Tuesday, March 20, 2012

Mortgage-GIC Arbitrage

Recent musings at Blessed by the Potato about BMO’s 2.99% closed 5-year mortgage offering made me wonder about the possibility of running an arbitrage with a mortgage and a GIC.

Outlook Financial offers a 5-year GIC at 3.10%. It would seem that if you owned your home outright you could take out a mortgage, put the proceeds in a GIC, and make a free 0.11% per year for 5 years. On a $250,000 mortgage, this would be a total of about $1375. This won’t make you rich, but it’s not trivial.

There are a number of potential problems here. For one, the fine print on the BMO web page includes “If we require you to obtain an appraisal, the appraisal fee would increase your APR.” So, you may not be able to get 2.99%.

Another potential problem is hidden compounding assumptions. In Canada, most mortgage rates assume semi-annual compounding. This means that 2.99% is really 1.495% every 6 months. This compounds out to 3.012% per year. I was once offered a variable mortgage by BMO where the rate assumed monthly compounding. If that applied here, the compounded rate would be 3.031%. It could be that Outlook Financial’s GIC rates have built in compounding as well. In the end, I’m not sure what actual arbitrage spread is available.

A third potential problem is insolvency. Outlook Financial is backed by the Deposit Guarantee Corporation of Manitoba (DGCM) and not the Canada Deposit Insurance Corporation (CDIC). At a 0.11% spread, if the odds of losing your GIC money within 5 years are more than 1 in 900, this arbitrage is definitely not worth it. How much lower the odds have to be for this arbitrage to makes sense is a personal choice.

The potential gains aren’t enough to entice me to try this arbitrage, but it makes me think.


  1. Or what about investing in BMO stock, currently yielding a dividend of better than 4.5%

  2. @Andy R: That's another way to go, but I was looking for a riskless arbitrage.

  3. Are you sure about your "2.99% is really 3.012%" interpretation of compounding mortgage interest? I was under the impression that the posted rate already took compounding into account, such that the effective rate paid by the borrower ends up being less than what is posted. I have an old blog post about this:


    With this interpretation, 2.99% would actually work out to 2.97% (if paid/compounded bi-weekly).

  4. @Loonies and Sense: Yup, I'm sure. I've confirmed this with every mortgage I've ever had, and just be be safe, I checked with BMO's online calculator:


    For a $500,000 mortgage at 2.99% over 25 years, the calculator says the monthly payments are $2363.66. I repeated this calculation using my own formulas for 3 cases:

    Annual compounding: $2358.02
    Semi-annual compounding: $2363.66
    Monthly compounding: $2368.46

    It's clear that BMO is using semi-aanual compounding, which means that the actual yearly rate after compounding is (1+0.0299/2)^2-1 = 3.012%.

  5. @Loonies and Sense: I just read your blog post. I was with yo until you said that the "true effective annual rate" for the 7% example was 6.90%. What you call the true effective annual rate is not what I mean when I calculate the yearly rate after taking into account compounding. In your example, if you make no payments for a year (and no penalties were charged), the amount you owe on your mortgage would rise by 7.1225%. This is what I call the annual rate after taking into account compounding.

    Many people seem to believe that the "real" yearly rate comes from multiplying the monthly rate by 12. We are charged compound interest, not simple interest; it makes no sense to report yearly rates that have little connection to how your debt grows.

  6. @Michael James: Ahhh... I gotcha. The only reason your "effective" rate ends up below posted is the payments you're making, effectively reducing the amount of cash you have earning money in a GIC. For your arbitrage scenario, you're using the correct rate.

    In order to get Excel's PMT function to replicate the monthly payment amount of $2,363.66 for your example, you need to enter a monthly rate of 0.0297/12, as opposed to 0.0299/12.

  7. @Loonies and Sense: Alternatively, you could enter (1+0.0299/2)^(1/6)-1 as the rate in the pmt function in Excel.

  8. Multiply by 12, and that's exactly the formula I used to get 2.97% (except that I squared and took the 12th root, instead of simplifying to the 6th root).

    Thanks for this post. I learned something new about about mortgage interest (or at least an adjustment to the way I think of mortgage interest), and got to debate financial calculations to boot.

    It's win-win! :)

  9. I must be missing something...how is a .11 percent per year return supposed to keep up with inflation?

  10. @Anonymous: The 0.11% per year is entirely free money (assuming that there is no default risk). You never have to put up any of your own money. So, comparing 0.11% to inflation is not the right comparison. The $275 you get each year might be worth a little less due to inflation, but that's about it.

  11. The 0.11% (or whatever difference) would be taxable and depending on your marginal tax rate you might only get just over half that amount.

    Also, you would have to make mortgage payments while your GIC money would be tied up for the 5 years, so you would have to ensure you had the cash flow for that.

  12. @Anonymous: You're right that the gains from the arbitrage would be taxed. I didn't want to complicate the post too much, but you could deal with the cash flow issue by borrowing a little extra on the mortgage to cover the payments. However, this would cut into profits as well.