Application of Net Cash Flow at Risk in Project Portfolio Selection
Perhaps the best-known and most
commonly used approach to estimate the level of risk is subjective
estimation. Here, we divide the data
into four categories: project cost,
initial required capital, project selling price, and production volume.
Then, by using statistical distributions, we fit the most appropriate
ones for each identified risk.
6. The next step is to generate the
variance–covariance matrix for the
objective data. Because of the interaction among historical data on factors, which derived from the market
and continuing existing relationship
during simulation, the variance–
covariance matrix must be used. If
the variance–covariance matrix is not
generated, there is no real relationship among simulated market factors, which can lead to an improper
7. We then specify the level of confidence (a) to optimize CFaR. Setting
the confidence level is very important
because it is a risk-aversion parameter and the model optimizes CFaR
based on it (the model’s objective
The modeling methodology is
shown in Figure 2 and explained as
1. Determine the prediction horizon
and then divide it into sub-periods.
2. Identify all investable projects of
each sub-period in the prediction
3. Identify all items that can affect
return, such as fluctuations in price,
inflation rate, production volume,
and project cost, and then analyze
the risk of the identified data. The
purpose of this phase is to provide
effective resources to respond to the
risk factors. Two types of data can be
identified: objective and subjective.
4. Objective data are those extracted
from historical data that do not
involve personal feelings. We divide
these data into two categories—
namely, product price and exchange
rate—and then fit the most appropriate distribution for each identified risk by time series models.
5. Subjective data are extracted from
expert judgments or expert opinions
that result from direct interviews.
is made for a time horizon in the future.
This distribution can be used to obtain
information about the worst scenarios
for the cash flow as well as the best ones
(Andrén et al., 2005).
CFaR can be calculated in a fashion
similar to the way VAR is determined.
The main difference is that CFaR uses
the expected cash flow instead of using
portfolio market values (Eydeland &
This study was conducted to improve
portfolio selection modeling based on
real-world problems by introducing the
concept of CFaR and by setting the risk
preference of the decision maker. Chance
constrained programming is used to deal
with the uncertainty of parameters and
also uses financial concepts, such as
covariance matrix, to generate a relationship among them based on real-world
limitations. We tested this model with a
case example (A) and then optimized to
find the best projects in each period. After
analysis of the model results, we used a
further case example (B) to draw conclusions about decisions for diversification.
Figure 1: VaR presentation.