A BS-Free Approach Finally Answers This Much Debated Question
Part 1 – Intro, Approach, and Assumptions
Click the hot links If you want to jump to Part 2 – Estimating rR & rB and Building the Spreadsheet or Part 3 – Results and Conclusions.
Is home ownership really something to aspire to, or could renting be the better path for most people? Googling “Rent vs Buy” is a proven method to expose oneself to a mountain of garbage arguments like few others (though for me, “How to choose a good real estate agent” still ranks #1). Most of the analysis-light articles encountered feel designed to sway opinions towards buying a home, getting pre-approved for a mortgage, hiring a real estate agent, opening a brokerage account, or raising eyebrows with a contrarian opinion that “the American dream of home ownership is dumb.”
There are hundreds of articles are chock full of gems, including:
- “…there is nothing like the satisfaction of homeownership…,”
- More recently, “…Zoom and work from home give people the ability to work wherever they want, and renting allows the flexibility to explore…,”
- “…the deductibility of mortgage interest and real estate taxes will result in a huge savings”
- And my favorite, “the S&P500 has been returning over 10% per year for the last 100 years, so clearly there is no better investment…,”
So I took the time to create a spreadsheet to analyze the concept for myself. This turned out to be way more complicated than I expected, and like ripping out a loose thread from an aging sweater: tug one and another comes loose.
Formulating the Hypothesis
The eureka moment came when I realized the best way to compare “Buy vs Rent” is to approach this from the perspective of “Buy minus Rent.”
Consider two people, person B and person R, with the same amount of cash at year 0, which we can call C0. B chooses to invest C0 as a down-payment on a home (which would also include attorney fees, bank fees, mortgage tax, application fees…etc.), and R chooses to invest C0 in the stock market and to rent something instead.
By subtracting R’s Return On Investment from B’s ROI, a number greater than 0 means B is better off, while less than 0 means B is not better off.
For math nerds like me, we are looking a solution to the following equation:
AdvantageROI = ROIB - ROIR
Where ROIB = C0 *(1 + rB)t and ROIR = C0 * (1 + rR)t
Here, rB is the rate of investment return for buyer B, and rR is the rate of investment return the renter R, and t corresponds to a time interval, which for our case will be number of years.
This is our hypothesis:
If ROIB - ROIR > 0, that means buying is better than renting, and if ROIB - ROIR <= 0 (AND THIS IS IMPORTANT) that means buying is not necessarily better than renting.
For the next step we have to figure out the rates of investment return rR & rB. Sounds easy, but the devil is in the details.
I tried to make intelligent estimates, and to account for every penny possible, but the US tax system is bracket based, with different rates on taxation as one jumps from one bracket to another, insurance varies company to company and is different for owners and renters, owners have higher maintenance costs, but renters spend more on moving costs, and this is just the tip of the iceberg.
The analysis is sufficiently rigorous, but every analysis requires the addition of an error term – which in this case would look something like this:
AdvantageROI = ROIB - ROIR + EBR
Where EBR is the sum of errors resulting from guess-work and assumptions required to come up with the ROI’s of B and R. Like the rest of the terms in our equation, it can be negative or positive.
If AdvantageROI is positive and EBR is negative, we know buying is better than renting (two negatives = positive), because ROIB must be > ROIR no matter how big EBR is. On the other hand, if AdvantageROI is negative and EBR is positive, we don’t know if buying is better, because a sufficiently large EBR can distort our findings.
Eliminating error is impossible, but one can control for its impact. Thus, when assumptions and guesstimates were necessary I chose decisions that would increase the ROI for the renter. Not because I prefer one over the other – but because ROIR is the negative term in our equation.
Remember the stated hypothesis:
If ROIB - ROIR > 0, that means buying is very likely better than renting, and if ROIB - ROIR <= 0, AND THIS IS IMPORTANT, that means buying is not necessarily better than renting.
By favoring ROIR, this would reduce the impact of a positive error term, and lend more certainty and credibility if the hypothesis is proven to be true.
Check out Part 2 – Estimating rR & rB and Building the Spreadsheet or Part 3 – Results and Conclusions...where I go over all of my assumptions, and where you will learn why this is such a robust approach.