9781118041581

government. Perhaps the greatest virtue of using decision trees in evaluating

and comparing risks is that it reminds us of the difference between good deci-

sions and good outcomes.

Features of the Expected-Value Criterion

The depiction of the risk in Figure 12.1 hardly could be simpler. Thus, it comes

as no surprise that the expected-value calculation is automatic, indeed, almost

trivial. Nonetheless, it is important to recognize the general properties of this

criterion, properties that apply equally to simple and complex risks.

The first (and most basic) feature of the expected-value standard is that it val-

ues a risky prospect by accounting not only for the set of possible outcomes, but

also for the probabilities of those outcomes. For instance, suppose the wildcatter

must decide whether to drill on one site or another. (There are insufficient

resources to drill on both.) The first site’s possible monetary outcomes are 800,

600, 160, 60, and 200 (all in thousands of dollars); these outcomes occur

with probabilities .05, .15, .2, .25, and .35, respectively. Thus, the expected profit

from drilling this site is (.05)(800) (.15)(600) (.2)(160) (.25)(60)

(.35)(200), or $77 thousand. The second site has the same five possible out-

comes as the first but with probabilities .05, .2, .25, .2, and .3. Notice that the

second site offers higher probabilities of “good” outcomes than the first site.

Clearly, then, the second site should have a higher value than the first. The

expected-value standard satisfies this common-sense requirement. Performing

the appropriate computation will show that the second site’s expected profit is

$128,000, a significantly higher figure than the expected profit of the first site.

Second, the expected value of a risky prospect represents the average mon-

etary outcome if it were repeated indefinitely (with each repeated outcome gen-

erated independently of the others). In this statistical sense, the expected-value

standard is appropriate for playing the long-run averages. Indeed, many man-

agers employ the expected-value criterion when it comes to often-repeated, rou-

tine decisions involving (individually) small risks. For instance, suppose you have

the chance to bet on each of 100 tosses of a coin. You win a dime on each head

and lose a nickel on each tail. This, you’ll no doubt agree, is the epitome of a

routine, often-repeated, low-risk decision. Here the expected-value criterion

instructs you to bet on each toss. If you choose this profitable (albeit somewhat

boring) course of action, your expected gain in the 100 tosses is $2.50. Your

actual profit will vary in the neighborhood of $2.50, perhaps coming out a little

above, perhaps a little below. The statistical “law of large numbers” applied to

the independent tosses ensures that there is no real risk associated with the bet.

Third, in decisions involving multiple and related risks, the expected-value cri-

terion allows the decision maker to compute expected values in stages.Figure 12.2

makes this point by presenting a “bushier” (and more realistic) tree for the

wildcatter’s drilling decision. The tree incorporates three risks affecting drilling

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