reality would be, in imagination the island provides a blank canvas without all the complexities and accumulated environmental damages of modern life. But that imagination is false, and Defoe knew it deeply and instinctively, while Wyss apparently did not.
The world is highly evolved, and no blank canvases remain. Whatever projects you undertake, you need to think through the consequences of everything you’re changing. Even if you cannot trace direct cause-and-effect relations, you have to respect the possibility that even markets fight to survive.
A completely different understanding of randomness underlies the field of statistical thermodynamics.
One popular way to think about the stock market is as a random number generator. News comes out about each company every day, which pushes its stock price up or down. The movement of an index like the S&P 500 is just an aggregation of the moves of the 500 stocks that make it up. The day’s move is treated like a random variable. You try to guess its distribution by studying past moves and using other information. The risk to a stock investor is that she gets an extreme draw from the left tail of the distribution – that is, a big down move, as large or larger than the big down moves in history.
That’s a fine story and useful for answering some questions about stock market risk. But what if you invert the story and say that the way things work is that macro financial variables such as interest rates and gross domestic product growth and inflation, along with other large-scale financial forces like total investor risk appetite, tax policy and leverage rules, all combine to determine the appropriate move in the S&P 500. Instead of being a random variable, the S&P 500 move is determined by economic forces. Now no one understands all the forces and no one can measure them precisely, so no one knows what tomorrow’s S&P 500 move will be, but just because no one knows something doesn’t mean it’s random.
The macro-economic variables that affect the stock market as a whole don’t put much direct pressure on the prices of individual stocks, which are still driven mostly by company-specific news. But because the S&P 500 is just the sum of the 500 stocks that make it up, if it goes up 1 per cent, the average of the 500 stocks must also go up 1 per cent.
The randomness in the stock market is how the market-level move determined by macro-economic forces gets distributed down to move individual stocks. When I say the individual stock moves are random, I don’t mean that something like a lottery is in place to determine which stocks go up and how much. Individual stock prices are still determined mostly by company news and investor opinions. But suppose that on days when the S&P 500 goes up investors underreact to any bad news that comes out about companies and overreact to good news. If a big investor wants to sell a stock for some reason on a good market day, the sale has minimal price impact, but if a big investor (or a lot of little investors) decides to buy on a good day, the price of the stock will jump up.
For what it’s worth (and it’s probably not worth much), this is how the market feels to many participants – that macro forces determine a market mood and the market mood affects how investors react to individual pieces of news or changes in supply and demand. In this view, the stock market isn’t a clearinghouse for evaluating news and balancing supply and demand, it’s a mechanism for translating macro-economic forces into specific individual transactions in specific stocks.
Now the risk to a stock investor is completely different. It’s not the risk that the stock market as a whole will get a draw from the left tail of some distribution because there is no distribution. The person who invests in the stock market over long periods of time will earn a return based not on randomness but on how good the economy is. However, people who hold concentrated portfolios of only a few stocks, and especially people who hold levered positions and derivatives, face the risk that their particular positions will be randomly selected to do worse than the market as a whole.
For risk managers, the big issue isn’t normal day-to-day randomness, but the possibility that the stock market mechanism may break down. A breakdown may cause a crash unrelated to macro-economic forces, or a flash crash, or a bubble, or a liquidity crisis. These risks are the major ones for professional investors, and they’re significant risks even for long-term, diversified buy-and-hold investors, because a single major event can wipe out many years of normal returns. But these risks cannot be studied in a bottom-up random walk model.
Physicists and economists want to make statements about the aggregate values. Physicists want to say that increasing the pressure by shrinking the jar will increase the temperature. Economists want to say that increasing inflation by cutting interest rates will reduce unemployment. But how does an air molecule know what the aggregate pressure is, and how can it use that knowledge to increase temperature? Also, if air molecules aren’t the things that react to pressure to increase temperature, what is? For economists, how does the inflation rate that the Bureau of Labor Statistics is going to announce in six weeks affect whether or not an employer takes on an additional worker?
The answer that physicists worked out at the end of the 19th century, and that risk managers came to appreciate about 80 years later, is that the macrostates like temperature or inflation rate are actually statistical statements about the likelihood of individual microstates, which are the motions of individual particles or the decisions of individual economic actors.
Okay, that’s pretty technical. (I think it’s fascinating, but you’re free to disagree.) What’s important to understand in order to understand risk management is that this concept of likelihood and statistics is an entirely new way of thinking about risk. There’s nothing random about particle movements or the unemployment rate, yet to understand the properties of a jar of air or the properties of an economy, you have to treat the particle properties and unemployment rate as random variables.
There is a difference between physics and finance. In finance, you typically talk about millions, or at most billions, of transactions. In physics, statistical thermodynamics is applied to systems with billions upon billions of particles or more. In physics, it’s entirely possible that a benign macrostate will, purely by random chance, select a microstate that puts all the air molecules in the same part of the jar, or at least enough of them to create a temperature and pressure that cracks the jar, thus changing the macrostate. However, so many particles exist that the chance of a measurable aberration from uniform temperature and pressure is negligible. In finance, you deal with systems small enough that these sorts of events are rare but do in fact occur from time to time.
A major risk in the financial markets is that the random distribution of macro forces to individual transactions will align by chance in a way that disrupts the markets, which in turn disrupts the economy, which in turn delivers additional shocks to the market. If that happens, it may be months or years before any kind of equilibrium is restored.
In the early 20th century,
