There are many factors which impact the decision to rent versus buy a home. The math is relatively easy, but the behavioural considerations are anything but.
There are two parts to this post:
1. A video which runs about nine minutes but is imperative to understanding the comparison. I strongly suggest watching it first.
2. A spreadsheet you can download so you can plug in your own numbers.
I’m posting a beta version of this rent vs buy calculator publicly, in the hopes that people can provide feedback for improvement, and for the masochists out there, let me know if any of the formulas or results are wrong. There are a lot of formulas and references in the spreadsheet, and in my experience, one person putting together something like this rarely gets it perfect the first time.
So help me try to break it, in the hopes that we can make it better and/or more accurate.
Some notes:
- This assumes you are a first time home buyer in the City of Toronto
- Therefore it assumes two levels of Land Transfer Tax (Provincial and Municipal)
- It also assumes you are eligible for a rebate
- You can model moving two times during the 25 years and all the transaction costs are automatically calculated (CMHC, Land Transfer Taxes, Realtor Fees, Legal Fees, etc.)
- The Monte Carlo simulations assume a normal distribution for both real estate and stock market returns. If you have suggestions on the variables to use for a non-gaussian distribution, let me know.
- There are cell comments for all the input fields
- I’ll add cell comments for the outputs later (if we think they are necessary)
- Please do not send your downloaded copy of the spreadsheet to others, instead refer them to this page where I will keep an updated copy of the spreadsheet
- Assume it is wrong until I have a few independent sources go over it in more detail (Another reason to not distribute it)
With house prices in Canada having had a spectacular run for a long time, and rents in some locations not increasing nearly as quick, at some point people will wonder if renting can make more financial sense in certain circumstances.
Most people have heard the usual rhetoric: “Renting is just throwing your money away” or “Why would I want to pay my landlord’s mortgage when I can pay my own?”. I am currently a renter and I’m confident that I’m not just throwing money away when you make a more apples to apples comparison, but I also believe that most people would be better off as owners.
To understand this somewhat paradoxical statement, I’ll refer you to a saying I have been known to trumpet from time to time: Managing your personal finances is 90% psychology, and 8% math. (The missing 2% is a testament to how unimportant that math is.)
In other words, if you took two otherwise similar homes where the only difference was one was for sale and one was for rent, then depending on your assumptions about growth rates and the ratio of the sale price to the monthly rent, you could see what would increase net worth faster: 1) Owning, or 2) Renting and taking all the upfront, and monthly cashflow differences and investing it. In one case your net worth would be driven by increasing the equity in your home. In the other, your net worth would be increased by how fast your investment portfolio grows over time.
While understanding that the projections are only as good as the assumptions (sketchy at best), far more important that the math are the psychological factors. For example:
- If renting and investing the difference is currently favourable, will you actually save the cashflow differences? In my experience, this is rarely the case except for the most disciplined of individuals.
- It’s *harder, but not impossible* to make mistakes as a home owner when it comes to getting the return available in the market. In other words, if there was a housing correction, most people wouldn’t panic and sell their homes. They would be more likely to ride out the downturn. The same is not true for people and their stock/bond/mutual fund portfolios. History has shown that investors do not often get the returns available in the market due to constantly making changes to their portfolios. (Edit: As per John Robertson, author of the new and recommended book The Value of Simple: A Practical Guide To Taking The Complexity Out Of Investing, “there’s an added risk on the home ownership side in that you can be forced to sell if you have to move to a different city for work or family reasons, but as a renter you can take your investment portfolio with you.”)
- On the other hand, some homeowners can sabotage themselves by accessing the equity in their homes too liberally. Some people renovate too much, fueled by rising home prices creating equity that can be tapped, oblivious to the fact that housing markets can correct, and sometimes viciously. Others may continually upgrade their homes by renovating or moving into more expensive houses time after time.
- There are less tangible benefits of owning: such as the pride of home ownership, having roots or a stable base for raising a family.
- Younger Canadians without families might also realize a benefit of renting instead: mobility. If you were offered a fantastic job in another province or country, are you more or less likely to take it if you’ve just bought a home? Is this important to you?
There are many other factors to consider, but for now, let me just say this: I don’t care if you own or rent. I have no horse in this race.
If you just want my opinion on what the average person should do, it’s this: Save up a healthy downpayment, make sure you find a place you don’t reasonably expect to move from for AT LEAST 10 years, buy a house that’s about 2/3 of the size of the mortgage you’re pre-approved for so you can be an owner and have money left over to invest in the stock/bond markets as well. Don’t over-think it.
Hi Preet, looks great!
On point 2, I’d just add that there’s an added risk on the homeownership side in that you can be forced to sell if you have to move to a different city for work or family reasons, but as a renter you can take your investment portfolio with you.
If you want to get super fancy, you can have the renter shelter some investment gains in a TFSA or RRSP (on the assumption that the owner will not be maximizing these). As an approximation, I use a lower marginal tax rate.
For the sheet, I have no idea how you made the Monte Carlo work, that is Excel wizardry beyond me.
My biggest issue is the output summary: it starts with a single trial above the fold, then the “real” results using all the trials is down below. Is it possible to graph the average or median results rather than a single trial? I may have just been unlucky, but I put in my numbers–which highly favour renting (as confirmed in the table below)–but 15 of 20 refreshes showed single trials where owning was the winner. This could be misleading (esp. as many users may not scroll down for the MC results or be confused by how the 95% avg/median results stack up) and wasn’t representative.
Is it useful to say renting (or owning) wins X times out of 1000 trials?
Property tax: the mill rate is held constant (so prop tax in $ goes down as house prices go down). I think it’s more likely IMHO for property tax in dollars to be set at today’s mill rate, then for the property tax in dollars to go up at ~inflation. Insurance may act more like that percentage-of-current-price though. Indeed, we’ve seen this in Toronto as prices go up faster than the city budget inflation, the mill rate has been decreasing.
Output: what is the graph showing? There’s a red line and a blue line, but which is which? Oh I see, the title has the colour coding. Could be more obvious.
Seems strange to me that the default std. dev. of house prices is higher than an investment portfolio (that fact alone is likely worth an article).
Hi Preet, looks great!
> Thanks!
On point 2, I’d just add that there’s an added risk on the homeownership side in that you can be forced to sell if you have to move to a different city for work or family reasons, but as a renter you can take your investment portfolio with you.
> Good point. I just recently from someone who closed and was transferred within a few months by his work. OUCH! I’ve added your comment above.
If you want to get super fancy, you can have the renter shelter some investment gains in a TFSA or RRSP (on the assumption that the owner will not be maximizing these). As an approximation, I use a lower marginal tax rate.
> I thought about that, and I think it can make a substantial impact, but as you know, the more complex the spreadsheet, the fewer people who will use it / use it correctly. Perhaps I will add a note to the cell comment that people can model lower tax drag using a TFSA by lowering the tax rates if they choose.
For the sheet, I have no idea how you made the Monte Carlo work, that is Excel wizardry beyond me.
>The inverse normal distribution function in Excel, using a nested Random number call function – then simulating multiple iterations using the Data Table function.
My biggest issue is the output summary: it starts with a single trial above the fold, then the “real” results using all the trials is down below. Is it possible to graph the average or median results rather than a single trial? I may have just been unlucky, but I put in my numbers–which highly favour renting (as confirmed in the table below)–but 15 of 20 refreshes showed single trials where owning was the winner. This could be misleading (esp. as many users may not scroll down for the MC results or be confused by how the 95% avg/median results stack up) and wasn’t representative.
> Good point. Perhaps I will switch the chart to appear below the fold. Graphing the range of possibilities would require increasing the computations from 1,000 operations to 300,000 (I think). Although there is probably a function that handles it more elegantly than I’m thinking in my head right now. Let me dig into that.
Is it useful to say renting (or owning) wins X times out of 1000 trials?
Property tax: the mill rate is held constant (so prop tax in $ goes down as house prices go down). I think it’s more likely IMHO for property tax in dollars to be set at today’s mill rate, then for the property tax in dollars to go up at ~inflation. Insurance may act more like that percentage-of-current-price though. Indeed, we’ve seen this in Toronto as prices go up faster than the city budget inflation, the mill rate has been decreasing.
>Okay, Let me think about a better way to model this.
Output: what is the graph showing? There’s a red line and a blue line, but which is which? Oh I see, the title has the colour coding. Could be more obvious.
>Added a legend.
Seems strange to me that the default std. dev. of house prices is higher than an investment portfolio (that fact alone is likely worth an article).
>Based on historical data, but likely the culprit is a non-normal distribution. Unless you are referring to the chart. In which case it’s due to leverage and possibly that part of the portfolio growth is linear (interest income, dividends, and annual realized capital gains distributions).
>Thanks for your feedback!
I know you’re hoping for technical feedback on your calculator, and I may yet provide some, but I was first struck by the expected real return of about 1.5% on real estate. According to Alan Blinder’s book, After the Music Stopped, the real return on houses in the U.S. from 1890 to just before the U.S. housing boom started was 0%. After the bubble burst in the U.S., the return eventually went back to 0%. Even if prices have risen a bit in the last couple of years, the annual compound average return since 1890 is still a small fraction of 1%. Anything is possible, of course, but even to hope to match inflation in Canada over the next decade seems optimistic. Of course, the roughly 3% real return on investments is optimistic for most people as well, but at least it is realistic for those who can avoid high fees.
Hey Mike, I agree running the numbers with 0% real growth on real estate makes sense. I’ve seen multiple sources as well showing no real growth over extended periods of time. I’m hoping people will do some of their own digging on what appropriate numbers are, but I also suspect many will come in with biases pre-determined to a certain extent.
Ditto with the rates on investments. One could make a pretty good argument on 0% real growth there as well depending on fees and behaviour :)
Thanks for the feedback.
With regard to return distributions, why not stuff actual data into a table and simply sample it? That is, for the stock market, put the daily returns from the TSX over the past couple of decades into a table and if you want to know the ten-year returns sample a random 2515-day interval (251.5 trading days per year)? You could presumably do something similar with home price data.
The advantages of this are: a) realism and b) pessimism. You’ll see the outliers on your Monte Carlo blow up badly for shots where returns catch a crash.
The disadvantage is that the data are pretty scarce and temporally inhomogenous: you will only have a few decades of meaningful data, and the data from 20 years ago will not be strictly comparable to those of today (market behaviours vary with time for all kinds of reasons.)
You can get around this to some extent by generating a histogram of one-year deltas, and then sampling that to generate multi-year returns. I know nothing about Excel (and treasure my ignorance deeply) but the way I’d handle this in any other language would be to generate a cumulative distribution function and do rejection sampling on it. I can go into more detail on that if it would be useful.
I have a couple of questions, why did you assume a rebate all the time on Land Transfer taxes?
Also, the assumptions of home ownership of 26 and 10 years don’t seem to fit reality. People turnover properties more frequently.
Wouldn’t commissions on sales reduce the spread more significantly if the person sold more frequently?
I really liked this spreadsheet. I have one similar but this one is much more robust.
What other spreadsheets do you have? I have an “Equity tracker” (for lack of a better name) that i created back in the 90’s and it’s grown a bit over the last 20 years.
I basically track my equity growth, available cash, retirement funds, debt, etc and I then graphed it.
I base all my money decisions on this. I’ve been looking to incorporate more intelligence into it, or make it more useful. I’m wondering if you have any spreadsheet similar to this.
Nice spreadsheet, good work Preet. Regarding the figures, that’s tricky, for example 3.5% real estate growth doesn’t happen for everyone. I see town homes in my area which would barely have 9 % appreciation for all 8 years so barely 1.1% per year. My approach in buy or rent comparison is to consider for housing all equivalent costs meaning I would not leave out heating, parking, etc which might be included in rental or have added cost. The buy or rent comparison should be actually called “invest by buying your home versus renting+investing”. Renters aren’t always saving the difference for an equivalent mortgage, same owning a home is not always an investment. For me I would say renting and investing makes sense as it fits better my lifestyle – no worries, flexibility and not splitting the paycheck with the bank is what I desire.