This came up in another thread in a discussion about rational investing, and I realized that some of you are really good with FIRECalc and cFIREsim and could give actually mathematical answers.

Most people agree that pre-paying a low-interest mortgage rather than investing is rationally incorrect. Over the long term, the market should return 7%, and a 3% interest loan is worth the cost in order to invest. It's easy to see that's correct over the typical 30-year mortgage period because the numbers are significantly higher for the market returns.

But there are also seem to be very few people who actually take the equity out of their house in the form of a HELOC to invest, even though the concept is exactly the same.

The latter seems scarier, even though we understand (or should understand) that rationally it's no different. And yet, our reliance on the 4% rule and investment portfolios to sustain early retirement is premised on being (at least relatively) risk neutral and trusting the numbers.

So what do the FIRECalc or cFIREsim numbers show about borrowing money to invest in the market?

If you have $750k in investments and can borrow $250k in home equity at a fixed 3% with a 20-year repayment period, does that always increase your odds of success? What kind of increases? Assuming the interest rate is locked and you're never going to get the equivalent of a margin call (i.e., being forced to pre-pay the loan or conduct a fire sale--excuse the pun), is there any situation in which borrowing the home equity doesn't make rational sense in the calculations?

I realized that, even though I consider myself a fairly rational investor, I'm not being rational by both (1) counting on the 4% rule, which requires a risk neutral acceptance of the numbers, and (2) refusing to consider investing home equity, because I don't like having debt. I'm now curious what the numbers show.

P.S. There was an example given in the other thread about a Boglehead investor who tried to borrow $200k in 2007 to invest early in his career, and it all melted down when a series of margin calls in late 2008 wiped him out. The quick reaction was don't ever do it, citing that example, but interestingly, that was a historically bad time to invest, and really not any different than citing the 5% failure rate as a reason not to follow the 4% rule. And even more interestingly, even though that was one of the worst times ever to invest, if he had not gotten the margin call, he probably would have made money on the loan through today, assuming a 4% interest rate or so on the loan.

Curious to see how this turns out.