point of view using historical data. They
used a Monte Carlo simulation–based
model to get a measure of downside risk
for different macroeconomic variables.
Their method is valuable when the market is stable for a long period of time.
The main contribution of this study
is that, for the first time, an application of CFaR is defined in PPS in which
financial concepts, such as price fluctuations and the correlation among
projects (assets) that exist in the portfolio, are considered important aspects of
portfolio risk management.
Unlike existing approaches in the
literature, which have focused only on
the risk of a single project, the main
concept of portfolio management is to
mitigate total risk, keeping in mind that
the simple sum of single-project risks
can be substantially different from the
overall risk of a portfolio. Therefore,
companies may fail to choose the optimal combination of risk and return for a
portfolio when projects are individually
considered, regardless of the correlation among them. The review of the literature does not reveal any application
of CFaR or similar tools in PPS.
Cash Flow at Risk
Using financial concepts to incorporate
risk in the project portfolio analysis is the
backbone of this study. Risk quantitative
measures allow decision makers to organize and compare investment schemes.
As a straightforward risk measure, Value
at Risk (VaR) is the most common way
to assess the potential loss of a portfolio
over a specified trading horizon and
with a given confidence level. If is
the selected confidence level, VaR corresponds to the 1 2 lower-tail level
(Jorion, 2007). Schematic VaR is shown
in Figure 1, in which represents the
confidence level (Du & Li, 2008).
The VaR can be achieved by simulating percent of the resulting return
distribution. An alternative for the VaR
in nonfinancial firms is CFaR. Firms use
the CFaR to measure the risk of receiving less than the expected cash flow.
The distribution of operating cash flow
Damghani and Tavana (2014) developed
an integrated approach for sustainable
and strategic PPS, which is composed
of two distinct but interrelated modules.
In the first module, they used strategic
planning and sustainability concepts to
select a set of promising projects. In the
second module, they used a PPS pro-
cedure to choose among the promising
projects identified in the first module.
Dou et al. (2014) proposed an integrated
technology-push and requirement-pull
model to focus on the problem of select-
ing an appropriate portfolio from sev-
eral candidate multifunction weapon
systems. Paquin, Tessier, and Gauthier
(2015) applied a probabilistic approach
to project portfolio risk diversification
and defined a project’s operational risk
by its probability of loss; they showed
conditions in which risk management
can help lower operational risk.
In the second part of the literature
review, Stein et al. (2001) proposed a
top-down approach to focus on over-
all cash flow fluctuations. They applied
the comparable-based method for
estimating CFaR and used a statisti-
cal methodology to predict probability
distribution for operating cash flow.
After that, Andrén, Jankensgård, and
Oxelheim (2005) estimated the sensitiv-
ity of cash flow from a macroeconomic
Some articles have proposed optimiz-
ing both risk and return simultaneously
(Chang et al., 2000; Maringer & Kellerer,
2003; Xia et al., 2000). In such articles, an
objective function has been developed with
a weighting parameter , usually known
as the risk-aversion parameter. Applying
the risk-aversion parameter, the objective
function can be updated as follows:
max( 12 )
The underlying assumption of modern portfolio theory is that decisions
are based on a tradeoff between return
and risk. One way to compute the return
is to measure the expected value of
the probability distribution of payoffs
for the assets or stocks involved in the
portfolio. Similarly, risk is measured by
the standard deviation or the variance
of the payoff distributions (Walls, 2004).
The above models can be applied to
financial assets to enable practitioners
to achieve lower risk levels with higher
expected returns. However, such models
are not sufficiently applicable in project
portfolio analysis because constraints
and relations are completely different from those in financial portfolios
(Archer & Ghasemzadeh, 1999). There
are many different techniques that can
help estimate, evaluate, and choose
projects for a portfolio. Some related
studies have been published; those are
examined in the following sections.
The literature review is presented in
two sections: first, the literature on project portfolio selection (PPS), and second,
the literature on cash flow at risk (CFaR).
Ghasemzadeh and Archer (2000)
proposed a decision support system that follows the steps of Archer
and Ghasemzadeh’s (1999) integrated
framework for project portfolio management (PPM). Gueorguiev, Harmon, and
Antoniol (2009) developed a software
project planning model formulated as
a bi-objective optimization problem.
Sak and Haksöz (2011) introduced a
copula-based simulation model for
supply portfolio risk in the presence
of dependent breaches of contracts.