BUSF_A01.qxd

Portfolio theory

Figure 7.6
The efficient frontier

Each point along the line EE represents the risk /return profile of some portfolio that is not

subject to any specific risk. The curves UxUx, UyUyand UzUzare the utility curves of three

different individuals. The graph indicates that each individual will seek to hold a different

portfolio of securities.

or all of the securities available in the economy as a whole. Efficiencyin this context

means that there is no specific (unsystematic) risk present; it has all been diversified

away.

None of the many portfolios represented by the efficient frontierhas any specific

risk; if they did, it would be possible to diversify further and get rid of it, thus push-

ing the frontier further to the top left.

Utility

Let us remind ourselves of what we discussed in Chapter 6 on the subject of utility. It

is possible (in theory at least), in respect of any particular individual and of any two

related factors, to represent that individual’s preferences as regards the trade-off

between the factors by a set of utility curves. If we assume both that investors are risk-

averse and that they are expected utility-of-wealth maximisers, then they would have

utility curves similar to those depicted in Figure 7.6 (UxUx, UyUyand UzUz).

Note that each of these three utility curves relates to different individuals (X, Y

and Z), all of whom are prepared to take on some risk, but who require compensation

in the form of increased expected returns for doing so. In each case, the investors

whose attitudes are depicted are risk-averse and, therefore, require increasingly large

increments in expected return for each successive increment of risk that they are pre-

pared to accept. This is why each of these curves slopes upwards to the right.

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