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How to Calculate your Average Annual Rate of Return

With Phase II of the Client Relationship Model (CRM II) fast approaching, Canadian investors will likely be on their own when trying to make sense of their reported rates of return (which will generally be meaningless for benchmarking purposes). The Modified Dietz rate of return calculator (available in the Calculators section of the blog) continues to be my recommended choice for DIY investors who want to calculate their annual return in a given year. But once they have a long string of annual returns, how do they go about calculating an average (or “annualized”) return?

Enter the geometric average annual rate of return. For those investors who still have their G-card, this can be a terrifying equation to tackle.  I’ll admit that the equation has no place in everyday life – it should be restricted to Excel spreadsheets and only allowed to see the light of day once a year (preferably after year-end).

Geometric Average Annual Rate of Return:

I find it best to just jump right into an example when trying to understand how to calculate this return. Let’s assume an investor has calculated the following annual returns over the past 10 years:

The investor now wants to calculate their 10-year annualized return in order to compare it to a suitable benchmark return. Here are the steps they would take using Excel:

Step 1: Enter the calendar year in column A

Step 2: Enter the corresponding annual returns in column B

Step 3: Enter an equation in column C that adds 1 to each annual return in column B:


Step 4: In a different cell, multiply all numbers from column C together (this can be done by using the PRODUCT function in Excel). Take the result to the power of 1 divided by the number of years in the measurement period (in our example, the number of years is 10). Subtract 1 from this result. This sounds confusing, but the equation in our example would simplify to:


This would result in a 10-year annualized return of 5.00%

By: Justin Bender | 2 comments

Norbert’s Gambit at NBCN

It’s been over two years since I first wrote about using Norbert’s gambit in client accounts to cheaply convert Canadian dollars to US dollars (and vice-versa). Various white papers followed, showing DIYers how to get around the big banks’ high currency conversion costs. I even spoke with a few advisors and portfolio managers who had recently started implementing gambits in their own client accounts.

After the switch-over from TD Waterhouse Institutional Services (TDWIS) to National Bank Correspondent Network (NBCN) in early 2014, I was forced to learn the process at yet another brokerage firm. I still tend to favour the Horizons ETF products (rather than inter-listed stocks) when converting currencies, but this choice is totally up to the advisor. I’ll start off by briefly discussing the products I use and then go through the various steps required to implement the Norbert’s gambit in a taxable NBCN account.


The Horizons U.S. Dollar Currency ETF (DLR) is an ETF that holds cash and cash equivalents that are denominated in U.S. dollars. It is traded on the TSX and priced and transacted in Canadian dollars.

The Horizons U.S. Dollar Currency ETF (US$) (DLR.U) is the exact same ETF as DLR. It holds cash and cash equivalents that are denominated in U.S. dollars and also trades on the TSX. The only difference is that it is priced and transacted in U.S. dollars.

Both DLR and DLR.U have the same International Securities Identification Numbers (ISIN), which is basically the DNA of the security. The first two characters are the country code (CA), the next nine characters are the Committee on Uniform Securities Identification Procedures (CUSIP) number (44049C302), and the final character is the check digit (1)

Now that you have a quick overview of the products we will be using, let’s walk through the steps an advisor would take if they needed to convert $50,000 Canadian dollars to US dollars in a client account at NBCN.

Step 1: Log-in to the NBCN member site at and obtain an exchange rate quote

In this example, NBCN was offering $43,591.98 US dollars in exchange for $50,000 Canadian dollars. In steps two and three, we will be determining whether implementing the gambit would be expected to generate more US dollars for our client than the amount offered by NBCN.

Step 2: Calculate how many shares of DLR you could purchase for $50,000 CAD at the current ask price

By dividing $50,000 by the current ask price of $11.35, we determine that we could purchase 4,405.2863 shares of DLR. This is a purely hypothetical calculation, as we cannot purchase partial shares.

Step 3: Multiple the number of shares from step two by the current bid price of DLR.U

If we sold 4,405.2863 shares of DLR.U at the current bid price of $9.94 USD, we would receive US dollar proceeds of $43,788.55. This transaction would leave the client with an additional $196.57 US dollars in their account ($43,788.55 minus $43,591.98). In this example, implementing the gambit would be the preferred choice.

Step 4: Buy 4,405 shares of DLR in the Canadian dollar “A” account

Since we can’t buy partial shares, we will round down the number of shares of DLR from step two to the nearest whole share. We recommend placing a limit order directly at the current ask price. Ensure that the market is “CDN” and that you are in the client’s taxable Canadian dollar account (the one ending in “A”). 

Step 5: Sell 4,405 shares of DLR.U in the taxable US dollar “B” account

Once you have noticed the purchase of 4,405 shares of DLR has been accepted, immediately switch to the US dollar “B” side of the same client account. Once there, place a limit order at the current bid price to sell 4,405 shares of DLR.U. One tricky part of placing this trade at NBCN is that the market must be “TF” (it stands for Toronto Foreign). If you type in “CDN” instead, the trade will be rejected.

Every so often, this trade will not be accepted right away. If this happens, feel free to pick up the phone and contact an NBCN trader, who will be able to push the trade through.

At this stage, you may also want to purchase a US-listed ETF with the US dollar proceeds; this is generally okay, as long as all trades settle on the same day. Beware of settlement periods that contain a market holiday for either the Canadian or US stock market.

Step 6: On T+4, log-in to iMOST Next Generation and transfer 4,405 shares of DLR from the Canadian dollar account to the US dollar account

In order to avoid debit interest, this step would be required by the trade date plus three business days (T + 3). Unfortunately, iMOST will not let advisors request a journal on T + 3 (it has to be done the next day). To get around this, change the effective date in the request to one business day earlier, giving the reason that iMOST did not allow you to request the transfer on the settlement date.

By: Justin Bender | 0 comments