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Unformatted text preview: Portfolio
Portfolio Selection
Chapter 8
Charles P. Jones, Investments: Analysis and Management,
Tenth Edition, John Wiley & Sons 81 Portfolio Selection
Diversification is key to optimal risk
management
Analysis required because of the infinite
number of portfolios of risky assets
How should investors select the best
risky portfolio?
How could riskless assets be used? 82 Building a Portfolio
Step 1: Use the Markowitz portfolio
selection model to identify optimal
combinations
combinations
Estimate expected returns, risk, and each
covariance between returns Step 2: Choose the final portfolio
based on your preferences for return
relative to risk 83 Portfolio Theory
Optimal diversification takes into
account all available information
Assumptions in portfolio theory
A single investment period (one year)
Liquid position (no transaction costs)
Preferences based only on a portfolio’s
expected return and risk 84 An Efficient Portfolio
Smallest portfolio risk for a given level
of expected return
Largest expected return for a given
level of portfolio risk
From the set of all possible portfolios
Only locate and analyze the subset known
as
as the efficient set
Lowest risk for given level of return 85 Investment Opportunity Set for Bond and
Stock
Stock Funds Investment Opportunity Set for Stock and
Bonds
Bonds with Various Correlations Selecting an Optimal Portfolio
of
of Risky Assets
Assume investors are risk averse
Indifference curves help select from
efficient
efficient set
Description of preferences for risk and
return
Portfolio combinations which are equally
desirable
Greater slope implies greater the risk
aversion
88 Selecting an Optimal Portfolio
of
of Risky Assets
Markowitz portfolio selection model
Generates a frontier of efficient portfolios
which are equally good
Does not address the issue of riskless
borrowing or lending
Different investors will estimate the efficient
frontier differently
El
Element of uncertainty in application 89 Two Asset Portfolio Return – Stock
and
and Bond r =w r +w r
r = Portfolio Return
w = Bond Weight
r = Bond Return
Weig h
w = Stock Weig htt
r = Stock Return
p B p B B S S B S S In General, for an nsecurity
portfolio
portfolio:
rp = Weighted average of the
n securities
securities
σp2 = (Consider all pairwise
covariance measures) Numerical Example: Bond and Stock
Returns
Bond = 6% Stock = 10%
Standard
Standard Deviation
Bond = 12%
Stock = 25%
Weights
Bond = .5 Stock = .5
Correlation
Correlation Coefficient
(Bonds and Stock) = 0 Return and Risk for Example
Return = 8%
8%
.5(6) + .5 (10)
Standard Deviation = 13.87%
[(.5)2 (12)2 + (.5)2 (25)2 + …
2 (.5) (.5) (12) (25) (0)] ½
[192.25] ½ = 13.87 The Single Index Model
Relates returns on each security to the
returns on a common index, such as
the
the S&P 500 Stock Index
Expressed R = α following e
by the + β R + equation
i i i M i Divides return into two components
a unique part, αi
unique
a marketrelated part, βiRM
814 The Single Index Model
b measures the sensitivity of a stock to
stock market movements
If securities are only related in their
common response to the market
Securities covary together only because of their
common
common relationship to the market index
Security covariances depend only on market risk
and can be written as: σ ij = 2
βi β j σ M
815 The Single Index Model (SIM)
Single index model helps split a
security’s total risk into
Total risk = market risk + unique risk
market
2
σi = 2
βi [σ M ] 2
+ σ ei MultiIndex models as an alternative
Between the full variancecovariance
method of Markowitz and the singleindex
model
816 Selecting Optimal Asset Classes
Another way to use Markowitz model is
with asset classes
Allocation of portfolio assets to broad asset
categories
Asset class rather than individual security
decisions most important for investors Different asset classes offers various
returns
returns and levels of risk
Correlation coefficients may be quite low 817 Asset Allocation
Decision about the proportion of
portfolio assets allocated to equity,
fixedincome, and money market
securities
Widely used application of Modern Portfolio
Theory
Theory
Because securities within asset classes tend
to move together, asset allocation is an
important investment decision
Should consider international securities,
real
real estate, and U.S. Treasury TIPS
and
Treasury
818 Implications of Portfolio Selection
Investors should focus on risk that
cannot be managed by diversification
Total risk =systematic
(nondiversifiable) risk + nonsystematic
(diversifiable) risk
Systematic risk
Variability in a security’s total returns directly
associated with economywide events
Common to virtually all securities Both risk components can vary over time
Affects
Affects number of securities needed to diversify
819 Portfolio Risk and Diversification σp %
Portfolio risk 35 20 Market Risk
0
10 20 30 40 ...... Number of securities in portfolio 100+ ...
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 Spring '08
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