Page 85 - DMGT207_MANAGEMENT_OF_FINANCES

Management of Finances

Notes

Notes Optimal Portfolio (Two Assets)

The investor can minimise his risk on the portfolio. Risk avoidance and risk minimisation
are the important objectives of portfolio management. A portfolio contains different
securities; by combining their weighted returns we can obtain the expected return of the
portfolio. A risk-averse investor always prefers to minimise the portfolio risk by selecting
the optimal portfolio. The minimum risk portfolio with two assets can be ascertained as
follows:

¶ 2 – Cov
W = B AB
A ¶ A 2 + ¶ B 2 – Cov AB
In continuation to illustration 9 we can calculate the proportion to be invested (W ) in
A
Security A.
2
16.31 – 84 182.02
= = = 0.875
2
2
(10.49 + 16.31 ) – (2×84) 208.06
Therefore, 87.5% of funds should be invested in Security A and 12.5% should be invested
in Security B, which represents the optimal portfolio.
Self Assessment

State whether the following statements are true or false:

10. The risk of a security is measured in terms of variance or standard deviation of its return.
11. Risk minimization is the only objective of portfolio management.

4.8 Portfolio Diversification and Risk

In an efficient capital market, the important principle to consider is that, investors should not
hold all their eggs in one basket; investor should hold a well-diversified portfolio. In order to
understand portfolio diversification, one must understand correlation. Correlation is a statistical
measure that indicates the relationship, if any, between series of numbers representing anything
from cash flows to test data. If the two series move together, they are positively correlated; if the
series move in opposite directions, they are negatively correlated. The existence of perfectly
correlated especially negatively correlated-projects is quite rare. In order to diversify project
risk and thereby reduce the firm's overall risk, the projects that are best combined or added to
the existing portfolio of projects are those that have a negative (or low positive) correlation with
existing projects. By combining negatively correlated projects, the overall variability of returns
or risk can be reduced. The Figure 4.3 illustrates the result of diversifying to reduce risk.
It shows that a portfolio is containing the negatively corrected projects A and B, both having the
same expected return, E, but less risk (i.e. less variability of return) than either of the projects
taken separately. This type of risk is sometimes described as diversifiable or alpha risk. The
creation of a portfolio by combining two perfectly correlated projects cannot reduce the portfolio's
overall risk below the risk of the least risky project, while the creation of a portfolio combining
two projects that are perfectly negatively correlated can reduce the portfolio's total risk to a
level below that of either of the component projects, which in certain situations may be zero.

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