# Price dynamics in commercial real estate

- Price dynamics in the absence of a risk model of commercial real estate
- METHODOLOGIES DERIVED FROM FINANCIAL ENGINEERING, MATHEMATICS, AND ECONOMETRICS
- GELTNER AND DE NEUFV1LLE (2018)’S EIGHT-FACTOR REAL ESTATE PRICE DYNAMICS
- The genetics-based model and the irrelevance of classical random walk for commercial properties

Now that we have introduced a risk model of commercial real estate and discussed methodologies to implement it, identifying real estate price dynamics to quantify uncertainty is the next step in the analysis. This point is especially important for deriving the ‘correct’ price of real estate derivatives. One fundamental issue here is to explore whether real estate follows a random walk, akin to financial assets, which would make it possible to apply well-known stochastic processes, such as the Brownian motion, for pricing real estate derivatives.

The concept of classical random walk introduced by Louis Bachelier (1900) and popularised by Burton Malkiel (1973) posits that asset prices exhibit a random walk whereby “successive price changes in individual securities are independent [...] A series of random walks implies that a series of stock price changes has no memory - the past history of the series cannot be used to predict the future in any meaningful way” (Fama, 1965).

This section starts by introducing models employed in the academic literature to simulate price dynamics in real estate markets. It then explores the random walk hypothesis in light of the genetics-based model.

## Price dynamics in the absence of a risk model of commercial real estate

Since real estate derivatives were reintroduced in the early 2000s, real estate finance researchers have looked for reliable models to capture real estate market price dynamics in view of quantifying real estate uncertainty and pricing real estate derivatives. This section briefly introduces two main categories of models: models derived from financial engineering, mathematics or econometrics, and models opting for a pragmatic approach of real estate risk (e.g. Geltner and de Neufville, 2018). These methodologies have in common not to rely on a risk model of real estate while assuming that real estate prices follow some kind of random walk.

### METHODOLOGIES DERIVED FROM FINANCIAL ENGINEERING, MATHEMATICS, AND ECONOMETRICS

Although the literature on pricing models of real estate derivatives is limited, Tunaru (2017) identifies three categories of models customarily applied in academic research:

- - Equilibrium models pricing contingent claims on a real estate index (e.g. Geltner and Fisher, 2007),
- - No-arbitrage models based on the no-arbitrage valuation principle which is applicable in markets assumed to be complete (e.g. Syz, 2008),
- - Econometric and mathematical based models which focus on econometric specifications rather than financial engineering specifications (e.g. Fabozzi, Shiller and Tunaru, 2009, 2012).

These models are designed for index-based derivatives, i.e. the most aggregated level in real estate analysis. Among the three categories, the third one is undoubtedly the most interesting insofar as it takes into account real estate prices’ empirical characteristics (i.e. serial correlation) whilst the other two categories are simply trying to make real estate fit into conceptual frameworks developed for other asset classes. Interestingly, all three categories of models tend to refer to a random walk process (e.g. Van Bragt et al., 2015 who mention a random walk with a drift).

Markedly, these models consider real estate in its financial dimension only. Fabozzi et al. (2012) affirm that “for a commercial real estate index describing the market in aggregate, it is better to model this asset as a financial asset”. When it comes to the hedonic value methodology and the related hedonic variables, they add: “In contrast [to residential property], commercial property prices are driven mainly by their investment attributes and the resulting economic value is related to both general and local economic conditions”. Hence, according to these models, one should not worry about underlying commercial properties’ characteristics such as size, age, location, and quality.

Considering real estate price dynamics at the aggregate level as a totally abstract process oblivious of actual physical assets and their space markets makes these three categories of models appear disconnected from the reality of real estate risk. Abstraction cannot make up for the lack of a comprehensive risk model of real estate informing these pricing models. In effect, notwithstanding their commendable search for scientific rigor, most models struggle to price real estate derivatives in a satisfactory manner. Case in point: no-arbitrage models assume a complete real estate market, which is notoriously not the case in practice since commercial real estate markets are inherently incomplete (Tunaru, 2017).

### GELTNER AND DE NEUFV1LLE (2018)’S EIGHT-FACTOR REAL ESTATE PRICE DYNAMICS

In contrast to the previous models’ extreme abstraction, Geltner and de Neufville (2018) propose an eight-factor model whose interest stems for its non-dogmatic approach to real estate market price dynamics. It is “as much an art as a science” affirm the authors.

The eight components are: (1) long-term trend rate, (2) volatility, (3) cyclicality, (4) mean reversion, (5) inertia (autoregression), (6) price dispersion (noise), (7) idiosyncratic shift, and (8) black swans. Components 1-5 as well as component 8 occur at the aggregate (index) level. They are systematic whereas components 6 and 7 occur at the property level and do not appear in indices. Once identified and modelled, these eight components can be put together to simulate real estate market price dynamics aiming for “the generation of future pricing scenarios that ‘look’ realistic and plausible [...]”. It is interesting to go over each component individually and point out important assumptions made by the authors:

- 1
*Long-term trend rate:*Structure depreciation affects property value negatively but might be more than offset by land value over time; - 2
*Volatility:*It “refers to the way prices change randomly, unpredictably from one period to the next”. It supposes that some degree of “memory less” random walk type influence applies to real estate price dynamics; - 3
*Cyclicality:*Real estate asset markets are notorious for their cyclicality which might or might not reflect the space market; - 4
*Mean-reversion:*Prices tend to ‘auto-correct’ and revert back towards the long-term trend in component 1 above. Powerful economic fundamentals in terms of structure and land might be at play; - 5
*Inertia:*Price changes in one period tend to echo price changes in the previous period though “autoregression”; - 6
*Price dispersion or noise*which occurs at the property level (individual transactions); - 7
*Idiosyncratic shift:*It occurs at the property level when “individual property paths evolve separate from and independent of the market value index”; - 8
*Black swans:*Also known as ‘fat tail events’ which rarely happen, and contrary to volatility, result in unexpected losses.

This combination of eight components yields a model-free methodology with many strong points. First, the model is firmly rooted in the behaviour of real estate markets and assets, especially assets’ physicality over time (component 1), and the asset market’s well-identified characteristics (components 3, 4, 5). Second, it accommodates property idiosyncrasies at the property level as a result of a transaction (component 6: impact on local real estate market) or a property’s uniqueness (component 7). But, it paradoxically combines a memoryless random walk (component 2) and long memory/memory-laden processes (components 1, 4, 5), which questions the actual nature of uncertainty in real estate. Geltner and de Neufville (2018) assert: “our pricing factors substantially enhance the traditional random walk process, by recognizing the special features of the dynamics of real estate markets”. It is undoubtedly the case. However, what does the eight-factor model mean with respect to the type of random walk applicable to commercial real estate assets?

When put together, the eight components seem to point at the impact of investment horizon on uncertainty with risk decreasing over long horizons?^{2} Indeed, real estate price dynamics appears a lot more uncertain in the short run than in the long run. So, does commercial real estate follow a time-varying enhanced random walk, i.e. relatively strong degree of randomness in the short run but mitigated by other potent processes in the long run? Notwithstanding its practicality and in the absence of an underlying risk model, the methodology cannot answer these questions, nor does it help in terms of risk factors to be used in order to hedge real estate risk.

## The genetics-based model and the irrelevance of classical random walk for commercial properties

In contrast to the models presented so far, the genetics-based model can help explain the nature of real estate price dynamics at the property level. The main contribution of the genetics framework is to fill in the gap left by the other models which almost exclusively focus on the macro-scale. As pointed out by Pai and Geltner (2007), the real estate industry understands “fairly well the big picture of what the typical or average real estate investment return should be - but not very well how a given property’s or market segment’s expected return should differ from that average”. Aggregate-level studies are fine for index-based derivatives, but they are of little value for property-level risk hedging. The analysis below focuses on the random walk at the micro-scale.

The classical random walk hypothesis which underpins the efficient market hypothesis has been applied to commercial real estate. Following in the footsteps of Alfred Cowles’s (1933) seminal study, Ling (2005) goes on “a random walk down main street” where he finds no evidence to support the predictability of private commercial real estate returns in US institutional-quality commercial properties. However, there is no decisive and consistent evidence in the literature to support the random walk hypothesis in real estate finance. First-order autocorrelation of appraised returns is a well-researched issue in real estate finance, an issue amply covered in the academic literature (e.g. Geltner, 1989). Private property markets are notoriously inefficient, plagued by asymmetry of information, illiquidity, and high transaction costs.

As a matter of fact, the random walk hypothesis, no matter how much one refines it (e.g. geometric random walk) is not conceptually compatible with direct commercial real estate. In its various incarnations (Ibe, 2013), the random walk hypothesis embodies a clear-cut disconnect between the ‘walker’ and the environment. This is the exact opposite to real estate where the environment

*Factorisation of commercial real estate* 53 is an integral part of a building’s ability to produce returns, and vice versa. The Brownian motion, as the continuous-time analogue of the random walk, might be a well suited diffusion process for liquid markets, but not for an illiquid and heterogeneous asset as physically and sociologically immersed in its environment as commercial real estate.

Nineteenth-century economists who questioned the use of physics, in particular equilibrium thermodynamics, in analysing economic systems shed an interesting light on this issue. For instance, Veblen (1898) suggests that the only rational approach to economic system is to consider they orderly unfold through “a cumulative process of adaptation of means to ends that cumulatively change as the process goes on, both the agent and his environment being at any point the outcomes of the past”. More concretely, Shiller (2008) who describes derivative markets for home prices explains that “other markets for liquid assets are nearly random walks” but not property which is so different “because there [might be] expectations of big price change”.

In this context, the genetics-based model proposes an alternative to the classical concept of random walk. In genetics, there is no ambiguity: the expression of a polygenic complex trait in a given genotype is not random. Lecomte (2007) explains:

Prices depend on assets’ genes, some of which cannot be easily altered or modified (e.g., land which is at the core of real estate’s physical dimension). Hence, what is randomness of assets whose returns are defined with what is essentially a deterministic model? [...] The concept of unqualified random walk in real estate is an aberration. Genetics defines randomness in a way that is not fortuitous but causal since linkages have known impact on traits.

Because of their essential physicality, real estate assets require a specific definition of randomness anchored in the space-time realm. Arrow (1951) brings an interesting perspective on the issue of uncertainty in real estate when identifying three classes of economic phenomena linked with uncertainty: (i) phenomena which are inherently concerned with uncertainty, such as gambling or insurance, (ii) phenomena “which are not related to uncertainty but nevertheless have no other conceivable explanation”, and (iii) phenomena “whose relation to uncertainty is more remote and disputable”. According to Arrow, contractual obligations such as leases fall in the second class.

One could argue that the application of the random walk in real estate is a misinterpretation of Arrow’s stance on uncertainty. Pricing models at the aggregate level treat real estate as a class one phenomenon (e.g. by proxying real estate uncertainty with ready-made stochastic processes and diffusion processes taken straight out of mathematics textbooks). More realistically, Geltner and de Neu-fville (2018) opt for a class two phenomenon whereby the random walk anchored in a few of real estate’s specific characteristics is enhanced and controlled. The genetics-based model selects the third class, arguing after Fisher (1930) that “risk varies inversely with knowledge”.

54 *Factorisation of commercial real estate *Lecomte (2007) asserts that genetics

has the potential to be to real assets what the Brownian motion is to financial assets, by defining and modelling randomness in process. [...] For any given environment, variability in [total] returns is deterministic, dependent on complex, though identifiable, patterns.

Thus, real estate follows a multifactorial causal walk, which is highly idiosyncratic, but not random. There is unquestionably the possibility that extreme idiosyncrasy at the property level be mistaken for randomness at the aggregate level.

The key to modelling real estate price dynamics at the property level is the ability to accommodate the changing nature of interactions between a building’s genotype and the space-time varying environment, i.e. to encapsulate real estate’s paradox of apparent stability amid constant changes. Kummerow (2000) sums it up as follows:

Processes [in real estate] are not strictly stationary in the long run, but they do have some structural stability and in normal times evolve slowly enough to allow imprecise forecasts. For these disorderly systems, parsimonious general models are more likely to fail than those that take account of local circumstances.

Hence, whatever process is selected should avoid a ‘one-size-fits-all’ solution. Ad-hoc micro-scale stochastic processes derived from the genetics-based model should replace a systematic top-down approach modelled after stochastic processes employed for pricing standardised financial derivatives. In that respect, the genetics-based model provides a fully consistent approach which encompasses a risk model as well as a wide-ranging notion of price dynamics to be used in real estate derivatives pricing. It is new in real estate finance, and unusual in finance to underpin a stochastic process by a risk model concerned with veracity in reflecting a particular asset’s behaviour inclusive of its environment at the micro-scale (e.g. property type and sub-type, local market). After all, the Brownian motion was originally inferred by Scottish botanist Robert Brown from observing small pollen particles in a drop of water, not the stock market (Ibe, 2013).

That said, the fact a stochastic process is disconnected from an asset’s true nature is not a problem in itself. Noticeably, according to Fama (1965), the random walk is unlikely to provide an exact description of the behaviour of stock market prices. But, it is still acceptable for practical purposes “even though it does not fit the facts exactly”.

Monte Carlo simulations of the genetics-based model can be run to infer a reasonable portrayal of price dynamics for a given property in a specific environment through simulated future scenarios. The ‘eyeball test’ of price paths mentioned by Geltner and de Neufville (2018) does matter here. Thus, the danger of this micro-scale experimental methodology is to claim generalisation that it is not entitled to. Simulation results are highly idiosyncratic and represent plausible

*Factorisation of commercial real estate* 55 asset-level price dynamics. To infer aggregate level price dynamics, interactions between proforma property type genotypes (standardised physical structure Cl and lease structure C2) and the least granular levels of location (G1 global, G2 country, G3 region on C3) would have to be selected instead and simulated within the confines of the model. Irrespective of the simulations’ aggregation level, interactions between genotype x environment will have to be defined through parametric rules part of genetics-based models. The complexity of these rules might range from simple (e.g. dominance of one gene not directly impacted by the environment) to complex (e.g. dominant genes directly impacted by modifiers and the environment) and extremely complex (e.g. polygenic and indirect environmental interactions with time effect). Comparative scenario-based simulations of total return paths under different controlled hypotheses (e.g. same building in different environments, different buildings in same environment) could then be envisioned. These pro forma models known as ‘avatars’ could serve as underlying to real estate derivatives. A market for pro forma genotypes in controlled environments known as ‘Market for Avatars’ is introduced in the section below. Suffice to say that a lot of research work will be needed to turn the genetics-based model from a conceptual framework to a practical tool catering to industry professionals’ hedging needs.