VEA vs XIN: Foreign Exchange Fees vs. Higher MER

A commenter named Blitzkrieg asked:

How do currency exchange fees factor into the decision between VEA and XIN? XIN’s MER is 0.35% higher than VEA’s, but it is purchased using Canadian dollars, so there is no exchange fee. VEA’s MER is nice and low, but don’t you immediately lose a few percentage points of your investment when you buy it due to currency exchange fees?

He’s exactly right. The answer to “which one is better, VEA or XIN, from a cost perspective” is “it depends.” In this case, it depends on how long you hold your investments.

I did some similar calculations to determine the “effective MER” of a foreign currency investment over time but this time I do it a bit more simply, to determine, simply, how long to I have to hold my VEA until it beats XIN.

When you buy VEA, you’ll pay a foreign exchange fee (spread). This varies depending on your broker but they range from 0.5% to 1.5% each way. Let’s assume it’s 1% each way. So when you use Canadian dollars to buy VEA they convert your dollars to USD but they take 1.5% for themselves. So our present value has gone down by 1.5%, or 98.5% of the original. When we sell your USD investment, VEA, in the future, the broker/banks will again take 1.5%. So your final value is also reduced by 1.5%. So originally, we had this:

FV=PV (1+i)^n

Our initial PV needs to get reduced to 0.985 of the original, and the result of the right-hand needs to be reduced by 0.985 (when we sell the investment). So what we end up with is this:

FV_{VEA}=(0.985)(0.985)PV (1+i)^n

If we invest in XIN, there are no foreign exchange, just an MER that is 0.35% higher. This 0.35% will reduce our annual return, so we get this:

FV_{XIN}=PV (1+i-0.0035)^n

We can get rid of PV (it won’t affect the result) and assume a return of 7% (i=0.07). It turns out that:

FV_{VEA} > FV_{XIN} \quad \textbf{if} \quad n\geq10

So if we hold onto our investment in VEA for 10 years or greater, we will end up better off, assuming a rate of return of 7% (note that the rate of return does not have much effect here, eg. 10% rate of return gives the same result) and a foreign exchange fee of 1% each way. The two variables that have the greatest effect here are the foreign exchange fee and the difference in MERs.