Harry Markowitz is one of the patron saints of modern finance, who's contribution is, according to the Nobel committee, for having "constructed a micro theory of portfolio management for individual wealth holders." Mark Rubinstein spoke at one of the innumerable conferences honoring Markowitz, and stated that
Near the end of his reign in 14 AD, the Roman emperor Augustus could boast that he had found Rome a city of brick and left it a city of marble. Markowitz can boast that he found the field of finance awash in the imprecision of English and left it with the scientific precision and insight made possible only by mathematics
In a speech given in 2009 (and many other writings), Markowitz notes rather casually that many use 'tracking error' rather than portfolio variability as the risk to minimize. Yet this leads to totally different implications. As I have demonstrated (see blog post here or article here), this leads to no risk-expected return relation in equilibrium. There is a trivial 'efficient frontier', aping the benchmark--everything else is inefficient.
Without the concave efficient frontier, James Tobin's two-fund separation theorem does not work, and without the two-fund separation theorem, the Sharpe-Lintner-Mossin Capital Asset Pricing model does not work. Of course, in practice, we all knew that, given that the two-fund separation theorem implied there would be one mutual fund, and it would be a value-weighted index, whereas instead we have more funds than equities that go into them. That theory was as falsified as Tobin's 'transactions model of money demand'. The empirical failure of the CAPM, is also well known. These models all have a certain attractive elegance to them, but as they don't explain the real world after 50 years of looking for relevance, an idealized scientist would ignore them.
'Risk' prior to Markowitz was not well defined, and he showed that in the standard, new models of consumers (specific utility functions, like von Neumann-Morganstern Utility), the dispersion of wealth was what mattered. Other conceptions of risk were inconsistent, applying to assets or portfolios, depending. It seemed clear that applying rigor to preferences via utility functions, and applying statistics to portfolios via this new metric of risk, would lead to a philosopher's stone. Like so many things, it hasn't worked out as expected. In Markowitz's thesis, he remarked that "risk" and "variance of return" were interchangeable, and up to 1990 or so this idea was defensible, but we know know it's a dead end, that 'risk' is now a correlation to several unagreed upon factors such as FX rates, yield curve spreads, or micro-cap value stocks.
Markowitz's seminal work contains a lot of what can charitably be called quaint empirical analysis, and algorithmic tricks to do matrix math to get to this to irrelevant frontier. He also spent a lot of time on looking at refinements to his assumptions--fat tails, different utility functions, but these forays led to his conclusion that "mean-variance approximation is so good that there is virtually no room for improvement" via these extensions.
His big idea, that one should look at a portfolio to evaluate risk, not the individual asset, remains. I agree that's a good big idea. The particulars he notes around that are as irrelevant as Newton's writings on alchemy or Playboy's interviews. He does not seem to grasp that this is his bon idée, the essence of his contribution to science, his only lasting insight. It highlights that a good idea in economics is rarely inextricably linked to deep mathematics--in this case it is clearly not, demonstrable via noting the Law of Large Numbers (a sample means volatility diminishes as the sample grows), and noting that the saying 'don't put all your eggs in one basket' is a good idea (there are apt quotes from Shakespeare to Aristotle on this).
As mentioned, even Markowitz has given up the ghost, noting that minimizing benchmark risk is more prominent, as if this is totally consistent with his thinking. Yet in spite of this factual divergence between theory and practice, finance remains enamored by what Rubinstein calls the "the scientific precision and insight made possible only by mathematics." The essence of a Journal of Finance article is its rigor, defined as abstruse mathematics, similar too but slightly different than the genre it discusses. A trivial, even silly, idea, is considered publishable if within this paradigm because a nice property of such models is they can be tweaked by other mathematically inclined economists and the publication bubble festers.
The bottom line is these models are not useful in the real world, Markowitz's focus--as opposed to his big idea--has been a distraction, irrelevant. I've been to private wealth manager conferences, those people who daily deal with customers who have more than $5MM in wealth. They don't know much math and don't care too much to learn more, seeing little need for it. They do know a lot about taxes, the law, and communication skills. It simply hasn't been the case that investing is highly influenced by "scientific precision" of these financial founding fathers, because the main issues--what asset classes to invest in, what managers to choose within these classes--remains a very qualitative affair. Deviations from the consensus at any level usually involve a qualitative story. As they say, in theory, theory and practice are the same; in practice, they are not.