Engineering Economic Analysis

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Risk 323

This equation is the square root of the difference between the average of the squares

and the square of the average. The standarddeviation is used instead of thevariancebecause

the standard deviation is measured in the same units as the expected value. The variance is

measured in "squared dollars"-whatever they are.

The calculation of a standard deviation by itself is only a descriptivestatistic of limited

value. However,as shown in the next section on risk/return trade-offs,it is useful when the

standard deviation of each alternative is calculated and these are compared. But first, some

examples of calculating the standard deviation.

Consider the economicevaluationof collision and comprehensive(fire,theft, etc.) insurancefor an

auto. One example was described in Figure 10-6.The probabilities and outcomes are summarized

in the calculation of the expected values, which was done using Equation 10-5.

EVaccidentw/ins.= (0.9 x 0) + (0.07 x 300) + (0.03 x 500)=$36

EVaccidentw/oins.= (0.9 x 0) + (0.07 x 300) + (0.03 x 13,000) = $411

Calculate the standard deviations for insuring and not insuring.

'SOLutiON:.- --.. - --.

The first step is to calculate the EV(outcome2) for each.

EV~ident w/ins.=(0.9X 02) + (0.07 x 3002) + (0.03 x 5002)=$13,800

EV;ccidentw/oins.=(0.9 X 02) + (0.07 x 3002) + (0.03 x 13,0002) = $5,076,300

Then the standard deviations can be calculated.

O"w/ins."=-/(13,800 - 362)= JI2,504= $112

O"w/oins.= -/(5,076,300 -4112) = -/4,907,379 =$2215

As described in Example 10-11, the expected value cost of insuring is $836(=$36+$800)

and the expected value cost of self-insuring is $411. Thus the expected cost of not insuring is
about half the cost of insuring. But the standard deviation of self-insuring is 20 times larger. It is
clearlyr,iskier.
Which choice is preferred depends on how much risk yoti are comfortable with.
As stated before, this is an example ofexpected values alone not determining the decision.

Buying insurance ,has an expected cost:::that ~is-$425=-peryear higher, but that "insurance lim-
its the maximum loss to $500 rather than $13,000. The $425 may be wortb spendiJ:!gto avoid
that risk.
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