I know this may seem like a silly question, but I’m just getting started on PM, and I am a little confused. Thanks.
No, the efficient frontier only includes the upper portion of the minimum variance frontier. Remember, the MVF is a fully convex (U shaped) curve. If you were to intersect with a vertical line, there would be 2 points (two equal values) where the variance was minimized, but one of those points would correspond to a much higher return than the other. It is not efficient to take a lower return for the same amount of risk, so the entire lower portion of the curve is inefficient. I hope that makes sense.
But if two portfolios have the same risk with different returns, then that generates an arbitrage opportunity in which you buy the higher return portfolio and sell short the lower return, right? So, how is that resolved within this model? It would seem that in an efficient market, there will only exist efficient portfolios. So, can we say that MVF includes inefficient portfolios that disappear in the long run?
Images speak louder than words: The EF is only the top portion of the frontier MVF: http://webpage.pace.edu/pviswanath/notes/investments/gif/assetalloc71.gif EF: http://i.infoplease.com/images/finance/aa-ideals_01.gif
Re: Is the Efficient Frontier the same thing as the Minimum Variance Frontier? Posted by: Dreary (IP Logged) [hide posts from this user] Date: January 31, 2009 07:03AM But if two portfolios have the same risk with different returns, then that generates an arbitrage opportunity in which you buy the higher return portfolio and sell short the lower return, right? So, how is that resolved within this model? It would seem that in an efficient market, there will only exist efficient portfolios. So, can we say that MVF includes inefficient portfolios that disappear in the long run? Dreary- the 2 portfolios do have the same risk with different returns I think b/c they aren’t the exactly same portolio, but rather different combinations of the assets in the portfolio to produce those results on the MVF. so as someone said above, if you have 2 portfolio combinations that have the same amount of risk but one produces higher returns, that is always the preferred portfolio- making the EF as the top part of that curve. i think “arbitrage” by definition would imply riskless, but here if they aren’t the same portfolio combinations, then there is risk to buy one portfolio and sell another short. I don’t think a true arbitrage opportunity is going to exist here buying one portfolio and selling the other short. the MVF portfolios where the combinations of securities on the lower part of the curve would be inefficient as compared to portfolios on the upper part of the curve b/c for the same risk, you can get a higher return.