The first is from MDM at the investment order thread: https://forum.mrmoneymustache.com/investor-alley/investment-order/
Pay off any debts with interest rates ~%3% or more above the current 10-year Treasury note yield.
The current treasury yield (as of writing) was 4.58%. Therefore, per forum wisdom, anyone with a rate >7.58% should be paying down their mortgage.
I just checked that thread, and
@MDM 's post (the 2nd post on the thread) says:
2. Pay off any debts with interest rates ~5% or more above the current 10-year Treasury note yield.
Maybe this advice changed to 3% downthread, but it's not material to my main comment.
My main comment is investing in 10y treasuries and paying down a mortgage are both risk-free investments from the perspective of a US-based person with dollars and a mortgage, and who is taking the standard deduction instead of itemizing. The two investments are equivalent in risk. So why wouldn't we go the treasuries route if treasuries were yielding even a fraction of a percent more than the mortgage? Why does the treasury option have to clear a 3% or 5% hurdle for us to start considering it? Is that hurdle arbitrary?
Some possible arguments:
1) Liquidity: This favors investing in treasuries, because funds paid into a mortgage cannot be quickly accessed in case of emergency or opportunity.
2) Inflation Hege: This favors investing in treasuries. As investors discovered in 2022, nominal bonds can lose value if rates rise quickly. AGG lost 14% in 2022. However, the people who paid off their 4% mortgages instead of investing in treasuries need not gloat, because they are now missing out on the opportunity to lock in 5% yields for many years. That missed opportunity to arbitrage a 4% debt against a 5% risk-free yield was probably worth more in the long run than was saved by not investing in bonds in 2021.
3) Abandonment Option in Non-Recourse States: This favors investing in treasuries. If you just put 3% down on a house in a non-recourse state, what should you do if housing prices crash -25%? Walk away and let the bank have it! In this way, a mortgaged house has a put option on it, limiting your maximum losses, whereas a house owned outright has no limit to losses. This option may also have value if the house is severely damaged and insurance won't pay.
4) Sequence of Returns Risk: This favors investing in the mortgage. It has been
mathematically demonstrated that your portfolio is more likely to survive a SORR event if you have less money and lower fixed housing costs, than if you have more money and higher fixed housing costs. Of course, I'm sure the advice has a crossover point where the house is so expensive or the mortgage payment so low that paying off the house leaves a person too vulnerable. But at normal house price to consumption values, the relationship holds. ERN used a $1M net worth, either a -$200k mortgage and +$200k extra in assets or no mortgage and only the $1M in assets, 4% WR, 2% inflation, and a 3.85% mortgage rate. A lot of those variables have changed since 2020.
5) Already Locked In Low Rate: This favors investing in the treasuries, and is no-brainer risk-free arbitrage. I'd choose this option anytime your mortgage rate < any duration treasury rate.
Invalid arguments:
1) Refi Opportunity: You can refi regardless of how much of your mortgage you already paid off. The amount you can refi is based on assessment, not existing mortgage balance.
2) Compounding: Aside from differences in the specific cashflows, compounding works both ways. E.g. you can reinvest the coupons from your treasury notes just like you can invest the savings from not having a mortgage. If the rates are the same, this is roughly a wash.
3) 25X or 4% Rules: This is invalid * in my opinion * because one should be optimizing wealth, risk, and inflation hedging, not rules of thumb. That means if it makes sense to have or keep a mortgage from an interest rates perspective, then your model for "when to retire" should account for the remainder of your mortgage payments and maybe make lower assumptions about the impact of inflation. This used to be hard, but is now easy thanks to sophisticated online retirement calculators that can account for mortgage payoff, social security, pensions, and other time-based changes.
The second is my own but fairly convention idea, pay down debts more than 1/CAPE10 + 10yr TIPS yield + 0.7%, which is historically the approximate return of the S&P500. 1/30+2.19%+0.7%= 6.22%. Per this rule, it is certainly time to be paying down the mortgage at today's rates.
Per these indicators, people with mortgage rates >7.5% and as low as 6% should be paying off their mortgages under these circumstances, certainly if they can do it with a lump sum. Depending on the liquidity and stability of the individual, it seems like many should also be putting money into the mortgage instead of investing in taxable accounts.
The problem here is we're comparing the prospects of a risk-free investment - paying down one's mortgage - with a far riskier investment in the stock market. Thus we're mixing (1) the issues discussed above for a decision between equally risky options with (2) a separate decision to increase or decrease the risk of one's AA.
The difference between expected and historical returns between bonds and stocks expands and contracts over time, so I'm reluctant to say a formulaic rule could cover all the scenarios where stocks are expensive/cheap, houses are expensive/cheap, mortgages are expensive/cheap, and alternative investments such as treasuries are expensive/cheap. I've seen various asset pricing models applying a fixed "equity risk premium" of 2% or 3% to compensate investors for the difference in risk between stocks and treasuries, but this does not guarantee any particular portfolio, which could encounter SORR and be devastated despite the premium. Risk is its own decision.