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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- Spring '16
- Standard Deviation, Variance, Supertech, Slowpoke