Morningstar Advisor - February/March 2009 - 44

Morningstar Conversation I don’t know when it’s going to start to straighten out, but ultimately, in the long run, stocks are a good investment. Roger Ibbotson in more recent years, it’s reached as high as 80% in this crisis. So I think you can resurrect this standard deviation framework, the mean-variance framework, but you have to recognize that the variance itself is stochastic; it’s changing. Mandelbrot: I am very pleased to see that, Mandelbrot: In that case, if you say that the probability of whatever, 2% or 1%, that everything is going to blow up, you can’t always do it. Every curve, if you say that you don’t have to follow it with all the zigzags, can be represented by a much smoother curve. Local averaging is a very common procedure. I have nothing against it. Cooper: Could I step in? I think we’re on a very interesting topic here. I became very interested in Professor Mandelbrot’s work when I was trying to make sense of how the financial markets were behaving and reading a lot of work by an economist called Hyman Minsky. I became fascinated when I saw that Minsky was suggesting a model of the financial markets and, particularly, the credit markets, that behaved at times in a manner exhibiting self-reinforcing phenomena, meaning that there was a dependence in behavior in the way that Professor Mandelbrot was talking about earlier. us a relatively benign view of how markets might behave have in large part led us into this financial crisis; those models suggest very much lower levels of real risk in the system relative to what can be delivered. If these events don’t teach us to revisit the statistics that we’re using for financial markets, then really we are not adhering to the scientific principle of allowing the data to force the theories to be corrected when they’re proven to be wrong. Mandelbrot: Yes, thank you. I second your opinion very strongly, and I very much regret that I didn’t know about Minsky until very recently. In the past few years, friends have been pointing out his work and I hope to read his books soon to get a feeling of his thinking. I understand, however, that it is largely qualitative. Kaplan: Dr. Cooper, please explain Minsky’s theories. Cooper: The essence of Minsky’s theories are really very simple. He claims—and I think the evidence supports him very strongly—that there are self-reinforcing processes operating within our economy, largely because of the way our economy is financed through debt. Those self-reinforcing processes mean that a credit expansion, when it starts, can act through what is known as positive feedback, which means that an effect intends to self-reinforce itself. If you can imagine as asset prices start inflating, you’re able to borrow more money against those higher asset prices and you’re able to then use that money to buy more assets, which creates higher asset prices again. after many years of denial, discontinuities are now allowed into mainstream economics. In a way, what you describe is an unmanageable way of interpreting my latest model. There, the observed function is an ordinary Brownian motion [the standard bell-curve model], but time itself is suitably compressed or decompressed; sometimes it runs lightning fast and you get a discontinuity, and sometimes it runs very slowly. But, of course, my representation doesn’t help unless the process ruling the intrinsic time—hence the discontinuities—is represented mathematically in manageable and realistic form. This is what I achieved with the concept of multifractal. The job is not by any means finished, but I did show how a small number of assumptions and intrinsic parameters can represent—and, hopefully, in due time, master—a great deal of complexity. This is a clear advance. Ibbotson: Benoit Mandelbrot, you deserve a lot of credit for all your work on this field, but I’m not ready to throw out all these other models, because I think they still have a lot of use. For example, in the options framework, if you’re valuing something over a relatively short time period, allowing for a very different standard deviation can often roughly correspond to what would be a good valuation of these options. These self-reinforcing phenomena could produce sudden jumps with very non-normal distributions. It struck me that there was quite a close parallel between what Professor Mandelbrot had discovered in the data and what Minsky was proposing for his financial instability hypothesis. It seemed to me that fusing the two together would lead to quite a substantial improvement in the way we look at things. With respect to Dr. Ibbotson on the idea that we can model the market with conventional Brownian motion and conventional Gaussian distributions, yes, you could do that in a piecemeal manner. But in practice, what we have seen is that those sort of models that give 44 Morningstar Advisor February/March 2009

Morningstar Advisor - February/March 2009

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