In short though, the entire thing is based on the idea that finance is based on guassians, whereas the evidence overwhelmingly suggests it's based on power laws instead. (And intringuingly, the consequence of the latter would mean that portfolio risk increases when you're diversified in many asset classes.)
Personally, I think the biggest problem with any ideal portfolio allocation tool are black swan events (Taleb).
Yes. Black Swans are certainly a problem. It's insane to think that investment returns are anything resembling a Gaussian distribution. In the financial crisis of 2008-2009, people were using phrases such as "a 9 sigma event" to describe the markets.
Wrong! Basically THERE'S NO SUCH THING AS a 9 SIGMA EVENT. Wikipedia gives the probability of a 6 sigma event as 1 in 500 million. So it the epitome of arrogance to think that we're so "special" that we just happened to be alive during a 9 sigma market move.
What it all really means is that the markets do not behave the way lazy eggheads want them to. Everyone understands Gaussian distributions and standard deviation. So they are eager to use that math where they shouldn't.
I'm sure you know all this. But for those people who aren't familiar with Taleb and want to read more, he wrote three pop books about it:
2001 Fooled by Randomness http://en.wikipedia.org/wiki/Fooled_by_Randomness
2007 The Black Swan http://en.wikipedia.org/wiki/The_Black_Swan_%28Taleb_book%29
2012 Antifragile http://en.wikipedia.org/wiki/Antifragile
I'm in the middle of reading Antifragile, and I am thoroughly enjoying it so far.
I often refers to a good paperon What has worked in investing [1]
I think Taleb criticism is right though and he demonstrates it through Mandelbrot fractal.
[1] http://www8.gsb.columbia.edu/sites/valueinvesting/files/file...
Nassim Taleb is a vocal critic of MPT.