Choosing Efficient Portfolios (Portfolio Theory)
A.
Portfolios of Risky Securities
i.
Mean-Variance Analysis
ii.
The Markowitz Efficient Frontier
B.
Risky Securities Plus a Risk-Free Asset
i.
The Tangent Portfolio
ii.
(Another) Separation Theorem
iii.
The Capital Market Line (CML)
FIN2200 Fall 2014 – Lecture 5
61

3.B.ii Risky Securities Plus a Risk-Free Asset: (Another)
Separation Theorem
The
optimal portfolio
choice problem can be separated into
two
independent
tasks
:
1.
Determining the
tangent portfolio
•
I.e. the portfolio of all risky assets with the
highest Sharpe ratio
•
This is a
non-personal choice
2.
Mixing
the
tangent portfolio
and
risk-free asset
to form an investor’s
optimal
portfolio
•
This is a
personal choice
; depends on the investor’s risk preferences
Separation Theorem
:
In a world with homogeneous expectations, the
tangent
portfolio
is the
same for everyone
All investors will hold the
same risky portfolio
!
(I.e. the efficient, tangent portfolio)
They can
separate
their level of
risk aversion
from their
choice
of the
risky
component
of their total portfolio
An investor’s
risk preferences
will determine
how much
to invest in the
tangent
portfolio
versus the
risk-free
investment
•
That is, all investors choose a point along the line
FIN2200 Fall 2014 – Lecture 5
62

3.B.iii. Risky Securities Plus a Risk-Free Asset: The Capital
Market Line
The
optimal portfolio
is a
combination
of the
risk-free
asset and
tangent
portfolio
Since the
tangent portfolio
is same for everyone, it
equals
the
market portfolio
When the
tangent line
goes through the
market portfolio
, it’s called the
capital
market line
FIN2200 Fall 2014 – Lecture 5
63
σ
P
E[
R
P
]
R
f
Market
Portfolio
The CML
While all investors invest in the market
portfolio, the
optimal portfolio
chosen
(on the CML) depends on their level of
risk aversion
Becomes an issue of
asset allocation
A risk-averse investor will invest more
in the risk-free asset
A less risk-averse investor will invest
more in the market portfolio
An investor may even borrow to buy
the market portfolio on margin, this
would be an even riskier strategy
Riskless borrowing and lending are
offset in the aggregate portfolio

To Summarize (Portfolio Theory)…
1.
The
investment opportunity set
is:
A
point
when there is
one
risky asset
A
curve
when there are
two
risky assets
An
area
when there are
many
risky assets
2.
When there is a
risk-free asset
:
Given the investment set, find the
tangency portfolio
by maximizing the
Sharpe ratio
The line connecting the riskless rate and the tangency portfolio is
the CML
and any portfolio along this line has the potential to be optimal depending
on the investor’s utility function
When there is a riskless and
only one risky asset
, the risky asset is the
“tangency portfolio” since it is the only risky portfolio available
3.
When there is
no risk-free asset
:
There is
no tangency portfolio
RSM 330 Winter 2011 - Class 6
64

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

Want to read all 64 pages?

- Winter '14
- JerrodFalk
- Finance, Standard Deviation, Corporate Finance, Portfolio Theory, Modern portfolio theory, The Tangent Portfolio