Note_04M.28-35 - 28 Case 3. Efficient Frontier with one...

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28 Case 3. Efficient Frontier with one Riskess Asset and two Risky Assets The efficient frontier discussed in case 2 considers only risky assets. What if we can include a riskless (risk- free) asset such as Treasury notes in the portfolio? Let be the yield of the riskless asset and be the fraction of fund to be invested in the riskless asset. We will denote the portfolio including the riskless asset by portfolio Q, and use , and for return, mean return and variance of the return, respectively. Since is not random, , and the return, mean and variance of the portfolio Q are Note that is the same as because is not a random variable. We have shown that the best portfolios of risky assets are on the efficient frontier. Therefore, we need to consider which portfolio of risky assets on the efficient frontier is the best choice to be included in the portfolio Q. Consider the portfolio that includes of risky assets in the figure below. We have shown earlier that the portfolio possibility curve of and riskless asset is the capital allocation line from to . Similarly, the PPC of riskless asset and risky asset is the line from to . This PPC line lies above the line that includes risky assets . Therefore, is a better choice than for a portfolio that includes riskless asset. Repeating this line of thought leads to the conclusion that the best portfolio of
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29 risky assets to combine with the riskless asset is the one at which the capital allocation line from is tangent to the PPC of risky assets. That is, it is the line that has the highest Sharpe ratio (slope of the capital allocation line). This is the most efficient portfolio of risky assets and it is shown as
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This note was uploaded on 04/05/2012 for the course ECON 445 taught by Professor Staff during the Fall '08 term at Texas A&M.

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Note_04M.28-35 - 28 Case 3. Efficient Frontier with one...

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