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Unformatted text preview: ght of the risky assets and their SD, as risk free assets
have a SD of 0. This suggests that the risk of B is linearly related to the SD of the P, and increases with the
weight allocated to P.
T HE RISK RETURN COMBINATION OF BALANCED PORTFOLIOS
Capital Allocation line (CAL) is a straight line that shows the risk return combinations of a set of balanced
portfolios that combine a risk-free asset with a portfolio of risky assets in different proportions. Point P is where y = 1 The introduction of a risk free asset enlarges
the set of attainable portfolios The risk return combinations of each set of B
lies on a straight line that extends from the
risk free rate of return to and beyond the
risk/return combination of the corresponding
portfolio of risky assets (point P) 5 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 T HE SEPARATION THEOREM The separation theorem states that:
• All efficient portfolios are on the CAL
The CAL is determined by the optimal risky portfolio
We pick the portfolio on the CAL that offers the amount of risk we want to take – this is done by
finding our choice of y This means, the portfolio choice problem can be separated into 2 parts:
2. Find the optimal risking portfolio
Choose how much risk we want by choosing the fraction of our wealth that we want to invest in that
portfolio, y T HE CHOICE OF PORTFOLIOS OF RISKY ASSETS IN THE PRESENCE OF RF ASSET
Where there is no risk-free asset, we select the portfolio of risky assets with the largest utility as the ORP. In
the presence of a risk-free asset, this criterion of selection from all the attainable risky portfolio is different. Once rf is available, the MRA investors may combine rf with another risky portfolio, labeled as ORP, to obtain a
balanced portfolio directly above point ORPMRA. Hence, this new point dominators ORPMRA as it earns a higher
E(r) with the same level of risk. Hence ORP is now the preferred portfolio of risky assets for the MRA investor.
This is the same case with LRA investors.
In summary: ORP is chosen as the optimal portfolio of risky assets irrespective of the degree of risk aversion of the...
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