An understanding of this formula is worthwhile. Although it refersto a portfolio of only two securities, it has great generality, since groupsof securities can be considered as a single security in thinking aboutand analyzing the problems of portfolio management. For example,if one is interested in understanding what the addition of a security does to the variance of an existing portfolio, one can think of theexisting portfolio as a single security. The simple formula then hasgreat expository power.A line which indicates theaverage relationship for these four times. Thisline has been drawn in such a way that the squared vertical distancesof the points from the line are minimized and the line is appropriately named a least-squares regression line.
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In order to see how different values of the covariance or correlationaffect the variance of a portfolio, consider the following simple examples: Assume that two assets (single securities or portfolios) havethe same rates of return and variances and that equal amounts areinvested in each. If the rates of return are 5 percent and the variancesare 2 percent, the expected return on the portfolio is 5 percent.
It has been seen that the attractiveness of a portfolio depends upon both its expected return and its riskiness. Risk, as measured by the variance in rates of return on a portfolio, depends upon the variances of the individual securities and the covariances of each security with each other security. Now it is possible to understand more fully what is meant by an efficient portfolio.