# 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%

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.

### 24 Responses to Calculating Foreign Returns in Canadian Dollars

1. Dan Hallett January 7, 2013 at 3:47 pm #

Great post Dan. This has been an area of confusion for investors and advisors alike for many years. One point worth adding is the format of the exchange rate.

You pointed out that there are different types of quotes – i.e. noon, close, etc. There are also different formats for each type of quote. Readers will want to make sure they’re working with a “Direct Quote” – where it tells you how much of your home currency (CAD) is required to buy a single unit of your investment currency (in this case USD).

Sometimes you may be given an “Indirect Quote” for foreign exchange – which in this case would be how many US dollars required to buy a loonie. That’s what’s commonly quoted in financial papers and on financial newscasts – even here in Canada. If you have an indirect quote, you simply take 1 and divide by your indirect quote to convert it to a direct quote, which can be used in the above formula.

Finally, since this might be easier for some to remember…the mathematical equivalent to Dan’s first formula is: (Ending Value / Starting Value) – 1

2. Canadian Couch Potato January 7, 2013 at 3:59 pm #

@Dan H: Thanks for the comment. Yes, currency quotes can be surprisingly confusing, especially when the two currencies are close to par and it’s not obvious which direction you’re going. How we yearn for the good old days when 1 CAD = 0.65 USD. 🙂

You would think there would be an easy place to look up the relative annual appreciation/depreciation of major currencies (i.e. “in 2012 the USD depreciated 2.43% against the CAD”) but I haven’t found one.

3. Dave January 7, 2013 at 7:31 pm #

> You would think there would be an easy place to look up the relative annual appreciation/depreciation of major currencies

If you visit http://finance.google.com and then search for CADUSD it will show the relative value of the Canadian dollar in terms of the US dollar throughout any period of time. You can do the same comparison with other currencies — for example, CADEUR will show the loonie vs. the Euro, USDJPY compares the greenback vs. the yen, etc. Simply set the time period appropriately.

4. Canadian Couch Potato January 7, 2013 at 7:40 pm #

@Dave: Thanks for the suggestion. Interestingly, for 2012 it’s showing a decline of 2.88% for the USD, which is quite different from my numbers.

5. Gupta January 8, 2013 at 5:53 am #

In converting ROI (USD) to ROI (CAD), one might want to factor in the currency conversion costs.

6. Canadian Couch Potato January 8, 2013 at 8:32 am #

@Gupta: If you are calculating your personal rate of return, you’re right: you would also factor in commissions and the timing of your purchases and sales. But these fund returns assume you held the position for the entire year, without adding or selling shares.

7. Reginald January 9, 2013 at 6:07 am #

Excellent site, learning lots.
I am not sure about the formula given to calculate the effective return. I think all returns should be expressed as greater than 1 but negative returns divide the positive returns instead of multiplying them. Using the vxus example above: (1+0.1822)*(1/(1+0.0243))-1 = 1.1822 * (1/1.0243) -1 = 1.1542-1= 0.1542

For the case study it would look like this: (1.51*1.38*1/1.21)-1= 0.7221. What do you think?

8. Canadian Couch Potato January 9, 2013 at 8:56 am #

@Reginald: Yes, there are different ways to express the formulas and still produce the same result.

9. Dan Hallett January 9, 2013 at 12:19 pm #

Yes, many different ways to calculate the same thing. Probably the most compact formula (and what I use) is…

(1 + USD return) x (Ending CAD:USD Exchange Rate) / (Starting CAD:USD Exchange Rate ) – 1

or using VTI

(1 + 0.1640) x (0.9968 / 1.0216) – 1 = 0.1357 or 13.57%

But Dan’s more expanded steps are better for those doing it the first time to see the steps and how the math fits together.

10. Canadian Couch Potato January 9, 2013 at 12:24 pm #

As one of my high school math teachers used to say, “Doesn’t matter whether you use a wrist shot or a slap shot, as long as you score the goal.” 🙂

11. Reginald January 9, 2013 at 3:51 pm #

Cool, Thanks, I like that compact formula (simple and effective), gonna use it

12. Trevor C January 10, 2013 at 9:01 am #

I just converted \$21,000 Canadian into US through Royal Direct. I’ve done this before and it infuriates me every time. XE.com shows the conversion rate to be \$1.014 and that the US dollar sits at 0.9857 Canadian. But Royal Direct converted that money as if the US dollar was \$1.0004 Canadian.

Unless I’m missing something, as far as I can figure that means I’m paying a conversion fee of 0.0144 per dollar, which is roughly \$300. But Royal Direct insists there’s no fee and that the dollars are essentially at par!

13. Freddie January 10, 2013 at 9:12 am #

But Royal Direct insists there’s no fee and that the dollars are essentially at par!

All banks usually charge about 1.5% on the currency exchange. Per se it’s not a fee; they just give you a bad exchange rate.

If you have a \$US and \$cdn trading acccount then Google for “Norbit’s Gambit”. Has worked fine for me at TD, sometimes you even make money on the exchange.

14. Canadian Couch Potato January 10, 2013 at 9:14 am #

@Trevor C: I’ve heard from several investors who were told there is no “fee” to convert currency through their brokerage. In a literal sense, I suppose that’s true. But if I buy an apple for 50 cents and sell it you for 60 cents, is that a 10-cent “fee,” or just my profit margin?

Brokerages buy USD for one price and sell it for a higher price. They call the difference the “spread,” but whether it’s a spread or a fee is just semantics. Either way it cost you \$300. Not sure if you’ve seen this post, but it explains this idea in more detail:

As I explain in that post, it makes no difference whether the currencies are at par or the CAD is worth 65 cents USD. Your cost is exactly the same (typically 1.5%). It’s just that you notice it more when the currencies are near par.

One thing RBC has going for it is that it’s the easiest brokerage for doing Norbert’s gambit. Definitely worth checking out that option.

15. Trevor C January 10, 2013 at 9:54 am #

Sorry, Dan. I actually meant to post my comment in that dollar-conversion item. The “Canadian dollars” in the headline above distracted me. I’ll consider Norbert’s Gambit next time.

16. Noel January 10, 2013 at 3:14 pm #

@Freddie – So true. I have friends who tell me their credit card, when used in the US, does not have an extra fee charged on top of the exchange rate. But, it’s just marketing. The fee is instead built into the exchange rate.

@CCP – Aside from Norbert’s gambit, RBC also has the advantage of allowing one to hold US funds in an RRSP. TD still doesn’t but apparently will sometime later this year. So. one has to wash any US trades in and out of TD’s TDB US savings fund.

17. Oldie January 12, 2013 at 9:49 pm #

@Noel, @CCP: with reference to RBC Direct RRSP’s allowing to hold USD and USD ETF’S, I have to make a decision whether to hold my RRSP in my professional association’s system (they don’t allow USD funds and USD’s) or go to RBC Direct for the RRSP. In my total portfolio I will hold Canadian Equity, World Equity and some bonds in the non RRSP account, and US Equities and the rest of the bonds in the RRSP. So is the 15% US withholding tax on dividends unrecoverable in the case of a Canadian based fund holding US equities enough of a drag to go the the hassle of splitting my investments by holding the RRSP in RBC Direct, to take advantage of holding USD US equities that forgive withholding tax on dividends if held in a Canadian RRSP?

18. Canadian Couch Potato January 12, 2013 at 10:11 pm #

@Oldie: The withholding tax amounts to an extra 30 bps based on a 2% yield. Whether that’s worth the added inconvenience is up to you. Remember, too, that RBC allows you to hold USD, but you still have to buy those USD in the first place and that’s not free.

19. Cary March 10, 2013 at 11:13 am #

i.e. i bought \$10,000 of VXUS when US/CAD was par – now US = 1.02 Cdn – I get a 2% pickup.

Is there a way to protect downside?

I think it must be a big issue now because a lot of Cdns probably bought US\$ the last 3 years.

thanks for your insight – great site. I just followed u on twitter! keep up good work Thanks.

20. Canadian Couch Potato March 10, 2013 at 1:35 pm #

@Cary: First it’s important to understand what downside you’re talking about. Are you worried the Canadian dollar will decline against the US? If so, that will boost the value of your holdings in VTI (in Canadian dollar terms). Or or are you concerned the Canadian dollar will rise even higher? If that’s the case, then you can use one of the many US equity ETFs that use currency hedging, such as XSP, ZUE or VUS.

The US/CAD exchange rate has no effect on VXUS:

If you’re investing for the short term you should simply avoid currency risk, and if you’re investing for the long term, it’s best to simply accept that currencies will fluctuate, and this adds diversification to an equity portfolio.

21. Rob March 19, 2013 at 1:29 pm #

Has any consideration been given to using ETFs hedged to the Cdn dollar? ie XSP iShares S&P 500 Would this take out some of the currency risk?

22. Canadian Couch Potato March 20, 2013 at 11:15 am #

@Rob: Yes, a fund that uses hedging would eliminate (or at least mitigate) the risk that a falling US dollar would detract from your returns in Us equities. Overall, however, the data are pretty clear that hedging in ETFs is expensive and imprecise, so it creates a long-term drag on returns: