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Efficient Portfolios

M noted above, the first step or the technical aspect of optimal portfolio selection is to determine risk-return opportunities available: to an investor, This is also referred to as the determination of the feasible set of portfolio at the portfolio opportunity set or the minimum-various portfolio opportunity set (not to be confused the minimum-variance portfolio of two risky asset, as discussed earlier). Graphically, these are summarized by the minimum-variance frontier of risky assets. Each point along the minimum-variance frontier represents the lowest possible variance that be attained for a given portfolio's expected return, The point to the left on the minimum-variance frontier represents the minimum variance portfolio. Similarly, the highest point represents the global maximum return portfolio, The line segment between the minimum variance portfolio and global maximum return portfolio condenses

the efficient frontier. It represents efficient portfolios, that is, portfolios having maximum return at each level of risk (standard deviation). Efficient portfolios dominate all other portfolios and individual assets, which lie below the efficient frontier. By definition, dominant portfolios offer maximum return for the given level of risk or, conversely, the minimum risk for the selected rate of return.

It may be noted that the efficient frontier is convex towards the vertical axis (axis of expected return) as all assets have a correlation between positive units and negative unity. It may be recalled from the discussion on portfolio diversification that assets with perfect positive correlation can only generate a linear combination of risk and return. The efficient frontier can never be concave to the vertical axis.
Delineation of the efficient frontier through the Markowitz portfolio analysis discussed above rests on four basic assumptions about asset selection behavior of investors.

(a) The rate of return from an investment is the most important outcome. Investors conceptualize the possible rates of return from an investment as a probability distribution of rates of return either consciously or subconsciously.
(b) Investors are averse to risks. They seek the highest level of return for a given risk class.
(c) Investors estimate risk in terms of the variability of expected returns.
(d) Investors base their decisions solely on two decision parameters expected return and variance (or its square root standard deviation):

Investors who conform to the preceding assumptions are termed Markowitz diversifies: They prefer efficient frontier portfolios.