Economic question:  A customer has a given lifestyle in mind. They have multiple paths they can take in gaining this lifestyle. We want to answer whether it is better to rent or to buy the same home to achieve that lifestyle. 

Buying a home =   a consumption decision for ongoing shelter and utility in the space + an investment decision on an appreciating asset (with maintenance) 

So the alternative, and opportunity cost, is renting to consume shelter and utility from the space, and investing in some alternative asset unrelated to real estate  that has a similar risk and return.

What we’ll do: Simulate the purely financial aspect of the decision so that the decision maker can decide if it is financially advantageous to commit to homeownership with a fixed-rate loan. Functionally, we’ll estimate the time horizon the buyer needs to maintain ownership to breakeven or if the difference in simulated costs on a short(er) horizon is at least at a price low enough to pay for the utility of full control of the property over that time. 

Optimality then implies that a renter becomes a buyer if and only if:

Where S^S_t=T, S^R _t=T denote the net present value for being a buyer and a renter respectively at time T, the intended years after purchase the buyer hopes to move again. The savings accrued from renting each period are the saved/invested funds that would have been used for a down payment and transaction costs invested at the risk-free rate plus the recurring costs of owning a home net the recurring cost of renting (rent, rent insurance, application fees, etc.)

Setting the price and rent at the time of purchase, t=0

As the average of the middle third of unbiased neural Zestimates within any region studied, the Zillow Home Value Index is our most reliable estimate of a “typical” home price within an area. So we set the price at purchase,

Practical realities to knowing the price and rent on the same house:

• Set of properties ever rented is distinctly different from the set of properties ever purchased.
• Only a subset of properties are sold or listed in every period.
• Set of properties listed for rent and for sale in the same period is negligible. 

Zestimation at Zillow

The Zestimate,

and Rental Zestimate

are unbiased property-level estimates of current home price and market-rate asking rent, respectively. They use advanced machine learning algorithms and neural networks trained with historical home prices or listed asking rents against property features to jointly minimize error (median absolute percent error, or MAPE) and minimize bias (median percent error) in predicting property valuation or rent. 

Advantages of neural networks:

• Improved performance at higher data volumes/histories
• Radical improvement in Zestimate bias (MAPE)
• Significant improvement in accuracy (especially at price tails)
• Enough advancement to learn underlying patterns along spatial and temporal dimensions
• Ability to extrapolate, like parametric approaches, but unlike traditional ML classification methods
• Zestimate accuracy[https://www.zillow.com/z/zestimate/]

So we should be able to exploit the estimates, with some reservation discussed later, on the same individual homes to estimate a “true” or at least “truer” price-to-rent ratio than previously available. With these property-level estimates of price and asking rent, our preferred method for evaluating the breakeven simulation at scale (for many different regions and scenarios) is to set rent in the first year such that

In which K is the total number of housing units (single-family, townhouses, condos and co-ops; excludes mobile homes) in the region.

Why not just use the Zestimate and Rental Zestimate at the property level? 

The computer processing load to estimate the full simulation is too great to reliably run the buy vs. rent break even simulation at the property level for public production. So we apply the typical price-to-rent ratio to the ZHVI and only have to calculate the buy vs. rent simulation for each scenario for each metro once. The MEDIAN_i=1,…,K(Z^R_i,t=0/Z^FS_i,t=0) also has public metrics potential for other applications by researchers beyond this one.

Alternatives used to demonstrate the importance of estimating a ZHVI-comparable rent

• Median rent of households who moved in the past year to detached, two- to four- bedroom, single-family rentals (Zillow analysis of 2021 ACS, IPUMS.org). This estimate is typically the lowest for rent, including some very long or familial tenant-landlord relationships and other ways that tenants can experience lower “off-market” rents. 
• Zillow Observed Rent Index (ZORI): Rental-market propensity weighted average rental Zestimate. Propensity is conditional on property type, year built and bedroom count. ZORI is a very useful metric designed to capture the rented housing stock, not the full stock, to make it comparable to ZHVI. 

Remaining concerns in this approach

• One available listing on Zillow could represent multiple units, among other data quality differences between rental Zestimation and home price Zestimation, likely driving different distributions of errors. 
• A subset of all rental units is listed on Zillow in every period, and that sample is likely to be toward higher quality and larger properties. Low-end rentals are more likely to go straight to Craigslist. In contrast, we likely see a more complete sample of homes that hit the for-sale market due to our for-sale market’s maturity. However, rental stock is systematically higher quality and larger than for-sale stock. At the moment, we do not know if these dynamics balance each other out.

Setting future price growth

The user will purchase the typical home in the metro (ZHVI) with only 20% down on a 15- or 30-year fixed-rate loan. The buyer will then earn appreciation on the full purchase price. To account for the user’s level of risk and what they’re willing to accept about the future of home price growth, they can choose three different home price path scenarios that will set Pt as the consumer holds the home after purchase:

• Data-forward in the short run, optimistic in the long run 
  • ZHVF (Zillow’s one-year forecast for ZHVI) over the first year, after which the growth rate moves toward the long-term historical growth rate along a cubic spline over five years.  
• Data-forward in the short run, more practical/conservative for the long run 
  • ZHVF (Zillow’s one-year forecast for ZHVI) over the first year, after which the growth rate moves toward half the long-term historical growth rate along a cubic spline over five years.   
• Conservative in the short run and the long run 
  • Flat over the first year, after which the growth rate moves toward half the long-term historical growth rate along a cubic spline over five years.   

Costs and benefit streams of buying

Transaction costs at purchase 

3% x P₀ at purchase and 8% x P_t=n at sale

• Assumed to include commissions, fees (title, mortgage fees and points, etc.), excise taxes, etc., and can vary greatly by individual, state and local jurisdictions. 
• Ongoing work: Estimating “true” or observed transaction costs for home buyers from Zillow’s database. 

Interest portion of mortgage payment 

Assumes a 15- or 30-year fixed-rate loan, mortgage rate locked at t=0. Mortgage rate is set in the simulation to explore before the pandemic (3%) and now (7%). (We will use this 4 percentage point change to explore the sensitivity to many of the parameters set in the simulation.)

Property taxes 

Assumed 1% x P_t annually 

• This is a dramatic simplification since property taxes vary widely across different and unique sets according to county, city and school district.
• Ongoing work: Effective property taxes within these overlapping boundaries was recently estimated but are not incorporated in this simulation yet.

Property insurance 

Assumed 0.5% x P_t annually

• Ongoing work: 
  • Insurance premiums are also available in public records within the same region cross-sections to estimate property taxes above. 
  • A potential collaboration with Allstate Insurance Company as well as climate risk information providers should increase the transparency in this area, especially as it relates to home purchasing decisions in locations impacted by the climate crisis. 

Maintenance costs 

Assumed 1% x P_t annually

• This is an oversimplification. Maintenance costs are likely highly personal as it is dependent on the human capital or professional network of the potential buyer, the costs and availability of help/skilled labor in the region, and/or the age of the house. 

Capital gains taxes on profit above $375K 

Assumes half of the household is married, so can deduct the average of $500K and $250K, when applying the capital gain exclusion for the primary purchase. The estimated taxes use the local median household income to set the tax rate, but this is almost always 15%.

Condo or HOA fees 

Assumed 0 in our simulation

• Fair and healthy HOA costs and management are likely critical to homeowner success where an HOA is in place. 

Property tax and mortgage interest deductions 

These are only triggered in the simulation if property taxes and mortgage interest exceed the standard deduction (data on other itemized deductions not incorporated). Since new limits on SALT deductions and the doubling of the standard deduction, at the median, this is almost never triggered without other itemized deductions to overcome the standard, so this is more or less negligible in the simulation.

Renting and investing

Rent growth

Because of relatively short rent histories within Zillow’s database, we do not yet have a formal forecast for asking-rate rent. To explore the impact of rent growth, we allow the user to choose 2% or 6% in the first year before splining to 2% annual growth by the fifth year. 

Rental broker fee 

Assumed 0

Rent deposit: 

You get it back, but used in opportunity cost calculations together with 1st and last months rent required at signing (and so tied up instead of invested in our simulation logic) 

Renters insurance 

1% of rent monthly

Opportunity cost and the renter’s investment stream

A major contribution from this work is to disentangle the investment streams of this decision from the more salient if still not totally certain upfront and monthly costs of the two options: rent or buy. 

To make a comparable decision to buying, as a renter, we assume that the renter is fully investing the money that would have been used to buy a home. 

Rates of return available in the simulation

• Risk free 2% over all time
• Risk free 6% over all time

The money invested by the renter includes any “savings” (the difference in monthly costs between buying and renting) each month. To keep it fair between the choices, the renter also then has to take money out of their investments to cover the difference during periods when out-of-pocket renter’s costs are larger than the homeowner’s for a similar property. The easiest way to mechanically code this is to estimate what the buyer would have earned as a return in the alternative asset with all the money they spent on housing. We then do the same thing for the renter. 

The renter’s investment gains are then the buyer’s opportunity cost (what would have been earned in the stock market after capital gains taxes but can’t be earned if it’s locked up in housing as an owner) minus the renter’s opportunity cost (what they didn’t earn from stock markets because their money was tied up in renting). 

Investment value of the renter 

       =     After-tax interest earned investing everything they spent to buy and own  

• After-tax interest earned investing everything they spent to rent 

• Original upfront costs for the buyer 

• Original upfront costs for the renter

The buyer’s comparable investment gain is their home equity (home price at sale minus the mortgage balance) minus the transaction costs and taxes they pay to liquidate the asset and get the return, and minus the down payment which they made in the first place.           

 Investment value of the buyer 

• Home value at sale

• Mortgage balance at sale

• Seller transaction costs      

• Capital gains tax of the owner after sale