Page 84 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 2: Risk and Return

If the securities are equally weighted, how much is the risk and return of the portfolio of these Notes
three securities?
Solution:

Expected Portfolio Return
= (25 × 1/3) + (22 × 1/3) + (20 × 1/3) = 22.33%

2
2
2
2
2
(30) (1/3) +(26) +(24) (1/3) + 2(1/3)(-0.5)(30)(26) 2(1/3)(1/3)(0.4)(26)(24)
2 =
P 2(1/3)(1/3)(0.6)(30)(24)
2 =100 + 75.11 + 64 – 86.67 + 55.47 + 96 = 303.91
P
= 303.91 = 17.43%
P
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
B AB
W = 2 2
A Cov
A B AB
We can also calculate the proportion to be invested (W ) in Security A.
A
16.31 2 84 182.02
= 2 2 = = 0.875
(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.
2.6 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 illustrates the result of diversifying to reduce risk.

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