Most paths go quickly to near zero. A few soar up far beyond the expected one per cent rate for a while, but all eventually crash. If you run the simulation longer, all paths would become indistinguishable from zero. To a risk manager, this bet is terrible – one that leads to certain disaster. The more times you repeat it, the worse it gets, not the better. Your psychology, your risk appetite, has nothing to do with it. This bet is worse than just losing all your money quickly because the paths that soar attract imitators and cause all kinds of foolish overreactions.

      The problem is simple. If you win half your bets, you lose money. If you win 20 per cent, you turn £1.00 into £1.20. If you then lose 18 per cent, your £1.20 falls to £0.984. (The order doesn’t matter. If you first lose 18 per cent to turn £1.00 into £0.82, then a 20 per cent win turns £0.82 to the same £0.984.) Every pair of win and loss costs you 0.6 per cent of your wealth. In the long run, you’re virtually certain to have nearly 50 per cent wins and losses, so you’re virtually certain to wipe out your wealth.

      How does the median 0.3 per cent loss per bet square with the expected 1 per cent return? It’s absolutely true that your expected wealth increases 1 per cent each time you repeat this bet, but in the long run this fact results from a microscopic probability of winning an astronomical amount of money. You’re virtually certain to be broke, but theoretically have enough chance of winning far more money than exists in the universe that your expected value is positive.

      This example is oversimplified, of course. With real risks, you never know the exact probabilities and outcomes. You don’t repeat them an infinite number of times, and the results are not independent of each other. You don’t bet constant fractions of your wealth each time. I use the example only to make the point that you can ask two different questions about any risk:

      The answers to these two questions are independent. Some risks increase average utility if taken once but can’t be accepted as part of a systematic strategy that leads to success, and some risks fit perfectly into systematic strategies but are unattractive as individual propositions. The only risks worth taking are the ones that make sense on their own and as steps in the long-term strategy. That’s why you need both line risk takers to ensure the first, and risk managers to ensure the second.

      I emphasize that this is a practical result discovered by experience, not a theoretical one. The mathematical example was invested to illustrate the idea; it's not the source of it. Quantitative risk managers learned that it was possible to analyse real risk-taking histories of real risk takers without assuming anything about probabilities or future possibilities or risk preferences and determine accurately whether they were on paths to riches or ruin. First they learned with their own risk taking, often from bitter experience, and then they learned it was possible to prove their contentions to risk takers, even when markets were in the peaks of success or the depths of slumps. This was the birth of the modern field of quantitative risk management.

      Working with Financial Risk

      The topic of this book is financial risk. Financial risk is created by people. It can represent natural risk: for example, an insurance company writing hurricane insurance or a venture capital investor taking on some of the economic risk of a start-up company. But most financial risk is entirely contained within the financial system, such as a futures trader making zero-sum bets with other futures traders or a government bond portfolio manager speculating on changes in interest rates.

      Even when financial risk represents physical risk, it represents the virtual version, not the real thing. An insurance company writes checks after a hurricane; it isn’t pinned under a fallen tree without fresh water available. A venture capitalist writes off his investment if the company fails; he doesn’t fire people and auction off the office furniture.

      The idea of converting physical and economic risk to virtual form and trading it is revolutionary. It allows people to shed their excess concentrated risk, such as that their company will fail or their house will burn down, and to take on opportunities in a diversified portfolio of other people’s risks. Done properly, the good risk – the innovation, the opportunity, the creation – is maximised for everyone’s benefit, and the bad risk – the ruin, the disaster, the catastrophe – is diversified into broadly shared affordable losses. This diversification is not always done properly, unfortunately, but it sometimes is. And whether the finance is done well or badly, it deals with risk, and risk must be managed.

      In managing financial risk, you need to distinguish between the risk of the financial product – the stuff that’s bought, repackaged and sold – from the risk of running a financial business.

      

A printing company has a contract with the government to print money. On one day it prints a billion pounds worth of bills to send to the government, and earns £100,000 for the job. If you ask the CEO how much money the company made, the answer is £100,000, not one billion pounds. If the CEO forgets this distinction and starts spending the money his company prints for the government, he goes to jail.

      The distinction between types of risk is easiest to see with the manager of an S&P 500 index fund. The manager doesn’t make judgements about securities, he just promises to take investors’ money and use it to buy the 500 stocks that make up the index. (Investing in an index is slightly more complicated than this, but that doesn’t matter for this example.)

      One risk, of course, is whether the S&P 500 basket of stocks goes up or down. However, this risk isn’t to the index fund manager. He sells this risk to his investors. His investors want it. This is like the billion pounds of bills the printing company printed for the government.

      The index fund management company has a risk manager. The risk manager doesn’t spend time thinking about how risky the S&P 500 stocks are. That’s not his job. He is, however, concerned with the liquidity of the S&P 500 stocks because the index fund needs to trade in order to honour new subscriptions and redemptions. He worries a lot about valuation because errors may result in underpayments or overpayments. He pays attention to counterparty risks, such as what happens if a dealer fails to honour a trade, a custodian goes suddenly bankrupt or a stock-lending counterparty is unable to return borrowed shares. A host of other risks are present as well. The point is that the risk manager’s concern is that the management company does what it promises – deliver the risk of the S&P 500 to its investors – not whether the risk of the S&P 500 is a good or bad risk.

      Investing with a mutual fund company that picks and chooses among stocks in an attempt to beat the S&P 500 is a bit more complicated. Now the company is selling a more complicated risk, a combination of S&P 500 risk