probably done through high-frequency trading and is only possible by the really large, institutional investing firms that can afford the infrastructure to manage this type of trading.
– RLH
Commented Sep 5, 2014 at 11:11

There's another dimension here as currency conversion isn't necessarily the final answer. As stated by others, converting money between the three should theoretically end up with the exact same value, less transactional costs.

However the kink is that the price of most products are not updated as the currencies change. In many cases the price difference is such that even accounting for shipping and exchange fees, purchasing a product from a distributor in a foreign country can be cheaper than just picking it up at the local store.

You might even be able to take advantage of this when purchasing at a single store. If that store is set up to accept multiple currencies then it's a matter of looking at the conversion rates the moment you are buying and deciding which one is the cheapest route for you. Of course, this generally will not work for smaller purchases like a cup of coffee or a meal. Primarily because the fee for the exchange might eclipse any savings.