The Portfolio Allocation Problem
•
The first step in this process is to find the expected returns,
standard deviations, and covariances of all assets under
consideration.
•
Next, we combine the risky assets available to us in a
portfolio. This is accomplished by finding the portfolio of
risky assets, among all possible portfolios, that has the
highest Sharpe ratio. This is the optimal portfolio of risky
assets, also called the tangency portfolio.
•
Finally, we combine the tangency portfolio with the riskfree
asset. This is accomplished by taking the riskaversion of the
investor into account. The more riskaverse the investor is,
the less he will allocate to the tangency portfolio.
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View Full DocumentPortfolios
•
Portfolios are collections of assets. Suppose we hold a
portfolio P of A and B with weight w in A and (1w) in B.
•
Then:
P
A
B
R
w *R
(1 w)*R
=
+

P
A
B
E(R )
w *E(R )
(1 w)*E(R )
=
+

2
2
P
A
B
AB
2
2
A
B
A
B
AB
V(R )
w *V(R ) (1 w) *V(R )
2w(1 w)
w *V(R )
(1 w) *V(R )
2w(1 w)
=
+

+

σ
=
+

+

σ σ ρ
•
The advantage of forming portfolios is a reduction in the
overall variance of the investment. This is the diversification
effect.
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 Spring '09
 Clarke
 2W, 1  w, R T, 1w

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