Monday, July 19, 2010

Harry Markowitz Inconsistent

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.


paul b said...

Eric, I really like your blog and I identify with most of the things you write about. (I'm always looking for evidence to confirm my priors.. ; ) but if you could humor me a faithful reader, please read Fischer Black's discussion of Risk page 45-47 in his book "exploring general equilibrium.") I think he makes some good points.


Eric Falkenstein said...

I don't have that book lying around...can you summarize the point made?

paul b said...

I could but you'd miss the beauty of his prose so I'll just include a few sentences.

"Risk and expected return are related. The risks we bear unwillingly seem associated with low expected return; while the ones we choose are most often associated with high expected return. That's why we choose them." ... "the general equilibrium approach doesn't restrict the sign of the correlation between risk and expected return, across countries or through time; and it especially doesn't restrict the sign of the correlation between risk and actual return."

Risk comes from many sources (political, technology, firm, projects etc) and the risk we can't choose can dominate the risks we can choose, whence the ambiguous sign.

It goes without saying that I think the book is well worth reading.


Eric Falkenstein said...

first, I agree that people take risks, however defined, based on higher-than-average expected returns. This is why every stock that's a 'buy' has a higher than average expected return, even though in theory there should be just as many stocks that are buys with lower than average returns (but much lower than average risks).

as to "the general equilibrium approach doesn't restrict the sign of the correlation between risk and expected return, across countries or through time", I don't quite follow. At any point in time, every g.e. model I have seen has a strictly positive linear relationship. If he's saying that the correlation across countries or time is positive or negative because of the risk premium, ok, fine, but still there should be a positive relationship, on average, between risk and return cross sectionally over time.

Drewfus said...

The status of, and demand for "experts" and expert authority in any domain, is independent of the level of scientifically validated knowledge of those experts.

Anonymous said...

This is a general question but relevant to this post: What should I get out of my finance PhD program?

Eric Falkenstein said...

Well, learning econometrics, the nature of time series, the dangers of overfitting, how parochial issues like the bid-ask spread, time-varying volatility, etc. affect results, these are valuable skills that outsiders don't have. You do learn a lot about dead ends. Basically, you learn how to deal with crappy data.

And perhaps most importantly, as a phd you show 1) you can program and handle large datasets and 2) you are reasonably smart.

But, there's no really good technique that industry really needs, like GMM or ARCH.

Anonymous said...

I would propose that under certain conditions, minimizing benchmark risk at the mutual fund level is consistent with Markowitz's ideas. If the CAMP assumptions hold, investors would want to hold the market and the risk free instrument. It's only reasonable that funds would want to be as close to the market as possible in that case, thus making minimization of benchmark risk at their level the optimal strategy.

I'm not saying that the CAPM assumptions DO hold, but you have to wonder why index funds are so popular...