Fig 3 the Efficient FrontierThat any portfolio below the efficient frontier has a lower return than the portfolio on the
efficient frontier vertically above it. The efficient frontier thus dominates all other
portfolios. Applying the dominance rules, only the portfolios on this frontier would be
chosen by investors, as for a given level of expected return or volatility, they represent
the best choice an investor can make. For example, no investor will invest in portfolio Q,
given that for the same level of risk he can obtain a higher return if he invests in portfolio
P (Fig.3).
If we consider the portfolios on the efficient frontier itself, no portfolio is dominated by
any other. How would an investor choose between them? The answer is that the choice
must be based on the investor’s willingness to assume risk. In Fig. 3, we have shown the
portfolio choices of three investors A, B and C. A is a very conservative investor who
wishes to keep his risk low; he chooses a point close to the left end of the efficient
frontier. Investor C is more interested in increasing his return than in containing his risk.
His choice is close to the right end of the efficient frontier. B is not given to such
extremes as A and C; he is a believer in the ‘golden mean’, and chooses a point close to
the middle of the efficient frontier.
It can be shown that the opportunity set must always assume the shape of a broken egg
placed smooth side towards the ‘north-west’, as in Fig 3. For example, if the graph were
to plot with the smooth side pointing towards north-east, as shown in Fig 4, then portfolio
P will completely dominate portfolio Q, since the former has a lower risk and a higher
expected return, so that nobody will ever want to invest in Q, driving this security out of
the market. Therefore, such a shape of efficient frontier is not possible.