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Roger Ibbotson, Benoit Mandelbrot, and George Cooper

Our distinguished economics panel debates the value of current risk models.

Paul D. Kaplan, 02/02/2009

We value your feedback. Send comments, questions, and criticism to advisorquest@morningstar.com.

To investors who lost mightily, the stock market crash of 2008 was a shock to the system. To Drs. Roger Ibbotson, Benoit Mandelbrot, and George Cooper, the decline was just the latest in a long string of the market's fits and starts. And if investors are finally awakening to the risks they incur when they invest in stocks, these three distinguished academics long ago observed that the market is a lot riskier than it may seem. Ibbotson is the founder of Ibbotson Associates, which is a wholly owned subsidiary of Morningstar, and professor of finance at the Yale School of Management. He is chairman and CIO of Zebra Capital Management, a manager of quantitative equity hedge funds.

Mandelbrot, the inventor of fractal geometry, is Sterling Professor Emeritus of Mathematical Science at Yale and co-author, with R.L. Hudson, of The (Mis)behavior of Markets (Basic Books, 2004).

Cooper, principal of Alignment Investors, is the author of The Origin of Financial Crises (Vantage Books, 2008), which The Economist calls "a must-read on the origins of the crisis."

From Chicago, we invited them to participate in a conversation, via conference call, about the crisis, economy, and the long-term ramifications for investors. On Dec. 17, Ibbotson called from New Haven, Conn., Cooper from London, and Mandelbrot from Boston. The discussion has been edited for clarity and length.

Paul Kaplan: The Fed took a dramatic step yesterday in lowering its funds rate to close to zero. What does that say about the current state of our financial system? How'd we get here?

Roger Ibbotson: Obviously, it's in really bad shape right now. I don't think the Fed funds rate has ever been that low. We are trying to regenerate the economy and save the financial system.

As I look back, it's looking more and more like the 1930s in terms of the financial markets. We haven't seen these large daily price movements in the market since the Great Depression. We had some really bad results in the stock market in the 1970s; we had the crash of 1987; and we were down 45% in 2000-2002.

But why I go back to the 1930s here is that both crises were created by the financial market. Most of the recessions that we have had were not oriented around a breakdown of the financial system. It's only this one and the one in the 1930s that were related to a breakdown in the financial system. In both cases, you had an overleveraged economy with a lack of transparency and a meltdown of various types of financial instruments. In the 1930s, a large number of banks failed and companies were overleveraged. We have that same sort of leverage today, not so much in companies, but both on the household level and, particularly, in the financial sector. This leverage was packaged and put in complex forms of derivatives, which wasn't always transparent to investors, and sold off around the world. So this crisis is not local to the United States, but it's a global financial crisis in both developed and emerging countries.

What's different this time is that the government is taking action. The government was paralyzed in the beginning of the 1930s, but today, it's acting. Maybe what the government is doing is not coherent or structured enough--there seems to be a lot of one-off actions and some panic--but certainly officials are doing a tremendous amount to try to alleviate this crisis. Part of that was what happened yesterday with the Fed rate.

George Cooper: What the Fed did yesterday is part of the necessary policy response here. They clearly have little choice, other than to use monetary policy and fiscal policy to attempt to prop up the financial markets and the economy more broadly.

What worries me, though, is that we're enacting these very aggressive policy responses without really stepping back and analyzing the problem or the reason that we got into this problem. We should go back a few years to when Ben Bernanke was giving speeches about how he could avoid a deflation problem in America by lowering interest rates and injecting liquidity into the economy; he claimed then that the deflation threat could be offset by stimulating more and more borrowing, which he and Alan Greenspan at the time did by lowering rates to 1% and triggering a boom in the housing market.

What was missed in that analysis was that by generating credit, Bernanke and Greenspan created a temporary boom in the economy. But once the credit needed to be repaid, you created a greater slump in the future. We are now reaping the rewards, if you like, of trying to fix the Nasdaq problem with a housing boom, which has compounded the problem into the current mega-credit cycle.

I think it would be very helpful if we step back and recognize that the problems in the 1930s and the problems we're facing today are a result of excessively loose credit policies in the previous decades. That's a missing piece of analysis. I think we need to fix the problems with the policies being used now, but as we do that, we need to recognize that once the fix is enacted, we need to run monetary policy in a fundamentally different way.

Kaplan: Dr. Mandelbrot, since the early 1960s, you've been building statistical models of asset returns. Your models differ very significantly from the ones that are taught in business schools. You use fat-tailed distributions, long-term memory, and so on. One of your students was Eugene Fama, who wrote his doctoral dissertation based on your research. Today, of course, Fama is very much in the mainstream of financial economics. Please describe your research. Why is it important for financial advisors to be familiar with it?PAGEBREAK

Benoit Mandelbrot: While working for the IBM Research Center in New York, I became motivated to look very carefully at cotton prices over a fairly ordinary period of five years. I observed that those prices' changes had been always very much dominated by special events that provoke sharp, even overwhelming, discontinuities. Then, I found that the same is true for the prices of wheat, stocks, and a multitude of other price series. The standard theory of price variation assumed continuity, but the data were very discontinuous. I became hooked on this problem and have worked on it ever since.

By training, I am a mathematician, but a very peculiar one, for an easily identifiable reason. During World War II, I studied by myself, up in the mountains and not in proper school. Therefore, I read many things that nobody else read, and I didn't learn many things other people learned, consciously or not. So I decided to look more and more carefully at price changes and see whether the fact that anything close to the simplest random walk fails to catch the variability of the process was something particular to the data I dealt with, or more widespread. Kaplan: What you're saying, Dr. Mandelbrot, is that when you began to look at financial data, you observed that contrary to the standard models, which say that returns follow a bell-curve distribution and move in a continuous fashion, the data were dominated by lurches and discontinuities. Today, of course, there's a lot of talk about "black swans," and you've coined the term "gray swans" to indicate events that differ significantly from the norm and should be planned for.

Mandelbrot: That's correct. When asked to comment about this, I always say that I've been studying gray swans, just because the problem is not just with one specific extreme event. You may say there are swans of every level of blackness, from almost white to completely black, and "completely black" has no limit.

Kaplan: Dr. Mandelbrot's thinking is very different from what is taught in business schools. Nobel Prizes have been awarded for mean-variance analysis, the capital asset pricing model, the Black-Scholes model of options pricing--all of which are based upon this notion that prices move in a continuous fashion. Should Dr. Mandelbrot's work be taught in business school?

Ibbotson: It's fine to teach it in business school, but let me say that I don't think you have to throw out all the standard deviation work because there are jumps and discontinuities in return series. I don't think there's any doubt that we have jumps and discontinuities and special events.

If you think of the implied volatility in the Black- Scholes model, that implied volatility takes on widely different numbers at different times. It's not a constant, and in fact, where we typically have standard deviations of, say, 20% implied in the stock market, or even 15% 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.PAGEBREAK

Mandelbrot: I am very pleased to see that, 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.

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.

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 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.PAGEBREAK

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.

This asset inflation and credit creation can spiral on the upside and create, for example, a housing boom, as we've just seen, or a Nasdaq boom, as we saw in the previous decade. But equally, when they go in the opposite direction, they can spiral in a negative manner and create asset price deflation with credit destruction, as we're witnessing now.

The essence of Minsky's theory--and I would say Minsky's theory is really just an extension of Keynes' theories--is that the financial economy is fundamentally unstable. This is directly opposite to what I would describe as mainstream economic thought, which is that our economic system is fundamentally self-stabilizing.

The reason that I find this fascinating, and what is a lot of the topic of my recent book, is that if we examine what the central banks are doing--which is trying to manipulate and control the economy under conventional economic theory--those actions should not be necessary if the economy is self-stabilizing.

We have a quite fascinating confusion at the moment in that we have a theory that says the economy is self-stabilizing and we don't need central banks, but then we have these central banks attempting to stabilize it. Unfortunately, because they are operating to this efficient market theory, the central banks are getting that stabilization process wrong because they're working to the wrong paradigm.

Kaplan: Dr. Ibbotson, is the economy fundamentally unstable or does it self-stabilize? It is curious that economists of every stripe right now are calling for aggressive government action regardless of what theory they seem to normally subscribe to.

Ibbotson: The economy has lots of self-stabilizing features, and it has other features that are destabilizing. Most of the time the economy is stabilizing, but certainly, I won't argue that the situation is stable now; instead, we have discontinuities here of an extreme sort.PAGEBREAK

But there are also behavioral aspects of this. I think the risks are definitely much higher than you might think of just looking at standard deviation, not only from the mathematical aspects of other measures of risk, but also from the way people react when they have the bad result. People often have the bad result at the same time they are losing their human capital income. They're losing all of their wealth at the same time, so they tend to be much more risk-averse than standard economics would show them to be. There is a lot of risk, and there's more risk than we think. I agree with both Benoit and George on these points.

Kaplan: If you were to receive a phone call from President Obama asking for your advice, what should policy be going forward, both in terms of fiscal policy and monetary policy?

Ibbotson: This process is so complicated that I don't have a ready solution as to how he should organize all these things. There's not much monetary policy left to be played here because they've already cut the rates to near zero. There's a lot of fiscal policy in Obama's plan, but I worry about the government being involved too much in the private sector. I think the likelihood of the government being able to straighten out this situation completely is not high; there will be a vast amount of waste in how they spend that money. Putting money into failing companies may be temporarily stabilizing, but it creates long-run problems.

Cooper: Well, like Roger Ibbotson, I don't believe that there is a quick, painless fix available. I think there are different routes that can be taken, but none of them are going to be pain-free. If I were advising President Obama, I would suggest that he acknowledge that we've had an excess accumulation of debt and that we now have little choice but to alleviate the burden of that debt through controlled monetization. That is, to inflate away the debt.

As we recognize that, however, we must recognize that this also represents a failure of previous monetary policy, and that once we have monetized the debt away, we will have to enact a radically different approach to monetary policy--one that pays close attention to credit cycles and not just to managing consumer price inflation.

Kaplan: Our readers are getting a lot of questions from their clients about what they should do. What kinds of things should advisors be discussing with their clients?

Ibbotson: I would be saying that when markets pull out of calamities, they often have their highest returns. We had the highest return ever in 1933 in the midst of a severe depression. You get the extreme pullout when things start to get a bit better. The markets in general move ahead of what's actually happening in the economy. The risk premium on stocks has gone way up because of the fact that investors now recognize that there is much more risk in the market than they had recognized. Stocks may not be done dropping, especially in light of what's happened to the financial system, and I don't know when it's going to start to straighten out, but ultimately, in the long run, stocks are a good investment.PAGEBREAK

Cooper: What I would say is that if we look back through history, yes, we had a crisis in the 1930s, especially in America, and look what happened to America afterwards. America was the most powerful, strongest growing economy for many, many decades.

I think if we step back from the financial side of things, and we focus on what really generates wealth for people in the long run, which are technological improvements, we'll realize that we're still living through a fantastic environment. Emerging markets are opening up to inward investment and adopting free market principles, allowing investment and allowing human potential to be used more efficiently.

I think there's very good reason to believe that, for example, China has entered its own industrial revolution. I think over the coming decades, there's very good reason to believe that the growth of the emerging markets will be a genuine powerhouse to improve the living standards of everybody on the planet. But there's no doubt about it; we're facing a very tough few years in the near term.

Kaplan: Dr. Mandelbrot, in your book, The (Mis)behavior of Markets, you point out that the truly risky nature of stock market investing, which is not really adequately captured by the standard models, could provide an explanation for the so-called "equity risk premium puzzle." As Dr. Ibbotson has documented, stocks over the past century have garnered enormous returns compared with fixed income. Yet, it's a puzzle because we can't square the theory with the data using models based on standard deviation.

You suggest, however, that investors, without the mathematical training that you have, do have some notion that stock markets are risky; they are aware that these crises occur and that the market moves erratically. Therefore, if you're going to be a long-term stock investor, you deserve to get a high equity risk premium. So the problem is with our models.

Mandelbrot: Indeed, the problem resides in the models. They began more than 100 years ago in the works of a man named Louis Bachelier. Little is known about him, but in 1900, he earned a Ph.D. in mathematics with a dissertation that put forward a theory of speculation. Unfortunately, his model for price variation was already very elaborate and I am sure far too mathematical for his time, so it fell into a black hole.

Soon afterwards, however, the same process was reinvented in physics by Norbert Wiener, and a huge theory developed on this basis. In a certain sense, it came to be viewed as the most basic and manageable model of variability that one can have. It was taught everywhere, and for reasons that are too complicated to explain, it became known as the Brownian motion.PAGEBREAK

Now, I have the greatest admiration for Bachelier and Wiener. But the only data Bachelier mentions concerned a very peculiar and highly controlled market. He had limited experience in running some very small investments. He was so isolated that no one knew him well.

In the 1960s, I found that the bell-curve models concerned only a part of nature. In particular, the standard Brownian models failed to apply to the real world of finance. Therefore, very thorough rethinking was necessary. I wrote a great deal on this topic, but, clearly, I did not speak loudly or convincingly enough.

Kaplan: But financial advisors need some way of explaining to the ordinary investor what are the risks of different kinds of investments. Is there a way to explain the risks and rewards of the market to an investor who has no mathematical training, so that the next time a crash happens, it won't be such a surprise?

Ibbotson: I think the simple message is that there's much more risk than there appears to be and that the standard deviation doesn't capture all the risk. Whether it's creating more-sophisticated statistical measures or whether it's just using behavioral economics and seeing the way people behave in crisis situations versus how they react on a questionnaire--all these sorts of things suggest that there's much more risk and much more risk aversion in markets than is revealed in the ordinary way we look at economics.

To me, there's never been a risk premium puzzle, because I've always thought that the risks are much higher and that there should be a payoff for this kind of risk. We'll see that people will be much more averse to risk going forward and much more averse to the stock market going forward.

If there is a positive equity risk premium, and I certainly think that's the case, this crisis will make it more obvious. The crisis itself is creating a big negative return, but going forward in the long run, I'm quite confident that stocks will outperform bonds.

Paul D. Kaplan, Ph.D., CFA, is Morningstar's vice president of quantitative research and a frequent contributor to Morningstar Advisor.

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