My Math Forum portfolio optimization, efficient frontier

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 September 23rd, 2011, 01:13 PM #1 Newbie   Joined: Sep 2011 Posts: 1 Thanks: 0 portfolio optimization, efficient frontier Hello, 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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