Quantitative Risk Analysis


Quantitative risk
analysis is a way of numerically estimating the probability that a project will
meet its cost and time objectives. Quantitative analysis is based on a
simultaneous evaluation of the impact of all identified and quantified risks.
The result is a probability distribution of the project’s cost and completion date based on the risks in the project.

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The quantitative
methods rely on probability distribution of risks and may give more objective
results than the qualitative methods, if sufficient current data is available.
On the other hand, qualitative methods depend on the personal judgment and past
experiences of the analyst and the results may vary from person to person.
Hence the quantitative methods are preferred by most analysts.
risk analysis considers the range of possible values for key variables, and the
probability with which they may occur. Simultaneous and random variation within
these ranges leads to a combined probability that the project will be
unacceptable Quantitative risk analysis involves statistical techniques that
are most easily used with specialized software. Quantitative risk analysis is
to assign probabilities or likelihood to the various factors and a value for
the impact then identify severity for each factor.


When thorough
quantitative risk analysis is necessary it can take two alternative approaches
(Kuismanen, 2001):


1.   Risks can be
quantified as individual entities while looking at the big picture. This way
can include the cumulative effects (to certain accuracy) into each individual
risk and thus make more accurate estimations of the net value of the risks.


Alternatively modeling the mathematical properties of
the interrelations from the bottom up can be started and then calculate the net
impact of each risk including the effects of interrelations.


In Figure 2.4 the basic steps of a
quantitative risk analysis and a simplified relationship between risk analysis,
risk assessment and risk management is presented.


·      Basic Steps of quantitative risk analysis


As discussed previously, the aim of
risk analysis is to determine how likely an adverse event is to occur and the
consequences if it does occur. When quantitative risk analysis is to be done,
it is attempted to describe risk in numerical terms. To do this, it should go
through a number of steps:


1.   Define the
consequence; define the required numerical estimate of risk.


2.   Construct a
pathway; consider of all sequential events that must occur for the adverse
event to occur.


3.   Build a model –
Collect data; consider each step on the pathway and the corresponding variables
for those steps.

4.   Estimate the
risk; once the model has been constructed and the data collected the risk can
be estimated. Included in this estimation will be an analysis of the effects of
changing model variables to reflect potential risk management strategies.


5.   Undertake a
sensitivity and scenario analysis; Undertaking a risk analysis requires more
information than for sensitivity analysis.


·      Methods of Quantitative Risk Analysis


Any specific risk analysis technique
is going to require a strategy. It is best to begin by providing a way of
thinking about risk analysis that is applicable to any specific tool might be


·      Probability Analysis is a tool in investigating problems which do not have a
single value solution, Monte Carlo
Simulation is the most easily used form of probability analysis.


·      Monte Carlo Simulation is presented as the technique of
primary interest because it is the
tool that is used most often.


·      Sensitivity Analysis is a tool that has been used to great extent by most
risk analysts at one time to another.


·      Breakeven Analysis is an application of a sensitivity analysis. It can be
used to measure the key variables
which show a project to be attractive or unattractive.


·      Scenario Analysis is a rather grand name for another derivative of
sensitivity analysis technique which
tests alternative scenarios; the aim is to consider various scenarios as



Sensitivity Analysis and Monte Carlo
Simulation are discussed briefly:



·      Sensitivity Analysis


Sensitivity analysis is a
deterministic modeling technique which is used to test the impact of a change
in the value of an independent variable on the dependent variable. Sensitivity
analysis identifies the point at which a given variation in the expected value
of a cost parameter changes a decision. Sensitivity analysis is performed by
changing the values of independent risk variables to predict the economic
criteria of the project. Sensitivity analysis is an interactive process which
tells you what effects changes in a cost will have on the life cycle cost.
Sensitivity Analysis is the calculating procedure used for
prediction of effect of changes of input data on output results of one model. It
does not aim to quantify risk but rather to identify factors that are risk


Sensitivity analysis enables the
analyst to test which components of the project have the greatest impact upon
the results, thus narrowing down the main simplicity and ability to focus on
particular estimates. The advantage of sensitivity analysis is that it can
always be done to some extent. Specific scenarios of interest can be reasonably
well described. Extreme outcomes, like the maximum or minimum possible costs,
can often be estimated.



































Figure 2.4 Simplified relationship
between risk analysis, risk assessment and risk management.


The major disadvantage of
sensitivity analysis is that the analyst usually has no idea how likely these
various scenarios are. Many people equate possible with probable, which is not
the case with sensitivity analysis.




·      Monte Carlo Simulation


Simulation is a probability-based
technique where all uncertainties are assumed to follow the characteristics of
random uncertainty. A random process is where the outcomes of any particular
process are strictly a matter of chance. The Monte Carlo process is simply a
technique for generating random values and transforming them into values of
interest, the methods of generating random or pseudo random numbers are more
sophisticated now and the mathematics of other distributions is more complex.
Different values of risk variables are combined in a Monte Carlo simulation.
The frequency of occurrence of a particular value of any one of the variables
is determined by defining the probability distribution to be applied across the
given range of values. The results are shown as frequency and cumulative
frequency diagrams. The allocation of probabilities of occurrence to each risk
requires the definition of ranges for each risk. Following are the risk
analysis simulation steps:


1.   Start with a
project estimate done for each cost account.


2.   Decide on the
most likely cost, pessimistic costs, and optimistic costs.


3.   Insert data
into simulation software, then run the model.


4.   Determine
contingencies based on desired risk level.


5.   Prioritize “risky” cost accounts for risk response planning.



This method of sampling (i.e. random
sampling) will, lead to over- and under-sampling from various parts of the
distribution. In practice, this means that in order to ensure that the input
distribution is well represented by the samples drawn from it, a very large
number of iterations must be made. In most risk analysis work, the main concern
is that the model or sampling scheme we use should reproduce the distributions
determined for the inputs.



2.6   Risk Response Practices



PMI (1996) suggested three ways of
responding to risk in projects, they are as follows:


·      Avoidance:
eliminating a specific threat, usually by eliminating the cause. The project
management team can never eliminate all risks, but specific risk events can
often be eliminated.


·      Mitigation:
reducing the expected monetary value at risk events by reducing the probability
of occurrence (e.g., using new technology), reducing the risk event value
(e.g., buying insurance), or both.


·      Acceptance:
accepting the consequences. Acceptance can be active by developing a
contingency plan to execute should the risk event occur or passive by accepting
a lower profit if some activities overrun.


Abu Rizk (2003) suggested some
actions to be taken in response to residual risks. Actions can include:


·      Reduce
uncertainty by obtaining more information, this leads to re-evaluation of the
likelihood and impact.


·      Eliminate or
avoid the risk factor through means such as a partial or complete re-design, a
different strategy or method etc.


·      Transfer the
risk element by contracting out affect work.


·      Insure against
the occurrence of the factor.


·      Abort the
project if the risk is intolerable and no other means can be undertaken to
mitigate its damages.



2.6.1 Risk Avoidance


Risk avoidance is sometimes referred
to as risk elimination. Risk avoidance in construction is not generally
recognized to be impractical as it may lead to projects not going ahead, a
contractor not placing a bid or the owner not proceeding with project funding
are two examples of totally eliminating the risks. There are
a number of ways through which risks can be avoided, e.g. tendering a very high
bid; placing conditions on the bid; pre-contract negotiations as to which party
takes certain risks; and not bidding on the high risk portion of the contract
(Flanagan & Norman, 1993).


2.6.2 Risk Transfer


This is essentially trying to
transfer the risk to another party. For a construction project, an insurance
premium would not relieve all risks, although it gives some benefits as a
potential loss is covered by fixed costs (Tummala & Burchett, 1999) Risk transfer
can take two basic forms:


·      The property or
activity responsible for the risk may be transferred, i.e. hire a subcontractor
to work on a hazardous process;


·      The property or
activity may be retained, but the financial risk transferred, i.e. by methods
such as insurance and surety.



2.6.3 Risk Retention


This is the method of reducing
controlling risks by internal management (Zhi, 1995); handling risks by the
company who is undertaking the project where risk avoidance is impossible,
possible financial loss is small, probability of occurrence is negligible and
transfer is uneconomic (Akintoyne & MacLeod,1997). The risks, foreseen or
unforeseen, are controlled and financed by the company or contractor. There are
two retention methods, active and passive;


a.   Active retention (sometimes referred to as self-insurance) is a
deliberate management strategy after
a conscious evaluation of the possible losses and costs of alternative ways of
handling risks.


b.   Passive retention (sometimes called non-insurance), however, occurs
through negligence, ignorance or absence
of decision, e.g. a risk has not been identified and handling the consequences
of that risk must be borne by the contractor performing the work.



2.6.4    Risk


This is a general term for reducing
probability and/or consequences of an adverse risk event. In the extreme case,
this can lead to eliminate entirely, as seen in “risk avoidance”.
However, in reduction, it is not sufficient to consider only the resultant
expected value, because, if potential impact is above certain level, the risk
remains unacceptable.