The return result depends on about 81 metro-level measurements and a single 2015 image of each city. Memarian, Vergara-Alert and Benetti connect firms' stock returns to urban density and the scope for further densification in their home cities. Their new satellite-based measure is associated with lower factor-adjusted returns. They say firms with more room for density growth "are perceived as less risky", with an effect "stronger for smaller and younger firms". The main text does not establish that investors price lower risk. Stock-price volatility appears among the appendix's alternative outcomes, whose results we did not see. Once firm productivity enters the regression, the OLS coefficient halves and the IV shrinks by about a third.
The paper makes no trading claim.
Measuring the room to build
The economic argument is straightforward. Partly built land already served by roads and utilities gives a growing firm room for facilities and workers. That capacity should reduce local firms' exposure to the cycle and, in turn, the return investors require.
The authors use 2015 Google Earth images, with about 15 cm per pixel in dense areas. Their universe consists of the 86 US metros whose populations exceeded 500,000 in 2000. Around each main city hall, they draw a polygon covering one hour's off-peak drive, then manually mask water, parks, reserves and steep slopes. A color-segmentation algorithm classifies the remaining land as high-developed, developed or low-developed. Potential density increase, or PDI, divides developed land by the sum of developed and low-developed land. It measures how much of the land still available for building already has urban infrastructure. New York's polygon spans 10,291.7 km2: 2,650.26 km2 is developed and 4,687.38 km2 is low-developed, producing a PDI of 36.14%.
The correlation between PDI and metro population density is only 0.41. Los Angeles and New York each have more than 1,000 inhabitants per km2, yet their PDIs are 81.34% and 36.14%. Some rankings are surprising. Chicago records 82.06%; Charlotte records 1.59%. Chicago and Phoenix have comparable high-developed shares, 15.82% and 18.51%, while their PDIs differ sharply at 82.06% and 21.65%.
For returns, the authors regress monthly excess returns on MKT, SMB, HML and UMD. Each firm-year's annualized residual becomes the dependent variable, with the top 1% trimmed. Headquarters ZIP determines a firm's location. The 2010-2019 panel contains 21,510 firm-years, representing 3,426 firms across 82 metros. There are 11,789 observations in the main regressions.
What does a 2.28-point annual residual decline tell us?
The pooled OLS coefficient is -0.090. Raising PDI by 10 points corresponds to 0.90pp less annual residual return, roughly the gap between New York and Minneapolis (36.14% versus 25.67%). The instrumented coefficient reaches -0.228, equivalent to 2.28pp. Against a residual standard deviation of 37.5pp, the effects amount to 1.83% and 4.63%.
Those 11,789 observations overstate the amount of independent information. Each metro contributes a single, time-invariant PDI measurement. Errors are clustered across 81 metros, and the subsamples have between 55 and 80 clusters.
The dependent variable is a realized residual from one decade. Lower expected returns could explain a lower realized residual. Cash-flow news or mispricing that ran against high-PDI cities during the 2010s could explain it equally well. The authors acknowledge both possibilities: excess returns, they write, "originate from the inherent unpredictability of firms' operational profitability or due to inaccuracies in market pricing." Yet they interpret low residuals as evidence of low risk. Neither beta nor volatility appears on the left-hand side in the main tables. Adding revenue and EBITDA growth as controls reportedly changes little; that check addresses growth news, while leaving mispricing unresolved.
Saiz's instrument leaves the mechanism unsettled
The instrument uses Saiz's housing supply elasticity. In the authors' account, elastic cities used up spare land as rates fell during 2000-2010, leaving less partly developed land in 2015. The first-stage coefficient of -0.157 fits that account. Its Kleibergen-Paap F is 17.858 and its partial R2 is 0.142.
The exclusion restriction is less convincing. Housing supply elasticity could directly affect house prices and wages, both of which affect firm risk. The authors test the house-price channel: controlling for the annual change in the house price index yields an IV coefficient of -0.187 (OLS -0.103). All regressions already compare firms with similar real estate ratios. Local wages remain uncontrolled. The paper cites Davidoff (2016), whose title argues that supply constraints correlate with many demand factors.
Geographic and regulatory controls produce an adjusted R2 of 45.7%; the full geographic set raises it to 65.3%. According to the paper, state fixed effects increase that figure further, and the main regressions include them. Identification therefore draws on less than the third remaining. The authors describe the residual simply as location-specific factors.
The IV coefficient is about 2.5 times the OLS coefficient. The authors suggest offsetting wage and congestion costs enter OLS. They also argue that "the instrument reduces the attenuation bias of the OLS estimates introduced by classical measurement error." They interpret the heterogeneity splits as consistent with the wage explanation, although the paper measures neither local wages nor congestion.
Productivity sorting has the larger bearing on the result. With Olley-Pakes firm TFP and 2000 population added, OLS falls to -0.044 and IV to -0.147 across 10,097 observations. The authors acknowledge that productivity sorting "is relevant". They defend the result because the coefficient remains negative and significant. But the IV's two stars sit beside 0.147 and a standard error of 0.080, implying a t of about 1.8. OLS presents the same issue: -0.044 and a standard error of 0.025 imply a t of about 1.76, despite its three stars.
I would treat the splits as suggestive. For firms below median market cap, IV is -0.509 across 4,133 observations; for large firms it is -0.050. Recently listed firms have a coefficient of -0.582 on 3,490 observations, compared with -0.113 for seasoned firms. Among low physical-capital firms, the sign reverses to +0.260, which the authors ascribe to wage and congestion costs. Some first stages are weak: the F falls to 8.506 for small-employee firms. The same table's note says every partial F exceeds the standard threshold of 10, contradicting the reported 8.506.
A separate check works in the result's favor. Excluding New York, Los Angeles and Chicago increases the magnitude of OLS to -0.203 and IV to -0.293. Excluding Los Angeles, San Francisco and San Jose also strengthens the estimates, leaving OLS at -0.128 and IV at -0.268. The largest, densest metros therefore do not account for the finding.
A 2015 land measure against returns starting in 2010
The images date from 2015; the return series begins in 2010. The authors defend that timing by arguing that the built environment changes slowly. For the risk argument, the defense is reasonable. A trading desk faces a different constraint: a book held in 2010 could not use a photograph taken in 2015.
The authors' placebo makes the slow-change argument harder to maintain. For 2001-2009 returns, OLS is -0.015 (SE 0.067), a result they view as supportive. If PDI changes little, that null suggests the relationship was absent during the earlier decade. The standard error is nevertheless too large to reject -0.090. The placebo IV tells us little, since its first-stage F collapses to 0.088. Such a collapse is odd for fixed metro attributes like PDI and elasticity, given the 2010-2019 F of 17.858.
We could not test the result ourselves. We lack both dated satellite land classifications and a point-in-time mapping of headquarters to metros. Using the single 2015 snapshot in any backtest before 2015 would mean trading on future information.
We did not find a portfolio sort, long-short spread or cost estimate in the paper. A small-cap PDI sort would change my view if its imagery preceded the return window and its long-short spread survived costs.