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      You have various ways to measure the spread illustrated by this graph. You can compute a standard deviation, a mean absolute deviation, an interquartile range or something else. For that matter, you can just reproduce the graph. However, there’s something misleading about representing the data this way: You cannot see the essential risk on this graph, and the risk you think you see is largely irrelevant.

      

In round terms, the stock market has turned £1 into £100 over the last 50 years. On about 99 days out of 100, the market moved less than 3.5 per cent in either direction. But consider the 80 days on which the market went up more than 3.5 per cent. They’re barely visible on the chart, but collectively they caused about a 4,000 per cent increase in wealth. All other days were responsible for about a 150 per cent increase. If you consider the 60 days when the market went down more than 3.5 per cent, they collectively turned £1 into £0.03.

      Now the 150 per cent increase from the 99 per cent of normal days isn’t insignificant. However, most of the action, especially to a risk manager, happens in the 1 per cent of extreme days, which are nearly invisible. This percentage isn’t true just of stock market returns, but also true of many important things in the world.

      Consider the risk going forward, which of course is what matters. Suppose that you’re considering an investment in stocks with a 1,000-day horizon – about four years of trading days. You expect to get 990 normal days in which the market moves less than 3.5 per cent. You may get 996 or 987 or even 1,000 such days; but you won’t get much different from 990. Also, getting a few days more or less won’t matter much because the average return on these days is 0.04 per cent, and no day can make a difference of more than 3.5 per cent. With 990 or so events and limited range, you’re highly likely to get something quite close to the expected outcome. Moreover, you have lots and lots of historical data on what happens on normal days, so you’re reasonably confident you know what the expected outcome is. There just isn’t a lot of risk in 99 per cent of the days, and what risk does exist can be easily handled by front-line risk takers. After all, if they couldn’t handle the stuff that happens 99 days out of 100, you’d have noticed long ago.

      You also expect to get about five days when the market loses more than 3.5 per cent, plus about five days when the market gains more than 3.5 per cent. However, there’s a lot of potential variability around those numbers. You might get 2 or 8 or even 0 or 10 or more of either one. Each one of these days is significant as they average about a 5 per cent move, and may be as large as -28 per cent or +18 per cent. With only a few events, you can get outcomes far away from the mean. Moreover, you have little historical data, you don’t really know how big these days can get; and you can’t be confident that your front-line risk takers are prepared for them unless you check.

      

If you take a closer look, you have even more reason to be concerned about a small number of big days. Markets often don’t function properly. You may not be able to trade the way you usually do or at all. Financial intermediaries may fail. Trades may be reversed after the fact. Events may trigger investigations and fines. Financial instruments don’t move together as they usually do – correlations are different on big days.

      Another problem is that the big days in the market can seldom be tied to observable economic events. On normal days, some fraction of stock price movements occurs in discrete jumps after clear news events such as central bank actions or corporate earnings announcements. A lot of unexplainable noise (price movements that cannot be easily explained) is evident too (which doesn’t stop commentators from jumping in with explanations after the fact), but it’s possible to imagine that prices are changing in response to economic news. On many of the biggest days, no news turns up at all, and on others, the extent and timing of the price move is inconsistent with the news the market is supposed to be reacting to.

      If that weren’t enough, not all the days the stock market makes big moves are abnormal; some are just normal big moves. On the other hand, on some abnormal days, the market behaves strangely but prices don’t move a lot by the end of the day, such as the Flash Crash of May 2010 or the Quant Equity Crisis of August 2007. In addition, you need to consider days missing from the graph because the stock market was closed, such as the days after the 9/11 attacks.

      The point is that almost everything a risk manager is concerned about is missing from the graph in Figure 1-1, or is nearly invisible on it. Therefore, any measurement of the graph is of only marginal use to a risk manager. Doing sophisticated analytics on the 99 per cent of normal days can be useful to line risk takers, but it’s false precision to a risk manager.

      

Consider Nassim Taleb’s example of a casino that can measure the risks of the bets it makes with its customers at the roulette and craps tables. This risk averages out quickly, and a risk manager who focuses on it would be wasting his time. The three biggest losses of one particular casino in one year were:

      ✔ The star performer was mauled by a tiger.

      ✔ The owner’s daughter was kidnapped and held for ransom.

      ✔ It was discovered that a long-time, low-level employee, for unexplainable reasons, had been stuffing tax reporting forms in his drawer rather than sending them in to the IRS for years, which resulted in large penalties.

      None of these things would have shown up in a graph of profit and loss from table games bets. None of these risks could have been reasonably measured before the fact.

      

Never confuse risk measurement with risk management. If you can measure it, you probably don’t have to manage it.

      People often like to segregate calculated risk from other types of risk. Calculated risk covers situations

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