Efficient Frontier

# Efficient Frontier - 10.4 The Efficient Set for Two Assets...

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10.4 The Efficient Set for Two Assets Our results for expected returns and standard deviations are graphed in Figure 10.2. 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. The box or "El" in the graph represents a portfolio with 60 percent invested in Super- tech and 40 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 10.3. Figure 10.2 Expected Returns and Standard Deviations for Supertech, Slowpoke, and a Portfolio Composed of 60 Percent in Supertech and 40 Percent in Slowpoke Figure 10.3 Set of Portfolios composed of Holdings in Supertech and Slowpoke (correlation between the two securities is -0.1639) Expected return (%) Supertech b Slowpoke I I I I Standard 11.50 15.44 25.86 deviation (%) Expected return on portfolio (%) I I I I 1 1.50 25.86 deviation of portfolio's return (%) Portfolio 1 is composed of 90 percent Slowpoke and 10 percent Supertech (p = -0.1639). Portfolio Zis composed of 50 percent Slowpoke and 50 percent Supertech (p = -0.1639). Portfolio 3is composed of 10 percent Slowpoke and 90 percent Supertech = -0.1639). Portfolio l'is composed of 90 percent Slowpoke and 10 percent Supertech (p = 1). Point MY denotes the minimum variance portfolio. This is the portfolio with the lowest possible variance. By definition, the same portfolio must also have the lowest possible standard deviation.

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Consider portfolio 1. This is a portfolio composed of 90 percent Slowpoke and 10 p cent Supertech. Because it is weighted so heavily toward Slowpoke, it appears close to 1 Slowpoke point on the graph. Portfolio 2 is higher on the curve because it is composed 50 percent Slowpoke and 50 percent Supertech. Portfolio 3 is close to the Supertech pol 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 argued that the diversification effect occurs whenever the correlation between the two securities is below 1. The correlation between Supertech and Slowpoke is -0.1639. The diversification effect can be illustrated by comparison with the straight line between the Supertech point and the Slowpoke point. The straight line represents points that would have been generated had the correlation coefficient between the two securities been 1. The diversification effect is illustrated in the figure because the curved line is always to the left of the straight line. Consider point 1'.
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## This note was uploaded on 03/02/2011 for the course BMGT 340 taught by Professor White during the Spring '08 term at Maryland.

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Efficient Frontier - 10.4 The Efficient Set for Two Assets...

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