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- 2011-7-11
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- 2013-9-27
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2#
发表于 2011-7-13 16:27
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Ok here’s my understanding.
1) Minimum variance frontier – this curve represents the portfolios with the lowest level of risk for a certain level of return. Ie if you considered all of the risky assets in the world, and formed them into portfolios, the MVF would show you the “best” you can get in terms of the lowest risk (at each level of return).
2) The global minimum variance portfolio is on the MVF, at the lowest level of risk (the MVF looks like a C, and the global minimum variance portfolio is at the most left-hand point of the C, if that makes sense). It is the lowest risk you can have, amongst all risky assets (note this DOESN’T include adding a risk-free asset, we’ll get to that later.)
3) Now think a bit more about what the ‘C’ shaped curve (the MVF) actually shows us – returns are on the Y axis and risk is on the X axis. Because of the ‘C’ shape, there are two parts on the curve where risk is the same, but returns are different. Why would you want to invest in the portfolio on the ‘bottom half’ of the C, which essentially has the same risk but worse returns? That’s how we get to the Markowitz efficient frontier – if you cut the C in half from left to right through its middle, the efficient frontier is the top half.
4) Now if you look at a graph that just shows the efficient frontier (the top half of the ‘C’). The risk free rate is on the Y axis somewhere. What you want is the risky asset portfolio that results in the steepest slope between the RFR and the efficient frontier (because a steep slope suggests that returns are growing faster than risk). You’re going to get that at the point of tangency between the efficient frontier and a straight line drawn from the RFR. (less steep and you’re not maximising returns, more steep is unattainable).
That point of tangency defines the market portfolio, ie the best possible risky portfolio to invest in.
5) The CAL and the CML show the same thing except the CAL graphs the combo of the risk free rate and ANY risky portfolio whereas the CML shows the risk free rate and the market portfolio.
6) To work out where on the CML each investor should be, you use the point of tangency with indifference curves .
hope that helps.... |
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