Note_04M.17-20

Note_04M.17-20 - 17 Opportunity Set Portfolio Possibility...

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17 Opportunity Set: Portfolio Possibility Curve (PPC) We have an initial investment fund and allocate it to different assets. Let be the fraction of fund to be invested in the risk-free asset, and , , etc. be the fractions to be invested in risky assets 1, 2, etc. If short sales are not allowed, allocation weights must be in a unit interval ( ) and sum to one. If short sales are allowed, the weights can be negative and can be greater than 1, but they have to sum to one. The rates of returns are denoted by for the risk-free asset, and etc. for risky assets. Since the amount of fund invested in asset i is and its gross rate of return is ( ), the value of the portfolio, , for the case of three assets is given by where is the random rate of return of the portfolio. We assume that our investor is an expected utility maximizer. We also assume that the utility function is a CARA and a normal distribution of , or a CRRA utility function with a log-normal distribution function, or a quadratic utility function with any distribution. We have shown that, under these assumptions, investors are concerned only about the mean and variance of . Therefore, we need to find the opportunity set in
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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.17-20 - 17 Opportunity Set Portfolio Possibility...

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