Intermediate Financial Management (with Thomson One)

88 • Part 1 Fundamental Concepts
Figure 3-7
The Capital Market Line (CML)
Expected Rate
of Return, r p
r M
r RF
0
σM
M
CML: r = r +
P
RF
r M – r
σ
Risk, σp
Note: We did not draw it in, but you can visualize the shaded space shown in Figure 3-6 in this graph, and the CML as
the line formed by connecting r RF with the tangent to the shaded space.
assets, such as the market portfolio. 11 It is possible to take the equations for the
expected return and standard deviation of a multi-asset portfolio and show that
the required return for each individual stock, J, must conform to the following
equation in order for the CML to hold for the market portfolio:
The CAPM defines the beta coefficient of company J, b J , as follows:
11The percentage of the investment in asset i is wi, the expected return for asset i is ˆr i, the standard deviation of
asset i is i , and the correlation between asset i and asset j is ij . The expected return for a portfolio with N assets
N
is and the variance of the portfolio is .
2 rˆ p a (wi rˆ i)
p a (wiwjijij) i1
JM J M
2 M
r J r RF (r M r RF)
M
JM a J b
M N
a Cov (r J, r M)
M
rRF (rM rRF) a Cov (rJ,rM) 2 b
M
Covariance between Stock J and the market
bJ
Variance of market returns
N
i1 a
j1
b
M
RF
σp
Cov (r J, r M)
2 M
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