Every System Has Instabilities: Another Look at Johnson

Everywhere I look over the past few days I see a copy of Simon Johnson's paper The Quiet Coup. Even David Brooks at the Times has decided to write about it. Then there is the writing of Felix Salmon on the Li Formula which measures risk in complex portfolios. There is also the brilliant but under-publicized book by MacKenzie called An Engine, Not a Camera (MIT Press 2008) which looks at the 1987 crash from an historical and philosophical view. Finally there is also the overview of depressions and recessions recently by Muller.

However, the Johnson paper recounts what happened. But there is also a layer below this which is more fundamental. MacKenzie recounts the establishment of the mercantile exchange and the necessity of railroads and the requirement to have a commodicized whet or corn product so that corn was corn and wheat was wheat so that one could then write futures independent upon a specific bushel of corn or wheat. This established the first break in the nexus between the commodity, the good, the property is you will, and the financial instrument which was then collateralized against it.

A contract was no longer on a specific bushel of corn from a specific farmer. It was just corn of a certain specification. Yet what was preserved was the basic issue of money for goods, hard assets were always at the core. One had to remember that of you traded commodity contracts you never wanted to hold the contract at the end, it made you buy the wheat. Even if you lived on Fifth Avenue, the railroad care was now yours!

We now make a few observations which we believe extend the Johnson model and world view.

1. Financial Contracts Were Unlinked from Real Assets

If you have a mortgage on a house if all else fails you still own the house. If you have an option to buy eggs at the end you own the eggs, albeit costly, and you either make a large omelet or try to sell them at a loss. But when you created new financial instruments which were based on the performance of another set of financial instruments you moved from owning something to betting on a horse at Belmont. If you bought an option on an interest rate, albeit secured by some complex instrument, you just as easily could have bought a ticket for Lucky Larry in the 4th at Belmont. At the end of the race you won or lost and your relationship to the horse and the jockey remained unchanged, you had none. The development of these new instruments made more money for the purveyors but they were just bets. It was gambling. Everyone knew that. Land is land, that is why people like it, gold is gold, but a bet is just a bet.

2. Derivatives are Both Derived from Something Else and a Mathematical Derivative

Derivatives evolved as complex sets of new securities which were derivative from some set of reality based securities. A short, especially a naked short, is just that. But there is a second definition of derivative which applies. Namely the mathematical derivative. Namely dx/dt. We all know that if x(t) is a stock price of house price that dx(t)/dt is its derivative and we can get higher and higher derivatives. They go up fast and they go down really fast! Worse if x(t)=z(t)+w(t) where w is some noise in the system, well, hold onto your hat. Taking derivatives of noise is a sure guarantee to see things just go crazy. The white noise, Wiener process, that is assumed in the quants models when differentiated is unstable. The differentiate if n times and what do you get, Armageddon.

3. Every thing in the world is a System

Everything in life is a system. Cells are systems, genes are systems, the stock market is a system. A system is a set of interrelated and dependent states which can be measured and characterized and which has a dynamic set of interactions which evolved over a period of time. Some systems are easy to understand. A radio is a system where a signal comes via an antenna and is converted by a small set of electronics to a sound we hear. The simple observation about systems is that everything is connected. Every action has a consequence whether you know it or not. Tell a three year old not to touch a hot stove and then five minutes latter they do and come screaming that they burned their hand. Hopefully they do not do it again. However Financial managers seem to be unresponsive three year olds, they just keep touching the stove.

4. Systems Have Feedback Paths

The system we look at have paths that feed back on other elements. Push here and it pops up there. Some paths are negative and reduce effects and some are positive and increase them. Some paths are delayed and the delay can cause jerky hesitation. Some complex delayed feedback can cause instabilities.

5. Systems with Feedback are Unstable

Every engineer is shown a picture of the Seattle Tacoma Narrows Bridge collapse and told to beware of this phenomenon. There is unstable feedback that cause collapse. Engineers sped their careers looking at the past and looking to avoid these problems. That is why they over design things. That is why Apollo 13 returned. Financial managers are clueless. They are Masters of the Universe who never look behind. They could never be a spy, they never look back to see who is following them, and often times it is the instabilities of the very systems they are playing with. The quants were for the most part physicists and mathematicians. The engineers, real engineers, are just too cautious. I recount a prior article on my comments on the Black Scholes model in 1973.

6. Systems are Stochastic, Random

Every system has random elements. They are random either because we can never really model them or because things just happen. Cancer in many cases is a rand event. In Chronic Myelogeneous Leukemia there is a splitting of a chromosome in the stem cells in the bone marrow. A fragile part of one chromosome breaks off and attaches to another. This is considered random, it just happens. Perhaps if we knew more about it we could deterministically say it has a deterministic cause, but maybe it just happens. All systems have these characteristics. The Quants modelled randomness in a Gaussian manner. The Gaussian world assumes that every event is independent and that they add up in such a manner and that clustering of "stuff" is impossible. There are various theorems which lay this view out in detail. The Gaussian world is a kind world, bad things happen independently and infrequently. In the really world clustering of event are all too common. It is this un-modellable world that we live in.

7. Random Systems with Feedback Can Be Really Unstable

If deterministic systems can be unstable then random feedback systems can be really unstable.

8. "S..t" Happens! Unstable Systems can result from the confluence of Events.

Well all of the above may just sound risky enough but there is also the favorite problem, we engineers call it Murphy's Law, the unexpected. It always happens. I remember Apollo 13 which I had designed the optical guidance system at the last minute and I thought it would never be used. Who'd da thunk! Things just have the habit of clustering. It is like telephone traffic was on mothers day. We all knew it and we planned for it. But then when the second all digital switch was deployed in Beverly Hills in 1966 they forgot about the fact that 1 PM in Beverley Hills was 4 PM in New York and everyone called their stock broker that day because of the glitch in the Stock Market and the switch failed because of an overload. This stuff just happens.

Thus Johnson is spot on in his analysis and the world of Bonfire of the Vanities lingered. The Financial Managers never got the point. They just went further and further and created their own world akin to the Oligarchs of Russia. The Fannie Mae and Freddie Mac bonus problem is another example of this arrogance. It continues and it is permitted to continue. Johnson observed the human side of the problem. My points articulated here is an attempt to detail a few of the laws of nature related to this problem. By the way, the same will apply to the current budget process. Thus beware!