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608 CHAPTER 15 RISK AND INFORMATION
two properties of probability just described. However, different decision makers might
have different beliefs about the probabilities of possible outcomes of a given risky
event. For example, an investor more optimistic than you might believe the following:
• Probability of A 0.50 (there is a 5 in 10 chance that the stock’s value will go
up by 20 percent).
• Probability of B 0.30 (there is a 3 in 10 chance that the stock’s value will stay
the same).
• Probability of C 0.20 (there is a 2 in 10 chance that the stock’s value will go
down by 20 percent).

These subjective probabilities differ from yours, but they still obey the two basic laws
of probability: each is between 0 and 1, and they add up to 1.

EXPECTED VALUE
Given the probabilities associated with the possible outcomes of your risky invest-
expected value A ment, how much can you expect to make, that is, what is the expected value of the
measure of the average investment? The expected value of a lottery is the average payoff that the lottery will
payoff that a lottery will generate. We can illustrate this with our Internet stock example:
generate.
Expected value probability of A payoff if A occurs

probability of B payoff if B occurs
probability of C payoff if C occurs

Applying this formula we get
Expected value (0.30 120) (0.40 100) (0.30 80)

100
The expected value of your Internet stock is a weighted average of the possible pay-
offs, where the weight associated with each payoff equals the probability that the
payoff will occur. More generally, if A, B, . . . , Z denote the set of possible outcomes
of a lottery, then the expected value of the lottery is as follows:

Expected value probability of A payoff if A occurs
probability of B payoff if B occurs . . .
probability of Z payoff of Z occurs

As in the coin tossing example, the expected value of a lottery is the average pay-
off you would get from the lottery if the lottery were repeated many times. If you made
the same investment over and over again and averaged the payoffs, that average would
be nearly indistinguishable from the lottery’s expected value of $100.

VARIANCE

Suppose you had a choice of two investments—$100 worth of stock in an Internet com-
pany or $100 worth of stock in a public utility (an electric company or a local waterworks).