## Diversification

Suppose that you plan to take a part-time job selling appliances on a commission basis. You can decide to sell only air conditioners or only heaters, or you can spend half your time selling each. Of course, you can't be sure how hot or cold the weather will be next year. How should you apportion your time to minimize the risk involved in the sales job?

The answer is thatriskcan be minimized by diversification-by allocating your time toward selling two or more products (whose sales are not closely related), rather than a single product. Suppose that there is a fifty-fifty chance that it will be a relatively hot year, and a fifty-fifty chance that it will be cold. Table 5.5 gives the earnings that you can make selling air conditioners and heaters.

If you sell only air conditioners or only heaters, your actual income will be either \$12,000 or \$30,000 but your expected income will be \$21,000 [,5(\$30,000) +. .5(\$ 12/000)]. But suppose you diversify by dividing your time evenly between the two products. Then your income will certainly be \$21,000, whatever the weather. If the weather is hot, you will earn \$15,000

TABLE 5.5 Income from Sales of Equipment

Hot Weather

ColdWeather

Air conditioner sales Heater sales

\$30,000 12,000

\$12,000 30/000

from air conditioner sales and \$6000 from heater sales; if it is cold, you will earn \$6000 from air conditioner sales and \$15/000 from heater sales. Hence, by diversifying you eliminate all risk.

Diversification is not always this easy. In our example heater and air conditioner sales were inversely related-whenever the sales of one were strong, the sales of the other were weak. But the principle of diversification is a general one. As long as you can allocate your effort or your investment funds toward a variety of activities whose outcomes are not closely related, you can eliminate some risk..

We have seen that risk-averse people will be willing to give up income to avoid risk. In fact, if the cost of insurance is equal to the expected loss (e.g., a policy with an expected loss of \$1000 will cost \$1000), risk-averse people will want to buy enough insurance to allow them to fully recover from any financial losses they might suffer.

The reasoning is implicit in our discussion of risk aversion. Buying insurance assures a person of having the same income whether or not there is a loss. Because the insurance cost is equal to the expected loss, this certain income is equal to the expected income from the risky situation. For a risk-averse consumer, the guarantee of the same income whatever the outcome generates more utility than would be the case if that person had a high income when there was no loss and a low income when a loss occurred.

To clarify this argument, suppose a homeowner faces a 10 percent probability that his house will be burglarized and he will suffer a \$10,000 loss. Let's assume he has \$50,000 worth of property. Table 5.6 shows his wealth with two possibilities-to insure or not to insure.

TABLE 5.6 The Decision to Insure

Insurance Burglary (Pr = .1) No Burglary (Pr = .9) Expected Wealth

Yes 49,000 49,000 49,000

### Insurance

The decision to purchase insurance does not alter his expected wealth. It does, however, smooth it out over both possible outcomes. This is what generates a higher level of expected utility for the homeowner. Why? We know that the marginal utility in both the no-loss and loss situations is the same for the man who buys insurance (because his wealth is the same). But when there is no insurance, the marginal utility in'the event of a loss is higher than if no loss occurs (recall that with risk aversion there is diminishing marginal utility). Therefore, a transfer of wealth from the no-loss to the loss situation must increase total, utility. And this transfer of wealth is exactly what the purchase of insurance accomplishes.

Consumers usually buy insurance from companies that specialize in selling it. In general, insurance companies are profit-maximizing firms that offer insurance because they know that when they pool policies, they face relatively little risk. The ability to avoid risk by operating on a large scale is based on the law of large numbers, which tells us that although single events may be random and largely unpredictable, the average outcome of many similar events can be predicted. For example, I may not be able to predict whether a coin toss will come out heads or tails, but I know that when many coins are flipped, approximately half will turn up heads and half tails. Similarly, if I am selling automobile insurance, I cannot predict whether a particular driver will have an accident, but I can be reasonably sure, judging from past experience, about how many accidents a large group of drivers will have.

By operating on a large scale, insurance companies can assure themselves that over a large enough number of events, the total premiums paid in will be equal to the total amount of money paid out. To return to our burglary example, a man knows that there is a 10 percent probability that his house will be burgled; if it is, he will suffer a \$10,000 loss. Prior to facing this risk, he calculates the expected loss to be \$1000 (.10 X \$10,000), but there is substantial risk involved, .since there is a 10 percent probability of a large loss. Now suppose 100 people are similarly situated and all of them buy burglary insurance from an insurance company. Because they are all similarly situated, the insurance company charges each of them a premium of \$1000 for the insurance. This \$1000 premium generates an insurance fund of \$100,000 from which losses can be paid. The insurance company can rely on the law of large numbers, which tells it that the expected loss over the 100 individuals is likely to be very close to \$1000 each. Therefore, the total payout will be close to \$100,000, and the company need not worry about losing more than that.

Insurance companies typically charge premiums above the expected loss because they need to cover their administrative costs. As a result, many people choose to self-insure rather than buy from an insurance company. One way to avoid risk is to self-insure by diversifying. For example, self-insurance against the risks associated with investing usually takes the form of diversifying one's portfolio, say, by buying a mutual fund. Self-insurance against other risks can be achieved by spending money. For example, a person can self-insure against the risk of loss by putting money into a fund to cover fu-

lure loss. Or one may self-insure against the loss of future earnings by pulling funds into an individual retirement account.

EXAMPLE 5.3 THE VALUE OFlriTLE INSURANCE WI^N ■4 v BUYING A HOME ri-'k v-irx ; '' - ■■

Suppose a family is buying its first home. The family knows that to close the sale of the house they will need a deed thai gives them the clear "Litic11 to the house. Without such a clear title, there is always a chance that the seller of the house is noi its true owner. Of course, the seller could be engaging in fraud but is more likely to be unaware of ihc exact nature of his or her ownership rights. For example, the owner may have borrowed heavily, using the house as "collateral" for the loan. Or the property might carry with it a legal requirement thaL limits the use to which it may be put.

Suppose the family is willing to pay \$150,000 for the house bui believes ihcrc is a one in ten chance thai carcful research will show that ihc currcni seller docs not own the property. The property would then be worth only \$50,000. If there were no insurance available, a risk-ncutral family would bid at most \$140,000 for the property (.9[\$150,000] + .1[\$50,000]). However, a family that expects to tic up most of their assets in ihcir house would most likely be risk averse and would therefore bid substantially less to buv the house, sav, \$120,(XX).

In situations such as this, it is clearly in ihc interest of the seller to assure the buyer that ihcrc is no risk of a lack of full ownership. The seller does this by purchasing "title insurance.11 The title insurance company researches the history of the property, chccks to-scc whether any legal liabilities arc attached to ii, and generally assures itself that, there is no ownership problem. The insurance company ihcn agrees to bear any remaining risk that might exist.

Because the title insurance company is a specialist in such insurance and can collect the relevant information relatively easily, the cost of title insurance is often less lhan the cxpccicd value of the loss involved. A fee of \$1,000 for title insurance is not unusual, and the cxpccicd loss can be substantially higher. Clearly, it is in the interest of the sellers of homes to provide such insurance, because all but the most risk-loving buyers will pay substantially more for the house when it is insured than when it is not. In fact, most stales require sellers to provide title insurance before ihc sale can be complete.

9 Because such risk^ arc also of concern to mortgage lenders, they usually require new buyers to have title insurance before they will issue a mortgage.

## Lessons From The Intelligent Investor

If you're like a lot of people watching the recession unfold, you have likely started to look at your finances under a microscope. Perhaps you have started saving the annual savings rate by people has started to recover a bit.

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