Strange attractor in the Auckland commercial property market

Publication Date14 May 2020
AuthorMoshe Szweizer
SubjectProperty management & built environment,Real estate & property,Property valuation & finance
Strange attractor in the Auckland
commercial property market
Moshe Szweizer
Research, CBRE Group Inc, Auckland, New Zealand
Purpose The purpose of this study is to provide a chaos theory-based framework, which can be used to
model commercial property market dynamics.
Design/methodology/approach The paper is presented in two parts. In the first, rigorous mathematical
reasoning is entertained, so to derive an attractor describing a set of feedback formulae. In the second part, the
attractor definition is used to model the Auckland commercial office market. The model is exposed through a
set of seven scenarios allowing for analysis of the market behaviour under various exogenously imposed
Findings The general behaviour of the model is in agreement with the commercial property market conduct
observed in Auckland. The model provides information related to the market turning points and allows for an
explanationof some intricate market dynamics. These include the anatomy of a market peak and its response to
the liquidity oversupply.
Practical implications The model may be used to expand our understanding of the market performance
under various exogenically imposed conditions, which allows for planning of market interventions in a more
refined manner.
Originality/value The paper is original, in the way the chaos theory is applied to the property markets
modelling and allows for expanding the understanding of the market behaviour.
Keywords Entropy, Chaos, Auckland property market, Market turning points, Property market modelling,
Strange attractor
Paper type Research paper
In this paper, the chaos theory is employed to model property markets. The work is divided
into two parts. In the first part, strict mathematical reasoning is applied to derive general
entropy-based feedback formulae that can be used in chaos modelling. In the second part, the
model is applied to the Auckland property market so as to reproduce its most characteristic
The model relies on three endogenic variables, namely, vacancy, rent and yield, and
employs four exogenic parameters that are related to the market worth, economic conditions,
financial stimulus and the demand for space.
The purpose of the second part of the paper is to illustrate the workings of the model
through seven scenarios, each based on specific values of exogenic parameters, representing
corresponding market conditions. The scenarios include a comparison of top-quality stock
behaviour in the presence and absence of supply; a look at the interdependencies of endogenic
variables for top-quality properties; the behaviour of the market under the large liquidity
supply scenario; the influence of stock supply on the market dynamics; the anatomy of the
market peak; the response of the market to the changes in liquidity supply; and finally, the
building quality and the yield spread compression relationships.
A discussion of the results, the current state of the model development and the future
directions concludes.
The property models present in the current literature seek forecasting as the main
objective. The models may be grouped depending on the technique employed, with some
using multidimensional linear constructs such as auto regressive integrated moving average
(ARIMA), simple and multiple regression, vector autoregression and others, but also
The current issue and full text archive of this journal is available on Emerald Insight at:
Received 30 October 2019
Revised 21 January 2020
2 April 2020
Accepted 19 April 2020
Journal of Property Investment &
Vol. 38 No. 6, 2020
pp. 579-596
© Emerald Publishing Limited
DOI 10.1108/JPIF-10-2019-0138
nonlinear reduced models with endogenic parameters influenced through elasticities.
Reviews of the linear models with a comparison of their effectiveness as forecasting tools may
be found in Stevenson and Mcgarth (2003),Jadevicius and Huston (2015),Chaplin (1999).
Examples of the models may be found in Hendershott et al. (1999),Hendershott et al. (2000),
Wheaton et al. (1997),McGough and Tsolacos (1995).Jadevicius et al. (2012) provide a
comprehensive discussion of reduced-form modelling techniques and their relative accuracy.
The model presented here employs a fundamentally different approach to modelling and
seeks different goals when assessing its effectiveness. The classical models are intrinsically
connected to a time series and seek to extend such through forecasting. Here, the model is time
static and paintsa picture representing all possible market states as a time-independent
construct. This construct allows for the current market to be located as a system state
within the model through a specification of the model parameters. A change in the market
state, reflected through a change in the parameters, moves the model to a different location
within the construct. There is no time variable employed; therefore, the model does not
provide any indication of the duration of such a movement.
Another major difference lies in the ability to assess detail though the model. In the
classical models. averaged values of variables are used and predicted. Here, the model
represents a statistical distribution of data related to individual buildings. Therefore, one
may perform an analysis with an objective of understanding a state of a single building
within an evolving market.
The classical modelling techniques are concerned with the prediction of the future values
of endogenic variables. A chaos-based model attempts to describe all possible states of the
market as one entity and is concerned with the marketsstability. In a chaos-based model, the
current state of the market is represented through a collection of points within the model and
the question being asked is related to the movement of these points when the market
conditions change. A stable system is represented through the points far away from the
chaotic region in the model, while an unstable system is close to or within such a region. In
this respect, a chaos model relates to the ability to forecast, as a stable state of a system is
more predictable than the unstable.
One of the biggest differences between the classical models and a chaotic one is the way
the concept of market shocks is treated. These are introduced in a somewhat artificial manner
to the classical models, while are an intrinsic part of the chaos theory, being represented
through bifurcations (splits of trajectories).
Another difference is the ability of the chaos theory to zoom-in onto a specific detail within
the model. Like with the use of a magnifying glass, a researcher may select a condition being
studied and investigate the detail by running the simulation with a very tightly set parameter
ranges. In general, there is no theoretical limit as to how narrow these ranges may be set. This
provides means of investigating how small changes in economic conditions influence the
Finally, the classical modelling techniques use an educated guess, combined with a deep
understanding of market workings, to arrive at the most promising model formulations.
These are judged through the effectiveness of the models as forecasting tools. Here, the model
is derived from first principles, through an application of strict mathematical reasoning.
Entropy exists; therefore, it is a physical quality. However, entropy cannot be measured or
observed directly; therefore, it belongs to the non-physical world. If someone believes in the
existence of a spiritual world, one could think of entropy as being the medium through which
one of these worlds can influence the other. Entropy is a measure of order and information.
The higher the order, the lower the entropy.

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