What would you decide? The smart choice for one person may not be the smart choice for another. You might decide not to have the surgery, but your next-door neighbor might opt for it. It all depends on one’s attitude toward risk.
Understand Your Willingness to Take Risks
Your risk tolerance expresses your willingness to take risk in your quest for better consequences—in Rob’s case, better vision. It depends primarily on how significant you consider the downside— the poorer consequences of any decision—compared to the upside. If, like most people, you are risk averse, the poorer consequences will weigh more heavily in your mind than the better ones. The more heavily they weigh, the more risk averse you are. Thus, to reflect your risk tolerance in a decision you need to think carefully about how desirable you consider the possible consequences relative to one another.
To see this, consider how two people, one moderately risk averse (Ms.Wary) and one very risk averse (Mr. Cautious), would evaluate a simple risky choice. Both are offered the opportunity to accept or reject a 50-50 chance of either making $10,000 or losing $5,000. A coin will be flipped. If it lands heads, they will receive $10,000 in cash. If it lands tails, they will lose $5,000.
How should they decide? They must weigh the chances of the upside and the downside and the desirability of each. In this case, because the upside and the downside are equally likely, the decision should hinge on how desirable they believe the upside is relative to the downside.
Mr. Cautious is very concerned about the impact of losing, fearing he’d have to borrow money or forgo important purchases to pay the penalty. He decides that the good fortune of receiving $10,000 doesn’t compensate for the equally likely $5,000 loss. Ms. Wary would also hate to lose $5,000, knowing it would mean delaying her long-cherished plans to remodel her condo, but she likes the potential offered by a $10,000 windfall. With the extra cash, she could take her remodeling to the next level. The upside is desirable enough that she is willing to take the risk.
The same logic applies to all risk profiles, not just this simple one with two outcomes and consequences described in terms of a single objective, money. The basic principle is this: the more desirable the better consequences of a risk profile relative to the poorer consequences, the more willing you will be to take the risks necessary to get them.
But making the smart choice also requires balancing the desirabilities of the possible consequences with the probabilities that they will occur. If the chances in the decision above were changed to 90 percent in favor of gaining $10,000, even Mr. Cautious might be tempted. The downside remains just as undesirable relative to the upside, but because it is now much less likely, the improved chance of success will, for many people, more than compensate for the imbalance in desirability.
Once again, this logic applies to all risk profiles. The more likely the outcomes with better consequences and the less likely the outcomes with poorer consequences, the more desirable the risk profile to you.
Incorporate Your Risk Tolerance into Your Decisions
To take your risk tolerance into account in comparing risk profiles, follow three simple steps:
•First, think hard about the relative desirability of the consequences of the alternatives your’re considering.
•Second, balance the desirability of the consequences with their chances of occurring.
•Third, choose the most attractive alternative.
Taking these three steps enables Rob Goldman to reach a final decision about cataract surgery:
1.Think hard about the desirabilities of the consequences. Rob believes that restoring 20/30 vision without fuzziness would make a huge difference to him. He could resume driving at night, and tennis and traveling—two of his favorite pastimes—would become much easier. And although dropping to 20/100 would be bad—no question about it—he feels he has already made so many adjustments to weakened vision that it wouldn’t be the end of the world. He therefore decides that, in terms of desirability, the negative consequence of deteriorated vision only slightly outweighs the positive consequence of improved vision.
2.Weight desirabilities by chances. More fully stated: weight the desirabilities of the consequences by the chances of their associated outcomes. If the odds of success were only 50-50, Rob wouldn’t undergo the surgery. But the odds aren’t even. Rob concludes that the fact that the upside is nine times more likely than the downside more than compensates for the fact that the undesirability of failure slightly outweighs the desirability of success.
3.Compare and choose. When Rob now compares the surgery risk profile with the no-surgery alternative, his choice becomes abundantly clear: he calls Dr. Eddy’s office to schedule the surgery.
Quantify Risk Tolerance with Desirability Scoring
Suppose that, after having developed risk profiles and thought hard about the desirabilities of the consequences and the probabilities of the outcomes, you still can’t decide. At this point, you need to be more precise about the relative desirability of each consequence. You need to move from a qualitative analysis, like Rob Goldman’s, to a quantitative analysis. You follow the same general steps Rob did—determining desirabilities, weighting desirabilities by chances, comparing and choosing—but you use numbers to express the desirability of each consequence and, in turn, each alternative. Let’s walk through the process.
1.Assign desirability scores to all consequences. You begin by comparing the consequences and ranking them from best to worst. You assign the score of 100 to the best and 0 to the worst consequence. Then you assign a score to each of the remaining consequences that reflects its relative desirability. If, for example, you conclude that the desirability of a consequence is exactly halfway between that of the best and worst consequences, you’d assign it a score of 50. Check to be sure that all your scores are consistent, and adjust them as needed to reflect your true feelings about their respective consequences.
2.Calculate each consequence’s contribution to the overall desirability of the alternative. Outcomes with a low chance of occurring should have less influence on an alternative’s overall desirability than outcomes with a high chance of occurring. Hence, you need to account for each outcome’s chance of occurring—its probability. Now, to determine a consequence’s contribution to the alternative’s desirability, multiply its associated outcome’s probability by its desirability score assigned in the first step. If your best consequence (desirability score of 100) had an outcome probability of 30 percent (0.3), its contribution would be 30 (i.e., 100 × 0.3 = 30). When an alternative results in a sure thing, its outcome has a probability of 1.0, and the contribution of its consequence will equal its desirability score.
3.Calculate each alternative’s overall desirability score. Now, add the individual consequence contributions to arrive at an overall desirability score for each alternative. (Note that the overall desirability score of an alternative is the average of the desirability scores of its consequences, weighted by the chances of their associated outcomes.)
4.Compare the overall desirability scores associated with the alternatives and choose. Now you have a solid, quantified basis for making a decision. Compare the overall desirability scores of each alternative, and choose the alternative with the highest score.
Use Desirability Scoring to Make a Tough Decision
Going through the process of assigning desirability scores to consequences and calculating overall desirability scores for alternatives won’t be necessary for most decisions. But for resolving some of life’s most important and most complex decisions, it can be invaluable. Consider the situation facing Marisa Reyes, a graduate student in business administration who must decide within a matter of days between two attractive job offers, each involving a major uncertainty. One job is with the global accounting firm where Marisa worked for three years before leaving for graduate school. The other is with an international management consulting firm.
The career prospects and financial rewards at both firms are essentially
equivalent. Marisa’s decision therefore hinges on the nature and location of her initial job assignment. She has identified a number of objectives relating to the job assignment: good living conditions, including cultural and social attractions, quality housing, and interesting places to vacation; a challenging job with substantial responsibilities; and an opportunity to contribute to society by helping people.
The actual assignment she’ll receive, however, is uncertain. Because she won’t start for six months, neither of the companies will commit beforehand to a specific assignment, but each has narrowed the possible postings down to two. The consulting firm might initially post her to London—her dream—but it might also post her to Buenos Aires. The accounting firm would start her either in New York or in Santiago. Each alternative, in other words, leads to an uncertainty with two possible outcomes.
Marisa carefully evaluates the possible assignments at each firm, and using the techniques outlined in Chapter 7, she creates the risk profiles shown below. To judge the chances of each job posting, she talks in depth with the manager of human resources at each firm.
Marisa is unable to decide by simply comparing the risk profiles. The qualitative descriptions don’t provide her with enough information. Therefore, she decides to compare the choices quantitatively. Before assigning desirability scores, she ranks the four possible consequences from best to worst, a good practice. As shown in the table below, she ranks the consequences associated with London first, New York second, Buenos Aires third, and Santiago last. She assigns a desirability score of 100 to the London consequences and 0 to the Santiago consequences, the best and worst of the locations. She then assigns to the Buenos Aires consequences a score of 50, judging its desirability to be halfway between that of Santiago and that of London. She then decides that the desirability of New York’s consequences lies 60 percent of the way from the Buenos Aires consequences to London’s, and so she assigns a score of 80 (80 is 60 percent of the way between 50 and 100). As a consistency check, Marisa asks herself whether all four of the scores reflect her true feelings, and she decides that they do.
Risk Profiles for Marisa’s Job Decision
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ALTERNATIVE: ACCOUNTING FIRM
Uncertainty: Office Assignment
ALTERNATIVE: CONSULTING FIRM
Uncertainty: Office Assignment
Ranking and Scoring the Consequences of Marisa’s Job Decision
* * *
Determining the Overall Desirability for Marisa’s Risk Profiles
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Accounting Firm
Consulting Firm
Marisa then calculates the overall desirability score for the alternatives. She first multiplies the desirability score of each of the consequences by its associated outcome probability, which yields its contribution, as shown in the table above. She then adds the contributions of New York (72) and Santiago (0) to arrive at an overall desirability score for the accounting firm (72). Likewise, she adds the contributions of Buenos Aires (37.5) and London (25.0) to calculate the overall desirability score for the consulting firm (62.5). Relying on her calculations and the careful thought that preceded them, Marisa makes her choice. She accepts the accounting job, and six months later she is posted to New York .
The Desirability Curve: A Scoring Shortcut
Marisa had only four consequences to consider, so assigning the initial desirability scores was fairly easy. When you have many possible consequences, however, the assignment of desirability scores can become difficult and time consuming. Fortunately, there is a shortcut: the desirability curve. After plotting the desirability scores of a few representative consequences—five, typically—you connect them on a graph to form a curve. You can then use this curve to determine the desirability scores of all other possible consequences.
There’s one important limitation to the use of desirability curves: you can use them only when each of the consequences can be expressed using a single, numerical variable, such as dollars, acres, years, or lives saved. They can be used, for example, to chart the payoffs of investments in terms of dollars made or lost, the potential environmental impact of a proposed development in terms of square miles affected, or the possible consequences of open-heart surgery in terms of years added to the patient’s life.
Desirability curves can be so useful, however, that it will often be worthwhile to use the even swap method to convert consequences described by multiple variables into a single, numerical term. (Remember that Karen, the accident victim, did this in the Application at the end of Chapter 7. She converted the time and psychological impacts of a trial into equivalent dollar amounts, enabling her to describe her consequences using a single variable: money.)
An Investment Example. To see how desirability curves work, consider the decision problem facing Jim Nance. Jim makes his family’s investments, guided by the dual objectives of growth and preservation of capital. Through an investment club, he now has the opportunity to make a one-year investment of $10,000 in a private venture, unrelated to the securities markets, on which he can make as much as 87.5 percent or lose as much as 37.5 percent. In other words, over the year, his $10,000 could grow to $18,750 or shrink to $6,250. Before learning of this opportunity, Jim had planned to buy an insured one-year certificate of deposit (CD) paying 6 percent interest, which would deliver a sure $10,600 in a year.
While the potential payoffs of $18,750 and $6,250 represent the extremes for the private-venture investment, Jim knows that there are a multitude of other possible payoffs between the extremes, and that each will have its own probability of occurring. Using a simple software program and drawing on publicly available industry data, Jim and some of his fellow investment clubbers develop a risk profile for the investment, showing a range of possible payoffs (which can be used to describe both the outcomes and consequences in this case) and their chances. The risk profile is represented by the first two columns of the table on page 148. Analyzing the risk profile, Jim sees that each of the first three payoffs in the list would all lose money, making the overall chance of suffering a loss 21 percent (2 + 6 + 13). On the other hand, the last seven payoffs earn more than the CD, making the chance of beating the CD’s return 64 percent (18 + 17 + 11 + 9 + 4 of beating the CD’s return 64 percent (18 + 17 + 11 + 9 + 4 + 3 + 2).
Risk Profile for Jim Nance’s Potential Investment
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The risk profile for this decision is clear and unambiguous (numbers usually are), but the decision isn’t. Should Jim invest in the risky venture, or should he go for the safe CD?
To answer that question, most financial analysts would first compute the ‘‘average monetary payoff’’ of the private-venture investment. To do this, they’d simply multiply the dollar amount of each payoff by its chances, as shown in the last column of the table, and then they’d add up all the resulting figures to arrive at the average payoff. In Jim’s case, the average monetary payoff of the venture investment is $11,775. Because this amount is only $1,125 higher than the $10,600 that would be delivered by the CD, many financial analysts would advise Jim to take the CD. They would reason that a sure 6 percent return is too good to turn down given the high risk of the private venture.
There’s a big problem with this approach, however. It doesn’t take into account the risk tolerance of Jim and his family. It may be that the potential gain of the private venture is worth the risk to Jim. This may be so even if, like most people, he is risk averse and the loss of a given amount of money may have a far greater impact on his family than the gain of that same amount.
The desirability curve can deal with this. What you do is:
•Construct a desirability curve (often referred to in the literature as a utility curve) that assigns a desirability score to each payoff that reflects the subjective desirability of money to you.
•Use the desirability scores of the possible payoffs and their chances to calculate an overall desirability score for each alternative.
•Choose
by comparing the overall desirability scores of the alternatives.
We’ll show you how this is done for Jim Nance’s investment.
Create a Desirability Curve. Because Jim is working with numbers, ranking the consequences is easy. When it comes to money, more is better, so he just assigns 100 to the highest payoff, $18,750, and 0 to the lowest, $6,250. Now, to avoid having to figure out the desirability scores for such a large number of consequences, Jim plots a desirability curve.
He uses a simple graph, illustrated below, with the horizontal axis showing the range of possible payoffs (the consequences) and the vertical axis showing the desirability score associated with each payoff. He first plots the two extreme points: point A represents the score of 0, assigned to $6,250, and point B represents 100, assigned to $18,750. These mark, respectively, the beginning and the end of the curve. He then uses his judgment to establish a midpoint for the curve corresponding to a desirability score of 50. Since preservation of capital is a prime objective, Jim decides that going from $6,250 to $9,000 is as desirable as going from $9,000 to $18,750. He thus assigns a desirability score of 50 to $9,000 (point C).
Creating Jim Nance’s Desirability Curve for Money
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Jim uses similar thinking to divide the ranges above and below $9,000 into equally desirable ranges to establish payoffs for the 25 and 75 scores. He assigns 75 to $12,000 (point D), which he decides is the midway desirability point between $9,000 and $18,750. He assigns 25 to $7,500 (point E), his midway desirability point between $6,250 and $10,000.
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