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September 23rd, 2011, 01:13 PM   #1
Joined: Sep 2011

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portfolio optimization, efficient frontier


I am trying to understand something:
I learned that for a risky portfolio, the efficient frontier is a parabola (sigma is function of E).
Also, when there is a riskless esset, the efficient frontier is a line.
Its tought that in order to find that line, one needs to find a line that passes through point (E=m, sigma=0, when m is the expectation of the riskless esset), and the line should be tangent to the parabole. That parabola is the one given when excluding the riskless esset.

My question is:
Why should there be a tangent point?
Why would that line and the parabola share some certain E with the same sigma?
Couldn't it be that for every possible E, the portfolio with the riskless esset will have smaller sigma?

Thank you.
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