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1、1 of 39WHAT YOU WILL LEARN IN THIS CHAPTERchapter: 212009 Worth PublishersUncertainty, Risk and Private Information2 of 39WHAT YOU WILL LEARN IN THIS CHAPTERThat risk is an important feature of the economy, and that most people are risk-averse.Why diminishing marginal utility makes people risk-avers
2、e and determines how much premium they are willing to pay to reduce risk How risk can be traded, with risk-averse people paying others to assume part of their risk How exposure to risk can be reduced through diversification and poolingHow special problems are posed by private informationsituations i
3、n which some people know things that other people do not3 of 39The Economics of Risk AversionIn general, people dont like risk and are willing to pay a price to avoid it.For example: insuranceBut what exactly is risk? And why dont people like it? To answer these questions, we need to look briefly at
4、 the concept of expected value and the meaning of uncertainty.4 of 39Expectations and UncertaintyA random variable is a variable with an uncertain future value.e.g. a persons medical expenses for the coming year.Lets assume that theres a 50 percent chance that this person will get sick and his high
5、medical expenses will materialize. He may face medical expenses of $10,000.5 of 39Expectations and UncertaintyThe expected value of a random variable is the weighted average of all possible values, where the weights on each possible value correspond to the probability of that value occurring.In this
6、 example, the expected value of the medical expenses is: (0.5 $0) + (0.5 $10,000) = $5,0006 of 39Expectations and UncertaintyTo derive the general formula for the expected value of a random variable, we imagine that there are a number of different states of the world.A state of the world is a possib
7、le future event.Then the expected value of the random variable is:7 of 39Expectations and UncertaintyRisk is uncertainty about future outcomes. Most people prefer, other things equal, to reduce risk. Well focus here on financial risk, in which the uncertainty is about monetary outcomes, as opposed t
8、o uncertainty about outcomes that cant be assigned a monetary value.But, why do people feel that risk is a bad thing?8 of 39The Logic of Risk AversionThe answer to the question of why people feel that risk is a bad thing lies in the concept of diminishing marginal utility.To understand how diminishi
9、ng marginal utility gives rise to risk aversion, we need to look not only at the medical costs but also at how those costs affect the income the family has left after medical expenses.If we assume that the family income is $30,000, the expected income after medical expenses is: (0.5 $30,000) + (0.5
10、$20,000) = $25,000.9 of 39The Logic of Risk AversionExpected utility is the expected value of an individuals total utility given uncertainty about future outcomes.Expected utility of the family is less than it would be if the family didnt face any risk and knew with certainty that its income after m
11、edical expenses would be $25,000.The following graph and table illustrates this point more clearly.10 of 39The Utility Function and Marginal Utility Curve of a Risk-Averse FamilySHHSUtility functionMarginal Utility Curve(a) Total Utility01,080920800560400IncomeTotal utility (utils)30,00020,000$10,00
12、0Utility in state H, UH(b) Marginal Utility070605040302010IncomeMarginal utility (utils)30,00020,000$10,000 Marginal utility in state S Marginal utility in state H$20,00021,00022,00023,00024,00025,00026,00027,00028,00029,00030,000Total Utility(utils)9209459689891,0081,0251,0401,0531,0641,0731,080Inc
13、omeUtility in state S, US11 of 39The Logic of Risk AversionMost people in real life, are risk-averse: they will choose to reduce the risk they face when the cost of that reduction leaves the expected value of their income or wealth unchanged.They would be willing to purchase a fair insurance policy
14、for which the premium is equal to the expected value of the claims.The purchase of a fair insurance policy increases expected utility and this is due to the concept of diminishing marginal utility. The reason is that a dollar gained when income is low adds more to utility than a dollar lost when inc
15、ome is high.12 of 39The Effect of Fair Insurance on the Lee Familys Income Available for Consumption and Expected Utility13 of 39The Logic of Risk AversionAlmost everyone is risk-averse, because almost everyone has diminishing marginal utility. But the degree of risk aversion varies among individual
16、ssome people are more risk-averse than others.Differences in preferences and in income or wealth lead to differences in risk aversion.The following graph illustrates this point14 of 39Differences in Risk AversionThe difference (reflected in the differing slopes of the two mens marginal utility curve
17、s) means that Danny would be willing to pay much more than Mel for insurance.Mels utility functionDannys utility function Mels marginal utility curveDannys marginal utility curve(a) Total Utility(b) Marginal UtilityIncomeTotal utilityIncomeMarginal utilityIncome rises by $1000LDNLMHMHDIncome falls b
18、y $1000Current incomeCurrent income15 of 39Paying to Avoid RiskDifferences in risk aversion have an important consequence: they affect how much an individual is willing to pay to avoid risk.A risk-neutral person is completely insensitive to risk.Depending on the size of the premium, a risk-averse pe
19、rson may be willing to purchase an “unfair” insurance policya policy with a premium larger than the expected claims. The greater your risk aversion, the greater the premium you are willing to pay.16 of 39Buying, Selling, and Reducing RiskLloyds of London is the oldest existing commercial insurance c
20、ompany.Originally formed in the 18th century as a commercial venture to help merchants cope with the risks of commerce (i.e. storms, pirates, etc). Lloyds matched ship owners seeking insurance with wealthy investors who promised to compensate a merchant if his ship were lost. In return, the merchant
21、 paid the investor a fee in advance; if his ship didnt sink, the investor still kept the fee.17 of 39Buying, Selling, and Reducing RiskLloyds performed the functions of a market. The fact that British merchants could use Lloyds to reduce their risk made many more people in Britain willing to underta
22、ke merchant trade.18 of 39Buying, Selling, and Reducing RiskThe insurance industry rests on two principles:The first is that trade in risk, like trade in any good, can produce mutual gains from trade; in this case, the gains come when people who are less willing to bear risk transfer it to people wh
23、o are more willing to bear it. The second is that some risk can be made to disappear through diversification.Lets consider each principle in turn19 of 39Trading RiskThe funds that an insurer places at risk when agreeing to provide insurance is called his or her capital at risk.There are gains from t
24、rade in risk, leading to an efficient allocation of risk: those who are most willing to bear risk place their capital at risk to cover the financial losses of those least willing to bear risk.Lloyds made money by matching wealthy investors who were more risk-tolerant with less wealthyand therefore m
25、ore risk-averseship owners who wanted to purchase insurance.20 of 39Quantity of policiesPremium of policyS43210115110105100More risk-averse investorSlightly risk-averse investorRisk-neutral investorThe Supply of Insurance21 of 39D3210200190180170Most risk-averse shipownerSlightly less risk-averse sh
26、ipownerStill less risk-averse shipownerQuantity of policiesPremium of policyThe Demand for Insurance22 of 395,0000200130100SDEQuantity of policiesPremium of policyThe Insurance Market23 of 39The Power of DiversificationHow were the British merchants able to survive the risky routes they took?One imp
27、ortant way was reducing their risks by not putting all their eggs in one basket: by sending different ships to different destinations, they could reduce the probability that all their ships would be lost. A strategy of investing in such a way as to reduce the probability of severe losses is known as
28、 diversification. As well now see, diversification can often make some of the economys risk disappear.24 of 39Two possible events are independent events if each of them is neither more nor less likely to happen if the other one happens. When independent events are involved, a strategy of diversifica
29、tion can substantially reduce risk.An individual can engage in diversification by investing in several different things, so that possible losses are independent events. Diversification is made easier by the existence of institutions like the stock market, in which people trade shares. A share in a c
30、ompany is a partial ownership of that company.The Power of Diversification25 of 39DiversificationA strong form of diversification, relevant especially to insurance companies, is pooling. In pooling, an individual takes a small share in many independent events. This produces a payoff with very little
31、 total overall risk.26 of 39Limits of DiversificationEvents are positively correlated if each of them is more likely to occur if the other one also occurs.When events are positively correlated, there is a core risk that will not go away no matter how much individuals diversify.Here are some of the p
32、ositively-correlated financial risks that investors in the modern world face:Severe weatherPolitical eventsBusiness cycles27 of 39ECONOMICS IN ACTIONWhen Lloyds Almost Lost ItAt the end of the 1980s, Lloyds found itself in severe trouble.The premiums the investors accepted were too small for the tru
33、e level of risk contained in the policies. But the biggest single problem was that many of the events against which Lloyds had become a major insurer were not independent. For example: U.S. companies involved in a torrent of asbestos lawsuits, many of them paid by Lloyds investors.28 of 39Private In
34、formationMarkets do very well dealing with risk due to uncertainty: situations in which nobody knows what is going to happen, whose house will be flooded, or who will get sick.However, markets have much more trouble with situations in which some people know things that other people dont knowsituatio
35、ns of private information.29 of 39Private InformationWhy should such differences in who knows what be a problem? It turns out that there are two distinct sources of trouble: Adverse selection Moral hazard30 of 39Adverse SelectionAdverse selection occurs when an individual knows more about the way th
36、ings are than other people do. Private information leads buyers to expect hidden problems in items offered for sale, leading to low prices and the best items being kept off the market (e.g. used car market).Adverse selection can be reduced through screening: using observable information about people
37、 to make inferences about their private information.31 of 39Adverse SelectionAside from screening, adverse selection can be reduced by revealing private information through signaling, or by cultivating a long-term reputation.A long-term reputation allows an individual to reassure others that he or s
38、he isnt concealing adverse information.32 of 39Moral HazardMoral hazard occurs when an individual knows more about his or her own actions than other people do. This leads to a distortion of incentives to take care or to expend effort, especially when the individual is insured.In the case of insuranc
39、e, it leads individuals to exert too little effort to prevent losses.33 of 39Moral HazardInsurance companies deal with moral hazard by requiring a deductible. They compensate for losses only above a certain amount, so that coverage is always less than 100 percent.A deductible in an insurance policy
40、is a sum that the insured individual must pay before being compensated for a claim.34 of 39ECONOMICS IN ACTIONFranchise Owners Try HarderMost fast food restaurants are franchises. An individual must put up a large sum of money to buy the license and to set the restaurant up. Therefore, becoming an o
41、wner requires a lot of risk.Why doesnt Taco Bell hire a salaried manager? Franchise owners work harder. In other words, there is a moral hazard problem when a salaried manager runs the Taco Bell. The result:Companies rely on franchises despite higher costs.Individuals are compensated with higher rew
42、ard.Companies compensated with higher sales and thus higher licensing fees.Moral hazard sometimes prevents diversification.35 of 39SUMMARY1. The expected value of a random variable is the weighted average of all possible values, where the weight corresponds to the probability of a given value occurr
43、ing.2. Risk is uncertainty about future events or states of the world. It is financial risk when the uncertainty is about monetary outcomes.3. Under uncertainty, people maximize expected utility. A risk-averse person will choose to reduce risk when that reduction leaves the expected value of his or
44、her income or wealth unchanged. A fair insurance policy has that feature: the premium is equal to the expected value of the claim. A risk-neutral person is completely insensitive to risk and therefore unwilling to pay any premium to avoid it.36 of 39SUMMARY4.Risk aversion arises from diminishing mar
45、ginal utility: an additional dollar of income generates higher marginal utility in low-income states than in high-income states. A fair insurance policy increases a risk-averse persons utility because it transfers a dollar from a high-income state (a state when no loss occurs) to a low-income state
46、(a state when a loss occurs).5.Differences in preferences and income or wealth lead to differences in risk aversion. The greater your risk aversion, the higher the premium you are willing to pay.6.There are gains from trade in risk, leading to an efficient allocation of risk: those who are most will
47、ing to bear risk put their capital at risk to cover the losses of those least willing to bear risk. 37 of 39SUMMARY7.Risk can also be reduced through diversification, investing in several different things that correspond to independent events. The stock market, where shares in companies are traded,
48、offers one way to diversify. Insurance companies can engage in pooling, insuring many independent events so as to eliminate almost all risk. But when the underlying events are positively correlated, all risk cannot be diversified away.8.Private information can cause inefficiency in the allocation of
49、 risk. One problem is adverse selection. It creates the “lemons problem” in used-car markets. Adverse selection can be limited through screening of individuals, through signaling that people use to reveal their private information, and through the building of a reputation.38 of 39SUMMARY9. A related
50、 problem is moral hazard: individuals have private information about their actions, which distorts their incentives to exert effort or care when someone else bears the costs of that lack of effort or care. It limits the ability of markets to allocate risk efficiently. Insurance companies try to limit moral hazard by imposing deductibles, placing more risk on the insured.39 of 39The End
