A 9% Mortgage Does Not Lose to 10% Stocks

There is a rule of thumb that circulates whenever someone asks whether to pay down a mortgage or invest the money. It goes: stocks have averaged about 10% a year, so any debt costing less than 10% should be carried rather than repaid. Personal Finance Club states it about as cleanly as anyone has:

“Mathematically speaking, if your interest rate is below 10% and assuming that investing will get an average return of 10%, you’re better off investing.”¹

The 10% is right. The word doing the damage is “mathematically,” and you can see why using the same index, over the same century, that the claim invokes.

The claim, with its own caveats

It is worth quoting the surrounding paragraph, because the post is more careful than the sentence that gets extracted from it. Immediately after the claim it adds that “the market is not consistent and it could give you a negative return for multiple years in a row,” and it closes by calling the choice “a decision based on personal preference.”¹ Earlier in the same post it concedes the key economic point in the other direction, that paying off high-rate debt is “essentially giving yourself a guaranteed return on your money.”

The post plainly understands that risk exists. The trouble is one sentence saying “mathematically” sitting beside sentences that concede the maths does not work that way, and the extracted sentence is the one that travels.

One attribution note, since fact-checks should get this right: that post is signed by two of the site’s writers rather than by Jeremy Schneider, who founded Personal Finance Club. The claim belongs to the publication.

Why an average is not a promise

Paying down a loan returns the loan’s rate, after tax, with certainty. Buying an index fund returns a distribution whose mean has historically been around 10% nominal and whose annual standard deviation has been about 19%. Comparing the mean of the second to the certainty of the first leaves out the entire reason anyone is paid an equity premium in the first place. We work that framework through in Debt Is a Time Machine and The Risk-Free Rate Is Your Hurdle Rate, so what follows here is the measurement rather than the theory.

The academic treatment builds the risk match into its setup rather than arguing about it. Amromin, Huang and Sialm, examining whether households should prepay a mortgage or contribute to a tax-deferred account, are explicit that the comparison runs against “an asset with similar risk properties.”² Their arbitrage result is real, and it is constructed over risk-matched assets. Swap in equities and it is no longer the same claim.

The test, on 98 years of returns

Take the annual total returns of the S&P 500 from 1928 to 2025. The geometric average is 10.02%, which is where the 10% comes from. Now ask a different question: across every overlapping holding period of a given length, how often did buying and holding actually beat a guaranteed return?

Our calculation from data/sp500_returns.json, reproducible with scripts/guaranteed_vs_equity_windows.py. Windows overlap, so they are not independent observations; the pre-1957 index is a reconstruction; taxes, the mortgage interest deduction and the fact that repayment happens on a schedule are not modelled.

Against a guaranteed 9%, stocks won 50 of 89 ten-year windows and lost 39. Over twenty years they lost 26 of 79. A strategy that fails a third of the time over two decades is a reasonable bet. It is not a mathematical result, and the difference matters most to the person who lands in the third.

The average people quote is not the average in the calculator

There is a second arithmetic problem hiding underneath. The same 98 years produce an arithmetic mean of 11.85% and a geometric mean of 10.02%. The geometric figure is the one that describes what a buy-and-hold investor actually compounded at; the arithmetic figure is higher because volatility drags terminal wealth below the average of annual returns. Anyone who takes an arithmetic average from a table and puts it into a compounding calculator overstates the result, and the gap widens with volatility. Our house planning number, and why it is lower than either figure, is in What Real Return Should You Assume for Stocks?

Where the rule is right

Read the top row again. At a 3% mortgage, investing beat the guaranteed alternative in 90% of ten-year windows and 99% of twenty-year windows. For the millions of households who refinanced into a 2% or 3% loan, the advice to invest instead of prepaying is not just defensible, it is close to overwhelming, and a reader who followed the rule of thumb got the right answer.

The rule breaks where it matters most, which is at high rates. That is also where people are most anxious and most likely to go looking for a rule. Somebody carrying 9% debt is being told by the version of this claim that circulates that the maths favours investing, when the historical record puts it near a coin flip over a decade.

Run it with your own rate

This calculator models the investing side as a distribution rather than a point estimate, which is the whole disagreement. It starts at a 9% debt rate against a 10% expected return.

What we recommend

Compare the debt rate to a return you could get with matching certainty, which in practice means a Treasury or a high-yield savings rate, not the stock market. If the after-tax debt rate is above that, repaying is a good risk-free trade. If it is far below, the historical case for investing instead is strong and the table above shows how strong.

In the middle, which for most of the last two years has meant mortgage rates around 6% to 7%, treat it as a genuine judgment call rather than a calculation. The record says investing wins most of the time at those rates and not all of the time, and how much you care about the difference depends on your job security, your other liquid assets, and how you would feel in the windows where it did not work. There is no version of this where a single threshold number settles it.

Frequently asked questions

Should I pay off my mortgage or invest?

Compare your after-tax mortgage rate to a safe yield, not to the stock market’s average. Above that safe yield, prepayment is a guaranteed return that is hard to beat on a risk-adjusted basis. Well below it, the historical case for investing is strong. Liquidity matters too: money in a brokerage account can be reached in an emergency and home equity generally cannot.

Is the 10% stock market average wrong?

The number is broadly right as a nominal, US-only, geometric figure over a long history. It is the wrong input for planning, because it is nominal rather than real, US-specific rather than global, and backward-looking. A lower real number is the appropriate planning baseline.

Does the mortgage interest deduction change this?

For most households now, very little, because the standard deduction means they do not itemize. If you do itemize, use your after-tax mortgage rate on the debt side of the comparison, which lowers the hurdle.

What about carrying debt to invest more generally?

The same logic applies with more force, since the borrowing is usually at a higher rate and the leverage magnifies the bad windows. That case is in Debt Is a Time Machine.

Key takeaways

• A certain return and an expected return are different goods. Comparing the mean of one to the certainty of the other omits the reason the equity premium is paid.
• Over 1928 to 2025, the S&P 500 beat a guaranteed 9% in 56% of ten-year and 67% of twenty-year overlapping windows. These are outputs of one historical test with overlapping windows, not a probability forecast.
• At low rates the rule of thumb works. Against a guaranteed 3%, stocks won 90% of ten-year windows. The advice is usually right even where the reasoning is not.
• The threshold that matters is a safe yield, not the stock average. That is a much lower bar than 10%, and it moves with rates.
• Quote the geometric mean, not the arithmetic one. The same 98 years give 10.02% geometric and 11.85% arithmetic, and the higher figure overstates compounding.

Related guides

• Debt Is a Time Machine the guaranteed-versus-expected framework in full, with a crossover calculator.
• Do You Need a Paid-Off Home to Retire? the same question at the point where liquidity starts to dominate.
• What Real Return Should You Assume for Stocks? why our planning baseline is well below 10%.
• Good Heuristics, Bad Theorems the series this belongs to, and the scale we grade claims on.

Author disclosure

Summitward publishes a debt payoff planner, so we have an interest in readers treating this as a decision worth modelling. We have tried to give the rule of thumb its strongest case, which is the 3% row, as prominently as its weakest. Nothing here is personalized financial advice.

Sources

1. Personal Finance Club, “Pay down high interest debt before you start investing,” July 13, 2023, signed by Vivi and Shane. Read September 14, 2026; the page shows no later update. personalfinanceclub.com
2. Amromin, G., Huang, J. and Sialm, C. (2007). “The tradeoff between mortgage prepayments and tax-deferred retirement savings.” Journal of Public Economics 91, 2014–2040. The arbitrage result is constructed over assets with similar risk properties, which is the point relied on here. mccombs.utexas.edu
3. S&P 500 annual total returns, 1928 to 2025, as stored in this project at data/sp500_returns.json. The window test is scripts/guaranteed_vs_equity_windows.py.

Editor’s note

Educational content, not financial or tax advice. The percentages in the table are historical frequencies over overlapping windows in a single market, which makes them a description of the US record rather than a probability of any future outcome. They ignore taxes, fees, the mortgage interest deduction, and the schedule on which debt is actually repaid, and they compare a lump sum against a lump sum. Quotations from personalfinanceclub.com were read on September 14, 2026. Talk to a professional about your own situation.