I've never seen a list of competing theories and it seems that most firms on some level build off the modern portfolio theory, efficient frontiers, or whatever the kids are calling it these days. MPT is old (outdated?). So, I ask...In the realm of portfolio optimization, what are some competing theories (in practice or not) to modern portfolio theory?

I think that what has probably happened was, in the 1950's when the building blocks for the MPT framework were first introduced, these optimization techniques were very unique and revolutionary, especially in an environment where computing power was very expensive and available to only a few. So it was relatively easy for a handful of men to garner accolades and widespread notoriety by exploring and expounding on these concepts, building it into MPT, and publishing extensively on it. Since so few people had access to being able to effectively computationally tinker with optimization, it was natural for these academics (Markowitz, Sharpe, et al.) to be seen by the financial academic community and investors as the clear innovators in this area.From the 1980's onward, however, there has been an obvious explosion in the amount of computational ability available to academics and practitioners. In many firms across the world, portfolio management groups and risk management departments are putting together very sophisticated optimizations and simulations on their desktops that could only be dreamed about several decades ago. However, since so many people now have access to the tools, it is difficult for any one of them to obtain the "academic air time" for their own approaches to reach widespread understanding and acclaim. Add to that the obvious tale of if a practitioner truly has anything of value, it may be being used sight unseen to generate profits, rather than release it to the public (the age-old finance debate of seeking either academic immortality or exploiting a proprietary model). While the analogy is imperfect, I liken this to the idea that it was easier to have a hit show in the United States when there was only the "Big Three" networks rather than the glut of channels now available on TV and Internet outlets; now producers are competing with tens of thousands of other producers and content developers for the finite share of viewership. With regard to the use of variance as a measure of risk, it is now not uncommon to see many other optimization techniques employed that can optimize to any number of other measures of risk. The optimization algorithm techniques available now can solve for very complex solution spaces. As the number of specialized needs and considerations in the industry has increased, I think you are seeing a lot of very custom and specific solutions that are having a difficult time to be generalized into a mass-appeal academic framework.

In 2000 Shefrin and Statman published 'Behavioral Portfolio Theory' which tries to go beyond MPT by postulating that investors have multiple goals (rather than just the maximization of return subject to risk) and different ways of looking at risk. The overall portfolio then consists of various 'subportfolios' designed to meet particular goals. You might have one very safe subportfolio to ensure that you don't starve and another riskier one to try to make some money, for example.Other writers have developed versions of this. Jean Brunel calls it 'goal based wealth management', A. Chhabra refers to 'comprehensive wealth allocation' and Dan Nevins calls it 'goal based investing'.However, so far this theory has not developed very far in my humble opinion, and consists of high level conceptual material and relatively little in the way of specific mathematical results. And the cost of generalizing the Markowitz framework may be that there is no longer a clear-cut solution, just many issues to be considered that are specific to each investor (in a way this is actually a step backwards from Markowitz). I am reading this material now and although it is interesting I have not yet decided whether it will be useful to me or not.

Adding to the previous observations, MPT is hard to implement in practice due to difficulties in estimation (especially the mean return vectors). The Black Litterman extension of the framework lets one impose their own views. But if you think about it, seeing as mean returns are not observable, any estimation is by definition subjective. I would opine that modern approaches to asset allocation have ditched MPT and instead lean toward exploiting market asymmetries and inefficiencies (or even seeking to create them - e.g. high speed trading).