A conversation like this is quite likely to have taken place in Washington D.C. sometimes in the late 1990s^{i} :

Robert Rubin : I don't believe that anything, absolutely anything, in this world is a "provable certainty".

Alan Greenspan : That's a dangerous path you are treading, Bob. If you say that nothing is a "provable certainty" in this world then uncertainty is itself uncertain thereby rendering your argument false. By the way, I am sure it’s Wednesday today. There is nothing uncertain about it.

Robert Rubin : Of course, the cognitive issues are important here. I would have to take your word for it and perhaps the words of millions of others that today is Wednesday and I would also stipulate the same, given that I can see it is Wednesday. It’s something one still cannot prove, show with certainty, that it is Wednesday. Based on the assumption that Wednesday comes after Tuesday, I’ll have to assume that today is Wednesday.

Alan Greenspan : Actually, what you trying to say, Bob, is that conditional on the fact that Wednesday comes Tuesday and that yesterday was indeed Tuesday, the probability that today is Wednesday is one.

Robert Rubin : Perhaps, you could say so, but it is all probability, isn’t it?

Alan Greenspan : Yes, it is and the funny thing is that probability always catches up with you.

Alan Greenspan and Robert Rubin, two men revered and held in very high esteem until quite recently are now vilified and despised by the banking and investment community at large. Heroes have become villains. These two men lived in a probabilistic world and, perhaps, ultimately succumbed to the turbulence and the uncertainties of the financial markets.

In the end, the theory of probability caught up with them. In the end they were felled by the same axioms of probability that they so strongly espoused.

Greenspan was a Bayesian. He believed in the Bayesian philosophy and the Bayesian approach to probabilistic analysis. His entire career at the Federal Reserve, it seems, was predicated on this philosophy.

There is nothing like an objective measure of probability. In an absolute sense, no one knows whether it will rain or not today; it is impossible for any human being to say – in an absolute sense – whether it will rain or not. However, we make predictions about rainfall day in and day out. How does the Weather department do that? They can make predictions based on data and information; based on their experience and the study of historical data about clouds, weather pattern and the month of the year they have an opinion – a "probabilistic estimate" if you will – about how likely is it that it will rain today or this week. Then they get fresh information and physical data about the weather and alter their analysis and change that "probabilistic estimate" to a new estimate. There is no objective answer to whether it will rain or not. All we have is an opinion, a belief, about the occurrence of rain from some *a priori* probability distribution but that opinion, belief, gets modified by the observation of data and we form *a posterior* distribution – a framework for analysis, if you will – using certain rule. That rule is the Bayes’ rule.

To Greenspan, the world was probabilistic, but only conditionally so. The concept of probability exists only as our subjective beliefs and these beliefs get continuously modified by new data and observations. The question that we should ask is not *"what is the probability that it will rain today"* but rather* "conditional on our prior beliefs and on the presently observed data what is the confidence with which we believe that it will rain today."* Just as in life, so it is in economics and economic theory. To Greenspan, the world of money and finance was characterized both by a "Knightian uncertainty" in which probability distribution of outcomes is unknown and the "risk" where the uncertainty of the outcomes is demarcated by a known probability distribution. How does one make a decision in such a world?

This was Greenspan’s predicament. He would conjecture about issues – such as growth of productivity in the United States – long before, such conjectures became accepted truths. This required him to make informed decisions based on the large volume of information that kept flowing in from the markets and economy and keep altering his existing beliefs. There was always a prior probability distribution to reflect his beliefs about the variables in the economy – productivity, interest rates, money supply, etc. The crucial task was to get the uncertainty intrinsic in (model) assumptions in a quantitative model and then exploring how uncertainty affects alternative model decisions. It was a classic Bayesian approach to study the economic variables and then take decisions based on his beliefs. These beliefs, mostly expressed as quantitative assessments, came from a mathematical model which analyzed data from the economy as well as which factored in assumptions from a prior probability distribution and then “evaluating an utility function describing how uncertainty affects alternative model decisions.”

Greenspan’s beliefs were not only based on some objective probability assessment about events and economic variables (which came from past observations and experiments) but also on what was happening in the economy at present, how the dynamics between economic variables were changing and impacting outcomes thereby altering the existing beliefs. It was a form of dialectic, something like the Hegelian dialectic, thesis and antithesis giving rise to synthesis, which befuddled the mind. Most people termed this kind of reasoning “Greenspan speak” or the “Fed speak”. If the world we live in is continually in a state of flux, then why shouldn’t our thinking be also in a state of flux? Alan Greenspan inhabited a Bayesian world.

Robert Rubin believed in a probabilistic world too.

Rubin remained a risk arbitrage trader all his life. As a trader in Goldman Sachs he dealt with risk every day of his life and this is where his probabilistic thinking got crystallized. Nothing was certain, or as he likes to term, “provable certainty.” Early on in his career he was aware of the asymmetry that existed in the markets and our inability to deal with these asymmetries.

For example, even though, generally speaking, the value of a fixed income, interest rate product, such as a bond or a mortgage security will go up if the interest rates drop, there is no certainty that if you are long a certain fixed income product you’ll always make money if the rates drop. He had learned his lessons in risk from the financial markets. In 1986, as losses at the fixed income division of Goldman Sachs mounted to $100 million, Rubin discovered that there are implicit interest rate options embedded in many fixed income products. If the rates drop then homeowners would refinance their mortgage at lower rates and corporations would exercise their call provisions to refinance their bond debt. Therefore, if a trader has a long position in these assets he would not make as much money as he would expect to. And if the trader was hedging with short positions in Treasury securities then his losses would be big due to the price rise.

To Rubin, here was the asymmetry in the markets; here was the risk. How does one cope with such a risk? How does one model such a risk?

Like Greenspan, Rubin was aware that the world was enveloped in a Knightian uncertainty. And it was not just the world of finance and economics. Rubin’s world stretched far beyond that, into politics, into statesmanship and hard diplomacy. This was a world where no one can prove an axiom or a theory one way or the other. A model is as good as the guy who builds it and therefore in the end, as far as risk management is concerned human cognition reigns supreme. Your knowledge, your experience, your interaction with your environment and sampling from that environment, the entire cognitive process culminates into your decision making; and that interactive and heuristic process is best suited to incorporate, not just objective probabilities about events, but the entire space of Knightian uncertainty.

Greenspan is gone, his myth shattered and his charisma tattered by the extreme turbulence which he himself never expected nor ever encountered before. Perhaps, he spoke about the "**Age of Turbulence**" too soon.

Robert Rubin, too, has incurred the wrath of Citigroup shareholders and its Board of Directors and his reputation has taken a severe beating. Twenty years of hard work in building up his own reputation and legacy has been flushed down the tube. After all he grossly underestimated the perils of living "**In An Uncertain World**."

**Reference**: Bayesian Methods in Finance by Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, Frank J.

^{i} See the interview of Robert Rubin in the Fortune magazine, December 8, 2003

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