256 CHAPTER 11 MANAGING RISKS

It’s normally like this

If statisticians have added anything to human knowledge, it is their insight about what

you normally find when you look into a bucket of numbers. In case you are unfamiliar with

this, I will elaborate. It is a masterpiece of observation. But do not dismiss it lightly. It pro-

vides a great tool for understanding present and future events that affect your business.

It allows you to say with confidence, I am 95% certain that sales will be between $80,000

and $100,000. There is only a 12% chance that R&D will fail to deliver (you must have excel-

lent boffins). There is an 80% likelihood that profits will exceed $5 million. And so on. You

can use this tool to qualify any such statement. First, the mechanics. Remember, this is all

painfully obvious logic.

SYMMETRICAL OR SKEWED?

Take any measurement that is affected by a large number of independent influences. This

could be heights of mature trees lazing in a sunny forest, diameters of ball bearings roll-

ing off a production line, teenage girls’ spending on cosmetics. The measurements are

always clustered evenly on either side of the average.

If you plotted a chart showing these observations, you would have a bell-shape curve.

(See Figure 11.1.) It is called the normal curve because it is what you normally find in such

situations.

A digression. Sometimes observed values are not distributed so neatly. For example, a

chart of annual salaries would be skewed with a hump on the left – comparatively few lucky

tycoons earn big money. However, any set of data can be described with just three statistics.

1 The average (a measure of the middle or most usual value).

2 The spread (the range, between the smallest and the largest).

3 The shape of the distribution (normal, skewed).

17 Cash flow. Not enough kills. Too much, poorly deployed, reduces return on

investment.

18 Interest rates. Increases raise the cost of capital, reduce demand and damage

profits (unless you are a bank).

19 Exchange rates. Changes affect the cost of inputs such as materials;

can reduce the cost of imported competing products; can reduce your

competitiveness overseas.

20 Natural disasters. What would happen if flooding or an earthquake closed

your computer centre or your supplier’s factory?

IT’S NORMALLY LIKE THIS 257

If you are a number-cruncher and someone tells you these three facts about any set of num-

bers, you can instantly visualise the data and make all manner of wise pronouncements. It is

not dissimilar to looking at dice and knowing how they will roll. Sounds useful?

Most of us spend our lives comparing ourselves with averages (average income,

weight, height) and we know well enough what they are. You will have gathered that I am

focusing on the normal shape. This just leaves measures of spread, which I will talk about

for a moment because the terminology is less well known.

MEASURING SPREAD

There is a neat measure of spread with a horrible name – standard deviation. Do not be

put off. This is just a way of presenting a range as a standardised average. It is calculated

very simply. You will probably never need to do it manually, but the calculation is shown

on page 259.

If you work out this standardised average range (i.e. standard deviation) for any nor-

mally distributed data it is always the case that:

68.3% of all values are within one standard deviation of the mean;

95.4% of all values are within two standard deviations of the mean;

99.7% of all values are within three standard deviations of the mean.

This is incredibly useful. Turning it into English. If the average height of trees in a hill-top

copse is 10 metres and the standard deviation of tree heights is 1 metre:

just over two-thirds of trees are 10±1 metres high – that is, between 9–11 metres;

95% are 30±2 metres high, or between 8–12 metres;

nearly all trees (99.7%) are 10±3 metres high, or between 7–13 metres.

Blinding insight

If measurements are distributed normally, and if you know their average and

standard deviation, you have the key to unlocking everything there is to know

about them. Turn this upside down. If you make a central and a worst-case forecast,

and if you attach a probability to the worst-case, you can predict the probability of

every other outcome. (Your central, or most likely, forecast is the ‘average’.) Your bank

manager ought to be impressed.

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