Currency conversion remains one of the biggest rip-offs in banking and investing. It’s made worse by the lack of transparency: if you call your discount brokerage they’ll quote their current rates, but it’s still hard to calculate the actual cost of your transaction. Don’t expect your brokerage to help with the math.

The first key point is, in practical terms, there isn’t a single exchange rate. While we might say “the US and Canadian dollars are at par,” that’s never quite true. On a day when the two currencies are theoretically equivalent, it might cost you \$1.01 CAD to buy \$1 USD, and if you sell \$1 USD you might receive \$0.99 CAD. That’s because currencies have a bid-ask spread just like stocks and ETFs that trade on an exchange.

There’s a simple formula to calculate the size of the bid-ask spread in percentage terms:

Note that the bid price is always the lowest of the two rates you’re quoted. So if we plug in the numbers in the example above, the math works like this:

= (1.01 – 0.99) ÷ 1.01 × 100
= (0.02) ÷ 1.01 × 100
= 0.0198 × 100
= 1.98%

The bid-ask spread in this example works out to 1.98%, which represents the brokerage’s profit. But it’s important to appreciate that any time you buy or sell an asset with a bid-ask spread, your cost is only half the spread:

• If you convert \$1,000 CAD, you receive \$990.10 USD (that’s 1,000 ÷ 1.01). So your cost is \$9.90, or 0.99% of the transaction.
• If you then convert your \$990.10 USD back to loonies, you would receive \$980.20 CAD (990.10 × 0.99), for another loss of 0.99%.
• Overall, the round-trip transaction turned your \$1,000 CAD into \$980.20 CAD, for a total loss of \$19.80, or 1.98%. But each individual transaction cost you only half as much.

The above example is very straightforward: the two currencies are theoretically at par, and the bid-ask spread is a tidy two cents. In the real world things are rarely that simple, so let’s consider an example using numbers obtained last week from RBC.

For transactions less than \$50,000:

• Selling \$1 USD gets you \$0.9689 CAD

For a \$100,000 transaction:

• Selling \$1 USD gets you \$0.9770 CAD

Plugging these numbers into the formula, we get the following for transactions less than \$50,000:

= (0.9969 – 0.9689) ÷ 0.9969 × 100
= (0.28) ÷ 0.9969 × 100
= 0.0280871 × 100
= 2.81%

And for a \$100,000 transaction, we get the following:

= (0.9888 – 0.9770) ÷ 0.9888 × 100
= (0.0118) ÷ 0.9888 × 100
= 0.01193378 × 100
= 1.19%

Assume you’re an investor who wants to convert \$10,000 CAD to US dollars. How much would it cost? You can calculate this by dividing the spread by two (2.81% ÷ 2 = 1.405%) and multiplying that by the amount you’re converting (\$10,000 CAD × 0.01405). That works out to a cost of \$140.05 CAD.

If you exchange \$100,000 CAD, you benefit from the tighter spread. Now the cost of a one-way transaction is 0.595% (that’s 1.19% ÷ 2), which works out to a cost of \$595 CAD.