Calculating Foreign Returns in Canadian Dollars

Global diversification was a huge benefit to investors in 2012, as Canadian equities lagged well behind the rest of the world. Two core funds in the Complete Couch Potato are the Vanguard Total Stock Market (VTI) and the Vanguard Total International Stock (VXUS), and last year these funds delivered returns of 16.40% and 18.22% respectively.

But these figures are misleading, because they’re expressed in US dollars. A Canadian investor is likely to be more concerned about how their US-listed ETFs performed in terms of our own currency. And that information isn’t easily available, so you need to do the math yourself. It’s a two-step process:

1. Determine the annual change in the exchange rate. Your first step is to learn how much the value of $1 USD changed over the year. That means looking up the exchange rates on December 31 of both 2011 and 2012. There are several sources for these data, but I’ve used XE.com. If you use another (such as the Bank of Canada or OANDA) you’re sure to get slightly different numbers: there are noon rates, closing rates, bid prices, ask prices and midpoints, all of which makes this more complicated than it might seem. But as long as you’re within 10 basis points or so, that’s adequate for benchmarking your portfolio.

According to XE.com, $1 USD fell from $1.0216 CAD on December 31, 2011 to $0.9968 one year later. Here’s how to express this decline as percentage:

= (end value – start value) / start value
= (0.9968 – 1.0216) ÷ 1.0216
= –0.0243
= –2.43%

2. Multiply this currency change by the USD return. The next step is to multiply this change in the exchange rate by the fund’s annual return in USD. Use this formula, where y is the USD return and z is the percentage you calculated in the previous step:

((1 + y) × (1 + z)) – 1

For the Vanguard Total Stock Market (VTI), we take our 16.40% return in USD and our currency change of –2.43% and calculate as follows:

= ((1 + 0.1640) × (1 – 0.0243)) – 1
= (1.1640 × 0.9757) – 1
= 0.1357
= 13.57%

And for the Vanguard Total International Stock (VXUS), which returned 18.22% in USD:

= ((1 + 0.1822) × (1 – 0.0243)) – 1
= (1.1822 × 0.9757) – 1
= 0.1535
= 15.35%

Understand your currency risk

As you can see, the decline in the US dollar during 2012 resulted in lower returns for Canadian investors in VTI. But it’s important to note the performance of VXUS was not affected by the decline in USD relative to Canadian dollars. This idea is frequently misunderstood by investors who buy US-listed ETFs that hold international stocks.

Although VXUS trades in USD, its underlying stocks are denominated in a host of native currencies, including the euro, yen, pound, Swiss franc and Australian dollar. The only relevant exchange rates are between these currencies and the Canadian dollar; the US dollar does not factor into the equation. Several foreign currencies declined relative to the CAD in 2012, including a drop of more than 13% in the yen. For more on this confusing issue, see my previous post on international currency expose and this case study, which explains the math.

I’ll be posting complete 2012 returns for all of the model portfolios—adjusted for Canadian dollars—as soon as all the data are available.