This comparison suggests that the two percentages (growth rate and interest rate) are applied to the same balance each year. The math isn't nearly that simple. After the first year, those balances are unlikely to ever be the same again.
Mortgage interest is calculated by multiplying the interest rate (4% in this case) by the current principal balance, which declines predictably and gradually for the first ten years or so, but is paid down faster over time. Portfolio returns are calculated by multiplying a highly variable annual rate of return by a current balance that can grow or decline substantially over time. They're two very different animals.
The simple math would work better if the earnings were risk-free. But, when the annual returns vary as stock returns do, the math switches from simply subtracting percentages to dealing with random variables.
To explain my point, I modeled real stock and bond returns and historical mortgage rates1 for 76 ten-year rolling periods from 1928 to 2013. Each year, I assumed that an investor borrowed a 30-year fixed rate mortgage (FRM) at the average mortgage rate that year and held the mortgage for 10 years. (The average mortgage gets paid off after about 7 years.)
I assumed that the investor then invested the $100,000 in a portfolio of 50% S&P 500 index and 50% 10-Year U.S. Treasury Notes. At the end of ten years, the investor cashes in the portfolio, pays off the mortgage balance and I calculate his profit or loss, as shown in the chart below.
Although the annual FRM mortgage payments remain a constant dollar amount throughout the term, I converted those payments to the value of dollars from the first year of the period. In inflationary times, mortgage payments get paid with cheaper dollars over time, and with more expensive dollars over time when there is deflation. The model accounts for this.
The average mortgage rate during this time was 7% and the annualized real return on the 50/50 portfolio was 4.6%. The annualized nominal 50/50 portfolio gain was 7.8%.
If portfolios returned 7.8% and mortgages cost 7%, you might expect this mortgage-to-invest approach to generate a 0.8% a year profit and if lots of people had tried this at lots of times since 1928, the average gain from this strategy for all of those investors combined would have been about 0.8% annually.
But, if you were one of those investors, you might have seen gains much different than 0.8%. A $100,000 investment earning 0.8% for 10 years would generate a gain of $8,294. Instead, you would have ended up with one specific outcome from the chart above. Those outcomes range from a loss of $37,733 to a gain of $133,287. The median profit was $26,937.
Nearly 40% of the outcomes were below the return you might expect when portfolio returns exceed mortgage rates by 0.8%.
A range of outcomes that broad is far from risk-free.
If we sort the periods by mortgage rates, about 8% of the negative outcomes occur when the mortgage rate is below the median of 5.8%, demonstrating that the strategy can lose money about one out of twelve times even when the mortgage rate at which we borrow is historically low.
The failure rate, however, increases to 17% when mortgage rates are above the median. This suggests an obvious strategy: don't mortgage to invest when mortgage rates are historically high, but that should be obvious.
The failure rate is 22% when the market return for the 10-year period is lower than the median 4.74%, and only 3% when returns fall into the upper half. These returns aren't knowable when you invest, of course, so this information doesn't help with your investment decision. Market returns explain about 90% of profitability and mortgage rates explain about 20%.
The worst case outcome was the 10-year period beginning in 2000 when 30-year mortgage rates were 8% but the market would only return a real 1% per year for the following decade. The mortgage-to-invest strategy would have shown a $37,700 loss.
The best outcome came from executing the strategy in 1989 when mortgage rates were at 10.3% and the market would return 11.4% annually over the boom decade of the nineties. The strategy would have shown a profit of more than $133,000. That's an enormous range of outcomes, which is to say that it's a risky investment.
William Bernstein has noted that an individual's success in financing retirement is largely dependent upon the year when he or she is born. The magnitude and sequence of investment returns can change dramatically if those returns are shifted a single year.
Starting a ten-year period with this mortgage-to-invest strategy can also be greatly impacted by a shift of a single year. Take a look at the ten-year period beginning in 1987, in which this strategy netted a profit of $59,388 and the one beginning in 1988 that netted a $106,937 profit, an increase of $47,549. Why such a large difference?
As you can see from the following table, the period beginning in 1988 jettisoned the 3.18% portfolio loss in 1987 and added the 19.22% gain from 1997, resulting in an improvement of outcomes near $48,000 if you started a year later. The strategy worked much better from 1988 to 1997 than from 1987 to 1996, even though mortgage rates were nearly identical at 10.2% in 1987 and 10.3% in 1988.
Don't overlook foreclosure risk.
If you mortgage your home so you can invest in stocks, you increase the risk that you will not be able to repay your mortgage and lose your home to foreclosure. The risk is multiplied when the failure of your mortgage-to-invest strategy coincides with an economic downturn, which is highly probable. Failure of this strategy means you probably had a high mortgage rate and/or experienced low market returns. Your chances of losing your employment increase at those times, as well.
Late in 2007, home values crashed, stocks crashed and unemployment soared simultaneously. A lot of people lost their homes.
I am not recommending that you do or do not "mortgage to invest". I only suggest that you understand the risks and rewards before you do. This strategy is far from a sure thing.
This is not ground-breaking analysis. I present it for two reasons. First, many readers will not have read the previous studies and should be advised of the risks. And, second, this example builds the foundation for what I really want to talk about: the difference between implementing this strategy while you're still working and executing it after you retire.
I'll cover that in Selling Stocks to Pay the Mortgage.