Risk models - more information

In the previous two posts (here and here) I wrote about mathematical risk models and how they contributed to the financial crisis of 2008. This post contains references to more information.

I recommend the following three books, all written before last year's financial crisis:

Against the Gods: The Remarkable Story of Risk, by Peter Bernstein (1996). This is a very readable history of the mathematics of risk. It is surprising how much of this history is from the study of gambling. This book is the source of the graph of monthly changes in the S&P 500 stock index in this post. The illustration on the cover of the book is Rembrandt’s painting of “The Storm on the Sea of Galilee.” Now there’s an example of risk!



The Black Swan: The Impact of the Highly Improbable, by Nassim Nicholas Taleb (2007). Dr. Taleb was a practitioner of mathematical finance, and gives an inside view of the profession. This book was a New York Times bestseller. Dr. Taleb calls the normal distribution the "GIF": the Great Intellectual Fraud (chapter 15).

Dr. Taleb dedicated The Black Swan to the author of the third book that I recommend: "To Benoit Mandelbrot, a Greek among Romans."



The (mis)Behavior of Markets: A Fractal View of Financial Turbulence, by Benoit Mandelbrot and Richard Hudson (2004). Benoit Mandelbrot is a famous mathematician, known for his work with fractals and the Mandelbrot set. He was not originally known for his work with the mathematics of risk. In a twist of fate that we in Farm Credit can appreciate, Dr. Mandelbrot became interested in the mathematics of risk when studying the volatility of cotton prices. He tells that story in Chapter VIII "The Mystery of Cotton."

Dr. Mandelbrot writes that there is a spectrum of risk, from "mild" to "wild." He says that the normal distribution is sufficient for analyzing mild risk, but that there is no mathematics currently available that is adequate for analyzing wild risk. If a mathematical tool is ever to be developed that will help us analyze wild risk, Dr. Mandelbrot believes that it will be found in fractal mathematics.

Of the three books, The (mis)Behavior of Markets is the most insightful. But The Black Swan has the most delightful quote—on p. 225 Dr. Taleb says: "Likewise, the government-sponsored enterprise Fanny Mae [sic], when I look at their risks, seems to be sitting on a barrel of dynamite, vulnerable to the slightest hiccup. But not to worry: their large staff of scientists deemed these events 'unlikely.' " Dr. Taleb wrote that in 2007. Here's what happened in 2008.

I also recommend the following newspaper and magazine articles, all published during and after the financial crisis:

“The 1% Panic,” by L. Gordon Crovitz, Wall Street Journal, 10/13/08 (may require subscription to read). Discusses two of the three books mentioned above.

“The End,” by Michael Lewis, portfolio.com, 11/11/08. No math, but an interesting discussion of people.

“Risk Mismanagement,” by Joe Nocera, New York Times, 1/4/09. Discusses one of the three books mentioned above.

“Recipe for Disaster: The Formula That Killed Wall Street,” by Felix Salmon, Wired Magazine, 2/23/09. Discusses more esoteric math than I have written about on this blog.

If you wish to play around with the normal distribution, there is an excellent Excel file that you can download here. I used this file to generate the graph of the normal distribution in this post.

Risk models - some math

In the previous post I wrote about how the failure of mathematical risk models contributed to the financial crisis of 2008. That post did not include any math. This post is about some of the math.

Modern financial theory purports to be able to calculate probabilities associated with risk with a high degree of precision. There is much more to modern financial theory than I understand, but it is primarily built on the foundation of the normal distribution, also called the bell curve:

The normal distribution is a wonderful piece of mathematics. If you know only two numbers — the mean and the standard deviation — you can calculate all kinds of probabilities with precision.

You may have encountered the normal distribution in high school or college. Even if you didn't study it formally, you may have heard about grading tests "on a curve." This is the curve! The normal distribution describes many phenomena in our world, including the distribution of test scores. For example, the Scholastic Aptitude Test (SAT) is graded according to the normal distribution. Scores on the SAT are calibrated to have a mean of 500 and a standard deviation of 100. There is only a 2.3% probability of scoring 700 or higher (two standard deviations above the mean). That is the kind of calculation that is possible with the normal distribution.

The basic insight of modern financial theory is that changes in the price of an asset (i.e., the volatility of that price) can be modeled using the normal distribution. There will be many small changes clustered around the mean. There will be fewer large changes, far from the mean.

This works a lot of the time. The problem is that it doesn't work all the time. Below is an example of when it doesn't work. This graph shows monthly changes in the S&P 500 stock index (source p. 147):

The changes far from the mean (what are called the "tails" of the distribution) do NOT decrease to virtually nothing as in the normal distribution; they actually increase! A mathematical risk model based on the normal distribution will significantly underestimate the amount of risk in the world, especially in times of high volatility—i.e., in the tails.

So why do financial institutions use mathematical risk models that are ultimately based on the normal distribution? Two reasons. First, it does work well a lot of the time. And second, we don't have any better tools in our mathematical toolbox. There simply isn't any mathematics available that adequately describes risk in times of high volatility, like last fall.

For a list of references with more information, see this post.

What went wrong?

The following column appears in the Fall 2009 issue of Financial Partner magazine:

The Financial Crisis of 2008: What went wrong?

What caused last fall’s financial crisis? What lessons can we learn?

In this column, I discuss one of many contributing factors: The mathematical models that financial institutions used to manage risk were not up to the task. Don’t worry, this column isn’t about mathematics. It’s about the risks of thinking we know more than we actually do.

Some things in our world can be calculated with precision and some cannot. Farmers know this intuitively. We can calculate exactly what time of day and where on the horizon the sun will rise three weeks from next Tuesday. (I use “we” loosely. I mean that someone in our society is capable of such a calculation, and the rest of us can look it up on the Internet.) But we cannot calculate with any certainty at all whether that sunrise will be visible or obscured by a cloud.

Can financial risk be precisely calculated like the motions of heavenly bodies? Or is it as unpredictable as the weather?

A typical way to measure financial risk is in terms of the volatility of the price of something. The “something” can be almost anything that can be owned, such as stocks, bonds, commodities or real estate. Or it can be a derivative financial instrument based on such things as stocks, bonds, commodities or real estate. Trillions of dollars of such assets are traded regularly. One can observe the prices at which they trade and measure changes (or volatility) in those prices.

The next step is to estimate the probabilities of future price changes. There is a high probability of small price changes which represent little risk. Conversely, large price changes represent significant risk but occur infrequently.

We can calculate these probabilities using modern financial theory. (Again, I use “we” loosely.) The mathematics involved is well beyond high school algebra, so Wall Street employed an army of mathematics PhDs.

Even those of us who don’t understand higher mathematics often make investments based on information that incorporates the mathematics of modern financial theory, such as public ratings on bonds and other debt instruments. The result is that investors made trillions of dollars of investment decisions thinking that they understood the risk in their portfolios.

Alas, events proved otherwise. Many investments were far riskier than the mathematical models predicted. Large price movements occurred more frequently than expected and the theory underpredicted the likelihood of extreme events. As a result, several large financial institutions suffered unexpected losses that they couldn’t absorb, resulting in failure. And this cascaded through the financial system, causing more failures.

What are the lessons?

Should we tar and feather the mathematicians? Well, no. Mathematics is useful and successfully explains significant portions of our world. But we got ahead of ourselves in thinking that we fully understood the mathematics of risk. One very costly lesson learned is that we should be more cautious when thinking that we understand our world. Another lesson is that many financial institutions should hold more capital. The financial institutions that failed thought they had sufficient capital based on their mathematical models. Unfortunately, they were wrong.

At June 30, 2009, Yankee’s permanent capital ratio was 18.2 percent. While no amount of capital completely guarantees against all events, you should take comfort that this level is considerably higher than most other financial institutions, both inside and outside the Farm Credit System.

More discussion

The following two posts on this blog are also on this topic:
Risk models - some math
Risk models - more information

Senate Judiciary Committee Hearing

Senator Patrick Leahy held a hearing of the Senate Judiciary Committee in St. Albans today: “Crisis on the Farm: The State of Competition and Prospects for Sustainability in the Northeast Dairy Industry.” Senator Bernie Sanders also participated:

Senator Leahy dedicated the hearing to Harold Howrigan.

Much of the testimony concerned Dean Foods. Senator Sanders stated that Dean Foods held 70% of the fluid milk market in New England, and 80% or more in many other states.

The first panel of witnesses included Christine Varney, Assistant Attorney General for Antitrust, and Dr. Joseph Glauber, the Chief Economist for USDA. Ms. Varney said that the Dept. of Justice and the Dept. of Agriculture will be holding a series of joint workshops in 2010 to explore issues relating to competition in agriculture, including the dairy industry. (DOJ news release)

The second panel of witnesses included three Vermont dairy farmers (Bill Rowell, Paul Doton and Travis Forgues) and Bob Wellington, economist for Agri-Mark:

The following graph of dairy farm income and expense was on display at the hearing:

One of the policy issues discussed was the Dairy Price Stabilization Program (aka Growth Management Plan) proposed by Dairy Farmers Working Together, the Milk Producers Council of California and the Holstein Association USA.

The hearing was well attended, with many farmers, politicians and media present. Click here for links to all of the statements and testimony.

UPDATE 9/20/09: Burlington Free Press coverage of the hearing:
Milk processors under fire
Dairy industry antitrust issues not new
photo gallery
Roger Allbee's letter to the editor about the hearing

Anne Galloway's coverage of the hearing on vtdigger.org:
Antitrust division to probe complaints about Dean Foods’ alleged monopolistic practices
(includes YouTube video of some of the testimony)

UPDATE 9/21/09: Wall Street Journal coverage of the hearing (subscription may be required to read):
Top Antitrust Enforcer Supports More Scrutiny of Dairy Industry
Kylie Quesnel is quoted.

Dairy Industry News

Links to recent news items about the dairy industry (subscription may be required for Wall Street Journal links):

EU farmers in white heat over milk prices - Yahoo!News/AP 9/16/09

Farmers Want Industry Probe - WSJ 9/17/09

Hate Calculus? Try Counting Cow Carbon - WSJ 9/18/09

Senate Judiciary Committee hearing in St. Albans 9/19/09

Vermont Ag Hall of Fame

Four individuals were inducted into the Vermont Agricultural Hall of Fame on Sept. 2nd at the Champlain Valley Fair:

John Finley (deceased) — former Deputy Commissioner of Agriculture
Millicent Rooney and all of the Rooney and James families — Monument Farms
Everett Harris (deceased) — for his work with FFA
Dr. Henry Atherton — Professor of Animal Science Emeritus at UVM

Congratulations to the 2009 inductees to the Vermont Agricultural Hall of Fame!

This was the 7th annual induction ceremony. Here are all the inductees from 2003-2009 (click to enlarge):




UPDATE: The Champlain Valley Exposition web site has a page about the VT Ag Hall of Fame.

Musings about "This Milk Problem"

Federal milk marketing orders exist under the authority of the Agricultural Marketing Agreement Act of 1937. The current northeast order came into effect in the late 1930s after farmers voted for it in a referendum. In 1937 UVM Extension published a booklet titled "This Milk Problem" by Harry R. Varney to educate farmers so that they could make an informed vote. (Click on the photo to see a larger view.)

The booklet gives a good overview and history of the dairy industry in Vermont as of 1937. Times on the farm were difficult in the 1930s, as they are now. It is interesting to compare and contrast the situation in the 1930s with today. If any reader of this blog would like a copy of this booklet please contact Ruchel St. Hilaire for a paper copy.

The best minds in the northeast have been thinking about "this milk problem" for over 70 years. (Click here for a recent example.) It's still a problem, perhaps now more so than at any time since the 1930s. I certainly do not have the answer to the problem. But that doesn't mean I don't think about it. I have spent most of my life around dairy farmers, and yet there are many things about the marketing of milk that I don't understand. While I don't have answers, I certainly have questions. Please note that the questions below are only "George" questions. They are not "Yankee Farm Credit" questions.

I often hear it said that "the system is broken." I wonder if this is true. It seems to me that the system of federal milk marketing orders was designed to make sure that all farmers receive "equal" prices, adjusted for such things as milk composition and distance to market. No matter how good a job a farmer or his/her cooperative does in marketing milk, all farmers receive the "blend" price. The system was designed to make sure that all farmers benefit when market prices are high. And of course all farmers suffer when market prices are low. Isn't the system working exactly as designed? Maybe we should ask the question: Is it still the right system? Does the current system itself inhibit innovative thinking about marketing?

I also often hear it said that proximity to the Boston and New York fluid markets is a strength of the northeast dairy industry. The booklet "This Milk Problem" discusses the importance of the Boston fluid market in some detail. This was certainly a strength at one time. I wonder if it is still a strength or if it has become a weakness. Perhaps a mortal weakness. Does the northeast dairy industry's strong attachment to fluid markets inhibit innovative thinking when it comes to marketing?

A few observations lead me to wonder about this. First, it was not always this way. Before 1900 fluid milk shipments to Boston were not significant because there was no easy way to transport milk. Butter and cheese production were more important. In the 1890s the largest butter factory in the world was in St. Albans, Vt. ("This Milk Problem" p. 8) If fluid markets were not always king in the past, will they necessarily always be king in the future? Second, New Zealand did not become a world power in the dairy industry by selling fluid milk. They found a way to be profitable with other dairy products. Third, the parts of the northeast dairy industry that have become famous and (often) successful in recent years are not selling fluid milk. Examples: Ben & Jerry's, Stonyfield, Cabot, Jasper Hill and the many onfarm cheesemakers. Whether through old technology (cheesemaking) or new technology (ultrafiltration) maybe the value in milk is in the components. Does the current marketing system allow this value to be fully realized?

One last set of questions. I often hear it said that one goal of food marketing policy is to provide cheap food for consumers. I ask—why? The goal of a marketing policy should be to create and capture value. The organic sector has figured that out, and kudos to them for doing so. Perhaps the conventional sector could learn something about marketing from the organic sector. A question I would ask when formulating a marketing policy is: How does a policy of cheap food help farmers create and capture value?

Well, I'd better stop asking questions, and get back to my day job. I am only a banker. I leave the job of finding markets for the products that farmers wish to produce where it belongs: with the farmers themselves and their processing/marketing co-ops.