7. In Dode’s case:
The portfolio’s standard deviation will be at a maximum when the correlation between securities A and B is 1. That is:
7. If the efficient set were not concave, it would be possible to construct portfolio that dominate
portfolios on the efficient set. By definition, the efficient set contains portfolios that offer maximum expected return for given levels of risk and minimum risk for given levels of expected return. Yet if offer lower risk for a given expected return or higher expected return for a given level of risk, then the efficient set portfolios are not truly “efficient” –a logical inconsistency.
That one could construct such portfolios if the efficient set were not concave can be seen by referring to the situation in which all securities had correlations of 1. In this case, combination of two portfolios on the efficient set would lie on a straight line. If the efficient set had a “dent” in it, it would be possible to produce portfolios that lay to the northwest of the this “dent”. Because securities do not have correlation of 1, combination of efficient portfolios along the “dent” will lie even further to the northwest, again dominating the efficient portfolios and producing the logical inconsistency referred to above.
14. The market risk of a portfolio depends on events that influence all securities to some
degree. That is these events are systematic. Because all securities are affected by these systematic events, diversifying a portfolio will not reduce exposure to them. Only if the securities added to a portfolio had lower sensitivities to systematic events would diversification reduce market risk. But there is no reason to assume that randomly selected securities will have such lower sensitivities.
The unique risk of a portfolio depends on events specific to individual securities comprising the portfolio. These events are systematic in the sense that an event that impacts one security (in either a good or bad sense) is not expected to impact other securities. As a result forming a diversified portfolio tends to cause the net impact of these unsystematic events to cancel each other out. The more diversified is the portfolio, the greater will be this canceling effect, and the lower is the portfolio’s unique risk.
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