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Fig. 5.6 Sensitivities: scaffolding project

The horizontal line across the chart represents the base case NPV of $0.6m.

There are three Type 1 sensitivities. Each of these is shown to the P10/P90

probability range. The numbers for each are listed on the chart. In the case of

the selling price the base case assumption was $1,700. The judgement of the

project sponsor is that the P10/P90 range is symmetrical around this number

with the range being Â±$150. The impact on NPV is shown as the top of the

160 The five financial building blocks

light-coloured block and the bottom of the dark block. The second Type 1

sensitivity concerned the scrap value of the scaffolding. In this case the range

was not symmetrical as the low estimate was $0.5m while the upside sen-

sitivity was $2m. The chart shows that the most important sensitivity con-

cerns the sales volume. Once again, there was more upside than downside.

None of the individual Type 1 sensitivities was sufficient to force the NPV

below zero.

Two zero NPV cases are shown. These were for sales of 846 units in the

first year or a selling price of $1,492. In each case all other assumptions are

as per the base case.

A single Type 3 sensitivity is shown. This is for a $100,000 increase in over-

heads. This could, for example, represent a calculation of the benefit on the

project of not having to pay any rental for the land. The fact that this is not

shown as a Type 1 sensitivity suggests that special attention is to be paid to

this sensitivity. It is clearly not just a usual degree of uncertainty that sur-

rounds the overheads or else it would be shown as Type 1.

Part 2: Portfolio effects

Spreading your bets

Now we must turn to what I consider to be the almost magical way that finan-

cial uncertainty can be made to disappear.17 In the realm of finance the effect

is referred to as portfolio diversification. Once again this is something that I

believe is best illustrated via a simple example.

We know that if you toss a coin once the result can be heads or tails.

Suppose that heads resulted in a payout of $1 while tails gave nothing. A

single throw will pay out either $1 or $0. The range in relation to the average

outcome is very great. Now consider two throws each paying out half the

As a rational person, I do not believe in magic. I do, however, believe that it is possible to exploit

17

an individualâ€™s perceptions to make them think something â€˜mustâ€™ be magic because the outcome

appears to defy rational explanation. The usual cause is that there is something the individual is not

aware of or some perception of how things work that does not apply in this instance. In the case of

financial uncertainty what people do not perceive is the vast pool of money that is available to take

risk and the willingness of financial investors to offset a win on one investment against a loss on

1another. This works in the case of money but not in the case of serious accidents because people are

not prepared to tolerate these at all.

161 Building block 5: Risk

amount. We know that three different scores are possible and that there are

four possible ways that the tosses can turn out. We should also know that half

the time we will get $0.50. So the range remains the same but now we have

a good chance of a result in the middle. If there are ten tosses each for one

tenth of the prize there are 1,024 different combinations of heads and tails

and 11 possible scores. The full range of outcomes remains zero to one but

now each extreme only has less than a one-in-a-thousand chance of coming

about. The exact mid point comes up 252 times while the middle of the range

($0.40â€“$0.60) comes up 672 times.

What we have seen in this example is that spreading your bets does not

ensure that you will achieve exactly the mid-point but it does more or less

ensure that you will avoid the extremes. Put another way, the range around

the mid-point within which it is reasonable to assume an answer will lie will

gradually decline as one increases the number of times a risk is taken.

Statisticians define a term called standard deviation to represent the vari-

ability of a set of data. The smaller the standard deviation, the lower the vari-

ability. I do not propose to prove it, but the standard deviation will fall with

the square root of the number of items considered. This means that by taking

a tenth of ten coin tosses one can reduce the variability by an amount equal

to the square root of 10.18 Spread your bets across 100 coin tosses and vari-

ability is down by a factor of 10. A million small bets gives a thousand-fold

reduction. This is the sort of level where we can say that risk has been effect-

ively removed.

Now one might think that there are few games which are played a million

times over and which can benefit from the portfolio effect and create the one-

thousand-fold reduction in variability that I have just described. This would

be a misguided thought. Life is absolutely full of uncertainties and one does

not have to play the same game in order to spread risks. You could, for exam-

ple, mix the tossing of a coin with the rolling of a dice. The way that chance

works is such that it does not matter whether or not the games are the same,

you just need to play lots of games-of-chance to spread your bets.

Readers might think that they do not play many games-of-chance. A

game of chance does not have to involve obvious risks like the toss of a coin.

Anything that is subject to financial uncertainty is, as far as I am concerned,

a game-of-chance. Investing in a range of companies provides a great way

of allowing individuals to spread their bets. Each company will be taking

lots of small risks each day and a shareholder can gain exposure to lots of

The square root of ten is about 3.16.

18

162 The five financial building blocks

companies by buying a few shares in each or by investing in a fund that owns

many different shares.

Now before we get too excited and think that risk can be defeated through

the portfolio effect there are three points that must be considered. These con-

cern correlations, ability to take risk and transaction costs. We will deal with

each of these in the following sections.

The effect of correlations

A correlation exists when one variable is related to another. In the coin-

tossing example, suppose that instead of having a million tosses with the

resultant thousand-fold reduction in volatility, there were a million separate

games each with a payout of 1 for heads and zero for tails but that there

was just one coin-tossing shown in a grand televised event. If heads came

up there everybody playing a game would win while tails would mean that

everybody lost. All of the games are exactly correlated and we would get no

risk reduction if we spread our bets.

So we have identified an important condition to the way that the portfolio

effect works. Risks can be reduced as long as they are not correlated. The

stronger the correlation between outcomes the lower will be the portfolio

effect.

What can cause a correlation? In our coin toss TV extravaganza we have

an obvious cause of the link. Other links can be caused by the weather.19 In

the world of commerce there are some more subtle links. The world economy

tends to suffer from cycles. When the economy is booming most companies

will do well. When it is in recession, most companies suffer a decline in prof-

its. This means that the results of companies will tend to be correlated. There

will be a few exceptions such as debt collectors who will have more business

during a recession but there will be a general relationship for the majority

of companies. If this is the case then one would expect that spreading bets

across companies would not remove all of the variability. If companies were

totally independent of each other we would expect to see variability more or

less disappear if we spread our bets across many companies.

We can put this hypothesis to the test. There is a vast array of data on the

performance of company shares. A key factor for a share is the return that it

gives over a year. Readers should recall that the return is equal to the dividend

On a hot day sales of both sun-screen products and ice cream will do well. On a freezing cold day it

19

could be ski wear and warm drinks that sell better.

163 Building block 5: Risk

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