Risk is the problem, as others have pointed out.
Your fixed mortgage interest rate is for a set period of time only.
Let's say your 3% might be good for five years, because that's typical of fixed-rate mortages in Canada.
So, what happens in five years if your investment has dropped 50% due to a prolonged bear market, and interest rates have since moved up from 3% to 8%?
Your investment would be underwater, and you wouldn't have enough to pay off the loan and exit the failed strategy.
Rather, you might just be stuck with renewing the mortage at a rate that makes the strategy far less attractive, being more likely to lose money in the long run than to earn any.
Leverage, or borrowing to invest, amplifies your risk considerably.
If you invest your own money in the market, you might lose what you started with, but if you borrow to invest, you might lose much more than you started with.
There's also one very specific issue with the example investment you've proposed:
You would be borrowing Canadian dollars but investing in an index fund of U.S.-based companies that trade in U.S. dollars.
Even if the index has positive returns in U.S. dollar terms, you might end up losing money if the Canadian dollar strengthens vs. the U.S. dollar.
It has happened before, multiple times.
So, while this strategy has worked wonderfully in the past, it has also failed disastrously in the past.
Unless you have a crystal ball, you need to be aware of the various risks and weigh them vs. the potential rewards.
There is no free lunch.
money.stackexchange.com/users/3/Chris W. Rea
Well for a start funds don't pay interest.
If you pick an income-paying fund (as opposed to one that automatically reinvests any income for you) you will receive periodic income based on the dividends paid by the underlying stocks, but it won't be the steady predictable interest payment you might get from a savings account or fixed-rate security.
This income is not guaranteed and will vary based on the performance of the companies making up the fund.
It's also quite likely that the income by itself won't cover the interest on your mortgage.
The gains from stock market investment come from a mixture of dividends and capital growth (i.e. the increase in the price of the shares).
So you may have to sell units now and again or cover part of the interest payments from other income.
You're basically betting that the after-tax returns from the fund will be greater than the mortgage interest rate you're paying.
3 facts:
In the long term it is likely, but not certain, that a decent fund will return more than your mortgage rate.
In the short term stock market returns are volatile - dividends and stock prices can fall leaving you with less than you started with.
The mortgage has to be paid every month regardless of 2.
If you're comfortable with these 3 facts, go for it.
If they're going to keep you awake at night, you might not want to take the risk.
money.stackexchange.com/users/13720/Nigel Harper
Risk.
That's it.
No guarantees on the fund performance, while the mortgage has a guaranteed return of -3%.
I'm doing this very thing.
Money is cheap, I think it's wise to take advantage of it, assuming your exercise proper risk management.
money.stackexchange.com/users/20107/Ryan
Something very similar to this was extremely popular in the UK in the late 1980s.
The practice has completely vanished since the early 2000s.
Reading up on the UK endowment mortgage scandals will probably give you an excellent insight into whether you should attempt your plan.
Endowment mortgages were provided by banks and at their peak were probably the most popular mortgage form.
The basic idea was that you only pay the interest on your mortgage and invest a small amount each month into a low fee endowment policy.
Many endowment policies were simply index tracking, and the idea being that by the end of your mortgage you would have built up a portfolio sufficient to pay off your mortgage, and may well have extra left over.
In the late 1990s the combination of falling housing market and poor stock performance meant that many people were left with both the endowment less than their mortgage and their house in negative equity.
money.stackexchange.com/users/20770/Korone
Essentially, what you're describing is a leveraged investment.
As others noted, the question is how confident you can be that (a) the returns on the investment will exceed what you're paying in interest, and (b) that if you lose the bet you'll still be able to pay off the loan without severely injuring yourself.
I did essentially this when I bought my house, taking out a larger loan than necessary and leaving more money in my investments, which had been returning more than the mortgage's interest rate.
I then got indecently lucky during the recession and was able to refinance down to under 4%, which I am very certain my investment will beat.
I actually considered lengthening the term of the loan for that reason, or borrowing a bit more, but decided not to double down on the bet; that was my own risk-comfort threshold.
Know exactly what your risks are, including secondary effects of these risks.
Run the numbers to see what the likely return is.
Decide whether you like the odds enough to go for it.
money.stackexchange.com/users/12439/keshlam
I'm wondering if this investment strategy would work:   I get a mortgage loan for $300K at a 3% rate (realistic for current 5-year fixed mortgage rates here in Canada).  I invest the proceeds in a low-fee index fund, such as Vanguard's Total Stock Market Index.  I use the interest to cover the mortgage payments, and invest the rest of the returns.    This looks like it could work. Am I missing anything?  Thanks!
Pros/cons of borrowing money using a mortgage loan and investing it in a low-fee index fund?
money.stackexchange.com
<canada><mortgage><index-fund><investment-strategies><leverage>
money.stackexchange.com/questions/47832
money.stackexchange.com/users/28748/ramav
Your fixed mortgage rate is for a set period of time only. Borrowing to invest amplifies your risk. You might lose the money you borrowed. In addition, it is also quite likely that the income by itself will not cover the interest on your mortgage, which means that you may have to sell units or cover some of the interest payments from other income.  The stock market is volatile, but the mortgage has to be paid each month regardless. The stock market is volatile, but the mortgage has to be paid each month regardless. On the other hand, in the long term, a decent fund may return more than your mortgage rate, but there are no guarantees on fund performance, whilst the mortgage has a guaranteed return. A review of the UK endowment mortgage scandals might give you some insight into whether you should attempt your plan.  
A fixed mortgage interest rate is for a set period of time only. Essentially, what you're describing is a leveraged investment, which amplifies your risk greatly. Investing your own money in the market has the risk that you might lose what you started with, but if you borrow to invest, you might lose even more than you started with. Such income is  not  guaranteed and  will  vary depending on the performance of the companies making up the fund.   In addition, it is also quite likely that the income by itself will not cover the interest on your mortgage, which means that you may have to sell units or cover some of the interest payments from other income.  The stock market is volatile, but the mortgage has to be paid each month regardless. The stock market is volatile, but the mortgage has to be paid each month regardless. On the other hand, in the long term, a decent fund may return more than your mortgage rate, but there are no guarantees on fund performance, whilst the mortgage has a guaranteed return. A review of the UK endowment mortgage scandals might give you some insight into whether you should attempt your plan.  