BUSF_A01.qxd

Systematic and specific risk

If, however, half is invested in each project then there are four possible outcomes:

1 A(i) and B(i)

NPV =(£1 million ×+20%) +(£1 million ×+20%) =+£0.4 million

Probability =(0.5 ×0.5) =0.25

2 A(i) and B(ii)

NPV =(£1 million ×+20%) +(£1 million ×−10%) =+£0.1 million

Probability =(0.5 ×0.5) =0.25

3 A(ii) and B(i)

NPV =(£1 million ×−10%) +(£1 million ×+20%) =+£0.1 million

Probability =(0.5 ×0.5) =0.25

4 A(ii) and B(ii)

NPV =(£1 million ×−10%) +(£1 million ×−10%) =−£0.2 million

Probability =(0.5 ×0.5) =0.25

Expected value =(0.25 ×+£0.4 million) +(0.25 ×+£0.1 million) +(0.25 ×+£0.1 million) +(0.25

×−£0.2 million) =+£0.1 million

We can see that, as far as this example is concerned, diversification means that the

expected value starts to become a likely outcome. Diversification has also reduced the

chance of the best outcome occurring, and the worst outcome is also less likely (in both

cases down from 0.5 to 0.25 probability). There are three important points to note

about the effect of diversification in Example 6.4. These are:

l Diversification does not change the expected value (£0.1 million).

l Diversification does not alter the highest or lowest outcome (still +£0.4 million or

−£0.2 million) (outcomes 1 and 4).

l Diversification does, however, introduce two new possibilities (outcomes 2 and 3),

both of which would combine a favourable outcome from one project with an

unfavourable one from the other.

These two possibilities, between them, are 0.5 probable.

We shall see a little further on that most investors will readily accept a reduction of

expectations of high returns in order to reduce the likelihood of low ones.

6.5 Systematic and specific risk

How likely in real life is it that investment projects are independent of one another in

the way that spins of a fair coin are? Is it not quite likely that the very factors that will

cause one project to turn out unfavourably will similarly affect each of the others? In

Example 6.4, is it not true that outcome (ii) occurring in Project A, in real life, implies

outcome (ii) occurring in Project B as well, meaning that there would be no advantage

from diversification?

The answer to these questions seems to be that while there are factors specific to

each individual investment such that they will affect only its outcome, there are also

underlying factors that will affect just about all projects.

Specific riskis the expression used to describe the part of the risk that relates to the

particular project. This portion of the risk can be eliminated by diversification, in the

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