The objective of efficient portfolio diversification is to achieve an overall standard deviation lower than that of its component parts without compromising overall return.

In an ideal world portfolio theory should enable:

- Investors (private or institutional) who play the stock market to model the effects of adding new securities to their existing spread.

- Companies to assess the extent to which the pattern of returns from new projects affects the risk of their existing operations.

For example, suppose there is a perfect positive correlation between two securities that comprise the market, or two products that comprise a firm's total investment. In other words, high and low returns always move sympathetically. It would pay the investor, or company, to place all their funds in whichever investment yields the highest return at the time. However, if there is perfect inverse correlation, where high returns on one investment are always associated with low returns on the other and vice versa, or there is random (zero) correlation between the returns, then it can be shown statistically that overall risk reduction can be achieved through diversification.

According to Markowitz (1952), if the correlation coefficient between any number of investments is less then one (perfect positive), the total risk of a portfolio measured by its standard deviation is lower than the weighted average of its constituent parts, with the greatest reduction reserved for a correlation coefficient of minus one (perfect inverse).

Thus, if the standard deviation of an individual investment is higher than that for a portfolio in which it is held, it would appear that some of the standard deviation must have been diversified away through correlation with other portfolio constituents, leaving a residual risk component associated with other factors.

Indeed, as we shall discover later, the reduction in total risk only relates to the specific risk associated with micro-economic factors, which are unique to individual sectors, companies, or projects. A proportion of total risk, termed market risk, based on macro-economic factors correlated with the market is inescapable.

The distinguishing features of specific and market risk had important consequences for the development of Markowitz efficiency and the emergence of Modern portfolio Theory (MPT) during the 1960's. For the moment, suffice it to say that whilst market risk is not diversifiable, theoretically, specific risk can be eliminated entirely if all rational investors diversify until they hold the market portfolio, which reflects the risk-return characteristics for every available financial security. In practice, this strategy is obviously unrealistic. But as we shall also discover later, studies have shown that with less than thirty diversified constituents it is feasible to reach a position where a portfolio's standard deviation is close to that for the market portfolio.

Of course, without today's computer technology and sophisticated software, there are still problems, as we observed in previous Chapters (PTFA and PTFAE). The significance of covariance terms in the Markowitz variance calculation are so unwieldy for a well-diversified risky portfolio that for most investors, with a global capital market to choose from, it is untenable. Even if we substitute the correlation coefficient into the covariance of the portfolio variance, the mathematical complexity of the variance-covariance matrix calculations for a risky multi-asset portfolio still limits its applicability. So, is there an alternative?

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