1) It's true that you receive a 4% spread. It's actually a bit greater than that. The next two points will address why
- First, the mortgage interest is tax-deductible, so the after-tax borrowing cost is significantly lower. If you're already over the standard deduction, any additional mortgage interest you pay will result in additional tax deductions. As a result if you're in the 25% marginal tax bracket, your after tax borrowing cost would actually be 4.5%.
- While the investment in stocks will result in taxable dividends and/or capital gains, these can be minimized by choosing tax-advantaged investments. For example, index funds throw off relatively low dividend payouts, and have very low portfolio turnovers. So, the tax liabilities on these accouts would either be minimal or largely deferred. In other words, the after tax borrowing cost is significantly lower than 6%, and the after-tax return will be affected less than the after-tax interest cost.
3) I don't buy the statement that you've tied your house to your investments (except in the VERY loose sens of the phrase). In the event that you sell the house, you can liquidate sufficient funds from your portfolio to pay off the loan. The major risk would be if both the house AND your portfolio had gone down in value. Of course, this is a problem mostly if you've over-leveraged your house. So, leave yourself some slack.
In summary, it's probably not a bad strategy, but it's definitely not for the naive investor. A person would have to be very cognizant of the risks involved. I'd add that (since I believe in efficient markets, the best investment strategy would be a buy and hold, index fund strategy.