3.
Students often confuse the SML in
Figure 11.11
with line
in
Figure
11.9
. Actually, the lines are quite different. Line
traces the efficient set of portfolios formed from
both risky assets and the riskless asset. Each point on the line represents an entire portfolio. Point
is a portfolio composed entirely of risky assets. Every other point on the line represents a
portfolio of the securities in
combined with the riskless asset. The axes on
Figure 11.9
are the
expected return on a
and the standard deviation of a
. Individual securities do not
lie along line
.
The SML in
Figure 11.11
relates expected return to beta.
Figure 11.11
differs from
Figure 11.9
in at least two ways. First, beta appears in the horizontal axis of
Figure 11.11
, but standard
deviation appears in the horizontal axis of
Figure 11.9
. Second, the SML in
Figure 11.11
holds both
for all individual securities and for all possible portfolios, whereas line
in
Figure 11.9
holds only
for efficient portfolios.
We stated earlier that, under homogeneous expectations, point
in
Figure 11.9
becomes the market
portfolio. In this situation, line
is referred to as the
capital market line
(CML).
Summary and Conclusions
This chapter set forth the fundamentals of modern portfolio theory. Our basic points are these:
1.
This chapter showed us how to calculate the expected return and variance for individual
securities, and the covariance and correlation for pairs of securities. Given these statistics, the
expected return and variance for a portfolio of two securities
and
can be written as:
2.
In our notation,
stands for the proportion of a security in a portfolio. By varying
we can
trace out the efficient set of portfolios. We graphed the efficient set for the two-asset case as a
curve, pointing out that the degree of curvature or bend in the graph reflects the diversification
effect: The lower the correlation between the two securities, the greater the bend. The same
general shape of the efficient set holds in a world of many assets.
3.
Just as the formula for variance in the two-asset case is computed from a 2×2 matrix, the
variance formula is computed from an
×
matrix in the
-asset case. We showed that with a
large number of assets, there are many more covariance terms than variance terms in the matrix.
In fact the variance terms are effectively diversified away in a large portfolio, but the covariance
terms are not. Thus, a diversified portfolio can eliminate some, but not all, of the risk of the
individual securities.
4.
The efficient set of risky assets can be combined with riskless borrowing and lending. In this
case a rational investor will always choose to hold the portfolio of risky securities represented by
point
in
Figure 11.9
. Then he can either borrow or lend at the riskless rate to achieve any desired
point on line
in the figure.

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