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that's just the formula for the variance of the portfolio
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as a function of--Now, since they have to sum to 1,
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I can write this as x12 σ12 + (1 - x1)2 σ22 + 2x1 (1 - x1) σ12
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and so that together traces out--
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I can choose any value of x1 I want,
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it can be number from minus infinity to plus infinity.
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That shows me then for any value of x1,
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I can compute what r is and what σ2 is
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and I can then describe the opportunities I have
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from investing that depend on these.
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Now, one thing to do is to solve the equation for r and x1
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and I can then recast the variance in terms of r ;