224 THE HANDBOOK OF PORTFOLIO MATHEMATICS
You should complete the table for the certainty equivalent columns. For
instance, when you are on the second to last row, you are, in effect, asking
yourself how much you would be willing to pay not to have to accept a 10 %
chance of winning $20,000 with a 90% chance of losing $10,000. Since you
are willing to pay, you should enter this certainty equivalent as a negative
amount.
When you have completed the third column, you must now calculate the
fourth column, theComputed Utilitycolumn. The formula for computed
utility is simply:
Computed Utility=U*P(best outcome)+V*P(worst outcome)
(6.04)where: U=Given constant, equal to 1.0 in this instance.
V=Given constant, equal to−1.0 in this instance.Thus, for the second row in the table:Computed utility= (^1) . 9 − (^1) . 1
=. 9 −. 1
=. 8
When you are finished calculating the computed utility columns, your
table might look like this:
P P Certainty Computed
(Best Outcome) (Worst Outcome) Equivalent Utility
1.0 0 20,000 1.0
.9 .1 15,000 .8
.8 .2 10,000 .6
.7 .3 7,500 .4
.6 .4 5,000 .2
.5 .5 2,500 0
.4 .6 800 −.2
.3 .7 −1,500 −.4
.2 .8 −3,000 −.6
.1 .9 −4,000 −.8
0 1.0 −10,000 −1.0
You then graphically plot the certainty equivalents as the X-axis and the
computed utilities as the Y-axis. Our completed utility function looks as is
shown in Figure 6.4.
Now you should repeat the test, only with different best and worst out-
comes. Select a certainty equivalent from the preceding table to act asbest