ERD50, if you read again , what I said was I couldn't stomach risking my house, not that I couldn't stomach risk. We have a COLA'd pension as well as a 403b and other investments. I am probably more sensitive to the type of risk we are talking about because I am directly affected. My mother lost her life long home this same way and now lives with me because she has nothing left but a very small SS check. My SIL lost her husband due to cancer and received $150,000 in life insurance. Rather than pay off her house, she gave it to a financial advisor(who also suggested she pay off the house) and between the drop in the markets and living beyond her means, she filed bankruptcy and the house was foreclosed on. Risk leaves wreckage sometimes.
As the other posts have covered, it's not a "Yes/No" question. It depends on what other investments you have and your overall portfolio (basic AA). And making bad choices is simply making bad choices, market risk or not.
Take your SIL's unfortunate circumstance - for simplicity, let's ignore the 'living beyond her means', as that will sink anyone (by definition). And again for simplicity, let's say the house had $150,000 remaining on the mort.
So, we need to know about her AA and portfolio. If this is the only $150,000 she has, she needs to invest it conservatively. And that is unlikely to earn more than mortgage rates, so it's not real attractive.
OTOH, if it *is* all the money she has, and she pays off the mortgage, she has nothing to cover an emergency. The liquidity of that $150,000 is important and valuable. And it will pay the mortgage for many, many months (years) while she gets situated. If she plans to keep the house she is going to need an income stream to support it. Don't forget, if she does not pay off the house, she HAS that $150,000 (which should be in conservative investments).
For example, GNMAs are paying ~ 4.5%, they do vary some in NAV, but not much and are not 'risky'. So, even if that is less than the mortgage rate, you can look at it as paying a small fee for liquidity. What's the option if an emergency comes up or she loses her job and she paid off the house? There are still bills to be paid, ins, utilities, taxes, food on the table, gas for the car, etc. You are going to pay for liquidity at that point, and it will probably be more expensive than the difference in the mortgage and GNMA rates, if available at all.
So, if you want to rephrase this as "Should a person who would do a really bad job of investing the money pay off the mortgage instead?" Well, then I'd say yes - but it would be better if that person got a little education instead, and made an informed decision. But that could still leave them in a liquidity crisis, so maybe they just swapped one problem for another?
Now, let's look at the 'living beyond your means' aspect of your SIL's situation. OK, if your SIL invested that money at the exact peak, $150,000 in the market would still be worth over $65,000 at the recent lows. So, if she blew that $65,000, then I'm also sure she would have also got into trouble if the house was paid for - she would have racked up CC debt, taken out a HELOC, something. I don't think a paid off house is a solution for a spend mentality.
This is a financial tool, and like so many other things - don't condemn a "tool" because it can be misused by some.
-ERD50