Asset-Level Risk and Return in Real Estate Investments

Real estate is an important investment class. As of 2019, MSCI Inc. estimated that roughly US$9 trillion in global real estate assets were held for investment purposes under professional institutional management, while Savills estimated in 2016 that the potential stock of investable institutional-quality global commercial real estate (CRE) was US$19 trillion. Relatedly, CRE mortgages totaled over US$4 trillion in the United States alone as of 2019 and comprised 35% of all loans for (mostly regional) banks with assets under US$10B.

Despite the significance of CRE as an investment class, price dynamics for individual assets are not as well understood as those belonging to more liquid categories such as equities, fixed income, commodities, currencies, and derivatives. This gap is important to address because asset-specific price dynamics can significantly impact the pricing of nonrecourse mortgages, the concentrated portfolios held by many real estate investors, and the option-like features in investment management contracts prevalent among private equity funds.

The few papers that attempt to quantify attributes of property-level risk and return assume that an individual property's log-value evolves as a random walk with drift (RWD). This is consistent with the prevailing paradigm in asset pricing (Campbell, Lo, and MacKinlay 1997) and is the modeling assumption most widely adopted in the applied theory literature, going back to Williams (1993). This paper makes two contributions to the current understanding of CRE asset price dynamics, and the insights should generalize to other highly illiquid asset investments.

First, I demonstrate with an exhaustive series of empirical tests that the RWD assumption is far from an appropriate description for CRE asset prices. Second, I derive an equilibrium search-based model that is able to fit observed dynamics of prices and turnover statistics, as well as transaction dispersion relative to perceived market prices.

The literature is full of hints that real estate prices and those of other illiquid assets deviate from an RWD, but such findings have been typically dismissed or viewed as data artifacts (e.g., measurement error and/or missing variables). The calling card of an RWD is the scaling of the mean and variance of log-price changes with the time between changes (i.e., the holding horizon).

Case and Shiller (1987), Abraham and Schauman (1991), Goetzmann (1993), Goetzmann and Spiegel (1995), and Calhoun (1996) find that return scaling is violated for house price increases based on repeat sales and attribute the anomalies to missing variables (e.g., investment in the form of renovation activity or price mis-measurement). Using detailed property-level data from the National Council of Real Estate Investment Fiduciaries (NCREIF), which includes capital expenditures, I robustly demonstrate that CRE prices are inconsistent with RWD dynamics even after accounting for all cash flow events.

Specifically, both risk-adjusted mean (i.e., "alpha") and variance of property log-returns fail to scale with the return horizon, and both exhibit large positive atemporal components: Return means and variances remain significantly positive even when the holding period is extrapolated to zero. The atemporal variance of roughly 3% is two to three times the idiosyncratic annual diffusion variance. The atemporal alpha is absurdly high, extrapolating to double-digit percentage points as the holding period vanishes.

With perfectly liquid assets, the RWD anomalies would present an arbitrage opportunity consisting of sequentially purchasing and then instantly selling the asset an arbitrary number of times over a finite time interval. The illiquidity of real estate assets rules out the executability or profitability of such an exercise. Indeed, by providing strong evidence that their source is transactional, I am able to link the root cause of the return anomalies to illiquidity rather than missing variables or a host of other explanations.

The second main contribution of this paper is to provide the theoretical link between illiquidity and the observed deviations from RWD in real estate price data. I do this by deriving a search-based model featuring two key mechanisms. The first is dispersion in the relative valuations of randomly matched counterparties, which leads to idiosyncratic randomness in the transaction prices of otherwise identical properties. This accounts for atemporal variance and shows up in an asset's observed price series as variance that depends on the number of transactions observed and not only on the holding horizon.

Because random matching and bargaining are common devices, many search models exhibit atemporal variance. The second key mechanism is the presence of "intermediate"-valuation investors, coupled with the highly plausible assumption that private valuations change slowly. If a recent property buyer is slow to change his or her valuation, the holding period will be short only if a much better offer happens to quickly come along. This is most likely to happen to intermediate-valuation investors because "better offers" are not available to high-valuation owners, while low-valuation investors are rarely recent buyers.

The observed positive short-term "alpha" is earned by luck and not by design. Less fortunate investors do not sell after a short period of time and do not show up in a panel of short holding period transactions.

In the limit of a liquid market, the model exhibits RWD returns, highlighting the connection between illiquidity and atemporal return anomalies. To my knowledge, among existing search models in real estate (for a review, see Han and Strange 2015), mine is the first to incorporate the second key mechanism and is the only one able to explain the atemporal alpha (through selection bias in repeat sales holding periods). From that perspective, the model can be viewed as a novel contribution to the prodigious real estate search literature and opens the door to new theoretical and econometric analyses of transaction-level data.

The model allows for cyclical dynamics in the property market and investors' cost of capital. Beyond the qualitative economics, the model's steady-state equilibrium can be calibrated to fit a large set of transaction-based moments from NCREIF property data, conditional on boom or bust market states. Among these are holding period return moments for properties bought/sold at different cycle points, quarterly turnover, the fraction of properties sold after five years, the average transacted income-to-price ratio (or "cap rate"), and the distribution of transactions relative to perceived market prices (i.e., appraisals).

The model fits the data very well and fully accounts for atemporal alpha and variance. For the best fit parameter set, as the market moves from an expansion to a contraction, investors' discount rates increase and strongly revert toward consensus. The former leads to aggregate asset devaluation and the latter to a dramatic decline in liquidity.

In contrast with a liquid market, sellers in the model must trade off price and certainty of execution. I quantify this notion of transaction risk in various ways: The probability of transacting at or above the average transaction price, expected or median time on market given a reservation price, and expected discount conditional on a binding liquidation horizon. The calibrated model implies a reduction in high-valuation prospective buyers during periods of market contractions, and this makes the tension between price and speed of execution more severe as reflected across all measures.

The magnitude of model-imputed transaction risk and its pronounced cyclical variation has significant implications for the pricing of property derivative assets such as mortgage loans and mortgage-backed securities. These could be important to incorporate into the current literature, where RWD assumptions are prevalent.

The paper is organized into the following sections: empirical (Section 1), model (Section 2), calibration (Section 3), applications (Section 4), discussion (Section 5), and concluding (Section 6). Appropriate literature is discussed in each section, and supplementary details and analyses are provided in the Internet Appendix.