see riskstat in statwork for possibly later version CHAPTER 1-5 DEALING WITH RISKS People sometimes enjoy the experience of uncertainty. Some are even willing to pay for the thrill of gambling in a casino. More commonly, though, uncertainty is a negative consequence that people are willing to pay insurance premiums to avoid. There are several reasons why a person may prefer a sure outcome to a set of uncertain outcomes. You may dislike the shivery feeling of worry about what will happen. Or you might imagine yourself feeling regret or unpleasant surprise or disappointment if a particular outcome should come about which you could avoid by insuring against it. In contrast to these subjective matters which differ from person to person, there is an important objective fact that influences choice in risky situations: The market will generally pay you to bear uncertainty in the form of variability of results. That is, the more variable are the expected returns from an investment, the greater the payoff. For example, riskier securities such as stocks pay (on average) a higher return than do less-risky securities such as government bonds. Looking in the other direction, insurance companies will reduce the possible variability in your stream of income by selling you guarantees that if a catastrophe should occur to you, you will be recompensed; you pay them a premium to assume risk for you. Insurance does not enable you to avoid feelings of disappointment or surprise or regret aside from financial loss. Sometimes it might be possible to arrange with another individual to shoulder bad feelings for you, however. For example, you might arrange in advance for someone else to take responsibility if a decision should have an undesirable outcome, or for someone else to take the phone call and deal with the consequences if a catastrophe should occur. But your feelings are mainly yours to be borne alone. The strength of your desire to avoid risk is likely to depend upon your economic and life circumstances, and upon the size and nature of the risky outcomes. For example, your desire to purchase life insurance is likely to be different when you have young children from when you have children still of school age. For another example, you may feel no need to insure against the first $500 of loss in an auto accident because that loss would not disrupt your life. But to avoid larger possible losses you are willing to pay an insurance premium which costs more than the expected value of the loss, because such a loss could disrupt your life badly. For a third example, you are more likely to quit your lawyer job and join a partner in hanging out a shingle after you hear that an unknown Aunt Tillie died and left you a hefty bundle. Now that we have in hand the mechanism of expected value for analysing uncertain choices without consideration of risk, as described in Chapter 1-4, we are ready to allow for risk when we do not feel neutral about uncertainty, but instead prefer to avoid it. A preference for certainty over uncertainty may be thought of in various ways: a) You prefer to have a thousand-dollar bill rather than a 50-50 chance of $2000 or nothing. And you would be willing to accept a smaller sum for certain than the "expected value" ($1000) of the alternative whose outcomes are uncertain. More generally, you are not indifferent between payoffs with different probabilities but the same expected value. That is, you prefer a .5 chance of $10 to a .05 chance of $100. b) You would not pay twice as much for a given probability of winning twice as much. That is, you might be indifferent between $9 and a 50-50 chance of $20, but you would prefer $900 to a 50-50 chance of $2000. And c) An idea which often has been intertwined with the above ideas about uncertainty concerns the different meanings of sequential increments of the same amount of money. That is, the second thousand dollars does not seem to give as much good feeling as does the first thousand dollars; twice as much money often is not "worth" twice as much to you. This is the famous idea of "diminishing marginal utility". But though this idea seems intimately related to the above ideas about uncertainty, and though it has often been considered interchangeable with them in theory, the relationship is not obvious. In practical terms, we want to know which choice we should make in a particular risky situation, such as purchasing insurance, or opening a law office, or choosing among investment opportunities in three countries that differ greatly in political stability. There are two steps to a sound decision: 1) Understand the nature of the risk, and how it fits into the rest of your life [your business]. 2) Use appropriate devices for allowing for the cost to you of assuming the risk, or the benefit of avoiding it. In the simple two-choice yes-or-no examples mentioned above, you should first try to gain a clear idea of the basic notions of probability and expected value, next consider the choice in light of your entire economic and non-economic life circumstances (and especially your present state of wealth), and then choose according to your enlightened preferences. The last step sounds vague, but we will look at some techniques to make it less vague. Sometimes it helps, for example, to consider a hypothetical set of other choices and ask yourself what you would do if you faced them. You can then look for consistent patterns in your preferences that will help you make your choice. You can also ask yourself such questions as: How much would it take to make me twice as happy as an extra $1000? (See Simon, 1975 [?] or XXX for details on these techniques) Illusions, paradoxes, and apparent self-contradictions abound in the risky choices people make even when the choices are relatively simple. Often people's responses depend upon how the issues is posed - for example, whether the same amount is seen as a loss of what you have, or a non-gain, both of which are objectively identical but subjectively very different. Hence risky choices have fascinated economists, statisticians, and psychologists during the last decade or two. But these peculiarities need not detain us here. It comes down to the fact that your willingness to accept $900 (or $800 or even $700) rather than a 50-50 chance of $2000 is of the same nature as your choice to use public transportation and save money rather than buy a car. The $900 (or whatever) that you will accept in exchange for the 50-50 chance of $2000 or zero is called the "certainty equivalent" of the uncertain opportunity. It corresponds to the risk-adjustment portion of the discount factor discussed in Chapter 2. The extent to which the certainty equivalent is less than the expected value of the uncertain opportunity -- that is, the difference between $900 and $1000 in this example -- is a measure of the extent to which you are risk averse. Scholars in finance and economics have done a great deal of advanced theoretical thinking about risk aversion, but as yet no one has developed convenient ways of applying this work to everyday life for individuals. So we continue to bumble through these decisions, often making them differently than we would if we were to spend the effort necessary to think them through in a satisfactory fashion. The techniques can be left aside. I'll simply mention the competing principles used in these risk analyses, each associated with a different criterion goal for optimization: Maximization of "utility" The utility principle is the oldest and the most widely used device to allow for risk, especially among finance specialists, perhaps because it lends itself better to mathematical analyses than do the others; it aims to maximize your "utility" -- that is, the supposed satisfaction that you might achieve from the resulting sums of money. It systematically takes into account that twice as much money will not give you twice as much satisfaction, the appropriate adjustment depending upon your wealth and the extent of your dislike for risk. All this has little or nothing to do with the concept of utility that Jeremy Bentham proposed in the 18th Century, and from which the term originally comes. When you apply this principle, you reduce somewhat the expected value of the alternative you choose in order to reduce the variability among possible outcomes. Minimization of regret or disappointment or unpleasant surprise. These related principles aim at reducing the chance that you will end up feeling badly about the outcome. For example, if someone first tells you that you have won a lottery and then two minutes later tells you that it was an error, you are likely to feel worse than if you had never heard either message. (Similarly, hearing from a doctor that you do not have a disease that you thought you might have had is likely to send you out in a particularly pleasant mood.) You therefore choose in a fashion that you reduce somewhat the expected value of the alternative you choose in order to reduce the chance that the outcome will be one about which you will feel regret, disappointment, or unpleasant surprise. The mini-max principle. This principle applies to some situations which are head-to- head games with one or more other players, in which you expect them to actively try to out-fox you, and where your loss is their gain. This is unlike most situations in life (and in business), in which the relationship you are in with the relevant groups of individuals (such as impersonal customers) or with nature (for example, when you are drilling an oil well) is not game-like because your "opponent" is not actively trying to out-fox you. The mini-max principle is a very complicated mathematical strategy for obtaining a combination of relatively large gains while taking the chance of relatively small losses, by attempting to avoid the worst situation that your opponent might force you into. This principle may be appropriate for some very specialized games, and perhaps occasionally in war. But to my knowledge it has never been found appropriate in everyday life, despite all the inflated claims made for it. It is a classic example of the adepts of a fancy mathematical technique succeeding in a massive snowjob on people who do not understand the mathematics but are so insecure about their ignorance that they take it on faith that there must be something of value inside the mysterious mathematical black box -- something worth paying a high fee for. Unfortunately, cases like this are not rare in the world of "scholarship". The psychological bases for these principles link up with the discussion of feelings in Chapter 00. For example, the pain of a contemplated negative outcome which might yield regret or disappointment can be understood with the same mechanism of negative self-comparisons used to understand sadness and depression.1 The choice among these principles for dealing with risk depends upon your taste. But if your goal is to maximize profit in business, you will not make any allowance for risk other than warranted by market (rather than personal) considerations. Lending or investing money is a common situation in which risk is a crucial issue. When a bank lends working capital to an individual or a firm, the interest rate depends upon how risky the bank deems the loan -- that is, the bank's estimate of the chance that the borrower will default. Similarly, the bonds of firms that are unstable or have little collateral must pay higher interest rates than do bonds of firms that are more solid. The stocks of firms whose prospects are very uncertain sell at a lower price relative to the firm's earnings than do the stocks of firms whose earnings are stable and seemingly-assured from year to year. And the rate of return to preferred stocks is on average higher than the rate of return to bonds, because in case of a bankruptcy the preferred stocks would lose their value before the bonds would. (Common stocks are riskiest of all in this respect.) This structure is equivalent, from the point of view of the person supplying the funds, to a lower discount factor for a more risky situation. (Chapter 1-2 discussed the mechanics of using the discount factor and introduced its interpretation.) You can go beyond making a single risky choice by arranging your "portfolio" of risktaking activities so as to reduce the total risk. For example, instead of investing all your wealth in a single stock, you can diversify among a set of stocks. A life insurance company greatly reduces its risk by selling a great many insurance policies rather than just one. The prospect that any single individual will die this year is very risky, but the rate of death among (say) a thousand people of the same age is known in advance with high probability, being affected only by the small chance of a major catastrophe. And the insurance company forestalls some of that risk with a clause which protects the company against war loss which will greatly increase overall risk. Almost any diversification reduces the overall risk even while keeping the returns the same. But it is not possible to eliminate all risk with diversification. In the past few decades the study of finance has worked out a variety of devices for "portfolio analysis" to take maximum advantage of diversification. The most important element in a diversification program, however, is to remember to do it. More about all this in Chapter 8-0 on portfolio investment. about utility analysis. Construct utility function. Can do it by asking how much it will take to make twice as happy, or how happy twice as much money will make you. Also maximin, and regret functions.] When there is a sequence of decisions so that you need a decision tree, you must put risk-adjusted quantities into the circles and boxes. The certainty equivalent serves this purpose. Instead of each uncertain set of outcomes, you substitute the assured amount that accept instead. This explanation is too brief for you to fully understand it, but you can get the details when you need them from a standard text.[fn to ame] FOOTNOTE 1 See Bell in Bell et. al. for an interesting formal analysis which explains people's risk behavior in this fashion, behavior which otherwise seems inexplicable. Page # thinking risks15% 3-3-4d