## Tuesday, February 20, 2018

### Measuring Returns in Different Currencies

Thinking about returns of stocks in different countries and in different currencies can get confusing. If Canadian stocks rise (in Canadian dollars) and U.S. stocks rise more (in U.S. dollars), almost everyone would agree that U.S. stocks performed better, even if the Canadian dollar rose by enough to make up the difference. This way of thinking makes no sense to me.

Suppose that in a particular year, Canadian stocks rise 10% when measured the usual way in Canadian dollars. In the same year, U.S. stocks rise 15.5% when measured in U.S. dollars. But the Canadian dollar rises 5% during the year. Most would agree that U.S. stocks had superior returns.

However, let’s look at this from a few points of view, starting with a Canadian investor who thinks in Canadian dollars. The Canadian stocks case is easy: a 10% gain. Now let’s consider the case of a C\$10,000 investment in U.S. stocks with the Canadian dollar at 80 cents U.S. The investment is US\$8000 and it rises by 15.5% to US\$9240. But Canadian dollars rose 5% to 84 cents U.S. This converts to C\$11,000 for a gain of 10% measured in Canadian dollars.

So, from the point of view of a Canadian investor, stocks in Canada and the U.S. performed the same, a 10% gain. If we go through the same exercise for a U.S. investor, the gain for Canadian and U.S. stocks will both be 15.5% measured in U.S. dollars. The same will be true for investors in any other country. Everyone in the world will see Canadian and U.S. stocks giving the same performance. So how can it make any sense to decide that U.S. stocks performed better?

This scenario was created to give the same returns for Canadian and U.S. stocks, but we get similar outcomes in other cases. If a Canadian investor sees Canadian stocks perform 5% better than U.S. stocks, then U.S. investors and all other investors in the world will see the same 5% better performance for Canadian stocks over U.S. stocks.

People think that stock returns measured by the country’s own currency are somehow the “actual return”. But this way of thinking is misleading. Returns are always relative. If every investor in the world sees Canadian and U.S. stocks as performing equally well in a particular year, how can it make any sense at all to decide that U.S. stocks performed better? The answer is that it doesn’t make sense.