Who Buys High and Sells Low: Trading against Expected Returns and Wealth Inequality
What this paper finds — and why it matters
Layer 1: Overview
Research question and motivation: Wealth in the US is far more concentrated than income, even among the bottom 99%. In 2013, the next-49% (above the bottom 50%) earned 4.7 times the income of the bottom 50% but held 6.5 times the net worth (SCF 2013). Since housing is most Americans’ primary vehicle of wealth accumulation, differences in housing returns could amplify wealth gaps. Prior work studied heterogeneity in risk-taking in housing; this paper instead studies the timing (mistiming) of housing trades: do some households consistently “buy high and sell low” relative to EXPECTED asset returns, and what does that do to portfolio returns and wealth inequality? Theory is ambiguous: pro-cyclical credit supply (Mian-Sufi, Rajan) predicts poorer, credit-constrained households buy more in booms (when expected returns are low); extrapolative expectations (Barberis et al., Kaplan-Mitman-Violante) predict richer, less-constrained households buy more in booms. So it is an open empirical question.
Data and method: The author builds a novel annual balanced panel of real-estate ownership from CoreLogic (formerly DataQuick) assessor file (a 2012-2013 cross section, ~104 million records, ~94% of US population) plus transaction-deed records, working backwards from 2012-2013 to assign owners by year (owner on Dec 31). Owners’ wealth/permanent-income is imputed from surnames: household wage income averaged at the surname level in the 1940 full-count Census (the latest full Census and first to ask income) is a strong predictor of those surnames’ 2012-2013 wealth (Henry de Frahan and Sakong 2023). Surname population counts and racial shares come from the 2000 Census tabulations (in 2000, 151,671 surnames with 100+ people, covering 242M of 282M people = 85.8%). Two samples: a “long” sample 1988-2013 (148 counties, 674 jurisdictions, 11 states, ~21-25% of US population) and a “wide” sample 1998-2013 (36 states, >60% of US population). Expected asset returns are estimated following Cochrane (2011) by regressing one-year-ahead realized housing returns on the log rent-to-price ratio (rents from BLS owner-equivalent rent or imputed from IRS local income; house prices from CoreLogic HPI, with Case-Shiller and FHFA for robustness), at aggregate, CBSA, county and zip-code levels, using common or area-specific (heterogeneous) coefficients. The key estimand is the covariance between (residualized) log housing quantity held by a wealth group and the log expected asset return — the “active” timing component, decomposed via a lognormal first-order approximation (Calvet-Campbell-Sodini-style passive/active split). Specifications include group, time, and group-time-trend fixed effects to isolate cyclical-frequency timing from long-run trends and new construction.
Main findings (with magnitudes): (1) Over 1988-2013, lower-wealth (lower 1940-income-percentile) surnames consistently held more housing pro-cyclically — buying when expected returns were low and selling when high. Portfolio expected returns from active trades are increasing in wealth (decreasing in pro-cyclicality), especially pronounced for the bottom 20% of the 1940 income distribution. (2) Using more disaggregated expected returns raises the estimated gradient almost monotonically: the coefficient on surname 1940 income percentile rises from 0.089 bp (aggregate) to 0.180 bp per percentile (zip code, heterogeneous coefficients, wide sample — the preferred specification). Aggregate returns bias the estimate downward toward zero. (3) The gradient is larger where expected-return volatility is higher: a one-standard-deviation higher expected-return volatility roughly doubles the wealth gradient (Table 3a, zip codes); meanwhile the extent of buy-high-sell-low behavior itself is statistically unrelated to volatility (Table 3b, near zero). (4) The positive overall return-on-wealth slope is driven by BETWEEN-race differences (non-White groups own housing highly pro-cyclically, consistent with Kermani-Wong); WITHIN race, portfolio expected returns are slightly DECREASING in wealth. (5) Quantitatively, projecting 1940 income percentiles onto the 2013 wealth distribution (via average home value and a housing Engel curve from the 2013 SCF), a 10% rise in net-worth percentile is associated with ~13 bp higher annual portfolio expected return; across the interquartile range this is a 65-basis-point per year differential — about two-thirds of the ~1% total realized-return spread Fagereng et al. (2020) find for financial wealth in Norway, here from timing alone. (6) A back-of-the-envelope calculation (APC out of labor income cy≈0.25 from PSID, wealth-to-labor-income ratio W/Y≈10 from SCF) implies the 65 bp differential raises the wealth share ~9% above the income share, accounting for roughly 20% (a fifth) of residual wealth concentration above income concentration across the interquartile range. Implication: time-series volatility of housing markets widens wealth inequality beyond income inequality; dynamic trade timing, not just average returns or asset heterogeneity, matters for wealth levels.
Layer 2: Deep Dive
What is the core conceptual distinction the paper insists on, and why does it use expected rather than realized returns?
The paper measures ‘buying high and selling low’ as the negative co-movement between the QUANTITY of an asset held and the EXPECTED asset return on it — not realized returns on completed trades. Three reasons: (1) Over a finite period some households get lucky/unlucky on unpredictable realized returns, but those wash out over the long run; only co-movement with the PREDICTABLE (expected) component survives to affect long-run wealth accumulation. (2) Expected returns are imputed as a log-linear function of the local rent-to-price ratio, observable at local levels, rather than realized returns on a specific property. (3) It computes returns on the whole stock of housing owned, not only traded units, because non-traders earning 0% realized return must be averaged in for wealth-inequality purposes. Example given: from 2007, aggregate housing had a realized return of -8% (-20% vs the 12% time-series average) but a +8% one-year expected return (-4% vs average); the paper focuses on the -4% expected, not the -20% realized.
What is the identification/measurement strategy and what are the main threats?
Identification rests on (a) imputing owner wealth from surname-level 1940 Census average wage income, validated against 2000 Census zip-code incomes (Table 1: strong, expected correlations, e.g., owner-occupant 1940 log wage loads ~1.6-1.8 on Census median income; investment-home owners’ residence income loads positively even controlling for property-site income), and (b) estimating the covariance of residualized log quantity held with log expected asset returns at cyclical frequency, with group, time, and group-specific-trend fixed effects (equations 7-8) to strip out level differences, differential new construction, and long-run population/inequality/homeownership trends. Threats: surname-level estimates require additional assumptions to map to family-level behavior (handled via Henry de Frahan and Sakong 2023 framework; the author deliberately avoids 2010s surname income/consumption to prevent reverse causality with 1988-2013 trading); the samples are not nationally representative (more urban, larger boom-busts); expected returns are imprecisely estimated for short local time series; and new construction cyclicality could confound who-owns-when (argued orthogonal because the outcome is the portfolio expected-return differential — even if poorer residents buy new units in booms, they are acquiring risky assets when expected returns are low).
What are the two competing theoretical mechanisms, and does the paper claim to distinguish which one operates?
Mechanism A: pro-cyclical credit supply (market- or government-driven, Rajan 2011; Mian-Sufi 2009) relaxes constraints in booms, so credit-constrained POORER households buy/own more housing in booms (when expected returns are low). Mechanism B: extrapolative expectations (Barberis et al. 2015; Kaplan-Mitman-Violante 2017) make booms coincide with optimism, and RICHER, less-constrained households are better positioned to add exposure, so they own more in booms. The two give opposite cross-sectional predictions. The paper emphasizes that its quantification of the wealth-inequality impact does NOT depend on WHICH mechanism drives the pattern or why households buy high — it measures the covariance regardless. Empirically it finds the poorer-buy-in-booms pattern dominates, consistent with the credit-supply channel, but does not structurally separate the mechanisms.
What heterogeneity is documented?
Three dimensions. (1) Geographic volatility: areas with more volatile expected returns (California, Florida prominently) show steeper wealth gradients in portfolio expected returns; one SD higher volatility roughly doubles the gradient (Table 3a). (2) Time period: the positive wealth slope holds both pre-subprime (1988-2002) and during the boom-bust, but is larger during the more-volatile subprime boom-bust. (3) Race: the overall positive slope of portfolio expected return on wealth is driven by BETWEEN-race variation — non-White groups own housing highly pro-cyclically (consistent with Kermani-Wong 2021, who attribute lower Black realized returns largely to foreclosures) — while WITHIN-race the gradient is slightly decreasing in wealth. The bottom 20% of the 1940 income distribution shows the most pronounced pro-cyclicality.
What robustness checks are run?
Quantity units: results robust to using number of properties (baseline), number of bedrooms, or square footage. Price indices: aggregate results similar using CoreLogic HPI, Case-Shiller, and FHFA (Table 2a columns: 0.080, 0.063, 0.057 bp). Samples: long (1988-2013) vs wide (1998-2013) give similar aggregate estimates. Rent source: BLS owner-equivalent rent vs IRS-income-imputed rents both yield strong predictability and similar gradients. Estimation of expected returns: common vs heterogeneous (area-specific) prediction coefficients both work, with heterogeneous generally larger. Validation of surname-wealth mapping via three sets of Census 2000 regressions (Table 1). Geographic disaggregation robustness (aggregate to CBSA to county to zip) shows monotone increase, and restricting to CBSA counties with BLS rent for apples-to-apples comparison (Online Appendix Table OA.3a) preserves results.
How does this paper relate to and differ from closely related prior work?
It complements contemporaneous work on heterogeneity in REALIZED portfolio returns along income/race (Goldsmith-Pinkham-Shue 2020; Xavier 2021; Kermani-Wong 2021; Martinez-Toledano 2022; Wolff 2022) and the wealth-returns literature finding returns increasing in wealth (Bach-Calvet-Sodini in Sweden; Fagereng et al. in Norway; Garbinti-Goupille-Lebret-Piketty in France; Kuhn-Rios-Rull, Wolff in US). It differs by focusing on EXPECTED returns and the TIMING (covariance) channel rather than realized returns or asset heterogeneity, and by isolating the active-trade timing component on the whole housing stock. Its 65 bp interquartile differential from timing alone is ~two-thirds of Fagereng et al.’s ~1% total realized financial-return differential, highlighting that timing matters even absent asset heterogeneity. It also relates to cyclical homeownership-by-demographic literature (Goodman-Mayer 2018; Mabille 2023).
What are the policy/theoretical implications and their scope conditions?
Implication: because expected housing returns are time-varying and predictable, and lower-wealth households trade against them, trade timing widens wealth inequality beyond income inequality — and areas/periods with more volatile housing markets amplify this. Dynamic, asset-price-driven mechanisms (not just average returns) matter for wealth LEVELS, not merely their cyclicality. Scope conditions: the result requires expected returns to be genuinely time-varying and predictable (if EtR were constant, the covariance term vanishes); the lognormal approximation requires positive asset quantities (holds for housing, would fail for risk-free borrowing); the quantification depends on cy≈0.25 (PSID), W/Y≈10 (SCF), and the housing Engel-curve projection; samples are urban-skewed and not nationally representative; and the cross-sectional volatility-inequality prediction is only suggestively, not rigorously, tested (data limits on local wealth inequality).
What does the formal decomposition (Propositions 2-3) deliver?
Proposition 2 decomposes long-run average wealth return into (i) a participation term — the product of differences in average asset shares times expected returns (the focus of the risky-participation literature) — and (ii) a covariance term between asset shares and expected returns (this paper’s focus). The covariance term is nonzero only if expected returns are time-varying and asset shares vary across households. Proposition 3 splits the share-return covariance into a ‘passive’ part (price changes mechanically move shares opposite to expected returns) and an ‘active’ part (deliberate quantity adjustment), via a first-order lognormal approximation; a sufficiently contrarian active change can flip the covariance positive. The paper targets the active component, equation (4): E(mu) times cov(residual log quantity, log expected return).
What are the key caveats the author flags?
(1) Estimates are fundamentally at the surname level; family/household interpretation needs extra assumptions. (2) Expected returns are noisily estimated, especially locally with short series; heterogeneous coefficients add error but allow meaningful heterogeneity. (3) The wealth-inequality quantification is explicitly ‘back-of-the-envelope’ and depends on approximations (APC, W/Y ratio, Engel curve, household-vs-surname extrapolation assumption). (4) During the subprime boom-bust, realized returns were far more volatile than rent-to-price-predicted expected returns (Online Appendix Fig OA.1), so the expected-return measure deliberately understates realized volatility. (5) Aggregate expected returns bias the gradient toward zero, so even the preferred zip-code estimate is likely a lower bound if returns are heterogeneous at finer-than-zip levels. (6) Samples cover urban areas with larger boom-busts and are not US-representative.