Economics 106V
Investments
: Lecture Note-3
Daisuke Miyakawa
UCLA Department of Economics
June 27, 2008
3rd lecture covers the following items:
(1) The structure of optimal portfolio choice problem, (2) a
simple one risk-free asset and one risky asset model, (3) Capital Allocation Lone (CAL) & Capital Market
Line (CML), (4) multiple asset model, (5) optimal risky portfolio, (6) global minimum variance portfolio, (7)
e¢ cient frontier, and (8) diversi°cation e/ect. After discussing those items, we solve some exercise problems.
1
The Structure of Optimal Portfolio Choice Problem
In the previous two lecture, we have studied the tools necessary to discuss the optimal portfolio construction
problem.
1.1
Overview
Suppose we are asked to construct a portfolio, which is a set of risky assets and risk-free asset. For simplicity,
assume that there are only two risky assets and one risk-free asset. Figure-1 summarizes the structure of
this problem.
Risky Asset-A
r
A
&
Risky Asset-B
r
B
&
Risky-Free Asset
r
f
&
A
σ
B
σ
0
=
f
σ
Step-1: Optimal "Risky" Portfolio Construction
Step-2: Optimal Portfolio Construction
Figure-1: The Structure of the Problem
In order to construct an optimal portfolio, we need to follow the two steps. First, an optimal "risky" portfolio,
which consists of only the risky assets, is constructed. Then, we allocates our funds to the risk-free asset
and the optimal risky portfolio. Figure-2 is the road map for the material on this lecture. Note that there
1

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