We can now consider
portfolios that are
combinations of the
risk-free security,
denoted with the
subscript
f
and risky
portfolios along the
Efficient Frontier.
E[R]
σ
P
R
f

58
A+Lending
The riskfree asset:
riskless lending and borrowing
Consider combinations of
the risk-free asset with a
portfolio, A, on the
Efficient Frontier.
With a risk-free asset
available, taking a long
f
position (positive portfolio
weight in
f
) gives us risk-
free lending combined
with A.
Taking a short
f
position
(negative portfolio weight
in
f
) gives us risk-free
borrowing combined with
A.
σ
P
E[R]
R
f
A+Borro
wing
Portfolio A

59
The riskfree asset:
riskless lending and borrowing
Which combination of
f
and portfolios on the
Efficient Frontier is
best?
Portfolios along the
line tangent to the
Efficient Frontier
dominate everything
else. Now, the only
efficient risky
portfolio on the
Markowitz Efficient
Frontier is Portfolio M.
σ
P
E[R]
R
f
What is the optimal strategy
for every investor?
M

60
M: The Market Portfolio
The combination of
f
and
portfolios on the Efficient
Frontier that are best are…
combinations of
f
and M.
All investors choose a point
along the line…
each point is some
combination of the risk-free
asset,
f
, and the market
portfolio
M
.
In a world with homogeneous
expectations,
M
is the same
for all investors.
σ
P
E[R]
R
f
CML stands for
the
Capital Market
Line
M
CML

61
A new separation theorem
This separation
theorem
states that
the market portfolio, M,
is the same for all
investors. They can
separate their level of
risk aversion from their
choice of the risky
component of their
total portfolio.
All investors should
have the same risky
component, M!
σ
P
E[R]
R
f
M
CML

62
Given Separation, what does an
investor choose?
While all investors will
choose M for the risky
part of their portfolio,
the point on the CML
chosen depends on
their level of risk
aversion.
A very risk-averse
investor will choose a
point closer to R
f
(i.e., a
higher weight for
f
and
a lower weight for M).
A less risk averse
investor will choose a
greater weight in M.
σ
P
E[R]
R
f
M
CML
An investor may even borrow to
invest more in M, this would be an
even riskier strategy.

63
7. The Capital Market Line (CML)
The CML equation can
be written as follows:
Where
EP
i
= efficient portfolio i (a portfolio on the CML composed of
the risk-free asset,
f
, and M)
E[ ] is the expectation operator
R = return
σ = standard deviation of return
f
denotes the risk-free asset
M denotes the market portfolio
E
R
EP
i
R
f
EP
i
E R
M
R
f
M
Note: the CML is our first
formal relationship between
risk and expected return.
Unfortunately it is limited in
its use as it only works for
perfectly efficient portfolios:
composed of
f
and M.

64
8. The Capital Asset Pricing Model
(CAPM)
If investors hold the market portfolio, M, then the risk of
any asset, j, that is important is not its total risk, but the
risk that it contributes to M.

#### You've reached the end of your free preview.

Want to read all 71 pages?

- Winter '14
- JerrodFalk
- Finance, Standard Deviation, Capital Asset Pricing Model, Corporate Finance, CML, Modern portfolio theory, The Market Portfolio