second scenario, the firm decides to
invest in two industries that have the
most negative correlation. As shown in
the correlation matrix (equation 18),
copper and GBP/USD have the most
negative correlation ( 20.605). Also,
copper and aluminum have a high positive correlation (0.869).
To simplify, we disregarded the fact
that different projects have different
returns and supposed instead that three
projects have similar characteristics
from a project return viewpoint. That is,
based on reverse engineering, we consider the return of three projects as equal
to 200,000 monetary units. According to
the last selling price of products derived
from the market, the production volume of project 1 is 25. 27 tons of copper,
the production volume of project 2 is
98.06 tons of aluminum, and the return
of project 3 is 123,708 currencies GBP (a
project invested abroad that its return is
in currency). Therefore, project return
is calculated by the amount of currency
multiplied by the exchange rate to convert
the unit to dollars. The following correlation matrix helps make sense of the
relationship between prices. It should be
noted that correlation among factors is
achieved by their historical price.
this, we investigate the point in a second
case example (B).
Case Example B
In order to better show the effects of
correlation, we modeled two different
scenarios for investing. In each one,
the portfolio is composed of two projects and portfolio return is the simple
sum of the two projects. By modeling
these scenarios, we are able to highlight the importance and impact of different diversification strategies on the
portfolio. In the first scenario, the firm
decides to invest in two industries that
have a high positive correlation (the
biggest number in the matrix). In the
705397 ( 7.053 3 105). Other important
parameters such as standard deviation
and mean are also shown. This means
that, given a confidence level, the firm’s
cash flow in only 5% of the situations is
less than 705397 and the firm’s cash flow
(with a 95% certainty) will not be less
than 705397.
Multiple simulated examples were
run to determine which factors influence
the selection or rejection of projects in
a period. After analyzing the results and
selecting the projects in each period, we
get another important result: In the same
situation, the model selects projects from
the industries that have the least correlation to reduce risk (variance). To illustrate
Industries Projects Investment Period Selling Period
Industry 1 Project 1 1 3
Project 2 1 3
Industry 2 Project 3 1 5
Project 4 2 2
Industry 3 Project 5 4 5
Project 6 3 5
Industry 4 Project 7 — —
Project 8 5 5
Table 3: The determined times by model to invest in and sell the projects.
Figure 3: Simulation of portfolio cash flow.
Values in Millions
0.5
5
1.0
0
0.9
5
0.9
0
0.8
5
0.8
0
0.7
5
0.7
0
0.6
5
0.6
0
1.0
5
7
8
6
5
4
3
2
1
0
Val
ue
s×
1
0
– 6
5.0% 95.0%
0.7053 +∞
Minimum
Maximum
Mean
Std Dev
Values
586,763.01
1,034,951.09
795,264.75
55,770.34
30000