Usually, connecting just five points will produce a smooth, easy-to-read curve. If more points are needed, however, the ranges can be divided into new equally desirable ranges. To better define his curve, Jim adds a sixth point by establishing the desirability midpoint, point F, between points D and B, at $14,500. Its desirability score is 87.5, halfway between 75 and 100. He then connects the six points, producing the desirability curve (page 150).
The curve represents the desirability scores of all the potential payoffs falling between $6,250 and $18,750. Reading from the curve, the desirability score assigned to the certificate of deposit alternative, which has a monetary value of $10,600, is 65, for example. Before using the curve, though, Jim decides it would be wise to test some of its implications and, if necessary, adjust it. The curve implies that, for Jim, the following increases, representing desirability increments of 25, are equivalent: $6,250 to $7,500; $7,500 to $9,000; $9,000 to $12,000; and $12,000 to $18,750. Asking himself whether these increments reflect his true feelings about desirability and risk, Jim concludes that they do.
Use the Desirability Curve to Make a Decision. Jim is now ready to evaluate the proposed investment, taking into account his risk tolerance. First, he reads from the curve the desirability scores that correspond to the 11 payoffs, and he writes the scores on his risk profile, as shown in the table below. He then multiplies each payoff’s chances by its desirability score, as in the last column. Finally, he adds up the resulting figures to calculate an overall desirability score for the investment.
The resulting overall desirability score is 68.35. Since this exceeds the desirability of 65 from the certificate of deposit, Jim should choose the private-venture investment.
Get Additional Insights by Converting Desirability Scores Back to Money. Converting the overall desirability score back into money yields new insights and another way to think about making risky decisions involving a single objective. Take Jim’s risk profile for the venture as an example.
Computing the Overall Desirability Score for Jim Nance’s Potential Investment
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•Its 68.35 desirability score corresponds to a monetary value of $11,000 from Jim’s desirability curve. This says that the value of the venture to Jim is $11,000.
•Having a monetary value gives Jim an intuitive feeling for how much better the private venture is. Namely, it is worth $400 more to him than the certificate of deposit, worth $10,600.
•The values assigned to risk profiles can be used for decision making. A more risk averse member to Jim’s investment club might value the private venture at $10,000 and, as a result, choose the certificate of deposit.
•Someone who had no risk aversion at all would value the private venture as its average monetary value, $11,775 (see table on page 148). Jim’s value is less because he is risk averse. The difference between the average monetary value and Jim’s value, $775, is called his risk adjustment for the risk profile.
•For a given risk profile, the risk adjustment is an indicator of your risk aversion. The larger the risk adjustment for any given risk profile, the more risk averse you are and vice versa.
It may be tempting to assign a value directly to a risk profile without introducing desirabilities in a formal way. Using your intuition, you could directly assess a risk adjustment, then subtract it from the average monetary value to obtain the value of the risk profile to you. This might seem simple and direct, but you need incredibly good intuition to do it well. To arrive at an appropriate figure, somehow you would have to keep in mind all the payoffs and how desirable you consider each of them to be, as well as how likely each is. This is mind boggling.
The desirability curve approach breaks this thought process into manageable bites, allowing you first to carefully think about your desirabilities, then to blend them with probabilities to calculate an appropriate value.
Interpret Desirability Curves. Jim’s curve not only helps him make a specific decision, it also provides him with considerable insight into his attitude toward financial decision making in general. It shows, for instance, that avoiding the largest possible loss (that is, the loss from $10,000 to $6,250), with its desirability score of 60, outweighs obtaining the maximum gain (going from $10,000 to $18,750), which represents a 40-point score. Avoiding losses, it is clear, weighs more heavily in Jim’s decision making than achieving equivalent gains, indicating that he is risk averse.
In fact, the shape of your desirability curve is a very good indicator of your overall risk tolerance, as the figure on page 155 illustrates. An upwardly bowed curve indicates a risk-averse attitude with a greater risk aversion indicated by a greater curvature. A straight line represents a risk-neutral attitude, and a downwardly bowed curve connotes a risk-seeking attitude.
Watch Out for These Pitfalls
We’ve shown you some reliable, logical ways to account for your risk tolerance in making decisions. By using them, you can avoid being tripped up by old habits and other common pitfalls. Here are a few to watch out for:
Interpreting Risk Attitude from a Desirability Curve
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•Don’t overfocus on the negative. To avoid bad consequences (and the resulting regrets), some people give disproportionate attention to the downsides of their alternatives. They focus on avoiding trouble, even if it’s unlikely to occur. In many cases, however, the upside potential will far outweigh the downside risk. Lesson: Consider the full range of consequences, not just the bad ones.
•Don’t fudge the probabilities to account for risk. Some people, consciously or unconsciously, account for their risk tolerance by raising the probabilities of outcomes with bad consequences and lowering the probabilities with good ones—just to be safe. Every risk profile is thereby shaded toward a pessimistic view, and the resulting decision is likely to be overly cautious. Lesson: Judge chances on their own merits, without regard for your risk tolerance. Account for your risk tolerance separately.
•Don’t ignore significant uncertainty. Some people make their decisions based on the most likely scenario, attempting to eliminate complexity by ignoring uncertainty altogether. Without bothering to make a risk profile, they just assume that the most likely chain of events will occur, determine their best choice under those circumstances, and pursue it. If something else occurs, well, that’s just good or bad luck. The problem is that something else can and likely will occur. Effective decision making takes all viable possibilities into account. Lesson: When uncertainty is significant, develop a risk profile for each alternative which captures the essence of the uncertainty.
•Avoid foolish optimism. While some people assume that the most likely chain of events will happen, others assume that a very positive chain of events will happen. They see decisions through rose-colored glasses. Their wishful thinking may be a personality trait—we all have friends and associates who are perennially optimistic—but often it is simply due to a lack of thoroughness in thinking about what could occur. They might project the completion date for a project, for example, without thinking through all the possible delays. Lesson: Think hard and realistically about what can go wrong as well as what can go right.
•Don’t avoid making risky decisions because they are complex. Overwhelmed by complexity, some people throw up their hands. They may do nothing and live with the status quo, they may make a random or arbitrary decision, or they may get someone else to decide for them. Such ‘‘decisions,’’ unfortunately, will rarely be consistent with their objectives. Lesson: Don’t despair; you can deal sensibly with complexity and reach a smart choice.
•Make sure your subordinates reflect your organization’s risk tolerance in their decisions. Government agencies, businesses, civic groups, families, and other organizations all have institutional risk tolerances. Without guidance and the proper incentives, people in an organization may, by their decisions, either expose the organization to too much risk or forfeit attractive opportunities by acting too conservatively. Lesson: An organization�
��s leaders should take three simple steps to guide subordinates in dealing successfully with risk. First, sketch desirability curves that reflect the risk-taking attitude of the organization. Second, communicate the appropriate risk tolerance by issuing guidelines that include examples of how typical risky decisions should be handled. Third, examine the organization’s incentives to ensure they are consistent with the desired risk-taking behavior.
Open Up New Opportunities by Managing Risk
In making decisions at home and at work—especially financial ones—you may frequently find yourself facing a risk that exceeds your comfort level. If so, there may be ways to manage this risk to make it acceptable to you. Consider the situation of Harry Healy, a small business owner who makes a good living in the very risky business of drilling and producing shallow natural gas wells near Zanesville, Ohio. Harry faces enormous risks each time he drills a well. If it produces no gas, he can lose all of the $125,000 cost of drilling. Furthermore, the price of natural gas can fluctuate by as much as 300 percent in a single year.
Fortunately, Harry has learned to apply various techniques,used regularly by people dealing in the financial markets, to manage his risks. Like Harry, you should consider adding these techniques to your risk management repertoire.
Share the risk. When a good opportunity feels too risky, share the risk with others.
In Harry’s case, the risk profile for drilling a typical well shows a substantial downside risk, including a 10 percent chance of finding no gas, a 30 percent chance of recovering only a small percentage of the drilling costs, and a 20 percent chance of losing a modest amount. He breaks even about 10 percent of the time and thus actually makes money only about 30 percent of the time—though the profits in these cases can be substantial.
With a net worth of under $750,000, Harry is unwilling to risk $125,000 at a time, when the chances are 40 percent that he will lose all or most of his investment. He manages the risk, therefore, by sharing it with a group of investors, each of whom takes a proportional share of the costs and any earnings. Harry himself invests $25,000, a sum he is comfortable with, to keep 20 percent of each well.
Seek risk-reducing information. Try to temper risk by seeking information that can reduce uncertainty.
To reduce his risk, Harry targets drilling sites with better-thanaverage risk profiles. He routinely studies surface geology, information on gas production at nearby wells, and, for borderline sites, he orders a seismic test, costing about $12,000, which can reduce some of the uncertainty about whether and how much natural gas might be present.
Diversify the risk. Avoid placing all your eggs in just a few baskets. Look for ways to diversify.
Harry diversifies his assets, investing some in stocks and bonds, rather than subjecting them all to the vagaries of the gas business. In addition, by buying mutual funds rather than individual securities, he lowers his risk further, because mutual funds hold a number of securities, and the ups of some cancel the downs of others. Even on vacation, Harry diversifies. When he goes white-water rafting through wilderness areas, his party divides the food among each raft.
Hedge the risk. When fluctuations in market prices or rates (interest rates, exchange rates, and the like) expose you to discomforting risk, look for ways to hedge.
Fluctuations in the price of natural gas can result in large swings in Harry’s monthly income, and a few successive months of low prices can have serious repercussions. By buying contracts on the commodities exchange that put a floor on future prices, he can—at a cost—manage this risk. Alternatively, he can sign annual fixed-price contracts with the utilities that buy his gas. Harry typically sells over half of his gas at fixed prices and risks leaving the rest subject to market fluctuations.
Insure against risk. Whenever a risk consists of a significant but rare downside, with no upside, try to insure against it. But don’t overinsure.
Harry would be liable for substantial damage and injuries from a well blowout or other accident. Although the chances of such an occurrence are extremely low, a serious accident could wipe him out. Harry manages this risk by insuring against it. He doesn’t, on the other hand, insure his $18,000 pickup truck against collision or theft. Because he can afford such a loss, he figures the insurance isn’t worth its cost.
All of these techniques help to manage risk by enlisting others in transactions that reshape the original risk profile, making it more compatible with the decision maker’s risk tolerance. So, when you face an uncomfortable risk, ask yourself, ‘‘What transactions can I make with others that will improve my risk profiles?’’
APPLICATION
To Settle or Not to Settle?
Karen and her advisor, Jane, have come down to the final element of Karen’s decision: her need for money, which determines her attitude toward risk. Starting with the assumption that Karen, otherwise broke and in debt, has at a minimum assets equal to $210,000 (the settlement offer minus her lawyer’s fees), Jane begins to examine how Karen would use the money. How would it change her life? Karen is ready with answers.
‘‘I’ve thought about that a lot. First I’d pay off my debts: a $50,000 student loan, $25,000 for the surgery my health insurance didn’t cover, and $8,000 in taxes. Then I’d have some purely cosmetic surgery to make these facial scars less visible, and with any money left over, I’d get a used car and maybe pay more rent somewhere to get out of my dreadful apartment.’’
‘‘How’s your job? How much do you make?’’
‘‘It’s a dead-end job, you know that. I hate sales, and I only earn about $25,000 a year. I’d like to go back to school and learn something that would help me get a better job. I’d have to take time off, anyway, for the surgery.’’
Jane summarizes. ‘‘If you go to trial and lose—not the most likely outcome, but it has a chance of 30 percent—your life would be pretty bad. You’d be in debt; you couldn’t afford some of the things that would make you happier; you’d have to remain in your present job and keep your present apartment.’’
Karen interrupts. ‘‘Not to mention the humiliation of losing and my regret over not accepting the sure thing of $210,000. I’m in pretty bad shape now, but I’d be far worse off if I lost the trial.’’
‘‘But who says you’re going to lose the trial?’’ Sam barks.
Jane continues: ‘‘If you netted a lot more money from the trial, what would you do with it? How would it change your life? How much happier would you be?’’
‘‘If I had a lot more money, I’d still do all the things I said I’d do if I had the $210,000. But I’d get a condo rather than go on renting, I’d buy a new car instead of a used one, and maybe I’d buy some clothes and take a few trips to Europe and other places. And I’d definitely go to graduate school. But those things aren’t nearly as important to me as what that initial $210,000 would bring.’’
‘‘How much more money above the first $210,000 would give you roughly the same satisfaction it would?’’
‘‘Close to a million! At least $800,000.’’
Sam couldn’t contain himself. ‘‘You can’t be serious, Karen! You can’t equate having only about $200,000 with having another $800,000!’’
‘‘Yes, I am serious. Without the $210,000, I’m ruined. More would make me richer, but that’s not as important to me as getting an even start.
‘‘This has really helped me,’’ Karen says, turning to Jane. ‘‘When you force me to think about my attitude toward risk and the probabilities involved, not only do I see clearly that I should accept the $210,000 offer, but I have firm conviction in that decision. When I think about how I’d use the money, the peace of mind I’d get, I know that the possibility of gaining more in court isn’t worth the gamble of losing it all.’’
On the courthouse steps, before Sam could accept the $300,000 offer, the other side increased it to $325,000. Despite his strongly differing opinion on what she should do, Sam accepted on Karen’s behalf.
Lessons from the Applica
tion
Karen couldn’t identify the smart choice until she had examined her risk tolerance. But once she had thought hard about the relative desirability to her of various possible consequences, she was able to make a decision without further analysis. This is the case for most of the uncertainty decisions that most of us face. Using a little careful, qualitative thinking about the significance of the consequences almost always makes the smart choice obvious.
If Karen had been unable to decide after thinking through the risks and benefits qualitatively, she could use the desirability scoring method. She would assign scores to the possible consequences, compute the overall desirability of going to court and of settling, and base her decision on what the scores revealed.
Sam’s sharp disagreement with Karen about whether to accept the $300,000 offer reflected a correspondingly sharp difference in risk tolerance. (They agree on probabilities; after all, Sam was the source of these judgments.) With Karen’s risk tolerance, settling was the smart choice, but with Sam’s, settling was foolishly conservative.
It is good to have our advisors challenge our thinking on risk tolerance (as Sam did), but in the final analysis, it’s our own (or, in this case, Karen’s) risk attitude that matters in making a decision. You should certainly seek out information and guidance from informed advisors, but you should never let them make a decision for you. Sam’s recommendation to go to court was incompatible with Karen’s risk tolerance.
CHAPTER 9
Linked Decisions
MANY IMPORTANT DECISION PROBLEMS REQUIRE you to select now among alternatives that will greatly influence your decisions in the future. Your choice of a college major, for example, may strongly influence your future career options. Such decisions are linked decisions—to make the smartest choice about what to do now, you need to think about what you might decide to do in the future.
Smart Choices Page 13
