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Portfolio Selection with a Riskless Security
Investor Preferences
Outline
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1.
Portfolio selection with a risk
‐
free and 1 risky
security.
2.
Portfolio selection with a risk
‐
free and 2 risky
securities.
3.
Portfolio selection with a risk
‐
free and many
risky securities.
Systematic and idiosyncratic risk
The Single Index Model
‐
> last class
‐
> today
Outline
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Investment opportunity set
With many risky assets (3 to…)
With many risky assets and a risk
‐
free security
Optimal portfolio choice and two
‐
fund separation
Diversifiable and non
‐
diversifiable risk
(systematic risk)

Three risky assets – Intuition
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Efficient Set AB
Efficient Set BC
Three Assets Example
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Source: G. Saar
Three Assets Example
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Source: G. Saar

Three Assets Example
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Source: G. Saar
Three Assets Example
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Source: G. Saar
Investment Opportunity Set
with Many Assets
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Expected return
Standard deviation
Global Minimum
Variance Portfolio
Individual
Assets
Inefficient Frontier
Efficient Frontier
Handout 13
explains how to
construct the EF –
It’s optional.

Step 3B: Optimal Portfolio Selection with Many Risky
Assets and a Risk
‐
Free Asset (on board)
1.
Create the set of possible mean
‐
s.d. combinations from
different portfolios of risky assets
2.
Find the “tangency portfolio,” i.e. the portfolio with the
highest Sharpe ratio:
3.
Choose the combination of the tangency portfolio and the
risk
‐
free asset to suit your risk
‐
return preferences.
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Optimal Portfolio Selection with Many
Risky Assets and a Risk
‐
Free Asset
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Two
‐
Fund Separation
All investors hold combinations of the same two
“mutual funds”:
The risk
‐
free asset
The tangency portfolio
An investor’s risk aversion determines the
fraction of wealth invested in the risk
‐
free asset.