HEDONIC PRICING MODELS AND THE ART OF MICRO-VARIABLES SELECTION
Factor-based real estate hedges include not only macro-factors but also microfactors. The Hedonic Price Model (HPM) based on Lancaster’s (1966) consumertheory can be helpful in identifying micro-variables factored in commercial real estate prices. The hedonic price model has been used in commercial real estate for two purposes:
- - The construction of repeat-sales transaction based indices of commercial real estate (e.g. Fisher, Geltner and Webb, 1994; or Shiller, 1993) to account for fundamental alterations in-between sales, and
- - The analysis of real estate return drivers, in particular for a specific property type in a given location, e.g. Brennan, Cannaday and Colwell (1984) who study office rents in the Chicago CBD.
Triplett (1986) explains that
the [HPM] framework is derived from the idea that production or consumption of heterogeneous goods (or services, for that matter) can be analysed by disaggregating them into more basic, or elemental, units that better measure the dimensions of what is bought and sold- the characteristics.
Characteristics are supposed to be utility-bearing attributes, which are homogeneous and valued by both buyers and sellers.
As the hedonic price theory does not provide any indications with respect to the optimal choice of hedonic variables, the implementation of HPM in commercial real estate has been accompanied with a great diversity of variables in the models applied in past research. Shiller (1993) mentions:
In constructing such hedonic indices, one is inevitably struck by the arbitrary or judgemental decisions one must inevitably make. Not only is there the decision of which quality variables to include, but there are also decisions to make about allowing nonlinear effects of each and interaction effects (represented, say, by variables equal to products of characteristic variables) between them. [...] There is a fundamental problem of objectivity of such indices.
In his choice of hedonic variables to be included in hedonic repeated-measures indices of commercial real estate, Shiller (1993) focuses on “independent variables that identify the investment”, i.e. “identifiers of specific claims on future income or services”. Time-varying variables which “naturally change for existing properties” should be excluded even though nothing seems reliably set in stone when it comes to ‘normal’ hedonic variable selection. For instance, to account for market conditions, Shiller posits that “one might sometimes wish to use hedonic variables” and suggests that “time on the market” be included in the hedonic regression model. This suggestion leads to many troubling questions about the relevance of any hedonic price indices based on “human judgement” and, in turn, derivatives using them as underlyings. Shiller (1993) talks in-depth about hedonic variables in the construction of index numbers feeding a macro-market for commercial real
Factorisation of commercial real estate 25 estate assets. But, no references are made to a risk model of commercial real estate underpinning the process of hedonic variable selection. Interaction effects are mentioned in statistical terms but not explained in the context of real estate risk.
Markedly, the hedonic pricing theory is not a risk model. One should not assimilate HPM with proper endeavours to model commercial real estate returns and risk. Besides, HPM was never designed for extremely heterogeneous assets. This inevitably turns hedonic variables selection into an art rather than a science. Pragmatically, Shiller muses that the market will ultimately decide on the value of such model. “If people want to hedge in the market, then the index is a success” in line with the engine versus camera argument made by MacKenzie (2006). But, if they don’t, that’s another wasted attempt to launch property derivatives until there are none left, that is because market authorities become wary and investors jaded.
LOCATION IN SPATIAL HEDONIC MODELS
One string of academic research combines hedonic modelling with spatial econometrics (e.g. Ozyurt, 2014). Location in classic OLS hedonic models such as those presented in Appendix 1.3 customarily assumes that land is a two-dimensional smooth surface on which buildings sit (Pace, Barry and Simians, 1998). A myriad of indicator variables in the models embody different parts of the urban area. For instance, Brennan, Cannaday and Colwell (1984) select several location-related regressors such as distance to LaSalle Street in Chicago CBD and positioning of the building in East-West and North-South coordinates.
By employing spatial econometrics, researchers aim to account for each neighbourhood’s unique effect while modelling the hedonic price of real estate assets. In doing so, they have identified two spatial effects which impact hedonic pricing models. Wilhelmsson (2002) explains:
Spatial econometrics explicitly accounts for the influence of space on real estate, urban and regional models. There are two types of spatial effect, namely spatial dependence and spatial heterogeneity.
Spatial dependence derives from “spillover effects such as the impact of the price of one housing on the price of its neighbours [or] spatially correlated variables that have been omitted”. Spatial heterogeneity may derive from “spatially varying parameters”.
The resulting models are spatial hedonic models. Dubin, Pace and Thibodeau (1999) emphasise that by controlling for omitted variables in real estate price models, spatial techniques can significantly improve the predictive accuracy of hedonic models which would otherwise result in inefficient estimations. One point frequently mentioned is that spatial hedonic models tend to be more parsimonious in independent variables than classic OLS hedonic models. Pace, Barry and Sir-mans (1998) assess that the number of variables in a hedonic model increases as a direct proportion to the geographic scope of the study. For a dataset of 10,000 realestate transactions data (n), approximately 500 location-related indicators (n/20) would be needed (corresponding to a separate indicator for each neighbourhood). One way to circumvent the issue is to focus on one specific neighbourhood all the more so if this neighbourhood is dominated by a single economic basis (e.g. Lecomte’s (2014) replication and hedging of City of London office buildings).
Although mainly employed in housing studies, spatial hedonic models have also been used for commercial real estate assets, in particular retail properties for which site selection is “a classic spatial problem [...] that can be improved with spatial statistical techniques” (Dubin, et al., 1999). For instance, Desrosiers, Theriault and Menetrier (2005) identify complex interactions between endogenous determinants of shopping centre rents (e.g. agglomeration economies, retail mix and concentration, image and interior design) and exogenous space-related factors. In addition to size, retail mix, and image attributes, spatial determinants linked to neighbourhood and location attributes play a key role in explaining variation in shopping centres’ rents in Quebec City, Canada.
More generally, whether spatial econometrics contributes to a more bottom-up approach to commercial real estate modelling than classic OLS hedonic regression by focusing on real estate micro-markets instead of macro-economic markets remains an open question. One would expect spatial determinants to be anchored in their local context. Ideally, spatial effects capture micro-trends at property level, trends which, through complex and dynamic interactions, are ultimately underpinning properties’ rents and values.
Practically, spatial techniques can contribute to improving real estate modelling. Dubin et al. (1999) note that spatial autoregression techniques substantially improve “predictive accuracy, change in parameter estimates and their interpretation” in commercial real estate models, whereas OLS methods (e.g. hedonic methodology) in the presence of positive spatial autocorrelation result in “inefficient estimation and literally biased inference”.
Hence, in the absence of a widely agreed risk model of commercial real estate, relying on spatial techniques could be an interesting way to reduce the number of variables in factor hedges while improving the instruments’ overall hedging effectiveness. Interestingly, the theoretical underpinnings of spatial hedonic models are grounded in urban land economics. By positioning location at the core of commercial real estate analysis, these models support the view that land is central to real estate values, either as a variable with an absolute impact determined by a building’s unique location on the surface of the Earth, or as a variable with a relative impact depending on interactions with other factors within a wider external context (be it the immediate or broader neighbourhood, the Metropolitan Statistical Area or beyond).
MILES, COLE AND OUILKEY'S (1990) FIVE DETERMINANTS OF VALUE
Some researchers have been somewhat more conclusive in selecting microvariables based on HPM, e.g. Miles, Cole and Guilkey (1990) who adopt a very
Factorisation of commercial real estate 27 broad approach. Their choice of hedonic variables for commercial real estate sets free from the Hedonic Price Theory’s inherent vagaries by shifting the focus to “basic valuation methodology”. Their selected variables come from five different categories which are “essential determinants of real property value”6:
- - National location which takes into account “the health of the local market economy in which a particular property is located relative to that of other local markets across the nation”.
- - Metropolitan location such as central business district, major suburban concentration, access to rail line, airport. It is “the most difficult to assess without a personal assessment of each property and its neighbourhood”.
- - Physical structure to assess “how well a particular property is suited for its highest and best use”. This includes variables “chosen to proxy for remaining physical usefulness and functional obsolescence” such as physical age, date of last major renovation, number of stories, number of buildings, extra land available, gross and net leasable square footage.
- - Lease structure to account for the “variability of returns and value attributable to differing lease structures”. Four variables can be included: weighted average remaining lease maturity, tenant credit quality, weighted average percentage of expense increases that may be passed through tenants, and number of tenants. Noticeably, whilst in their strictest definition, hedonic variables tend to be structural and static, “lease structure” variables are essentially functional by capturing the dynamic process of income-generating at the asset level.
- - Financial structure with measurements such as net income, capital improvements, partial sales, and appraised value as a way to measure “the financial operating performance of each property”.
These determinants of property value are applicable to a building in its entirety, or to each unit making up the whole building. However, the selected variables are not unsystematic risk factors. Instead, they are “identifiable and observable proxies” selected for their high correlation with unobservable unsystematic factors. This caveat matters because (again) the list of variables is established without any reference to a comprehensive risk model of commercial real estate. Guilkey, Miles and Cole (1989) hypothesise that each of the four main commercial property types should have its own pricing equation built from the above-mentioned five determinants? However, how the five categories of determinants and corresponding hedonic variables fit within a comprehensive and dynamic framework aiming to explain unsystematic risks associated with ownership of real estate property remains a mystery, one that can only be approached by proxy.
REAL ESTATE PRICING MODELS, CAPITALISATION RATES, AND MICRO-VARIABLES
Instead of focusing on sale prices, appraised values, or rents, a few researchers have applied a multifactor approach to disaggregate the determinants of commercial real estate capitalisation rates (cap rates) after pioneering studies by Ambrose and Nourse (1993), Jud and Winkler (1995).
In contrast to the two former studies which are conducted at the macro-level (e.g. Jud and Winkler study cap rates from 21 MSAs in the USA), Crosby, Jack-son and Orr (2016) who study a large number of transactions in the London office market (2010-2012) design a multilevel framework which captures at the micro-scale “the variation generated by the characteristics of the real estate, its tenants, its purchaser and how wider macro-economic factors influence the expectations of purchasers with regard to individual investments”.
By modelling cap rates at the micro-level, they aim to capture “the impact of attributes specific to the transacted real estate [given] the wider contextual and behavioural factors that can affect the outcome of the pricing decision”. Macro- and micro-factors which impact investors’ expectations of investment performances belong to four categories: investment and capital markets, real estate market, sector and allocation, stock/asset.
Among the latter category, variables positioned at the micro-end of the risk scale include tenant (credit worthiness), lease (multi/single-let, review/user clause, period to expiry/review), location (micro location/ accessibility), and building (sustainability rating, obsolescence). Furthermore, real estate asset-specific variables cover transaction characteristics broken down into transaction traits (e.g. type of investment transaction, property sold as part of a portfolio) and purchaser traits (e.g. international experience of the buyer, type of buyer). Interestingly, Ratcliff’s (1961) real estate analysis specifically recommends a very similar approach. In parallel to each property being “structurally and locationally different and thus subject to certain special influences”, the second special circumstance explaining that no two transactions are the same in the real estate market is linked to the parties involved. These parties might have different “motivations, business judgement [...] and financial circumstances”.
To assess buildings’ expected depreciation in their pricing model, the authors select Co-Star building quality rating as an independent variable in the pricing model: from one star (very poor quality building) to five star (landmark building). Crosby et al.’s empirical findings show that real estate specific factors dominate variation in cap rates, even more so than locational differences across submarkets. Yet, surprisingly, building quality does not influence cap rates of London office buildings, which admittedly, might be a special case owing to the focus on London, one of the most sought-after global cities for real estate investment.