Quantitative methods for risk management in the real estate development industry

 
JPIF                                                          PRACTICE BRIEFING
30,6
                                         Quantitative methods for risk
                                         management in the real estate
612
                                            development industry
                                                   Risk measures, risk aggregation
                                                     and performance measures

                                     1. Introduction
                                     Investment in real estate is based on dynamic, uncertain and complex assumptions. This is
                                     especially true for real estate development given its speculative and entrepreneurial
                                     activity. Factors such as unknown future demand, risks and uncertainty are key elements
                                     of real estate development (Byrne, 1996; Isaac et al., 2010; Schulte and Bone-Winkel, 2002).
                                     Effective risk management is thus a decisive strategic success factor. Though not always
                                     evident during periods of strong economic growth, it is undoubtedly of paramount
                                     importance during economic downturns. The global financial crisis and the deterioration
                                     in real estate markets across large parts of Europe in 2008/2009 clearly demonstrated the
                                     significance of the real estate industry for the world economy. Despite the structural
                                     significance of real estate to the economy and even though risk management has been
                                     widely analyzed in academic research, there remains limited substantive research on risk
                                     management that pertains directly to real estate development. Further, even less empirical
                                     data exists that can provide an overview of industry practice with respect to risk
                                     management by major development organisations (RICS, 2003; Shun, 2000). This paper
                                     provides a comprehensive overview of risk quantification, which may be expressed by
                                     probability distributions, and the calculation of risk measures, such as “capital
                                     requirements” (value-at-risk). A key technique is the aggregation of risks by means of
                                     simulation that creates transparency about planning certainty.

                                     2. Definition of risk management and the importance of a sound risk
                                     assessment
                                     In the following risk is generally referred to as:
                                        [. . .] the uncertainty expressed through the significance and likelihood of events and their
                                        outcomes that could have a material effect on the goals of a real estate development
                                        organisation over a stated time horizon.
                                     in accordance with the definition provided by Wiegelmann (2012a) and is based on
Journal of Property Investment &     COSO (2004).
Finance                                 Enterprise risk management is defined by COSO (2004) as:
Vol. 30 No. 6, 2012
pp. 612-630
q Emerald Group Publishing Limited
                                        [. . .] a process, effected by an entity’s board of directors, management and other personnel,
1463-578X                               applied in strategy setting and across the enterprise, designed to identify potential events that
may affect the entity, and manage risk to be within its risk appetite, to provide reasonable                                 Practice briefing
   assurance regarding the achievement of entity objectives (COSO 2004, executive summary, p. 4).
Recent risk management standards and guidelines include inter alia: the risk
management standards of the Canadian Standards Association (1997), the Standards
Australian and Standards New Zealand (2004) or the Federation of European risk
Management Associations (2002). The Committee of Sponsoring Organisations of the
Treadway Commission (known as COSO) provides a comprehensive guide to effective                                                                  613
risk management. Also, the International Organization for Standardization (ISO) has
published the so-called ISO 31000: “Risk Management – Principles and Guidelines”.
All these standards are comparable in respect to a sound risk management process. In
general, each risk management framework constitutes a permanent, dynamic and
systematic process in the sense of a control loop, with the risk management process
essentially consisting of four phases, namely identification, assessment, control and
monitoring (Figure 1).
   Although each individual framework has these four core elements in common, the
terminologies, individual components as well as the complexity of the control loop
vary. The goal of the risk identification process is to identify possible risks, which may
affect, either negatively or positively, the objectives of the business and the activity
under analysis. Risk assessment is defined as the overall process of risk analysis and
risk evaluation and helps in determining which risks have a greater consequence and
impact than others as well as the probability of the event occurring. This is followed by
the risk control phase, which evaluates whether the level of risk found during the
assessment process requires management attention. Risk monitoring is the periodic
tracking of risks and reviews the effectiveness of the treatment plan.
   Risk assessment is the process of evaluating identified risks and the interrelation
between risks. During risk assessment the individual risk situation of a real estate
project, standing asset or portfolio is mapped and forms the basis for the subsequent
formulation of risk management and control strategies. It is necessary to quantify risks

                                          Safeguarding of corporate objectives

  Output-related corporate objectives           Financial corporate objectives                Social corporate objectives

    Appetite and                                                                                            Optimisation of
   capacity for risk                             Avoidance                                                 corporate security

                                                            Minimising
  Risk identification
                                                                                                            Risk monitoring
                                                                         Transfer

  Risk assessment                                                                   Accept/undertake

                                   Total risk                                 Remaining risk

                                                         Risk control
                                                                                                                                             Figure 1.
                                                                                                                                Risk management process
Source: Wiegelmann (2012a)
JPIF   in order to assess the potential economic value of risk management, in particular to
30,6   ensure a quantifiable quality improvement of corporate decisions by weighing up the
       expected returns and risks. A sound understanding about possible outcomes for a
       development project is crucial for the developer to judge about an adequate level of
       return to compensate for the risks (Atherton et al., 2008).
           The meaningfulness of the assessment models in the context of real estate development
614    used depends significantly on the amount of data available and the specific data quality
       (Wiegelmann, 2012b). The methods used for risk assessment depend on the quantity and
       quality of the available information. Assessment methods can be broken down into
       quantitative methods and qualitative methods. The quantitative approaches are based on
       mathematical methods and only apply if sufficient risk-specific data is available. In the
       ideal scenario and where sufficient data is available, both significance and likelihood of an
       event can be derived on a quantitative, and therefore more objective, basis.
           Quantitative assessment techniques can be broken down into benchmarking,
       probabilistic and non-probabilistic methods (COSO, 2004). The most rudimentary form
       of risk analysis takes the form of simple adjustments of development variables along
       the lines of a worst- and best-case scenario. For example, construction costs can be
       calculated higher than current estimates and rental values can be calculated lower than
       current figures. However, such rudimentary risk adjustment is deterministic and
       highly subjective, leading to rather questionable estimates. A more systematic
       approach to risk analysis is sensitivity analysis. Sensitivity analysis examines the
       effects on profitability of changes (such as high, low and medium values) of any of the
       key variables. It identifies the key variables and how changes in individual variables
       might impact the final value. Scenario testing is a methodical improvement on
       sensitivity analysis. Its aim is to examine how a combination of changes in the
       development variables of an appraisal affects its outcome.
           The consistent application of risk evaluation methods is a critical success factor for
       efficient risk management. What needs to be analyzed is the probability of occurrence,
       the possible extent of occur-ring risks and, at best, their quantification. The question is,
       however, how established the respective approaches are in business practice.
           In an empirical survey of 69 (response rate of 43.7 percent) of the leading European real
       estate development companies in Germany, France, the UK, Italy, Austria, Spain and
       Switzerland conducted by Thomas Wiegelmann in 2005, 98.5 percent of the survey
       participants (n ¼ 67) stated that an efficient risk management is the basis for sustainable
       success in real estate development. At the same time, 44.1 percent of respondents (n ¼ 68)
       stated that, from their perspective, they did not have a sufficiently comprehensive concept
       for risk assessment. With respect to approaches and possible methods of risk evaluation,
       Figure 2 shows the distribution of answers (multiple responses were possible).
           69.9 percent of the surveyed real estate development organizations (n ¼ 69) approach
       risk assessment from the primarily subjective and intuitive perspective of the developer.
       The personal experience of the evaluating person and his or her “common sense” or
       “gut feeling” is accorded a high value in this regard. Further established methods are
       scenario techniques as well as sensitivity analyses with each 43.5 percent. Reasons for the
       preference for these evaluation approaches and processes lie most likely in their practical
       and comparatively simple application. Traditional sensitivity analysis does typically
       assume best, business and worst case scenarios and their outcome on the expected
       outcomes, not taking into consideration uncertainty and the possible range of outcomes
Practice briefing

                                                                                                            615

                                                                                                          Figure 2.
                                                                                            Risk assessment methods
Source: Wiegelmann (2012a)

that may result (Atherton et al., 2008). It becomes obvious that simulation-based
methods with 10.1 percent and value-at-risk approaches with 7.2 percent can hardly be
considered widely established methods. The survey results indicate developers typical
approach towards the management of risks tends to be characterized by a lack of
formalization and coordination, relying largely on an individual judgment and experience.
The survey results therefore indicate a considerable potential for improvement with
respect to probability-based risk assessment.
   The level of risk in real estate development projects and also standing assets and
portfolios determines the risk-based capital structure (capital requirements),
the probability of default (rating), minimum required expected rate of return
(WACC) and the project value. Also the upper limit for the costs of risk management
JPIF   measures (e.g. insurance) is determined through the risk level. As a measure of success,
30,6   profitability and risk are typically expressed in one key figure, a number, a dollar
       amount (in e) or a return. Risks need to be quantified. It is a major challenge for risk
       analysis and risk management to describe risks quantitatively by appropriate
       “probability distributions” or “stochastic processes”.
           The quantitative description of a risk requires the use of frequency or probability
616    distributions (and accordingly in the case of multi-period stochastic process). Risk
       therefore deals with the inevitable possible deviations from plan because of the
       uncertain foreseeable future, which incorporates opportunities (potential positive
       deviations) and threats (potential negative deviations). To make risk easy to calculate, it
       is necessary to express various kinds of risks with a (positive and real) number that is
       easily interpretable – the so-called risk measure, which enables prioritization of risks.
           This paper will explain the most important methods in the context of the
       quantification of risks. First, in Section 2 the need to quantify risks – or the impossibility
       of the non-quantification of risks will be discussed. Section 3 shows, that predictable
       positive or negative deviations (opportunities and threats) should not only be the basis
       for quantifying risk, but demonstrate that risk quantification and prediction systems are
       closely connected to each other. Section 4 will briefly introduce the most important
       probability distributions that are suitable for the quantitative description of risks.
       Section 5 deals with the central technique of simulation-based risk aggregation for risk
       management, thus determining the total risk (e.g. capital requirements) based on
       quantified individual risks. Based on that, Section 6 explains by which risk measures the
       total risk can be expressed. The most important risk ratios are presented with these risk
       measures and reference is made to measures of risk-bearing capacity (such as the equity
       ratio). Finally, Section 7 deals with performance measures, i.e. with success benchmarks,
       constructed by the combination of:
           .
              a measure of risk; and
           .
              an earnings benchmark (expected value) – such as enterprise value (discounted
              cash flow), or a “risk adjusted” economic value added (EVA).

       3. The non-quantification of risks is not possible
       It is obviously desirable to have sufficient relevant historical data at hand which can be
       analyzed by suitable statistical methods when risks are to be quantified. However,
       often, the question arises how to proceed if no adequate data and comparables are
       available. The empirical evidence presented in this paper, proves that many real estate
       organizations have not established suitable methods to quantitatively describe
       inherent risks.
           According to Sinn (1980) the varying degrees of uncertainty (risk, probability) are
       always attributable to the scenario of a “certainly known objective probability”, which
       may subsequently be used for all further analyses and decisions. In the absence of
       other information, all potential situations are regarded as equally probable due to the
       principle of insufficient reason.
           This means that all risks are quantifiable even if no information exists. The absolute
       ignorance regarding a risk threatening an investment would have to be expressed as
       follows: the likelihood of risk is between 0 and 100 percent. And the extent of damage,
       if it occurs, is between 0 and about e200 trillion, which is the equivalent of all property
       items on earth. One would probably quite quickly reach the conclusion that it is possible
to restrict such two ranges significantly based on the information available. The realistic                             Practice briefing
ranges should be determined based on information available and in light of the
heterogeneous assessment of various experts. Making decisions aligned to risks should
only be based on the information available that is presented in an adequate manner –
pseudo-accuracy is never desirable.
    Where a decision maker is confronted with insufficient probability data, higher-level
probabilities will have to be applied (Sinn, 1980):                                                                                    617
    .
       where the probability distribution of probabilities is known, they may be
       translated for an objective first-level probability that is implicitly present; and
    .
       where, however, no probability of any level is known for the validity of a
       probability distribution, a uniform distribution that is known with certainty will
       have to be assumed.
The decision principle of “insufficient reason” (Sinn, 1980, p. 36) may thus be described
as follows:
        In the event of completely unknown probabilities for the status categories of the world, the
        decision maker will have to assess outcome vectors:
        .
            as if each status category occurred with equal probability, and
        .
            as if such probability was an objective quantity that is known with certainty.
In real business situations, because information is incomplete and historical data is
limited, it is often not easy to decide by what probability distributions a risk may be
quantitatively described in an adequate way (Gleißner, 2011b).
   Neglecting parameter uncertainties (meta risks) may result in inappropriate risk
underestimations. Capturing such meta risks is imperative in order to facilitate a
correct assessment of the risk scope of a company or an investment project.
   A distinction is made based on whether the type of probability distribution or the
parameters, respectively, are known or unknown.
   In the classic decision theory risk scenario both the probability distribution type
and all parameters are known with certainty (Figure 3):
   .
      A meta risk of type I underlies the scenario in which the probability distribution
      may be assumed as being known with certainty, whereas the parameters
      themselves by their nature are random variables.
   .
      For the meta risk of type II it is assumed that several probability distributions (with
      parameters known with certainty) are considered possible, whereas the probability
      that a corresponding distribution exists is unknown. This means there is also a
      second-level probability; thus it is necessary to model a probability distribution
      describing the probability for the respective first-level probability distribution.

8                                                                                      Required capital
7                                                                  500.000
6
                                                                   400.000
5
4                                                  Residuum plus   300.000
3                                                    Risk level
2
                                                                   200.000                                                         Figure 3.
1                                                                  100.000                                                  Risk and planning
0                                                                       0                                                            certainty
    0     2   4   6   8   10   12   14   16   18                         2007   2008       2009           2010   2011
JPIF                 .
                         The meta risk of type III combines the scenarios of type I and type II. This means
30,6                     there is initially uncertainty as to the validity of a probability distribution (which
                         calls for a probability distribution by means of the probability distribution), und for
                         each of the (first-level) probability distributions there is again uncertainty about the
                         model parameters, which here are also, again, regarded as random variables (Table I).

618               Risk analysis and risk management procedures must be pragmatic, as can also be shown
                  theoretically: risk quantification (and consequently decisions in line with risks) shall
                  always be based on best available information or information to be made available with
                  adequate effort. Using subjective (expert) assessments as the risk quantification basis is
                  acceptable in principle too. It should, however, be ensured in general that data quality, to
                  the extent possible and economically sensible, is improved, for example by imposing a
                  “constraint to give reasons” on experts or using a number of information sources.
                     In the end, however, a more or less pronounced “meta risk” will always remain, or in
                  other words the danger that a risk may have been quantified incorrectly. It is irrelevant
                  if a situation was predictable without certainty or could not be predicted merely
                  because of lack of information. Such uncertainty about the risk scope may – sensibly –
                  be accounted for by presenting a parameter uncertainty in an explicit manner.
                     Data quality deficits therefore do not pose a problem in terms of the risk
                  quantification; a problem however arises where the implications of available data, and
                  their quality for the risk scope relevant to a decision, are ignored due to specialised
                  method-related inability or psychology-related unwillingness.
                     The conclusion therefore is that uncertainty about the risk scope and deficits in the data
                  basis available for risk quantification will have to be considered in the decision-making
                  process. “Worse data quality” itself will have a risk-increasing effect and may, for
                  example, be accounted for by explicitly stating the parameter uncertainty of a probability
                  distribution. Neither uncertainty about the degree of a specific risk (of a probability
                  distribution) nor poor data, however, justify forgoing a risk quantification.

                  4. Risk quantification and prediction models, expectation formation and
                  time series analysis
                  Already the definition of risk as possibility of a planning variance shows that risks can
                  be quantified in terms of a particular, as explicit as possible to the planned value.
                     Risks are the result of the uncertain, (partially) unforeseeable future and planned values
                  and therefore the result of forecasts. Thus, planning, forecasting and risk management
                  systems are inevitably linked together. It is not task of risk management (as can be
                  read occasionally) to predict or forecast future development. This is the job of a

                                                                                 Distribution type
                  Meta risk                                                             Potential alternative types
                  types                                           Known                 assessable

                  Parameter         Known                         Classic risk          Meta risk type 2
                                                                  scenario
                                    Assessable as probability     Meta risk type 1      Meta risk type 3
                                    distribution
Table I.
Meta risk types   Source: Gleißner (2009)
forecasting system. And quantifying risk is dealing with the question to what extent              Practice briefing
deviations may arise from a (best) forecast. Risk is the possibility of deviation from plan. In
so-called “stochastic” planning or forecasting models (e.g. a “stochastic corporate
planning”) all (important) forecasts will be described by random variables, so that
expected value and risk measure can be derived from a common basis. The former
expresses what could happen “on average” and the risk measure describes the size of
possible deviations.                                                                                          619
    The so-called “unbiased” planned values, i.e. the forecasts that are “on average”
may occur, usually cannot be determined without the knowledge about opportunities
and threats (risks). Besides the “most probable values” the less likely scenarios, the
potential positive and negative deviations, should also be taken into account. It is
essential that business decisions (e.g. investment appraisals) are to be made on the
basis of expected values- and not just on the basis of a most likely value (or median).
Before the level of risk is quantified, a possible meaningful (unbiased) planned value or
projection should be determined, which is required by good forecasts, whereas “bad”
(e.g. biased) forecasts lead to an overestimation of the true risk volume.
    For the quantification of risks it is meaningful to separate the changes of variables in an
expected from an unexpected component, which represents the risk volume. Not the change
in a variable but the amount of unexpected change in the variable determines the risk.
    After quantifying the risk the possible deviations from predictions (residuals, time
series innovations) are only considered and described through an appropriate
probability distribution (Section 4). The risk measures (such as the standard deviation)
relate to unpredictable (unforeseeable) deviations – what is predictable is not a risk.

5. Quantitative description of risks through probability distributions
Under risk quantification one can understand the quantitative description of risk and
the derivation of a risk measure (an index/benchmark as presented in the following
Section), which makes risks comparable.
    Basically, a risk should first be described by a suitable (mathematical) distribution
function. Risks are often described by likelihood and amount of loss occurring, which is
a so-called binomial distribution (digital distribution). Some risks, such as variation in
maintenance costs and interest expenses, which may vary in amount with different
probabilities, are however described by different distribution functions (e.g. a normal
distribution with mean and standard deviation). The binomial distribution, normal
distribution, and triangular distribution are the most important distribution functions
in risk management in practice (Albrecht and Maurer, 2005; Gleißner, 2011a) (Figure 4).

Binomial distribution
The binomial distribution describes the probability that in n-times repeating,
a so-called Bernoulli experiment, the event A occurs exactly k times. A Bernoulli
experiment is characterized in that exactly two events A and B occur with probability p
and 1 2 p, these probabilities do not change during the experiment and the individual
trials are independent. An example of the occurrence of this probability distribution is
tossing a coin repeatedly.
    A special case of the binomial distribution is the “digital distribution”. Here are two
possible events consisting of the values, zero and one. In practice the risk is often
described by the likelihood and the amount of loss occurring (within a specified period).
JPIF                                  Risk quantification: description of a risk with a probability distribution
30,6
                                                Mean = 1.33                                                                               –3 s               +3 s
                                                                         (18 von 30=) 60%
                                                                                                                                                    99.7%
                                                                                                                                          VaR
                                                                                             (9 von 30=) 30%                                       –s   +s
620                                                                                                             (3 von 30=) 10%
                                                                                                                                                    68.3%

                               0.00   0.75    1.50    2.25    3.00

Figure 4.                       (a)       Triangular distribution           (b)             Scenario distribution                 (c)       Normal distribution

Quantitative description        • Allows a simple estimate of maximum,       • Number of cases with damage                         • Suitable for e.g. the risk in
                                  minimum and most probable value              above a certain level is evaluated                    planning (many small risks)

                               Normal distribution
                               The normal distribution is common in practice. This follows the so-called central limit
                               theorem.
                                  This means that a random variable is approximately normally distributed if this
                               random variable can be understood as the sum of a large number of independent, smaller
                               “individual risks”. For example, an organization has a large number of almost equally
                               significant customers whose buying patterns are not dependent on each other. We can
                               assume that deviations from the planned sales will be approximately normally
                               distributed. It is therefore in such a case unnecessary to consider each customer
                               individually, but the total turnover can be analyzed. The normal distribution is described
                               by the expected value (m), which indicates what “on average” happens, and standard
                               deviation as a measure of the “usual” dispersion around the expected value.

                               Triangular distribution
                               The triangular distribution can be applied without deep statistical knowledge – an
                               intuitively simple quantitative description of the risk of plan variables, such as a cost
                               position. Only three values for the risk-bearing variables must be specified: the
                               minimum value of a, the probable value b, and the maximum value c. This means that
                               an estimation of probability is not required. This implies through the three specified
                               values and the type of distribution. The description of a risk with these three values is
                               similar to in practice the kind of scenario technique, but probability density for all
                               possible values between the minimum and maximum is here calculated. The following
                               figure shows a triangular distribution as an example of the loss of key personnel
                               (Figure 5).

Figure 5.
Distribution for the loss of
key personnel
                                                       0      20.000     40.000             60.000             80.000 100.000 120.000
The quantification of risk in this case shows a loss of up to e125,000, if a key person                   Practice briefing
would leave the organization. However, there could be no increase in costs. e50,000 is
the most likely cost.
    The expected value of a p  triangular          distribution is calculated ffias: ((a þ b þ c)/3), and
                                  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
the standard deviation as: ða þ b þ c 2 2 ab 2 ac 2 bcÞ=18.
                                      2          2

    In addition to above mentioned, a whole range of probability distributions
exists and is important in risk management practice. For the quantitative description                                 621
of “extreme risks” (such as “crashes” or natural disasters) usually the (generalized)
Pareto-distribution is applied (Zeder, 2007).
    Instead of the direct description of risk through the (monetary) effects within a
planning period (e.g. one year) the description could also be through two probability
distributions, which should be first aggregated: one probability distribution for
frequency of loss and the other for the (also uncertain) amount of loss per claim, which is
common in insurable (event-driven) risks. For the mapping of more complex problems
combination of two distributions may also be appropriate. We can for example describe
a risk by a combination of the binomial distribution and the triangular distribution in a
liability process/suit. First, what is the likelihood that we will lose the process (binomial
distribution). Second, the possible loss amount will be specified given a minimum value,
probability value, and maximum value.
    For the evaluation of the risk we can apply risk effects (losses) occurred in the past,
and use either benchmark values in the industry or self-constructed (realistic) loss
scenarios, which accurately describe and explain possible quantitative impact on the
organization’s performance. As a matter of principle, the impact on the development of
sales and costs are considered.
    So far, probability distributions describe the effect of risk at a point in time or in one
period in the context of the quantitative description of the risk observed. The effect of
many risks is certainly not limited to a date or a period. For example, to capture the
exchange rate risk adequately, the entire uncertain future development of the
underlying (exogenous) risk factors, such as dollar exchange rate, should be taken into
account. The interdependency of the risk effect from period to period is therefore
considered. For example, an (unexpected) change in the dollar exchange rate in 2011
would have an impact on the exchange rate in the following year 2012. The dollar
exchange rate at the end of 2011 is namely the starting rate for 2012. In order to
describe the time evolution of uncertain target parameters or exogenous risk factors,
the so-called “stochastic process” is therefore necessary, which could be described as a
“multi-period probability distributions” (for the stochastic process, see for example
Albrecht and Maurer, 2005).
    The following simple example shows how risks can be described quantitatively.
The risk of potential losses is considered caused in a product-related liability process.
Here two probability distributions are combined. First, the probability is estimated
whether the legal process is lost at all (binomial distribution). Based on an expert
survey the CEO’s estimate the probability to lose the case is 30 percent. The amount of
the compensation payment in case of loss is also uncertain. This is estimated by:
    .
       minimum value of 1 million;
    .
       the likely value of 2 million; and
    .
       maximum value of 5 million (triangular distribution).
JPIF   In the determination of probabilities and bandwidths, different information sources
30,6   (different expert estimates) are used, as the heterogeneity of the expert estimates
       reveals valuable information about the risk perception. It is also possible (and
       often useful) to present the uncertainty about the probability of loss occurring on
       its own (parameter uncertainty). For example, the probability that the process is
       lost could be described also by range of possibilities for this outcome (from 20 to
622    40 percent).
           It should be finally noted that problems occur especially in a situation when data is
       insufficient or there is a need for the use of subjective estimates (Section 2), that is, the
       risk quantification itself must be estimated to be risky. There is therefore a “risk of
       second degree” (“meta risk”). This issue will be explained in detail in section “data
       problems and uncertain probability distributions in risk management”.
           In general terms, there are very flexible ways to describe each kind of risk by
       adequate probability distribution. It is not appropriate to determine a priori the type of
       probability distribution.

       6. Stochastic planning and risk aggregation using Monte Carlo simulation
       The objective of risk aggregation is now to determine the overall risk position of a
       project or an organization. The probability distributions of individual risks and a
       probability distribution of the target return to the organization (e.g. earnings or cash
       flow) will be combined. In a next step the risk measures for the entire organization can
       be determined, which characterize the total risk (Section 6).
           The evaluation of the overall risk enables us to make a statement about whether an
       organization’s risk-bearing capacity is sufficient to carry the risk and thus ensure the
       survival of the organization in the long term. Should the existing risk as identified,
       exceed the risk-bearing capacity of the organization, the additional measure of risk
       management is required.
           The risk aggregations are provided by the simulation, which is described by
       probability distributions of risks in the context of corporate planning, i.e. it is shown in
       each case, which position in the planning (succession planning) may cause dispersion.
       With the help of risk simulation methods (Monte Carlo simulation) a great
       representative number of possible risk-related future scenarios can be calculated and
       analyzed. So that it is possible to draw conclusions on the overall risk volume, the plan
       hedging, and the realistic bandwidth, e.g. the business performance.
           A key benefit of using the Monte Carlo simulation is that it allows the developer to
       achieve enhanced comprehensiveness and understanding on the risk position (Loizou
       and French, 2012).
           The Monte Carlo simulation provides a large “representative sample” of the
       risk-induced possible future scenarios of the organization, which is then analyzed.
       Aggregated frequency distributions result from the realizations of the target returns
       (e.g. earnings). Based on the frequency distribution of the earnings we can directly
       conclude the risk measures, such as capital requirements (RAC) of the organization
       (Section 6). To avoid over-indebtedness the required capital should be at least as much
       as to cover the losses, which may occur.
           The previously described risk aggregation model is always based on the corporate
       plan. Below are two (combinable) variations of presented risk assessment models:
(1) the direct consideration of the uncertainty related to the various planning items        Practice briefing
       (i.e. characterization of planning items with a distribution, such as a normal
       distribution); or
   (2) the separate quantitative description of risk by an appropriate distribution
       function (e.g. amount of loss and probability of event-driven risks) and the
       allocation of this risk in a second step to the planning items, where deviations
       may arise from the plan.
                                                                                                            623

With the “risk factors” approach there is another combined alternative to take risk into
account in the context of plan. In addition to the corporate plan, a model of the corporate
environment with the variables associated to the organization is constructed (Bartram,
1999). The corporate environment is described by exogenous factors such as exchange
rates, interest rates, commodity prices and economic situation (e.g. growth in demand).
For all these exogenous factors of the business environment, forecasts are made to create
a “plan-environment scenario”. The dependence of the plan variables of the organization
on the exogenous factors is captured for example by elasticity. These show how a
(uncertain) change in any risk factor impacts the plan variables (e.g. turnover).
      There are some important advantages of using a risk factors model. First, it greatly
simplifies the correlations (statistical dependence) which are difficult to estimate
amongst the uncertain (risk-bearing) variables in the income statement of an
organization. For instance, if two different types of uncertain costs, K~ 1 and K~ 2 , both
(with different elasticity) are dependent on the common (exogenous) risk factors R~ 1 and
R~ 2 , these two costs are thus correlated. A significant part of the correlations between
individual risks or risk-bearing planning items thus implicitly result from the
description of the dependence of exogenous risk factors in the business environment,
such as economy, exchange rates, and commodity prices.
      The development of simulation-based risk aggregation models (e.g. with Excel and
Crystal Ball simulation software) is therefore not difficult. The following simple example
illustrates the “bandwidth” of the profits of an organization that are determined in the next
fiscal year. The starting point is the very simple income statement shown in the following
figure. The planned turnover (10 million e) is risky and is described by a normal
distribution (standard deviation: 2 million). The variable costs are 50 percent of sales
and fixed costs (including interest expense) are described by a triangular distribution:
minimum value of 4 million, most likely 4.5 million, and maximum 5.5 million. To
aggregate these two risks – revenue and cost – the Monte Carlo simulation is used, which
means that the simulation software will for example calculate outcomes of organizations
future earnings for the 20,000 possible scenarios. The outcomes are presented in Figure 6.
      Two important findings can be observed:
      (1) The expected profit is on average only e0.33 million and thus lying below the
          planned profit of e0.5 million, because with the “fixed cost risk” the “threats”
          overweigh the “opportunities”.
      (2) The aggregate risk volume can be expressed by the amount of loss, for example
          with 95 percent confidence level a loss up to 1.4 million will not be exceeded
          (formally one here speaks of a “value-at-risk”, VaR, see Section 7).
JPIF
30,6

624

Figure 6.
Distribution of earnings
(in the sample case)

                           As seen from the example, the output of risk quantification makes it possible to derive
                           meaningful (unbiased) planned values and the range of possible (negative) deviations
                           from plan.

                           7. Risk measures
                           7.1 Fundamentals
                           Should decisions be made under uncertainty (risk), the alternatives must also be
                           evaluated with regard to their riskiness. Risk measures enable us to compare different
                           risks with different characteristics and with different types of distribution and
                           distribution parameters, such as amount of loss (Albrecht and Maurer, 2005).
                              The traditional risk measures of the capital theory (e.g. CAPM and Markowitz
                           Portfolio) consider the variance or standard deviation (the root of the variance) as
                           volatility measures. That is, they quantify the extent of fluctuations in a risk parameter
                           around the average development (expected value).
                              Variance or standard deviation are relatively easy to calculate and easy to
                           understand. They consider both the negative and positive deviations from the expected
                           value. Most investors are however more interested in the negative deviations. The
                           so-called downside risk measures are based on this approach. The (valuation-relevant)
                           risk is considered as a possible negative deviation from an expected value and thus the
                           downside risk measures only consider these deviations and include the value-at-risk,
                           the Conditional value-at-risk or lower semi-variance (one-LPM2 risk measure).
                              Risk measures can be classified in various ways. One of them is according to the
                           position dependence. Position-independent risk measures (such as standard deviation)
                           quantify the risk as the extent of deviation from a target return. Position-dependent
                           risk measures such as value-at-risk are however depending on the expected value.
                           Often, such a risk measure as “required capital” or “required premium” is considered as
                           risk coverage (Section 7.2).
Therefore, these two types of risk measures can be transformed into each other. For     Practice briefing
example, we apply a position-dependent risk measure to centerd random variable
instead of to a random variable (e.g. earnings). This results in a position-independent
risk measure. As in the calculation of position-dependent risk measures the expected
value is included, these measures can also be interpreted as a kind of risk-adjusted
performance measures.
   The main advantage of a position-independent risk measure is that the “height                        625
information” (expected outcome) and the “risk information” (deviation) are clearly
separated, so that the axes are independent from each other in a risk-return portfolio.
   Position-dependent risk measures are in contrast corresponding more to the
intuitive understanding about risk, since with sufficiently high “expected returns” the
possible deviations lose their importance, and since they do not so strongly lead to a
possible negative deviation from the target return (e.g. minimum expected return).

7.2 Specific risk measures
The value-at-risk (VaR) as a position-dependent risk measure explicitly investigates
the impact of a particularly unfavorable development for the organization. It is defined
as the amount of loss not exceeded within a certain period of time (“holding period”,
e.g. one year) with a fixed probability p (e.g. from a given target rating). Formally,
a value-at-risk is therefore the negative percentile Q of a distribution:
                                 VaR12p ðXÞ ¼ 2Qp ðXÞ
The position-independent counterpart of the value-at-risk is the deviation value-at-risk
(DVAR, or relative VaR), which is known as value-at-risk of X 2 E(X) (Figure 7):
                         DVaR12p ðXÞ ¼ VaR12p ðX 2 EðXÞÞ
The value-at-risk (and the required capital, which can be regarded as VaR in relation to
the organization’s earnings) is a risk measure without taking into account the entire
information of the probability density. What course the density below the desired
quantile (Qp) takes, i.e. in the range of extreme effects (losses), is irrelevant to the
capital requirement. Therefore, information that may be very important could be
neglected. In contrast to the aforementioned, the shortfall risk measures – particularly
the so-called Lower Partial Moments (LPMs) – consider often interesting parts of the

                        LPM1
               CVaR =           + VaR
                        LPM0

                                    DVaR
                         1-PD

                          CVaR Q(X)     E(X)                                                         Figure 7.
                                                                                               VaR, DvaR, CvaR
                                 =VaR
JPIF   probability density from minus infinite up to a given target return (target/upper bound c)
       for the risk evaluation. The understanding about risk reflects the perception of an
30,6   institution, and the threats of the shortfall set by it (such as required minimum rate of
       return). In general, we calculate LPM measure of order m as:
                                   LPM m ðc; XÞ ¼ Eðmaxðc 2 X; 0Þm Þ:
626    In practice, three specific cases are usually considered, namely, the shortfall probability
       (probability of default), i.e. m ¼ 0, the target shortfall or expected shortfall (m ¼ 1), and
       the target shortfall variance (m ¼ 2). In contrast to the variance, at the lower semi-variance
       only negative deviations from the expected value are included in the calculation.
          The aforementioned probability of default p (PD, probability of default), an LPM
       measure of order 0, indicates the probability that a variable (such as shareholders’
       equity) falls below a predetermined threshold value (here, usually zero), and
       characterizes a rating (Gleißner, 2011a):
                               SW ðc; XÞ ¼ LPM 0 ðc; XÞ ¼ PðX , cÞ ¼ PD
       The shortfall risk measures can be categorized into conditional and unconditional risk
       measures.
          While unconditional risk measures (such as the expected shortfall or the shortfall
       probability, SW) ignore the probability of falling below the target, they can flow into the
       calculation of the conditional shortfall risk measures (such as the Conditional value-at-risk).
       The Conditional value-at-risk (CVaR) is the expected value of a risky variable that lies
       below the value-at-risk (VaR12 p). The value-at-risk measures the deviation which is not
       exceeded within a given planning period with a given probability, in contrast to the
       Conditional value-at-risk that indicates which impact is to be expected upon the occurrence
       of this extreme case, i.e. when exceeding the value-at-risk. The Conditional value-at-risk
       takes into account the probability of a “big” deviation and the value of the deviation.
          Overall, it shows that a number of risk measures depend on a given restriction in the
       form of (e.g. by the creditor) a maximum acceptable probability of default p. The risk
       level expressed by risk measures like value-at-risk, Conditional value-at-risk, relative
       value-at-risk (Deviation value-at-risk) is thus dependent on the given rating, which is a
       specific LPM0-risk measure.
          Risk measures with VaR and CVaR can be economically interpreted simply as
       “risk-related capital requirements”.

       8. Consideration of risk information in performance measures
       Real estate development in general represents a very complex, dynamic challenge
       encompassing a variety of practice areas. Methodically adequate evaluation approaches
       as well as a well-grounded knowledge of the development process, related risk aspects
       and their assessment are indispensable for efficient risk management. Stochastic
       calculations enable an additional objectification of risk evaluation. Despite the available
       evaluation methods, the risk evaluation is primarily conducted based on the subjective
       assessment of the respective parties.
          In this respect, the available data and their specific project-related applicability are of the
       utmost importance. As a conclusion, it can be stated that a further establishment of risk
       management concepts as well as supporting instruments on a strategic level would also
       provide the operational business of a company with a significant potential for optimization.
It is the central concern of a value-oriented management that in the preparation of       Practice briefing
corporate decisions the expected returns and risks are weighed against each other. The
following figure shows this basic idea.
    Through the identification, quantitative description, and aggregation of risks of a
project, the total risk (on the x-axis) expressed for example in capital requirements
(VaR) can be compared with the expected return of the project. This quantification of
the risks enables to check whether the project associated with the aggregate total risk                        627
can be paid by the organization (maximum risk line, derived from capital and liquidity
reserves, i.e. risk-bearing capacity). Hence, a higher risk requires a higher amount of
expected profit (or higher returns). That is, the projects should have a favourable
risk-return profile to justify the implementation or investment.
    If we want to position a project or an organization on the risk-return diagram shown
in Figure 8 with one ratio, this will lead us directly to the performance measures.
A performance measure is obtained by the combination of the expected value of the
results (e.g. profit) associated with a risk measure.
    A performance measurement can be carried out either ex ante or ex post. An ex ante
performance measure is used as a projected success measure of the decision
preparation for (or against) an organization’s activity, such as an investment. By doing
so the uncertainty of any future forecast (on a target variable X) is explicitly taken into
account, which is the fundamental of any economic decision.
    Such performance measures are therefore indicators that results from combining
(through a function f ) the expected outcome E(X) (e.g. expected profit) with a suitable
risk measure R(X) such as standard deviation or value-at-risk. The risk measure shows
the extent of possible deviations from the plan:
                                P ea ðXÞ ¼ f ðEðXÞ; RðXÞÞ
                                                  Maximum risk line: Safety-First
         Expected
            profit
                                                              Strategy D

             20%
                                  Invest !
                                                                     Strategy C

                           Stragety B            Strategy A

             10%

                                                                   Do not
                                                                   invest !
                                                                                                            Figure 8.
                                                                                                    Trade-off between
                     0%                 10%                       20%
                                                                                    Risk            earnings and risk
                                                                                                (risk-return trade-off)
                                             (Risk measure: Capital requirements (VaR))
JPIF   In the simplest case there is a performance measure P(X) for the uncertain profits X where
       the expected value is reduced by a risk discount, which is directly dependent on the risk
30,6   measure R(X), e.g. the value-at-risk (of profits) or capital requirements. For example:
                                        PðXÞ ¼ EðXÞ 2 l · RðXÞ
       The deduction of the risk discount (l · R(x)) from the expected value is corresponding to the
628    procedure for the determination of so-called “certainty equivalents”, expressed from the
       perspective of the institution for which secure outcome is equivalent to the uncertain
       income X. If we choose for example the capital requirements as our risk measure, we can
       interpret the variable l and the “price of risk” as imputed (additional) cost of equity. Thus,
       corresponds to the risk discount just the imputed cost of capital or risk costs.
          Enterprise value (capital value/NPV), value added (EVA), and RoRAC or the Sharpe
       ratio (SR) are the performance standards:
                                                    Eðr A Þ 2 r f
                                            SRA ¼
                                                      sðr A Þ
       with:
          rA     ¼ a return on investment.
          rf     ¼ risk-free rate.
          s(rA) ¼ standard deviation or return on investment as risk measure.
       As an alternative to the Sharpe ratio performance measures are to be considered, where
       excess return (in relation to the risk-free investment) is considered in relation to LPM
       risk measures. Such performance ratios are called “Return to Short Fall” (RTS) ratios.
          The enterprise value is also interpreted as a performance measure because it is
       risk-adjusted by discounting the expected future earnings or cash flows. In order to
       consider the model-based calculated value as performance measure, it is necessary that the
       discount rate (or cost of capital) is actually derived from the future risks, and not from the
       historical capital market data (stock returns) within the framework of the so-called Capital
       Asset Pricing Model. In this approach we can regard the discount rate (cost of capital) as
       risk-based requirements for the return of a project or organization, i.e. the risk level is the
       requirement of return on investment (hurdle rate) by calculating the cost of capital. A higher
       amount of risks leads to potentially higher (negative) deviations from the plan or losses,
       resulting in a higher “capital requirements” and thus higher capital costs.
          RAVA stands for “risk adjusted value added”, a performance measure that can be
       interpreted as a position-independent risk measure. Unlike today’s conventional
       performance measures, such as EVA, with this performance measure an adequate and
       planning-consistent risk assessment is carried out (Gleißner, 2011a):
                               RAVA ¼ EðXÞ 2 r f · CE 2 l12p · EKB12p
       RAVA therefore reduces the expected profit (expected operating profit E(X) less the
       risk-free return on capital CE) by a risk discount EKB (risk-adjusted capital, also
       known as RAC) which is commonly employed as a measure of risk capital requirement:
                                           R12p ðxÞ ¼ EKB12p
       The application of the performance measure RAVA is simple. In a simple case study
       for risk aggregation (Section 6) an expected profit of the organization was e0.33 million
(after interest expense, rf · CE) and a risk-adjusted capital (required capital) of            Practice briefing
e1.4 million (value-at-risk under a 5 percent level) was determined.
    Assuming (for simplicity) a risk premium of the capital of 10 percent, in the
“performance assessment” of the organization the imputed cost of capital is 10 percent
£ e1.4 million, i.e. e0.14 million to be considered.
    RAVA is calculated according to:
                                                                                                           629
      RAVA ¼ expected profit 2 10% £ required capital ¼ 0:33 2 10% £ 1:4
           ¼ 0:19 Mio Euro:

9. Conclusion and recommendations
Although being a multi billion industry with high relevance for a multitude of
stake-holders, real estate developers appear to have an unstructured and ad hoc approach
towards the management of risks, and largely rely on individual judgement and
experience (Wiegelmann, 2012a). Real estate developers often base significant
investments on back-of-the-envelope calculations (Gimpelevich, 2011). The lack of
financing availability in the context of the Global Financial Crisis and the downturn in
investment markets have increased exit risks and pricing insecurity for many
development schemes. We expect development organisations, who fail to implement a
risk management system, will find themselves increasingly penalised by the capital
markets and financing partners if not dealing adequately with the identification,
assessment and management of risks. The quantification of risks can provide significant
economic benefits of a risk-based management, especially in supporting decision-making
under uncertainty. The apparent alternative of a non-quantification of risks actually does
not exist, because non-quantified risks are hardly just zero quantified risks.
   The quantification of risks starts with the quantitative description of the risks by an
appropriate probability distribution. As businesses, projects or entire companies are
generally subject to a number of risks; these must be aggregated to determine the overall
risk. This requires the use of Monte Carlo simulation, in which a large representative
sample of risk-bearing possible future scenarios is calculated. Risk-related information
therefore adds value to the “traditional” organization or investment planning. The total
risk the frequency or probability distributions are derived from the so-called
“risk measures” such as standard deviation or value-at-risk. In practice, it is particularly
convenient (based on the value-at-risk) to express the overall level of risk through capital
requirements, that is, the amount of capital as safeguard against risk. In such a way,
a risk-adjusted financing structure of a project or an organization will be determined.
Also the rating (to assess the threat to the organization) or risk-adjusted cost of capital
(as demands on the return) is easily possible to derive.
   The central benefit of quantitative methods in risk management is to enable us to deal
with the trade-off between expected returns and risks in the business decision-making
process. And since the quality of corporate decisions especially in an uncertain
foreseeable future largely determines a real estate development organization’s success,
the quantitative methods of risk management are a key success factor of the company.
                                                                   WernerGleißner
                                               FutureValue Group AG, Germany, and
                                                             ThomasWiegelmann
                                             FRICS, Bond University, Robina, Australia
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       Further reading
       Hoesli, M., Jani, E. and Bender, A. (2006), “Monte Carlo simulations for real estate valuation”,
             Journal of Property Investment & Finance, Vol. 24 No. 2, pp. 102-22.
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