Note_04M.21-27

Note_04M.21-27 - 21 Case 2 Two risky assets Following the...

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21 Case 2. Two risky assets Following the same procedure as in case 1, we allocate fraction of fund to risky asset 1 and fraction of fund to risky asset 2. The rate of return on portfolio is and its mean and variance are Both the mean and variance are affected by allocation weights and . The relation between and that describes the PPC can be derived as follows. (i) solve the mean equation for to derive (ii) Substitute these expressions into the variance equation Though this expression is complicated and is not very useful for our purpose, it shows that the PPC is a hyperbola in and . Two cases need a special attention. The equation for the PPC in the case of a perfectly correlated returns ( D =±1) becomes a simple equation. Perfect Positive Correlation ( D =+1) Perfect Negative Correlation ( D =-1). (i)

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(ii) If , the portfolio has a zero risk ( ). Proof. (A) Perfect Positive Correlation ( D =+1). The portfolio possibility curve is a straight line. In this case, the variance equation becomes which gives Solving this for , we can write Substituting this into the equation for the mean return we have And this is a linear equation in the and space, and the PPC is a straight line connecting point A and point B . (B) Perfect Negative Correlation (
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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.21-27 - 21 Case 2 Two risky assets Following the...

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