coin toss. You are saying that your CE for the coin toss is $25. This CE is signif-
icantly smaller than the expected value of the bet, $100. This being the case, we
would say that you are risk averse. An individual is risk averseif his or her cer-
tainty equivalent for a given risky prospect is less than its expected value.
Loosely speaking, the magnitude of one’s aversion to risk is indicated by
the shortfall of the CE below the expected value of the risky prospect; this dif-
ference (sometimes referred to as a discount for risk) measures the reduction in
value (below expected value) due to a prospect’s riskiness. Here the risk dis-
count is 100 25 $75. The discount depends on individual preferences as
well as on the size of the risk. For instance, a second individual might prefer to
avoid the coin toss altogether; that is, in a choice between the coin toss and
receiving $0 for certain, this individual prefers $0. This preference makes good
sense for someone who does not wish to bear the downside risk of the coin
toss. Suppose this individual is indifferent to the options of paying$20 for cer-
tain or taking the coin toss. (He or she is willing to pay $20 to avoid the risk of
the gamble.) Here the CE is $20, and the risk discount is $100 (20)
$120. Clearly, the second decision maker is more risk averse than the first.THE DEMAND FOR INSURANCE Risk aversion provides a ready explanation
concerning the demand for insurance. Insurance companies stand ready to
compensate their policyholders in the event of losses (specified in the insur-
ance contract) at a price in the form of the premium paid by the customer to
the company. Risk-averse individuals are willing to give up monetary income to
avoid risks. In effect, this is what they do when they purchase insurance.
To make the argument concrete, consider a couple who is about to pur-
chase fire insurance to protect their home (which is valued at $150,000). The
risk of a fire destroying their house is very small—about 1 in 300 in any given
year. Nevertheless, the loss of their house would mean financial ruin. Thus, the
couple finds it prudent to purchase insurance. In return for payment of a $500
annual premium, a 100 percent fire policy promises to pay whatever amount
is necessary to rebuild and replace the house in the event of fire. In purely
financial terms, the couple faces the following options. If they do not buy the
policy, their wealth at the end of the year will be $150,000 if there is no fire or
$0 if a fire occurs (a 1-in-300 chance). Their expected wealth is $149,500.
(Check this for yourself.) By purchasing the policy, their net wealth is $150,000
$500 $149,500 at the end of the year. Their wealth is certain. Regardless of
whether a fire occurs, they will have their house (or the money to rebuild it).
Notice that whether or not they purchase insurance, the couple’s expected
wealth is the same, $149,500. Because they are risk averse, the couple prefers
the certain $149,500 provided by insurance to the alternative of bearing the risk
of fire. Thus, they purchase full insurance.
In this example, the company has offered the couple “actuarially fair”
insurance; that is, the couple’s premium ($500) just covers the company’s
expected payout under the policy: (1/300)($150,000) $500. Because of their520 Chapter 12 Decision Making under Uncertaintyc12DecisionMakingunderUncertainty.qxd 9/29/11 1:34 PM Page 520