BUSF_A01.qxd

(Darren Dugan) #1
Portfolio theory

Figure 7.4
The risk /return
profiles of various
portfolios of
securities A and B,
with differing
assumptions
regarding the
correlation
coefficient


For example, all of the points along the line connecting A and B, labelled R=−0.5, represent
the risk and return of a portfolio containing some combination of securities A and B,
assuming a correlation coefficient of −0.5 between the two securities.

portfolios of them would do nothing to reduce risk, since the risk of the portfolio
is simply a linear combination of the risks of the constituent securities. This is evid-
enced by the straight line connecting A and B, representing the profile of expected
return/risk for R =+1 in Figure 7.4. In reality, securities with positive, but less than
perfect positive, correlation are what we tend to find. To that extent, column 6 of Table
7.1 is the most realistic. Here the correlation coefficient is +0.5, and combining A and
B provides some reduction in the total risk but by no means total elimination of it.
That part of the risk that reduces when A and B are combined in a portfolio is
specific risk. As we saw from Figure 7.1, combining two securities far from exhausts
the possibilities of specific risk reduction. Introducing further securities in appropriate
combinations into the portfolio would reduce the risk still further.

Extending the range of investments
Figure 7.5 shows three more securities, C, D and E, brought into the reckoning. The
various curved lines show the expected return/risk profiles of various combinations
of any two of the five securities. The line XB furthest to the top left of the graph shows
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