above the standard deviation of the index itself though a few of the securities

# Above the standard deviation of the index itself

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above the standard deviation of the index itself, though a few of the securities could have lower standard deviations than that of the index. Table 11.3 Standard Deviations for Standard & Poor’s 500 Index and for Selected Stocks in the Index
11.4 The Efficient Set for Two Assets Our results for expected returns and standard deviations are graphed in Figure 11.2 . The figure shows a dot labeled Slowpoke and a dot labeled Supertech. Each dot represents both the expected return and the standard deviation for an individual security. As can be seen, Supertech has both a higher expected return and a higher standard deviation. Figure 11.2 Expected Returns and Standard Deviations for Supertech, Slowpoke, and a Portfolio Composed of 60 Percent in Supertech and 40 Percent in Slowpoke percent invested in Slowpoke. You will recall that we previously calculated both the expected return and the standard deviation for this portfolio. The choice of 60 percent in Supertech and 40 percent in Slowpoke is just one of an infinite number of portfolios that can be created. The set of portfolios is sketched by the curved line in Figure 11.3 . Figure 11.3 Set of Portfolios Composed of Holdings in Supertech and Slowpoke
(correlation between the two securities is –.1639 Consider portfolio . This is a portfolio composed of 90 percent Slowpoke and 10 percent Supertech. Because the portfolio is weighted so heavily toward Slowpoke, it appears close to the Slowpoke point on the graph. Portfolio is higher on the curve because it is composed of 50 percent Slowpoke and 50 percent Supertech. Portfolio is close to the Supertech point on the graph because it is composed of 90 percent Supertech and 10 percent Slowpoke. There are a few important points concerning this graph: 1. We previously argued that the diversification effect occurs whenever the correlation between two securities is below 1. The correlation between Supertech and Slowpoke is –.1639. The straight line in the graph represents points that would have been generated had the correlation coefficient between the two securities been 1. Note that the curved line is always to the left of the straight line. Consider point 10 percent in Supertech the correlation between the two were exactly 1. There is no point has the same expected return as point Figure 11.3 .) Though the straight line and the curved line are both represented in Figure 11.3 , they do not simultaneously exist in the same world. straight line exists. In other words, though an investor can choose between different points on the line. 2. The point MV represents the minimum variance portfolio. This is the portfolio with the lowest possible variance. By definition, this portfolio must also have the lowest possible standard deviation. (The term is standard in the literature, and we will use that term.

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