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.

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:

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.