Chapter 6 • Risk in investment appraisal
There may be some individuals in the world who are risk-lovers. Such an indivi-
dual might, for example, be prepared to enter a coin-spinning wager standing to lose
£100 with only a 50 per cent chance of gaining £190. Such might be the desire to be
exposed to risk that he or she would be willing to take on wagers with negative ex-
pected value. Most of us are not.
Looking back at Example 6.4 on page 164, most people, because they are risk
averse, would prefer a combination of Projects A and B rather than an investment in
just one or the other. This is despite the fact that both strategies give the same expected
value. It is also despite the fact that the single-project strategy offers a 50 per cent
probability of an NPV of £0.4 million, whereas the diversification strategy (A and B)
offers only a 25 per cent probability of that desirable outcome. This preference for the
diversification strategy is connected with the relatively low probability of the negative
outcome.Evidence of risk aversion
There is quite a lot of evidence around us to support the assertion that most people
are risk-averse. People’s general desire to cover potential disasters by insurance is
an example. Most house owners, with no legal compulsion, choose to insure their
property against destruction by fire. Clearly, taking account of the potential financial
loss and the risk of fire, the premium must be more than the expected value of the loss,
otherwise the fire insurance companies would consistently lose money. For example,
if the potential damage from a fire for a particular house is £100,000 and the probabil-
ity of a serious fire during a year is 1 in 1,000 (that is, a 0.001 probability), the expected
value of the loss is £100 (that is, £100,000 ×0.001). Unless the house owner is prepared
to pay a premium higher than £100 p.a. the insurance company would not accept the
risk, yet most house owners seem to insure their houses. They are prepared to do this
because the loss of utility caused by paying the premium is less than the anticipated
loss of utility caused by the cost of a fire (if the house is uninsured) multiplied by its
probability of occurrence. This arises from the fact that, for risk-averse individuals,
utility of wealth curves are not straight lines: in other words, there is not a linear rela-
tionship between wealth and utility of wealth.Preferences of risk-averse investors
Figure 6.7 shows the range of possible outcomes for two investment projects, A and B.
Both have expected values of £15,000 (the outcomes of each are symmetrically arrayed
around this value); in fact, £15,000 is the single most likely outcome (the mode) in
each case.
Both of these projects would be acceptable to the investor as neither of them has a
negative NPV, irrespective of where in the range the actual outcome falls. Since most
of the human race seems to be risk-averse, Project A would be most people’s first
choice if they had to choose between the projects. This is despite the fact that Project B
holds the possibility of an NPV as high as £30,000 whereas Project A’s maximum is
only £21,000. The risk-averse investor’s eyes would be drawn to the lower end of the
scale where that person would note that Project A gives a guaranteed minimum NPV
of £9,000 whereas Project B’s outcome could be as low as zero. To the risk-averse, the
so-called downside risk looms larger than the upside potential. By contrast, a risk-lover