Let's say you have 100k in your house as equity.
S&P 500 pretty much guarantees a 10% reasonably safe return.
Interest Rates are at 2% to 3% on a home loan.

Let's say you do a cash out refinance and got that 100K in equity in cash and invested it in an S&P 500 fund.

It seems to me that the investment would earn more than the interest being paid on the loan. Your home appreciation wouldn't be changed. So you would net net 7% return on your equity that would normally earn nothing.

I know there are investments which would earn more money but with better returns come bigger risks so I like the S&P 500 for the lack of risk in this example.

It can't be that simple. I know I am missing something here.