Utility Maximization
with
a Riskfree Asset
~
Old Efficient
Frontier
Expected
Return
E(R.;)
Std dev
0";
Portfolios
on the Capital Market Line
•
An investor
holds a positive
proportion
of the two funds if the
tangency
between
an indifference
curve and the capital market
line lies between
the two funds
• An
investor
borrows
at the riskfree
rate and invests in the
market
portfolio
if the tangency
between
an indifference
curve
and the capital
market
line lies to the right of the two funds
~
Riskless
Asset
Old Efficient
Frontier
The Market Portfolio
(with 2 risky assets)
•
For two risky assets, we know that the portfolio
return
and
standard
deviation
are
given by
Tobin's
TwoFund
Separation
•
When the riskfree
asset is introduced,
all investors
prefer
to move from their originally
optimal
portfolios
to a
combination
of the riskfree
asset and the market portfolio
•
Alternatively
stated, combinatjons
of the riskfree
asset and
the market
portfolio
(JOm
1
r1
all other assets
and portfolios
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 Fall '10
 Sapp
 Linear Algebra, Vector Space, Capital Asset Pricing Model, The Market Portfolio

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