How the calculator works

Last updated October 24, 2026

This page explains exactly how the calculator turns your inputs into an estimate, where its data comes from, and what it leaves out. The examples use CAD to USD; USD to CAD works the same way with the two ETFs swapped.

1. How many shares you buy

Norbert's Gambit uses DLR, which trades on the Toronto Stock Exchange in Canadian dollars as DLR and in U.S. dollars as DLR.U. To convert CAD to USD you buy DLR at its ask price. The calculator first sets aside your broker's journaling fee and buy commission, then buys as many whole shares as the rest covers:

shares = floor((amount − journaling fee − buy commission) ÷ DLR ask price)

Any cash that doesn't make up a whole share stays in your account in the original currency. Journaling fees are always charged in Canadian dollars, so for USD to CAD conversions the calculator converts the fee to U.S. dollars using the DLR.U ask and DLR bid prices.

2. What you get when you sell

After your broker journals the shares to DLR.U, you sell them at the DLR.U bid price and pay the sell commission:

proceeds = shares × DLR.U bid price − sell commission

Buying at the ask and selling at the bid means you pay the bid-ask spread on both sides. That spread, plus the commissions and journaling fee, is the direct cost of the gambit.

3. The risk while you wait

Journaling can take several business days, and the price you'll sell at can move in the meantime. The calculator models that movement as a normal distribution. If the share price has a daily standard deviation of σ and journaling takes t business days, the price after t days has a standard deviation of σ × √t. The estimate for a given number of standard deviations z is:

proceeds(z) = shares × bid price × (1 − z × σ × √t) − sell commission

The headline range uses z = ±3, which covers 99.73% of outcomes under a normal distribution. The detailed explanation also shows ±0.5, ±1 and ±1.5 standard deviations.

This risk matters most for USD to CAD. There you sell DLR, whose Canadian-dollar price moves with the exchange rate, so a few days of currency movement can change your result noticeably. For CAD to USD you sell DLR.U, whose U.S.-dollar price barely moves, so the range is very narrow. Both volatilities can be changed under advanced settings.

4. Comparing with Wise

When you click the Wise comparison, the calculator requests a live quote for your amount from Wise, for a balance-to-balance conversion where the money is already in your Wise account. It then finds how many standard deviations (z) of price movement would make Norbert's Gambit return exactly the Wise amount, and uses the normal distribution to turn that into a probability:

chance Norbert's Gambit beats Wise = P(Z < z_break-even)

If break-even is more than three standard deviations away, the result is shown as "near 0%" or "near 100%".

Opportunity cost

Wise usually converts much faster, so the comparison can include the interest your money could have earned while Norbert's Gambit is in progress:

opportunity cost = amount × Wise rate × risk-free rate × (journaling days + settlement days) ÷ 261

261 is the approximate number of business days in a year. The risk-free rate defaults to 0%, so this cost is only included if you enter a rate under advanced settings.

Data sources

• DLR and DLR.U prices: the page loads a recent snapshot of bid and ask prices, and the "Refresh DLR Prices" button fetches current quotes through this site's server. The timestamp next to each price shows how fresh it is.
• Volatility: an estimate of DLR's recent daily price volatility, updated periodically. You can see and change it under advanced settings. DLR.U uses a small default (0.01%) because its U.S.-dollar price is very stable.
• Wise: the rate and fees come from Wise's API at the moment you request the comparison.
• Broker presets: commissions, journaling fees and typical journaling times for nine brokers, gathered from broker websites and other investors' reports. They're estimates and may be out of date, so check them against your broker's current pricing.
• About DLR: the Global X US Dollar Currency ETF product page from its issuer.

Limitations

• Real exchange-rate moves aren't perfectly normal; large, sudden moves are more common than the model assumes.
• It assumes you buy at the current ask and sell at the bid with no partial fills or price slippage.
• It doesn't include taxes, ECN or exchange fees, trading halts, or other market disruptions.
• Journaling and settlement times vary by broker and even by request; the presets are typical values, not guarantees.
• The Wise quote assumes the money is already in your Wise balance; funding or withdrawing can add fees and time.

Spotted a mistake or have a better data source? Please get in touch.