BUSF_A01.qxd

Chapter 6 • Risk in investment appraisal

A business has two investment projects (A and B) in each of which it can invest either £1 mil-

lion or £2 million. It has a total of £2 million to invest. This means that the business can invest

all £2 million in Project A, all £2 million in Project B, or £1 million in each of Projects A and

B. The characteristics of the two opportunities are as follows:

Project Outcome (NPV as % of investment) Probability

A (i) +20% 0.5

(ii) −10% 0.5

B (i) +20% 0.5

(ii) −10% 0.5

The outcomes from these two projects are independent of one another. This is to say that

outcome (i) occurring in Project A tells us nothing about the outcome of Project B.

If the business were to invest all of its £2 million in either Project A or Project B (they both

have the same possible returns), the outcomes would be either:

NPV =+20% ×£2 million =+£0.4 million

Probability =0.5

or

NPV =−10% ×£2 million =−£0.2 million

Probability =0.5

Expected value =(0.5 ×+£0.4 million) +(0.5 ×−£0.2 million) =+£0.1 million

Example 6.4

differed by much. In other words, where there is a large number of projects, the

expected value and the actual outcome are likely to be close, provided that the projects

are independent, that is, they are not affected by common factors.

The portfolio effect

Businesses typically hold portfoliosof investment projects: they have a number, per-

haps a large number, of projects in operation at any given time. They do this, among

other reasons, to diversify risk, that is, to seek to achieve the expected value of the sum

of the projects. Managers know that the expected value of each project probably will

not (probably cannot) actually occur but that ‘swings and roundabouts’ will cause the

sum of the expected values to be the outcome. Greene plc (in Example 6.3) may well

have many other projects, and it expects that the unlikely event of outcome C occur-

ring will be matched by an unexpectedly favourable outcome in another project. The

business would expect this in the same way as a coin landing heads up five times in

a row is possible (a 1 in 32 chance) but, over a reasonably large number of throws,

chance will even out so that heads will face upwards in only about 50 per cent of the

total number of throws.

Diversification

Holding a portfolio of investment projects with the aim of risk reduction is known as

diversification. We shall now see how diversification works by looking at Example 6.4.

‘

‘