The cost of converting Canadian Dollars to American Dollars with Norbert's Gambit

On Feb 26th, 2019, I initiated my first Norbert's Gambit at National Bank Direct Brokerage (NBDB).  The purpose was to exchange over 55k worth of Canadian Dollars (CAD) to American Dollars (USD) within my RRSP account. (Side story: I used the greenbacks to invest in a leveraged implementation of Dual Momentum)

My RRSP account at NBDB is segregated into two sub-accounts: a Canadian Dollar RRSP sub-account and a US Dollar RRSP sub-account.

The original funds were in my Canadian Dollar RRSP. There I bought 4,274 shares of DLR at $13.290 CAD; for a grand total of $56,801.46 CAD. 

I waited until the day after my trade settled (March 1st, 2019) and called NBDB requesting to transfer all 4,274 shares of DLR from my Canadian Dollar RRSP to the  US Dollar RRSP (resulting in 4,274 shares of DLR.U being transferred into the a US Dollar RRSP). I also asked them to include a note in the system so that I could sell all the 4,274 shares of DLR.U that same day. 

Shorty after the call I sold the 4,274 shares of DLR.U at $10.06491 USD for a grand total of $43,017.43 USD.

In summary, I got $43,017.43 USD for my original $56,801.46 CAD.

There were no transaction costs because trading more than a 100 shares of any ETF is free at NBDB.

The bid/ask spread when I bought DLR.TO was $0.01 CAD; incurring in a cost of $42.74 CAD because I bought at the ask price. 

The bid/ask spread when I sold DLR.U.TO was $0.01 USD; incurring in a cost of $42.74 USD because I sold at the bid price. Converted to CAD using the Bank of Canada (BoC) rate on March 1st ($1 CAD -> $0.7541 USD) this cost rounds to $56.68 CAD.

The MER of these ETFs is 0.56% annually; which translates to a cost of 0.0046% (3 * 0.56% / 365) of the market value for holding it 3 days.  For simplification let’s say we apply this tiny percentage to the initial dollar CAD amount: 0.0046% x $56,801.46 CAD = $2.61 CAD.

If the ETF was trading at a premium; then there would be a cost associated with such premium. I honestly don’t know whether the ETFs were trading for a premium or at a discount at the time I executed my trades.  If you execute Norbert's Gambit many times over your life as an investor; then this cost would probably balance itself.  So, I will assume this cost to be zero given that sometimes you would buy at a premium incurring in a cost or buy at a discount pocketing a gain.

Beyond the “typical” costs we need consider the capital gain or loss incurred by holding the ETFs for 3 days (the Forex market keeps moving). Here again I would simplify things by assuming that either the CAD/USD pair did not move significantly during these 3 days or that over a lifetime of executions of Norbert's Gambits the capital gains and losses would balance themselves.

So far the “approximate” “theoretical” cost of my Norbert's Gambit comes to $102.03 for exchanging 56,801.46 CAD. In percentage this cost rounds to 0.18% of the amount I exchanged.

That’s the theory, but what about in practice?

The BoC CAD/USD rate on Feb 26 was 0.7579 ($1 CAD -> $0.7579 USD). If we use this rate for our estimation, then we could have converted $56,801.46 CAD into $43,049.83 USD on Feb 26. This number is very close to the real amount of dollars I ultimately got converted ($43,017.43 USD). The difference is minus $32.40 USD; which could be interpreted as a “cost” of $32.40 USD ($42.97 CAD if we use the BoC exchange rate of March 1st). In percentage this cost rounds to 0.08% ($42.97 CAD / $56,801.46 CAD) of the amount I exchanged.

There are lots of simplifications and assumptions in the math above; but they are not outrageously out of place. My goal was not to calculate the cost of the Norbert's Gambit with scientific precision; but to show that it is a very cheap strategy to convert CAD to USD dollars and vice versa.