Should You Rent or Buy?
Emre Ergungor and Saeed Zaman
Should you buy a home? The answer depends greatly on individual circumstances. You need to consider factors such as your income, job security, existing debt, and tolerance for risk, as well as the condition of your local housing market. You may also want to consider the impact that buying a home will have on your household finances. We have created this calculator to aid you in understanding that part of the home-buying decision.
Our rent or buy calculator compares the cost of owning a home to the cost of renting one under various economic scenarios. It then presents a rough estimate of the financial benefit of homeownership relative to renting. What makes our calculator unique is that it doesn’t just give you the estimate, it also gives you a range of possible gains and losses around that estimate. This range captures the uncertainty that surrounds the future path of home prices, interest rates, and investment returns.
While we believe that the calculator can help people understand how renting or buying might yield different results over time, depending on how certain variables change, we must stress that the estimations produced by our calculator are rough and should not be used as investment advice.
How is our calculator different?
You may have already tried other rent or buy calculators on the Internet. Ours is different in that it accounts for potential fluctuations in variables that could affect the financial returns you might get when you buy or rent a home. Variables such as the rate at which your home appreciates, mortgage rates, and the yield you could earn on investments if you chose not to invest your money in a home help determine those returns, and they all fluctuate over time.
Our calculator allows you to account for these fluctuations by letting you specify ranges of potential outcomes instead of just one fixed variable that is expected to perform consistently over the duration of your homeownership. For example, if we look at the performance of stocks from 1950 to 2008, the average return was 11 percent.1Average inflation over this period was only 3.5 percent. In other words, stocks delivered returns that outpaced the decline in the purchasing power of the dollar. But assuming that returns in some particular period in the future will be similar to that average ignores the possibility of a decade of flat real returns (like the 1970s) or two decades of double-digit returns (like the 1980s and 1990s). That is just one example of the kind of fluctuating conditions we might experience over the next decade that could affect your decision to purchase a home.
You can also capture the impact of fluctuating variables using any typical buy or rent calculator, but it’s not easy. For example, suppose you believe that your house will appreciate 2 percent a year. You can feed that assumption into a typical calculator, along with other assumptions, and calculate your gain or loss from homeownership. You may then repeat the calculation for 3 percent, −1 percent, etc.; the possibilities are endless, and the process is very cumbersome. This is where our calculator can be useful. All you have to do is to specify a range of possible outcomes and our calculator will try several random possibilities within that range, which we call a “simulation run.” In each simulation, we pick one random outcome and calculate the gains or losses that would follow from it. After multiple simulations, all gains and losses realized under various scenarios will be reported.
Our calculator also allows the user to distinguish between short-term and long-term trends in the housing market. While housing trends are slow to change, they do change. To capture a shift in home appreciation rates, you can choose one set of values for the first three years and a different set for the years thereafter. The inputs you adjust for this are the range of outcomes and the degree of optimism.
Admittedly, our calculator captures fluctuating variables in a very simplistic manner. The results depend on the range of possible outcomes that you specify.2 This approach does not capture the dependence of one period’s observation on the periods preceding it. Home price appreciation rates show especially strong serial correlation; that is, periods of rapid appreciation are followed by periods of further appreciation, and periods of rapid depreciation are followed by further depreciation.
We have a simpler, albeit less accurate, approach. After you specify the minimum and maximum expected appreciation, we will also ask you whether you expect the realized outcomes to come from the low end or the high end of the distribution. If you are a pessimist, you may choose the pessimistic scenario, which is more likely to draw outcomes closer to the lower end of your range. Figure 1 depicts this feature pictorially. The blue-colored line represents the probabilities of pessimistic outcomes. A higher value of the blue line indicates that the corresponding outcome on the horizontal axis is more likely than outcomes for which the blue line has a lower value.
Notice that, under the pessimistic scenario, the most probable outcomes—the highest point in the blue line—are located at about one-third of the range you specified, which we plotted as the boundaries of the horizontal axis in figure 1. If you are an optimist, however, you can choose the optimistic scenario, which samples from the higher end of the distribution (red line). You will notice that, under the optimistic scenario, the most probable outcomes are located at about two-thirds of the range you specified. The neutral scenario samples mostly from the mid-range (green line).
Figure 1: How One’s Outlook Affects the Distribution of Outcomes
Finally, be aware that you can get different answers from the calculator even though you plug in exactly the same values. The answers vary less if you set the number of simulations higher, though going too high slows the calculator down.
It is because certain variables fluctuate that the average results you get from one set of simulations will not be exactly the same as the results of another set. Let’s look at the some sample runs to explain how it happens. We ran the calculator ten times, using the same inputs but changing the number of simulations. The inputs are presented in table 1 and the results in table 2. To obtain the first column in table 2, we executed 100 simulations in each run. The probability of a financial gain varied between 63 and 81 percent, which is a wide range given that we are not changing our inputs. However, as we increase the number of simulations in each run, the range tightens significantly. At 1,500 simulations per run, the probability of gain is between 65.1 and 68.5 percent. Increasing the number of simulations makes our estimates more precise, but the cost is the time it takes to run those simulations. While the speed will vary from browser to browser, we recommend at least 1,000 simulations per run as a balance point between speed and precision.3
Table 1: Default Inputs
|Short-term (first 3 years) estimated minimum annual appreciation||−4%|
|Short-term (first 3 years) estimated minimum annual appreciation||1%|
|Expected outlook for short-term appreciation rate||Neutral view|
|Long-term (after first 3 years) estimated minimum annual appreciation||0%|
|Long-term (after first 3 years) estimated maximum annual appreciation||7%|
|Outlook for long-term appreciation rates||Neutral view|
|Length of time you will own the home||20 years|
|Homeowner association fee (HOA)||$25 per month|
|Property tax||1.8% of home value per year|
|Maintenance costs||2% of home value per year|
|Homeowner’s insurance (HOI)||0.25% of home value per year|
|Length of mortgage||30 years|
|Do you pay Private Mortgage Insurance (PMI) ?||Yes|
|Fixed or adjustable||ARM|
|Initial mortgage rate||4%|
|Initial fixed rate period||2 years|
|Adjustment period after initial fixed||1 year|
|Initial adjustment cap||2%|
|Rate adjustment cap||2%|
|I/O period||0 years|
|Estimated lowest rate over the life of the mortgage||4%|
|Estimated highest rate over the life of the mortgage||12%|
|Outlook for future mortgage rates||Equally likely|
|Rent and anticipated rent inflation|
|Renter’s insurance||4% of monthly rent|
|Itemize your mortgage interest for tax deductions?||Yes|
|Marginal income tax rate||25%|
|CPI inflation||2% per year|
|Savings Rate||20% per year|
|Estimated minimum alternative investment yield||−-3%|
|Estimated maximum alternative investment yield||10%|
|Outlook for future investment yields||Neutral view|
Table 2: Percent gain from homeownership, using 10 executions with varying simulation runs (SR)
Interpreting your results
The various inputs that go in our calculations are described in the glossary. Here we will try to give you some pointers on interpreting the results.
The potential gains from homeownership relative to renting are the focus of figure 2, which shows the results obtained from a run with 1,500 simulations and the default settings of the calculator (listed in table 1). The first part of the figure shows that there is a 67.6 percent chance that you will be better off buying than renting. On average, our calculator puts the relative benefit of homeownership at $4,065, given these inputs.
Figure 2: Calculator Output
This calculator is for informational purposes only. The results should not be interpreted as investment advice.
There is a 67.6 percent chance that you will gain financially from homeownership, with an average expected gain of $4,065.
The chart below shows the possible outcomes from 1,500 simulations. The height of each bar indicates the fraction of the outcomes that fell within the range specified underneath. A higher bar therefore means that the corresponding range is a more likely outcome than the ranges with shorter bars. The overall probability of a gain from homeownership relative to renting (67.6 percent) corresponds to the fraction of positive outcomes in 1,500 simulations.
Note: Numbers enclosed in parentheses () below are negative.
All numbers below are in today’s dollars and average of 1,500 iterations
The chart in figure 2 shows the distribution of the relative gains or losses across all the simulations. The distribution is divided into multiple bins, and the label under each bin corresponds to the range of outcomes it contains, as listed in the table below the chart. For example, bin number 4 would contain the outcomes in the −$10,000 to −$5,000 range. A loss of $8,000 (or −$8,000) would be placed in this bin. A gain of $12,000 would go into the eighth bin. The height of each bar represents the frequency with which outcomes fall into a particular bin. For example, 20.93 percent of our outcomes were in the $5,000 to $10,000 range, or seventh bin. The number we report as the probability of a financial gain from homeownership relative to renting is the ratio of the number of positive outcomes to the total number of simulations.
The table at the bottom of figure 2 gives more detailed information about your rent or buy decision. The table labeled “purchase metrics” lists some details about the cost of the home and the loan: the mortgage is $189,000, you have to bring $23,500 to the closing, and the monthly principal and interest payment will be $902. The table labeled “sale metrics” shows that the estimated sale price 20 years after the initial purchase is $370,298, which means that the home will appreciate 2.877 percent per year on average. This will leave you with an equity position of $260,053. Note that these numbers are an average of 1,500 simulations, and results in individual simulations will vary (see “Some limitations,” above).
The next table (“homeowner expenses”) shows the estimated average costs of homeownership. Over the next 20 years (your ownership period), you are likely to pay $5,935 in homeowners’ association fees, $81,279 on maintenance and repairs, and $76,769 in property taxes. All of these numbers are in current (inflation-adjusted) dollars. Your net property taxes may actually be lower than $76,769 because the IRS allows you to deduct property taxes as well as your mortgage interest from your taxable income unless you are taking the standard deduction. Assuming that you are planning to itemize and you indicated this preference in your inputs to the calculator, the tax savings you realize from the interest expense and property tax deduction add up to $67,324. In total, homeownership will cost you $107,322 over 20 years. But this is not your net position; when you sell your house, you will get your equity back, which we estimate to be $169,970 in inflation-adjusted dollars ; that is, your equity of $260,053 is worth $169,970 today because of inflation. After paying your realtor his or her 6 percent fee to sell the house, you are left with $155,319. After deducting homeowner expenses, mortgage payments and private mortgage insurance, your net position, then, is a loss of $234,457.
So does this mean that homeownership is a bad deal? Not necessarily. Keep in mind that you have to live somewhere and if you don’t buy a house, you will have to rent one. In fact, over the course of 20 years, your rental expense would add up to $297,856, as shown in the table labeled “rent option.”
However, if you rent, you will be able to save for your down payment, points, and closing costs. On top of that, you can also save the money you would have paid for property taxes, maintenance, etc. The difference between your monthly rent of $1,300 and the principal and interest payment on your mortgage, $902, increases your savings from renting by $398, so overall, you get to save some money when renting. Assuming that you may dip into those savings from time to time (20 percent net savings rate), you will have saved, on average, $59,334 in 20 years. Thus, your savings reduces the cost of renting, and turns it into a net cost of $238,522. The cost of renting is greater than the cost you incur from buying, which we calculated as $234,457. The difference between the costs, $4,065, is your net gain from homeownership relative to renting. In other words, on average, you are still better off buying.
Now, our entire discussion about whether you are better off buying or renting is focused only on financial gains. This is clearly not the only driver of home purchases. There are many benefits and costs associated with homeownership that cannot be expressed in dollars. For example, on the benefit side, people like to have a home they can call their own, they like to work in their yards, and so on. On the cost side, some people don’t like to spend their time mowing the lawn or shoveling snow. We realize that the decision to buy or rent goes beyond a consideration of financial outcomes, but our calculator does not take those considerations into account. How can you ever put a price on the joy of shoveling 2-feet deep snow in 20-degree weather?
1. Calculated using Robert Shiller’s S&P500 composite index real returns (includes dividends). The average is calculated as a simple average of annual returns.[Return]
2 We assume a beta distribution over the range of possible outcomes that you specify. Realizations of monthly home appreciation rates, yield on investments other than housing, and interest rates are all drawn from beta distributions.[Return]