related questions need to be answered by a good portfolio manager. In this section we
proceed to provide answers to such questions.
Dominant Portfolios
The notion of dominance is based on two very easily understood statements: (i) if two
portfolios have identical expected return, then investors would choose the one with lower
volatility of return (measured through s), (ii) if two portfolios have identical volatility of
return, then investors would choose the one with higher expected return. Let us once
again consider our earlier illustration of securities X and Y on planet Earth, in which the
expected returns on securities X and Y are 20% and 30% respectively and their sās are,
10% and 16% respectively, with the coefficient of correlation between the returns of X
and Y being 0.5.
Neither share dominates the other since X has lower return and Y has lower risk. If
forced to choose between X an Y, some investors may choose X and some Y, depending
on the extent of risk they are willing to assume. But the situation changes when we look
at the portfolio combining X and Y in a ratio of 9:1. In Table 7.1, we see that when we
invest 90% in share X and 10% in Share Y, the expected return is 21% and the s is
9.90%. This portfolio dominates share X which has a lower return of 20% and portfolio
dominates share X which has a lower return of 20% and a higher risk of 10%. The
dominance principle allows us to say that no investor would invest 100% in share X.
This example involved only two securities. Conceptually, the notion of dominance can
be extended to all portfolios that are possible, by combining all the risky securities
available in the market, in various proportions. The result can be shown graphically as in
Fig 3, where return is on the vertical axis and risk on the horizontal axis. The enclosed
area in the figure is the opportunity set, i.e., the set of all possible portfolios. The upper
(concave) part of the boundary of the opportunity set of portfolios is known as the
efficient set or efficient frontier. It is visually clear