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Part I
Getting Started with Risk Management
Chapter 2
Understanding Risk Models
Getting Scientific with Risk

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It’s a little embarrassing philosophically that neither of the two main concepts of randomness actually exists. Dice rolls are determined by physics, not chance. We just pretend they’re random. And, although experts know less about the human mind than about simple physics, you can be confident that people do not have a consistent set of subjective beliefs about any possible eventuality. So Bayesian probabilities don’t really exist either. (See “Betting with Bayes” earlier in this chapter for an explanation of Baynesianism.)

However, in the 350 years since mathematical investigation of probability began, science has uncovered some important kinds of randomness that actually exist in nature. These models have been much more important to the development of risk management than traditional probability and statistics.

Evolving

Darwinian evolution is defined as random variation and natural selection. It was the random part that was revolutionary when Darwin published On the Origin of Species in 1859. The idea of random selection is what distinguished Darwin’s ideas from earlier theories of evolution and is what upset many religious people at the time.

The main difference between the randomness exploited by evolution and the randomness manufactured in a casino or used to model the uncertainty of an individual is that the mechanism of randomness is created and regulated by evolution. I’m not going to go into the complex theoretical and mathematical meaning of that, but I can illustrate it with three examples.

Stealing from a tiger

Consider the question of what the stock market will do tomorrow. A frequentist pretends that the result will be the draw from some probability distribution, and tries to guess the characteristics of that distribution. She knows that the actual outcome will be the result of a complex interaction of economic news and traders’ reactions, but she considered that too complicated to model in detail. To a Bayesian, the question is, ‘What do I think are the possible moves the market might make and what probability do I assign them?’ The frequentist treats the market like a roulette wheel and tries to guess what numbers will come up with what frequency. The Bayesian treats it as something she’s uncertain about and tries to quantify that uncertainty.

Both attitudes are unwise for someone managing risk. They fail to give the market the respect it deserves. Suppose instead that you think about the stock market as a highly evolved entity. In order to survive, it evolves defences against people guessing what it would do. If people make accurate guesses they can extract money, which comes from other participants who eventually leave the market. The market’s defences don’t have to be perfect – they can allow some people to make some money – but the defences have to be extremely good given the number of smart people devoting great resources to beating the market.

But the market has to do more than just defend against smart traders. It has to

✔ Encourage people to bring information to it

✔ Attract both issuers of securities and investors in securities

✔ Direct economic activity in reasonable ways

If the market fails in any of these tasks, it won’t survive. Of course, many financial markets have failed over the years.

If you think of the market as a roulette wheel, you think that all you have to do is predict its next number with a bit better than random accuracy. If you think that the market is a highly evolved entity threatened by any profits you extract, you think you have to snatch a piece of meat from a tiger. One of the formative events in the career of a risk manager is getting mauled by the market. I don’t mean losing money because you’re wrong – that’s justice, not a mauling. I mean getting blown up despite being right because you didn’t see the market’s defences.

A Bayesian approach disrespects the market in another way: it treats the market as something that can be understood, albeit with some uncertainty. You won’t get the meat by understanding the tiger and negotiating. What you want is inconsistent with the tiger’s survival. That’s what you have to understand.

Shorting the big one

Michael Lewis’ book The Big Short (WW Norton and Company) is an entertaining account of traders who managed to get rich during the 2007–2008 financial crisis by betting against subprime mortgages. If you don’t work on Wall Street, you probably think the hard parts of that are figuring out the right bet to make, and getting the money to back your opinions. But as the book shows, those two things were minor hurdles compared to figuring out how to place the bets and then to collect the winnings. Lots of people got the bet right and lost all their money anyway. In addition, all the successful bettors in Lewis’ book had to survive multiple crises, none of which had anything to do with the economics of their bet and any one of which may have gone the other way.

You can look at each of problem one at a time and ascribe it to a tricky detail of the market or regulation, or some shady practice by dealers or an attack by people on the other side of the bet. Of course, if you want to be a successful trader, you have to discover all the tricks that can be used to extract your profits when you win, so this analysing each factor makes sense. However, in another sense it misses the point. These people were all trying to take money out of the market. The market has evolved ways to make that difficult. Not all these market defences can be traced to rational actions by individuals; many of them are consequences of group behaviour.

On one extreme are certain academic thinkers who treat the market as if it doesn’t care what they own. At the other extreme are superstitious traders who believe that the market is always out to get them. For risk managers, the traders’ perspective is closer to right attitude. There’s an old military adage, ‘Prepare for your enemy’s capabilities, not his intentions.’ Sound financial risk management prepares for anything the market is capable of doing, not just what the market should do, or what you expect it to do, or what makes sense.

Getting shipwrecked

Most people are familiar with the stories of Robinson Crusoe and the Swiss Family Robinson about people who had to find a way to survive in a completely new environment. These stories offer an excellent contrast between treating risk as something that powers evolution versus risk as something manufactured in a casino or resulting from subjective uncertainty.

Daniel Defoe’s realistic Crusoe is thoroughly aware that he is thrusting himself into a foreign ecosystem that he must respect in order to survive. Mostly that means he must adapt himself, and while changing things on the island where he’s shipwrecked, he must make small changes and think the consequences through thoroughly before acting.

In contrast, Johann Wyss’s Robinson family sets energetically to the task of recreating the Swiss environment they came from on the tropical island they land on. In the novel, they’re completely successful. In real life, their strategy would have been a disaster.

The idea of being shipwrecked on a desert island has an enduring romantic appeal. However unpleasant the 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.

Going thermodynamic

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.

Atomic theory says that a jar full of air is really a jar full of molecules whizzing around and occasionally hitting and bouncing off the jar. You can measure properties of the air in the jar like temperature and pressure. But these properties do not apply to any individual particle; they can only be defined and measured on an aggregate level. An economic analogy is aggregate economic statistics, like the inflation rate or the unemployment rate. These rates are measured by compiling individual transactions. But in one sense, there is no inflation, there’s just a bunch of people buying and selling a bunch of different things – some at higher prices than yesterday, some at lower prices. No individual experiences the inflation rate directly; it’s something that can only be defined and measured as an average over many transactions. Similarly, no individual experiences the unemployment rate. A lot of people are in the job market – some have jobs, some don’t, some want jobs, some don’t; and a lot of people are in intermediate job states – employed part time, employed but looking for a new job, self-employed by choice or not by choice, student, retired and so on.

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.

Trading in uncertainty

In the early 20th century, physicists discovered an entirely new kind of randomness, quantum uncertainty, that didn’t obey the rules of macroscopic probability. Subatomic particles behave randomly, but not like coin flips or dice throws, and not like Bayesian bets.

When you flip a coin, the result is either heads or tails, it makes no difference if anyone looks at it or not. But in the quantum world, the coin is both heads and tails until someone checks to see which it is.

An analogy putting you as the detective in a murder mystery may make this difference clearer: Before you know whodunit, you’re suspicious of everyone, and you’re uncertain about events because the testimony of the murderer is likely false. Given what you know so far, you think you have a 66 per cent chance the duke did it and a 34 per cent chance the butler did it. If you knew it was the duke, you would lock up the duke; if you knew it was the butler, you would lock up the butler; but given your uncertainty you lock up no one. You don’t lock the duke up 16 hours in the day and the butler 8 hours. The point is that the actions you take under uncertainty are not the weighted average of the actions you take under each of the possible resolutions. The state of uncertainty is fundamentally different from any of the possible resolved states.


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Financial Risk Management For Dummies

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