Tuesday 29 October 2019

Markowitz the practical

The expected trajectory of the Markowitz story is, Harry gets randomly pointed to work on portfolio selection by an anonymous broker who he met in his supervisor's waiting room.  A couple of years later, randomly, William Sharpe turns up and asks Markowitz what should he work on for his own thesis, and out of this CAPM is born.   Both Sharpe and Markowitz get Nobel prizes for this, but, fast forward to 2005 and Markowitz publishes a paper which in effect, blows up the pure CAPM, his own baby.  No doubt, CAPM has been blown up many many times in the intervening 40 years, nonetheless it is somewhat surprising to see a 40 years later article from the father of modern portfolio theory criticising CAPM so roundly.

The paper in question is "Market Efficiency: A Theoretical Distinction and So What?".  Such a dismissive sounding title.  Unusually so given the academic norms, even for a publication like the Financial Analysts Journal.  I'm reading it as an argument which placed mean-variance efficient portfolios above CAPM-compliant market portfolios, and the attack is on the principle of unlimited borrowing (and/or shorting).  He very much assigns this assumption to his Nobel peer, Sharpe ( Lintner probably should be in that list too but he died seven years earlier).

He makes this rather bold claim: 
Before the CAPM, conventional wisdom was that some investments were suitable for widows and orphans whereas others were suitable only for those prepared to take on “a businessman’s risk.” The CAPM convinced many that this conventional wisdom was wrong; the market portfolio is the proper mix among risky securities for everyone. The portfolios of the widow and businessman should differ only in the amount of cash or leverage used. As we will see, however, an analysis that takes into account limited borrowing capacity implies that the pre-CAPM conventional wisdom is probably correct.
This in effect completely blows a hole in the primary element of CAPM and CAPM-related models which privilege the market portfolio as most efficient of all, and most universal.

I think Markowitz wants more life to accrue to mean-variance optimisation, for there to be more and varied applications of it, using credible, practical, defensible assumptions, assumptions which in the limit are person-specific.  He makes similar points in his Nobel speech when he says:
Thus, we prefer an approximate method which is computationally feasible to a precise one which cannot be computed. I believe that this is the point at which Kenneth Arrow’s work on the economics of uncertainty diverges from mine. He sought a precise and general solution. I sought as good an approximation as could be implemented. I believe that both lines of inquiry are valuable.

So his claim is he likes practicality, both in models and in assumptions.  It was at RAND, after all, where Sharpe met him, and where he met mister simplex, George Dantzig.  Optimisation research will get you prizes in computer science, but of course not in economics.  It is worth mentioning that Markowitz also made strides in operations research (which I think of as a branch of computer science) - for example he was heavily involved in SIMSCRIPT and invented a related memory allocation algorithm for it, together with sparse matrix code.  The buddy allocation system made its way into linux, and hence in to pretty much every phone on the planet.  The very term sparse matrix was in fact coined by Markowitz.  So as you can see, his interests were very much algorithmic and practical, whether this was inside or outside of economics.