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Note_04M.41-43

# Note_04M.41-43 - asset is 1 That is at the tangent point...

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41 Portfolio Frontier with a Risk-Free Asset Suppose there is a risk-free asset with the rate of return : 0 . A portfolio consists of a risk free asset and n risky assets with weights and , where w is an nx1 vector of weights on the risky assets and . The expected rate of return and the variance of the portfolio Q are Portfolio Possibility Curve (PPC) Method 1 Find the allocation weights and w that minimize the variance of the rate of the return for a given mean of portfolio. Let be the vector of excess returns of risky assets over riskless return. The risk minimizing allocation is given by and the variance One can construct the PPC by repeating this for various values of Method 2. The PPC curve (capital allocation line, tangent line) is given by a linear function where k is a positive or a negative root of Portfolio of Risky Assets The portfolio at the tangent point does not include risk-free asset and hence, the sum of the weights of risky

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Unformatted text preview: asset is 1. That is, at the tangent point, . This gives which gives 42 Expected Utility Maximizing Portfolio We will consider the expected utility of CARA utility function under the normality. The expected utility is where We have shown that the maximization of this expected utility is equivalent to the maximization of subject to the linear efficient frontier derived above Substituting this into the objective function, we have which is a function of only. Taking derivative with respect to and setting it to zero, we find the first order condition and the expected utility maximizing value of is The allocation weights are computed from The expected utility maximizing mean and variance of the wealth are 43...
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Note_04M.41-43 - asset is 1 That is at the tangent point...

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