Dr. Trance
11/2/2009
Portfolio Man.
Dr. Frank Jones
Project 1 – Optimization
1)
EF and CML
a)
CML = rf +((rmrf)/σm)*σp
b)
The PM:
Where:
Asset 1 = Ibbotson Associates Small Stock
Asset 3 = Ibbotson Associates All Value
Asset 4 = Ibbotson Associates Monthly Convertible
Asset 5 = Lehman Brothers Aggregate Bond
Asset 6 = Lehman Brothers HiYield
c)
There are negative numbers.
These numbers represent the need to short this
security as it is overpriced and we can get more return by investing more in
another security.
Thus we are investing over 100% as we borrow.
2)
a)
Personally optimal point = The PM is my personally optimal point.
b)
I selected this point because I am risk averse.
c)
The composition of my personally optimal portfolio is the same as the
Market Portfolio.
d)
By choosing the PM as my preferred portfolio I do not have to do any
borrowing or lending of the Risk Free Asset.
3)
Sharpe Ratio
a)
((rmrf)/σm) = ((11.015.02)/6.63) = .90346908
b)
Personal Portfolio is the same Sharpe Ratio
4)
+ 5%
a)
The compositions are the same we just have to borrow and lend the risk free
rate
b)
Sharpe ratios
i)
+5%
((rprf)/σp)= .90283749
ii) 5%
((rprf)/σp) = .90184049
c)
Yes these ratios do make me want to invest in a higher risk portfolio.
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a)
To measure superiority we shall use the Sharpe ratio
i)
6 asset Sharpe Ratio = .90346908
ii) 3 asset Sharpe Ratio = ((14.765.02)/16.26)
=
.59901599
b)
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 '09
 Jones,Frank
 Standard Deviation, Capital Asset Pricing Model, Modern portfolio theory, sharpe ratio, Ibbotson Associates

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