Things I’ve Worked On: Rent Above Replacement

Real estate, in all of its manifestations–buying, selling, renting, remodeling–has always been an interest of mine. I think the reason it’s so fascinating to me is because it so naturally embodies three often-disparate topics to which I’m inclined, namely econometrics, sociology, and design. I’ve at least tangentially addressed the design and sociology of real estate in past projects, but I have yet to do the same with econometrics. Therefore, in this article, I will explain a metric I developed to analyze the rent-investment dyad of metro D.C. neighborhoods: rent above replacement (RAR).

When purchasing an income property, there are two main price points to consider: the purchase price (and, eventually, selling price) and the amount for which you can rent it. Ideally, you want to buy a house that is cheap to purchase but that can still earn a high rent; however, typically, high-rent areas  also demand a high purchase price, so there is an apparent trade-off between these two price considerations.

At least one simple metric already exists to explore the extent of this trade-off within different contexts: the price-to-rent ratio, defined as the ratio of home prices to annual rental rates. If a house is worth $100,000 and can be rented for $1,000/month ($12,000/year), it’s price-to-rent ratio is 8.33. If a house is worth $200,000 and can also be rented for only $1,000/month ($12,000/year), it’s price-to-rent ratio is 16.67. Clearly, as a rule of thumb, the lower the price-to-rent ratio, the better the home will serve as an income property.

But this rule betrays the reality of an important aspect of economics: risk. That is, areas of low-cost housing also represent areas of higher risk when it comes to renting. And whatever gains can be made by buying a cheap home and renting it for a relatively high price could be lost by having the home go unrented for large periods of time and, later, be sold for a less-than-ideal price.

Therefore, there is a need to incorporate risk in a metric such as the price-to-rent ratio. I can do exactly that by looking to the marketplace at large using another metric: cost per square foot. Below, I chart cost per square foot vs. price-to-rent ratio for metro Washington D.C. neighborhoods over the last year, based on data from Zillow.

2018-11-02 (2)

This graph indicates a few things: First, there is considerable variability in the price-to-rent ratio for neighborhoods with homes of similar value (up-down variance). For example, Kent and Judiciary Square have the same average cost per square foot, but Kent has a price-to-rent ratio of 22.7 (rank 52 out of 131), whereas Judiciary Square has a price-to-rent ratio of 17.1 (rank 130), which represents a large difference in this context. Second, the price-to-rent ratio tends to increase as the cost per square foot increases. I hypothesize that this change in the ratio embodies the decrease in risk achieved by renting your property in a more economically prosperous neighborhood. That is, in more expensive areas, you must pay more in comparison to the rental price on the front end but you can avoid riskiness down the road. Third, this increasing trend isn’t exactly linear but it’s close.

To address point two, I can regress the price-to-rent ratio on the cost per square foot of D.C. neighborhoods, and to address point three, I can add a log-log transformation on top of the regression, which improves the r-squared and residual plot over a direct linear model, leading to the following:

2018-11-02 (4)

Note also that as a power series, the modeled relationship between the two variables can be expressed as follows: y = 1.7264 * (x ^ 0.3841).

Then, I can use the residuals (i.e., actual price-to-rent ratio – predicted price-to-rent ratio) of this regression to come up with a risk-adjusted metric of rentability for DC neighborhoods. Since a lower price-to-rent ratio is better, I’ll multiply the residuals by -1 and normalize the data to come up with my final metric, rent above replacement (RAR). In layman’s terms, RAR describes how much better or worse a neighborhood is for renting out homes. The higher RAR is, the better the neighborhood is for purchasing a rental property and renting it out.

Neighborhood City State RAR CostSqFt
Foggy Bottom Washington DC 3.03 574.08
Dupont Circle Washington DC 2.36 653.58
Columbia Heights West Arlington VA 1.99 251.75
Penn Quarter Washington DC 1.86 618.67
West End Washington DC 1.83 717.83
Logan Circle Washington DC 1.66 666.92
Downtown Washington DC 1.62 652.75
Shipley Terrace Washington DC 1.57 264.92
Southwest Waterfront Washington DC 1.53 485.83
U Street Corridor Washington DC 1.42 674.08
Colonial Village Arlington VA 1.41 457.42
Adams Morgan Washington DC 1.40 621.67
Judiciary Square Washington DC 1.38 629.00
Mount Vernon Square Washington DC 1.38 649.00
North Highland Arlington VA 1.32 425.50
Benning Washington DC 1.30 276.33
Buckingham Arlington VA 1.28 325.92
Carver Washington DC 1.22 441.58
Radnor-Ft Myer Heights Arlington VA 1.21 492.83
Benning Ridge Washington DC 1.18 318.25
Catholic University Washington DC 1.13 359.00
Long Branch Creek Arlington VA 1.08 407.33
McLean Gardens Washington DC 1.07 484.25
Cathedral Heights Washington DC 1.01 408.17
Hillbrook Washington DC 0.99 277.42
Douglas Washington DC 0.98 234.50
East Corner Washington DC 0.95 257.75
NoMa Washington DC 0.94 512.50
Benning Heights Washington DC 0.93 267.00
Wesley Heights Washington DC 0.87 502.33
Randle Highlands Washington DC 0.85 266.75
Fairlington-Shirlington Arlington VA 0.85 446.67
Ballston-Virginia Square Arlington VA 0.74 528.75
Woodley Park Washington DC 0.74 560.17
Capitol View Washington DC 0.69 259.25
Columbia Heights Washington DC 0.68 562.17
Columbia Heights Arlington VA 0.67 359.67
Deanwood Washington DC 0.65 270.08
Congress Heights Washington DC 0.63 240.50
Clarendon-Courthouse Arlington VA 0.62 581.08
Shaw Washington DC 0.57 651.67
Fort Dupont Washington DC 0.54 232.83
Georgetown Washington DC 0.54 798.75
Wakefield Washington DC 0.53 459.75
Bull Run Manassas VA 0.50 186.67
Brightwood Park Washington DC 0.34 415.58
Navy Yard Washington DC 0.32 587.42
Michigan Park Washington DC 0.28 398.75
North Michigan Park Washington DC 0.24 407.58
Town Center Reston VA 0.23 256.17
North Rosslyn Arlington VA 0.20 539.83
Glover Park Washington DC 0.20 540.50
Woodridge Washington DC 0.17 397.17
Riggs Park Washington DC 0.16 392.00
Edgewood Washington DC 0.13 454.50
Cleveland Park Washington DC 0.12 582.42
Burleith Washington DC 0.11 719.92
Stronghold Washington DC 0.11 501.33
Sunset Hills Reston VA 0.07 357.33
Kalorama Washington DC 0.04 681.33
Langdon Washington DC 0.02 370.83
Sudley Manassas VA 0.01 208.33
Petworth Washington DC -0.02 446.92
Kingman Park Washington DC -0.04 505.33
Dupont Park Washington DC -0.05 321.58
Park View Washington DC -0.08 494.00
Ledroit Park Washington DC -0.08 547.50
Truxton Circle Washington DC -0.12 508.08
South Lakes Dr – Soapstone Dr Reston VA -0.17 281.58
Claremont Arlington VA -0.18 464.25
Nauck Arlington VA -0.25 388.25
Capitol Hill Washington DC -0.29 596.42
Eckington Washington DC -0.32 482.33
Trinidad Washington DC -0.32 455.67
Manor Park Washington DC -0.34 400.92
Near Northeast Washington DC -0.37 555.92
Arlington Heights Arlington VA -0.37 465.50
North Cleveland Park Washington DC -0.46 608.67
Fort Lincoln Washington DC -0.47 234.33
American University Park Washington DC -0.49 597.67
Barney Circle Washington DC -0.53 561.25
Alcova Heights Arlington VA -0.56 415.00
Penrose Arlington VA -0.56 404.75
Glencarlyn Arlington VA -0.56 437.58
Arlington Forest Arlington VA -0.57 487.25
Friendship Heights Washington DC -0.60 583.58
Brightwood Washington DC -0.60 418.83
Dominion Hills Arlington VA -0.62 551.75
Mount Pleasant Washington DC -0.64 565.67
The Palisades Washington DC -0.66 573.58
Douglas Park Arlington VA -0.66 380.42
Lyon Village Arlington VA -0.67 589.50
Takoma Washington DC -0.67 381.92
Brookland Washington DC -0.67 422.75
Lyon Park Arlington VA -0.68 510.67
Bluemont Arlington VA -0.73 502.08
Ashton Heights Arlington VA -0.75 533.67
Barcroft Arlington VA -0.76 433.00
Glade Dr – Reston Pky Reston VA -0.77 290.83
Kent Washington DC -0.78 628.50
Aurora Highlands Arlington VA -0.80 443.75
High View Park Arlington VA -0.83 477.50
Forest Hills Washington DC -0.85 489.92
Berkley Washington DC -0.86 615.83
Sixteenth Street Heights Washington DC -0.87 431.83
Waverly Hills Arlington VA -0.87 409.00
Westover Village Arlington VA -0.87 515.75
Bloomingdale Washington DC -0.89 519.58
Chevy Chase Washington DC -0.89 523.08
Cherrydale Arlington VA -0.97 502.75
Hattontown Reston VA -1.00 267.92
Waycroft-Woodlawn Arlington VA -1.02 500.33
Spring Valley Washington DC -1.05 571.50
Madison Manor Arlington VA -1.07 481.25
Highland Park – Overlee Knolls Arlington VA -1.12 501.17
Barnaby Woods Washington DC -1.14 495.42
Tara-Leeway Heights Arlington VA -1.19 497.17
Yorktown Arlington VA -1.22 475.42
Leeway Arlington VA -1.24 477.25
Arlington-East Falls Arlington VA -1.24 466.75
Donaldson Run Arlington VA -1.26 473.58
Boulevard Manor Arlington VA -1.28 396.92
Arlington Ridge Arlington VA -1.29 373.58
Old Diminion Arlington VA -1.29 460.75
Olde Glebe Arlington VA -1.32 471.42
Rock Spring Arlington VA -1.35 466.50
Shepherd Park Washington DC -1.52 401.92
Wiehle Ave – Reston Pky Reston VA -1.55 291.25
Colonial Village Washington DC -1.97 412.50
Crestwood Washington DC -2.00 443.92
Lawyers Rd – Fox Mill Rd Reston VA -2.18 284.25

There are a number of logical extensions to this relatively simple measure. You could consider different or larger areas (USA instead of metro D.C.), you could consider different units of analysis (cities instead of neighborhoods), you could try exploring the relationship in a different way (e.g. a quantile regression), and you could incorporate additional measures into the model of the price-to-rent ratio, to name a few.