In Memory of Benoit Mandelbrot

As we all know he has recently passed on, but for years was more than a credible critic of classical finance theory. While the discussion of Gaussian dists and the argument against it with reference to BM was brought up here before: http://www.analystforum.com/phorums/read.php?1,830472,830494#msg-830494 Maybe it worth revisiting it, in “The Misbehavior of Markets” Mandelbrot mentions CFA curriculum and Gaussian dist in it … Considering the events of the Great Credit Crunch/Great Panic of 2008. Do you think it is time to address the problems with Gaussian dist in the exams ? Do you think that perhaps stochastic calc and alternatives to the Gaussian curve should be introduced? Perhaps some watered down version of Mandelbrot set … ?

What kind of Mandlebrot set question do you think is an appropriate one for the CFA exam? Can you write a sample question that would be clearly relevant in a practitioner setting?

Well, I cant. I am new to CFA curriculum, and I have not studied “Mandelbrotian” models. If Manderlbrot Set is not relevant then lets forget it. However, “The Misbehavior of Markets” Mandelbrot presented a very strong argument against Gaussian dist as a staple in financial theory and practice and particularly in the context of CFAs on one occasion. I think history proved him right to a certain extent. You think CFA curriculum should not “lead the way?” And only update to what is actually used in the field, and question the effectiveness ?

People know that normal distributions aren’t the way the world works in finance, but at the end of the day, most of the tools we have are designed to work with normal distributions. The CFA curriculum pretty much ends by making sure that candidates know that there are limits to the effectiveness of most statistical tests based on the fact that real distributions have fat tails, i.e. high kurtosis. Fractal geometry is not the only way to get at this. Nonparametric tests are another; another is to use other distributions like the t-distribution or Cauchy distributions or more exotic stuff in your regression estimations, etc. The level of mathematics that is required to get an understanding of fractal geometry is just a lot more work than one can realistically expect to put on an exam that has all this other stuff in it. The way most people try to deal with it is to use something like a normal distribution to describe the everyday process of things, and then have a separate analysis of what happens on non-normal days, and trying to get your risk control processes managed in such a way that you can at least recognize when a non-normal event is happening and switch into the “extremistan model.” That really gets you enough of the way that one can leave out the extra semester’s course in fractal geometry. As for the Mandelbrot set, it’s very pretty and all, and it’s a great example of how you can have sensitive dependence on initial conditions in processes that are iterative. Also, given the feedback loop between our psychology and the behavior of markets, which is surely nonlinear, it isn’t too hard to argue that similar starting points in markets can lead to highly disparate outcomes. But I’m not sure what else the Mandelbrot set actually tells you. I’ve heard that there is a one-to-one mapping between points in the Mandelbrot set and every fractal that there can be, but I find this hard to believe, because I find it difficult to believe that iterating Z = Z^2 + C has enough dimensionality to capture all possible fractals. Moments like this make one wish JDV hadn’t gone and disappeared again.

Dr.Mavashi01 Wrote: ------------------------------------------------------- > Well, I cant. I am new to CFA curriculum, and I > have not studied “Mandelbrotian” models. If > Manderlbrot Set is not relevant then lets forget > it. However, “The Misbehavior of Markets” > Mandelbrot presented a very strong argument > against Gaussian dist as a staple in financial > theory and practice and particularly in the > context of CFAs on one occasion. I think history > proved him right to a certain extent. You think > CFA curriculum should not “lead the way?” And only > update to what is actually used in the field, and > question the effectiveness ? Look, I obviously am a fan of contemplating risks in a non-linear mindset. The problem here is that non-normal models don’t really exist in a useful sense for measuring risks. Those that do generally fail to provide much useful insight. Again, I firmly believe that the world is built on a framework of fairly random and unpredictable power curves, but that’s nothing new, true thinkers have known that for long before Mandelbrot rephrased the argument using equations. In the end, if you’re going to be one of the non-Gaussian types, you can either say you know what, normal dist isn’t exist, therefore we keep the limitations in our minds as we make decisions but move forward with the tools we have (which is probably the proper way to look at it) or you can constantly say the tools are broken, we shouldn’t use them, but you have no suggestions, which in my mind, is somewhat counter productive behavior. I guess if you wanted to see good analysis independent of the gaussian framework however, you could look to Munger & Buffett. Based on Munger’s book, the guy thinks CAPM is crap, cost of equity is a hoax, doesn’t use forecasts, but instead focuses only on forming a qualitative analysis of the underlying business over a lifetime holding period (basically an enormous PE fund in that regard). When I started the CFAi, I thought I was smarter than the material, but by the end, after I’d learned a great deal, I realized that the material had pretty much been right and I’d been off base. I believe the CFA material does a great job of outlining the general uses and limitations of various investor tools, particularly in level II and III for the limitations part.

bchadwick Wrote: ------------------------------------------------------- > > Fractal geometry is not the only way to get at > this. Nonparametric tests are another; another is > to use other distributions like the t-distribution > or Cauchy distributions or more exotic stuff in > your regression estimations, etc. Do you think perhaps this icluded in the exam matterials/questions? > The way most people try to deal with it is to use > something like a normal distribution to describe > the everyday process of things, and then have a > separate analysis of what happens on non-normal > days, and trying to get your risk control > processes managed in such a way that you can at > least recognize when a non-normal event is > happening and switch into the “extremistan model.” Does one of the three exams cover this?

Dr.Mavashi01 Wrote: ------------------------------------------------------- > bchadwick Wrote: > -------------------------------------------------- > ----- > > > > Fractal geometry is not the only way to get at > > this. Nonparametric tests are another; another > is > > to use other distributions like the > t-distribution > > or Cauchy distributions or more exotic stuff in > > your regression estimations, etc. > > Do you think perhaps this icluded in the exam > matterials/questions? There are plenty of questions that make test whether you remember that the results of a particular analysis assume normal distributions and some of the harder ones may ask you to determine the direction of the bias that non-normality works. The questions don’t test whether you actually know these other distributions (other than the t-distribution, and even that is only for the traditional uses of the t-test). > > > The way most people try to deal with it is to > use > > something like a normal distribution to > describe > > the everyday process of things, and then have a > > separate analysis of what happens on non-normal > > days, and trying to get your risk control > > processes managed in such a way that you can at > > least recognize when a non-normal event is > > happening and switch into the “extremistan > model.” > > Does one of the three exams cover this? This stuff shows up more in the risk management material, which is primarily a Level 3 topic. However, I can tell from your previous posts here that you will likely find it insufficiently mathematical.