Risk models and price dynamics in commercial real estate

Whilst a graduate student in physics at Princeton, American physicist and Nobel Prize Laureate Richard Feynman attended an advanced biology class in which he was asked to discuss an academic paper on cat nerves’ impulses which the authors characterised as “sharp, single-pulse phenomena” (Feynman, 1985). As he prepared for his assignment, he reportedly asked Princeton librarians for “a map of the cat”. Feynman’s first instinct of mapping the underlying physical context of a complex dynamic phenomenon is classic in life sciences. For centuries, many scientists worked on mapping the human body and its various systems through extensive, albeit at times gruesome, dissections of cadavers.

To some extent, modern finance’s Capital Asset Pricing Model (CAPM) provides a ‘map’ of an asset. A relatively simple risk model underpins the single index linear pricing equation. Surprisingly, despite the CAPM’s and other financial models’ shortcomings in their application to commercial property, real estate finance has not felt the urge to come up with a holistic conceptual framework as a prerequisite to a thorough investigation into commercial real estate asset returns and risks. There are several rational explanations to that neglect. As mentioned before, the import of ready-made models from financial economics has resulted in aggregate thinking and a top-down approach in real estate finance, which does not encourage the granular modelling of property assets. Furthermore, faced with the mammoth task of modelling commercial real estate assets, there is a tendency to think along the lines of “too complicated to bother”. The absence of risk models in real estate finance is sometimes justified in the name of practicality: making empirical inferences from historical data should suffice to model real estate price dynamics. Geltner and de Neufville (2018) explain:

[...] Rather than attempting to model all the possible determinants of [the future value of an asset being built or invested in] in a causal structural model, we content ourselves with modelling the kind of dynamics and randomness that appear in historical data about property price evolution. [...] This does not mean that analysts should not consider, or indeed study and seek to understand, the underlying causal elements that affect prices and values. [...] But an ever-present challenge in effective, practical simulation analysis is to avoid excessive complexity. We must not “get lost in the weeds”, and we must not “lose sight of the forest for the trees blocking the view!”.

So, does real estate finance actually need to bother about a thorough risk model for commercial property? This book argues that the shortage of research about risk modelling in commercial real estate is one of the main reasons why real estate derivatives have not been successful, especially as hedging instruments for direct property investors. Indeed, it is impossible to hedge an asset whose overwhelmingly idiosyncratic variations in returns cannot be explained at the most granular level.

Risk models matter insofar as they define several crucial conditions which have to be met for real estate derivatives to succeed. Risk models provide the framework underlying any attempts to model factors and their wider interactions. They also underlie the choice of relevant stochastic processes to be used in pricing real estate derivatives. Without a solid risk model, pricing real estate derivatives is approximative at best. Real estate finance should undoubtedly aim to be right in practice about commercial real estate price dynamics. However, forgoing a conceptual approach to risk in commercial property has direct consequences for real estate derivatives.

For instance, one can simply consider US residential real estate derivatives’ lack of liquidity (Shiller, 2008). Liquidity in standardised property derivatives markets has been an unsolvable conundrum stemming from property’s heterogeneity. Fabozzi, Shiller and Tunaru (2010) assess:

Derivatives require homogeneity of the underlying for establishing liquidity in their trading. The lack of homogeneity in real estate markets has been one of the main obstacles to the development of property derivatives.

One way to overcome this obstacle is to develop a widely accepted risk model of commercial real estate, which can help make sense of property heterogeneity. A model does not aim for the truth but for a vision of reality that can be widely and systematically adopted by market participants, as CAPM was in the investment industry (Bernstein, 1995). Indeed, a model is an engine, not a camera (MacKen-zie, 2006). Short of designing its own models, real estate finance is condemned of having no engine at all or one that does not suit its needs. This section presents two factor-based models: the historical pricing model devised by Hoag in his seminal 1980 paper, and a genetics-inspired risk model proposed by Lecomte (2007). It then shows how the choice of a risk model can affect our understanding of random walk and stochastic process, two important concepts applied to the pricing of commercial real estate derivatives.

Hoag’s (1980) model of commercial real estate

Conceptual framework for index construction from a property valuation function

James W. Hoag is oftentimes credited for introducing the first multifactor asset pricing approach into real estate literature (Miles et al., 1990; Tunaru, 2017). The model presented by Hoag (1980) which focuses on industrial properties is first and foremost a valuation model akin to methods “utilized in common stock risk/ return analysis”. Hoag explains:

The method of analysis [...] leads naturally to a consideration of a property valuation function based on a vector of fundamental microeconomic and macroeconomic variables which affect property value. With certain reasonable approximations, the valuation model leads directly to an estimate of the market rate of return on real estate, the risk and return associated with each property and the market risk.

The full “conceptual framework for index construction from a property valuation function” encompasses the property asset’s micro-market defined as buildings’ specific characteristics and the broader macro-economic environment captured by national and regional variables. Five categories of variable are represented in the model: national economic, regional economic, locational, temporal, and property-specific characteristics.

Hoag explains that “initially, the list of valuation characteristics should be very broad, but as experience grows, many candidate characteristics will be cast aside”. Property-specific characteristics include location, physical characteristics, lease characteristics, financing characteristics, and appraised value. The macro-economic climate, including both regional variables (e.g. regional growth, population changes, regional transportation spending) and national variables (e.g. business inventories, mortgage interest rates and availability), interacts with other fundamental characteristics to impact the valuation function and estimated prices. The supply and demand sides of the real estate market are also part of the model with national variables such as available space/ vacancies, commitments, and investment by major participants. Hoag assesses that the locational variables “detract somewhat from the regional economic concomitants since each represent a localized measure of value. [...] Location interacts with specific regional macroeconomic variables such as transportation spending to provide a context for regional valuation [...]”. Hence, as mentioned before, locational variables can be a proxy for macro-economic variables at the micro-scale.

Individual risk measures are designed to assess a building’s responsiveness to fundamental characteristics.9 Hoag stresses that the objectivity of the model contrasts with appraisers’ subjective estimates of value and thus return. Markedly, the model is determined from an analogy with the “type of fundamental analysis [which] is accomplished on a daily basis by security analysts in the stock market”. Among Hoag’s objectives is the provision of index numbers that can be used “to utilize current investment technology (the Capital Asset Pricing Model - CAPM) to estimate a real estate investment”. In that sense, Hoag’s model, although characterised by its innovative use of a multifactor risk model in what is essentially a parametric methodology, is intrinsically biased towards a binary approach to commercial real estate returns and risks.

Hoag’s framework and factor-based real estate derivatives

By putting a conceptual framework at the core of the analysis, Hoag’s seminal research defines the way multifactor asset-pricing studies for commercial property should be designed. Hoag validates the notion that factors come from two broad categories: macro-variables and micro-variables which are property specific. Property specific does not mean hedonic inasmuch as property-specific factors also include lease and financing characteristics.

National and regional economic variables are designated as “concomitants of value” in the asset valuation function for industrial properties. This implies that economic variables form the context which interacts with fundamental characteristics to determine value. The latter are limited to before-tax equity cash

Factorisation of commercial real estate 37 flows and property-specific factors, especially lease characteristics. In that sense, Hoag’s framework implicitly follows a bottom-up approach to commercial real estate value. Hoag does not venture into a risk model per se as his framework is essentially designed to estimate a valuation function “at any point in time” (i.e. statically). But, by assessing “the responsiveness of property value to changes in fundamental factors”, the framework can double up as a dynamic risk model for commercial property.

Lecomte’s (2007) genetics-based risk model of commercial real estate

It should be clear by now that real estate is refractory to abstraction. This is the crux of a problem which has so far prevented academics and finance experts to successfully design and launch standardised real estate derivatives markets. The over-the-counter format of Total Return Swaps (TRS) can accommodate property heterogeneity. But, standardised markets, as we know them today, simply cannot. Property heterogeneity can be ignored by adopting aggregate thinking in the name of financial economics orthodoxy or for the sake of practicality.

Alternatively, property heterogeneity can become real estate finance’s central tenet. The underlying idea is simple. Let’s put aside everything financial economics has taught us and think in terms of “what if”. The first of a long series of “what if’ goes back to the very origins of economics: what if Cambridge economist Alfred Marshall’s focus on life sciences had become the dominant paradigm in economics at the turn of the 19th century, instead of physics? What would it mean for real estate?

In his Principles of Economics (1890), Marshall writes:

The Mecca of the economist lies in economic biology rather than in economic dynamics [...] Frequent use is made of the term “equilibrium”, which suggests something of statistical analogy [...] But, in fact [economics] is concerned throughout with the forces that cause movement: and its keynote is that of dynamics rather than statics. [...] Economics cannot be compared with the exact physical sciences: for it deals with the ever-changing and subtle force of human nature. [...] The laws of economics are to be compared with the laws of the tides, rather than with the simple and exact law of gravitation. [...] Economics, like biology, deals with a matter, of which the inner nature and constitution, as well as the outer for, are constantly changing.

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