Mandelbrot, what is wrong, and a solution

Friday, 23rd October 2009

Richard Beddard's post on a recent FT two part interview of Benoit Mandelbrot focuses on his comments on Bachelier and the efficient markets hypothesis.

Firstly, could those who are attacking the efficient markets hypothesis please tell us where all these profit opportunities are? In this particular case they are even attacking the weak form EMH. They are saying that they can predict future prices from past price movements (funnily enough, Richard also mentions even more evidence that technical analysis does not work in the same post). If they can really do this, they ought to be able to program it into a computer and watch the billions roll in.

Mandelbrot is undoubtedly right in many ways:

  1. Real life price movements are not continuous (prices move in ticks), and there are sudden jumps in prices. Assuming continuous time and price may be a bad approximation at least some of the time.
  2. The process by which prices move may not follow the formula that is usually used, so Black-Scholes etc. are wrong.

In addition there are other assumptions that can be challenged: that investors are risk averse and rational, for example. However dropping weak form efficient markets and no arbitrage seems a step to far for the moment.

No one has ever denied that markets can do not always function correctly (except, may be, some regulators). It is not at all true to say that the financial sector has been assuming efficient markets: the whole point of hedge funds is to find inefficiencies. The point is that the EMH is a normal situation, and deviations from it are opportunities to make a profit, because the market will tend to revert to efficiency.

As for dropping the assumption of continuous time (and price), you can derive a formula almost identical to CAPM assuming discrete time and price. It require very little in the way of assumptions (little more than no arbitrage). Mandelbrot and his followers also make much of the existence of large, sudden price swings (which can be adequately explained by fat tails). He also talks about clusters of price movements (e.g. lots of successive drops in price). This is harder to explain, and he could well be right that the underlying maths is scalable (fractal). The problem is that we are still a long way of being able to produce a useful model of this using fractals. I personally think that the key to explaining what is wrong with the market lies in agency theory. This is a subject I have long been interested in despite it not having been fashionable in recent years (I did my MSc dissertation on it despite my supervisor being less than encouraging). the reason it is unfashionable, is a problem that has damaged economics as a whole, not just financial economics. If it does not lead to lots of fancy maths, it was not taken seriously. Like economics, finance needs a return to thinking about fundamental concepts. The market needs better ways of persuading professionals to manage money well. I strongly believe that the solution is to rely on integrity rather than incentives, because it is impossible to get the incentives entirely right. The only alternative I see is to shut down the money management industry, and let everyone who does not want to choose their own investments put their money in trackers.

Comments

Richard Beddard
Friday, 23rd October 2009 8:03AM

Hi Graham, your comments on my blog and here have given me some cause for thought, unfortunately not very well formed thought! In particular I wonder whether Mandelbrot's ideas could undermine the weak form of EMH.

Technical analysis is not particularly interesting to me - a bit of a blindspot, but I did ask Mandelbrot about technical analysis and fundamental analysis when I interviewed him. He was fairly adamant that technical analysis didn't work, he was more accepting of fundamental analysis.

I think the evidence is much stronger against the semi-strong form of EMH, and particularly (as I say in the blog) the value effect, a fact (that value outperforms glamour), recently confirmed (apparently, I only found this research this morning, and have only read the summary): http://greenbackd.com/2009/10/23/iconic-value-vs-glamour-research-receives-an-update/

I think you're on to something about agency theory. I always thought institutional investors added their own inefficiencies to the market but not necessarily that they added to the overall level of inefficiency.

It's funny that Burton Malkiel - defender of the EMH thinks its the 'pros' that make the market efficient because they have enormous powers of analyis and the ability to act instantaneously.

But he even acknowledges elsewhere in his book that institutional investors have a huge influence on the market and can distort it. Presumably somewhere along the line he decided that their distorting effect was less important than their moderating effect. I don't know how!

That's the problem with EMH I think. Once you break out of its idealised framework, reality undermines it.

I admit Mandelbrot's models, as they are, don't give investors any tools to value shares, build portfolios, or manage risk, but they do at least recognise reality can be extreme, or 'rough' as Mandelbrot would say. That's all I'm claiming for them.

Richard Beddard
Friday, 23rd October 2009 8:10AM

PS - you mention assumptions that can be challenged. I think EMH is a mass of assumptions that don't stand up in reality. Not just that investors always act rationally, but also that prices respond instantaneously to new information. Piotroski demonstrated (to my satisfaction) that they adjust slowly - particularly for the kind of companies that he (and I) am interested in - deep value - i.e. unloved/unfollowed companies.

Graeme
Friday, 23rd October 2009 8:34AM

My own thoughts are still far from well formed over several of these issues: the application of fractals to finance, in particular.

I think the agency theory link you found recently (I think you twittered it: it showed up on Facebook) had evidence of professional investors making the market less efficient.

I think the explanation of the mis-pricing of value lies in agency theory. I think I have blogged or commented before on why pros like growth stocks.

I would say semi-strong EMH is true with some deviations. The reasons why the price rise in value shares is slow goes back to the agency issues again.

I agree about looking for unloved companies. One of my first ever blog posts talked about not following the herd: http://pietersz.co.uk/2005/03/good-analysts-and-stock-pickers

Not being interested in technical analysis is a sign of having some sense, not a blind spot!

I other words I am saying semi-strong EMH, with prices distorted by agency issues, and the maths quite likely to be fractal.

I am wondering about whether the price distortions caused by agency issues are necessarily a deviation from EMH. The prices still reflect all known information, it is that the prices also reflect the incentive investment managers have to take punts. It is really risk aversion that is in question.

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