Chapter 7 • Portfolio theory and its relevance to real investment decisions
Figure 7.7
The efficient frontier
with borrowing and
lending
The graph indicates how most investors will be able to reach a higher level of utility as a
result of the existence of the availability of borrowing and lending.Looking at the utility curves shows that individual Z is rather more risk-averse than
individual X. The latter is prepared to accept much more risk to achieve any given
level of expected return than is the former. Individual X is still risk-averse and there-
fore needs increasing amounts of expected return for each additional increment of
risk, but less so than individual Z.
Irrespective of their personal preferences, all of the investors (X, Y and Z) whose
attitudes are represented in Figure 7.6 would reach the highest level of utility
(satisfaction) by investing in some portfolio that lies along the efficient frontier (EE).
No one would want to invest in individual securities or portfolios lying below or to
the right of the efficient frontier because these all have some specific risk. It would be
possible either to obtain a higher return or have lower risk by investing in a portfolio
lying on EE.A risk-free asset
We now make another assumption, which is that there is a financial market that will
lend to and borrow from all investors. It will do this in unlimited amounts of money,
at an equal, risk-free rate(rf). This would transform the position from that shown in
Figure 7.6 to that of Figure 7.7. Now all investors would locate on the straight line rfS.
Investors whose preferences are similar to those of individual Z would choose to
put some wealth into risky securities and lend the remainder at the risk-free rate (see
Figure 7.7). Individual Y would invest entirely in risky securities despite the existence
of the risk-free asset. This is because this person’s utility curve just happens to be‘
‘