25
For use in two of the approaches to risk which will follow, the
probabilities will be those which quantify the occurrence of yields
and prices which fall short of (in bad years) or exceed (in good years)
their normal, or modal, values by some specified percentage. That is,
the frequencies are noted with which values above or below the normal
values of yield and product price are observed. These non-normal
values, grouped by percentile intervals, express the magnitudes by
which the observed values differ from the normal values. The proba
bilities of experiencing values above and below the normal value for
the activity are calculated.
In the example which follows the probability of a low and a high
yield is calculated, as well as the expected value of yield in any
a given year (Table 2). Based on these data the probability of having
a low yield is .20 (i.e., 8/40). G iven that a bad year will occur
the following probabilities can be calculated describing the magnitude
of yield loss: \
1. Probability of realizing .90 (i.e., 450/500) of a normal crop
is .25.
2. Probability of realizing .80 (i.e., 400/500) is .375.
3. Probability of realizing .70 (i.e., 350/500) is .25.
4. Probability of realizing .40 (i.e., 200/500) is .125.
The expected value of yield in a bad year (Y^) is
E[Yb] = 500 C-25(.90) + .375(.80) + .25(.70) + .125(.4o)D
= 500 C.75]
= 375.
Similarly, the expected yield in good years can be calculated. Given
a good year the probability that yield will be 550, or 1.10 of a normal