Chapter 6 • Risk in investment appraisal
Figure 6.5
Graph of the utility
of wealth against
wealth for a
particular risk-
averse individual
This person prefers more wealth to less wealth, because the curve shows increasing utility
for increasing wealth. It also shows the individual to be risk averse, because each successive
increase of £1 of wealth yields a smaller increase in satisfaction. This person would lose more
satisfaction from losing £1 than they would gain from gaining £1.Risk aversion
Figure 6.5 shows the utility-of-wealth curve for a risk-averse individual. Utility, as we
saw in the previous section, is a level of satisfaction. W on the horizontal axis repres-
ents the present level of wealth of this particular individual. To this individual, increas-
ing wealth by £100 would increase personal satisfaction (utility) by CB, but losing £100
would reduce that satisfaction by CD, a rather larger amount. This individual would
only become indifferent to the wager if the potential gain were x, so that the increase
in utility from the gain (should it arise) would equal the potential loss of utility from
the loss of the money (that is, CA =CD). The risk-averse person would need the prize
for the coin landing heads to be in excess of £200 to make the wager attractive.
The precise shape of a utility curve (and thus how much the prize in the above
wager needs to be) depends on the personal preferences of the individual concerned.
The curve in Figure 6.5 represents the preferences of just one hypothetical individual,
though all risk-averse individuals will have a curve of roughly the same shape. Note
that how much the prize in the wager would need to be, to tempt any particular indi-
vidual, depends both on that person’s utility curve and on the level of wealth of that
individual at the time that the wager is on offer.