HMGT 435 WK1

CHAPTER

55

4DESCRIBING, EVALUATING, AND MANAGING RISK

Learning Objectives

After reading this chapter, students will be able to

• describe the key features of a risky choice, • construct and use a decision tree to frame a choice, • calculate an expected value and standard deviation, and • discuss common approaches to managing risk.

Key Concepts

• Clinical and managerial decisions typically entail uncertainty about what will happen.

• Decision makers often have imprecise estimates of the probabilities of various outcomes.

• Decision makers must describe, evaluate, and manage risk. • Risk sharing and diversification are two ways to manage risk.

4.1 Introduction

Clinical and managerial decisions typically entail risk. Important information is often incomplete or missing when the time to make a decision arrives. At best, managers know the potential outcomes and the probability that each will occur. At worst, managers have little or no information about outcomes and their probabilities. Either way, managers must identify risks that are worth analyzing, risks that are worth taking, and the best strategies for deal- ing with them.

When outcomes are uncertain, decision making has three compo- nents: describing, evaluating, and managing potential outcomes. Because uncertainty is central to many areas of healthcare, the same techniques (e.g.,

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A l l r i g h t s r e s e r v e d . M a y n o t b e r e p r o d u c e d i n a n y f o r m w i t h o u t p e r m i s s i o n f r o m t h e p u b l i s h e r , e x c e p t f a i r u s e s p e r m i t t e d u n d e r U . S . o r a p p l i c a b l e c o p y r i g h t l a w .

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Economics for Healthcare Managers56

hedging bets, monitoring uncertain situations aggressively) are recom- mended for describing and evaluating potential outcomes regarding real investments (e.g., buildings, equipment, training), financial investments (e.g., stocks, bonds, insurance), and clinical decisions (e.g., testing, therapy).

4.2 Describing Potential Outcomes

The first step in any decision is to describe what could happen, including the probabilities and value of possible outcomes, and calculate descriptive statis- tics about the possible outcomes.

Description begins with an assessment of the probabilities of the pos- sible outcomes. Ideally, the assessment should generate an objective prob- ability—an estimate based on evidence about the frequencies of different outcomes. For example, if 250 out of 1,000 patients reported nausea after taking a medication, a good estimate of the probability of nausea would be 0.25 (250 divided by 1,000). More often, though, description assesses the subjective probability—the decision maker’s perception of how likely an outcome is to occur.

In some cases, decision makers have incomplete data. In other cases, the data do not fit the situation. For example, if a careful study of a drug in a population of young men finds that the probability of nausea is 0.25, what value should we use for a sample of women older than 65 years? In still other cases, individuals may feel that population frequencies do not apply to them. Someone who claims to have a cast-iron stomach may believe that his prob- ability of nausea is much less than 0.25. The decision maker with a cast-iron stomach may be correct in thinking that the population frequency does not apply to him, or he may just be overly optimistic.

In practice, decision makers predominantly use subjective probabili- ties. Unfortunately, these subjective probabilities are often inaccurate, even when the estimates are made by highly trained clinicians or experienced managers. Studies have found that physicians overestimate the probability of skull fractures, cancer, pneumonia, and streptococcal infections, and manag- ers are notorious for being overenthusiastic in their forecasts of how well new projects will fare (Segelod 2017).

For a variety of reasons, humans routinely misestimate probabilities, so examining data about population frequencies can significantly improve deci- sion makers’ choices. For example, even if you believe that your hospital is less likely than average to lose money on the primary care practices it has just purchased, knowing that the majority of hospitals lose money tells you that your hospital is still prone to loss. Moreover, in many cases, an honest assess- ment of the probabilities results in broad generalizations, not a point estimate

objective probability An estimate based on frequencies.

subjective probability An estimate based on judgment.

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 57

of probabilities. A manager may be able to say only that one scenario seems more likely than another. This information is still useful; general impressions can often clarify the situation and help managers make the best decision.

Managing Risk in Medicare Advantage Plans

Medicare Advantage (private insurance for Medicare beneficiaries) presents major risks for insurers. First, the Centers for Medicare & Med- icaid Services annually compiles performance data and assigns every plan from one to five stars. These star ratings have two effects: Higher- rated plans get higher payments and more customers. Because star rat- ings depend on the customer and clinical service offered by providers, who are usually independent contractors, profitability depends on fac- tors that insurers control imperfectly. Second, profitability in Medicare Advantage depends on Medicare spending levels, and no one can really forecast how payment innovations will change Medicare spending. For example, Medicare’s bundled payment for joint replacement reduced costs by 20 percent in some markets (Navathe et al. 2017). Changes that large could matter. Third, no one knows what will happen to Medi- care Advantage enrollment if Medicare’s benefits or payment systems change. Most insurers have profited from Medicare Advantage, benefit- ing from the enrollment of younger retirees, more efficient use of care, and more favorable contracts with providers. But some insurers, such as Catholic Health Initiatives, have posted large losses (Barkholz 2017).

Risk is intrinsic to the health insurance business. Insurers take on risk by selling coverage for consumers’ variable medical expenditures. When you average risk over the spending patterns of tens of thousands of consumers, however, the risk becomes less uncertain—in most cases. But in Medicare Advantage the insured populations are often small, and costs may be driven by a handful of beneficiaries.

But the main perils do not come from the operational issues men- tioned previously. The real risks spring from strategic decisions that could go wrong if an insurer misjudges the market.

Discussion Questions • What has happened to Medicare Advantage enrollment during the

past year?

Case 4.1

(continued)

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Economics for Healthcare Managers58

4.3 Evaluating Outcomes

The next step is to evaluate possible outcomes. This chapter focuses on financial outcomes, typically profits. While easier to forecast than many other outcomes, financial outcomes are difficult to predict. Skilled analysts com- monly arrive at different answers when forecasting costs and revenues for well-established products, and predictions are much less accurate for new products. A famous quotation, apparently of Danish origin, notes that “pre- diction is very difficult, especially if it’s about the future.”

The problems mount when no simple measurement system, such as profits, exists. How valuable is a new surgical procedure that reduces the chance of abdominal scarring from 0.12 to 0.08 but reduces the chance that the operation will succeed from 0.68 to 0.66? When a scenario involves opposing probabilities, evaluation becomes a challenge. Even though schol- ars have made progress in evaluating complex outcomes, considerable uncer- tainty remains. Chapter 14 will tackle this problem in more detail.

4.3.1 Expected Values Calculating descriptive statistics is the final step in the process of evaluating outcomes. The most common statistic (although not always the most use- ful statistic) is the expected value. To calculate an expected value, multiply the value of each outcome by its probability of occurrence and then add the resulting products. For example, suppose your organization is contemplating buying a skilled nursing facility that currently has profits of $20,000. The price of the nursing home is $1 million, meaning that the return on invest- ment would be only 2 percent, which is too low from your organization’s point of view. One of your managers, however, has identified a number of operational improvements that she forecasts will boost profits to $120,000.

expected value The sum of the values of each possible outcome weighted by probability.

return on investment Annual profit divided by the initial investment.

• Have any insurers pulled out of Medicare Advantage during the past year?

• Have any Medicare Advantage plans lost money during the past year?

• Is Medicare Advantage riskier than other forms of private health insurance?

• What other healthcare firms also face risks due to changes in government policy?

• What are the advantages of having private insurers manage Medicare? Disadvantages?

Case 4.1 (continued)

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 59

Although this manager’s improvements are reasonable, a consultant points out that, in his experience, ambitious proposals to increase profits fail about 40 percent of the time. The consultant estimates that the expected profit is $80,000 = (0.6 × $120,000) + (0.4 × $20,000).

This level of precision (e.g., “about 40 percent of the time”) is repre- sentative of the reliability of managerial forecasts—they are inexact at best. Despite imprecise forecasts, managers must make a choice. In many cases, calculating the expected profit and then conducting sensitivity and scenario analyses will help managers avoid bad decisions.

An expected value equals P1X1 + P2X2 + . . . + PnXn, where Pi repre- sents the probability that an outcome will occur and Xi represents the value of that outcome. An expected value differs from an average because the prob- abilities of some outcomes will be higher than the probabilities of others, so they get more weight. For example, the average of $120,000 and $20,000— the two estimates from our previous example—is $70,000. But the expected value is $80,000 because the probability of earning $120,000 is larger than the probability of earning $20,000.

Does buying the skilled nursing home make sense? It might. The expected return on investment is 8 percent. Given that the worst-case sce- nario is a 2 percent return on investment, this gamble will seem reasonable to many firms, depending on the alternative investments the firm is considering.

Good decisions usually require more information than just an expected value because typically the expected value is not the outcome that occurs. Most decision makers find that a list of the best and worst outcomes is valuable. A list of the most likely outcomes can also be useful. Graphs, too, can help decision makers understand their choices. Many people find a well-designed graph more valuable than a calculation. Finally, remember that estimates are estimates; writing them down does not make them more reli- able. The less mathematically sophisticated your target audience is, the more you need to emphasize that forecasts are imprecise.

This simple example can be illustrated with a decision tree, which is a way of presenting information about a choice. A decision tree visually links a decision maker’s choices with the outcomes that are likely to result. It is called a tree because the possible outcomes branch from a choice. For the analyst, much of the value lies in the process of constructing the decision tree because it highlights the analyst’s perceptions of what will happen and where the information is weakest. In addition, many people find that examining a decision tree helps them understand the issues involved because it lays out their best estimates of the cost or payoff and the probability associated with each possible outcome. As you can see in exhibit 4.1, the worst-case forecast is a profit of $20,000, which is less than ideal but not a catastrophe. Similarly, the best-case forecast is a profit of $120,000, which is good but not superb.

sensitivity analysis The process of varying an analysis’s assumptions to see how outcomes change.

scenario analysis Evaluation of payoffs under differing assumptions.

decision tree A chart that depicts the values and probabilities of the outcomes of a choice.

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Economics for Healthcare Managers60

As is usually the case, laying out the decision tree helps clarify the situation by making the probability and profit estimates explicit. It does not tell managers what decision to make. Alternatives have not yet been laid out, so a sensible decision cannot be made.

Calculating the expected values of alternatives is sometimes called rolling back a decision tree. Rolling back a decision tree means calculating its expected value. In exhibit 4.1, the expected return is $80,000.

Examples as simple as this do not require decision trees, but slightly more complex examples may require one (see exhibit 4.2). Suppose the probability that the state will reduce nursing home payments is 25 percent, or a one in four chance. With lower payments, profits will be $100,000 if the improvements succeed or $0 if the improvements fail, so expected profits fall to $75,000. The updated decision tree also displays the profit available from an alternative investment, in this case a short-term bond that returns $40,000. Most profit-oriented decision makers would prefer to invest in the nursing home because its expected profit is higher and the risks are modest.

To make sure that you understand exhibit 4.2, answer the following questions. Why does the probability that the improvements fail and rates are cut equal 0.10? Why is expected profit less in exhibit 4.2 than in exhibit 4.1?

4.3.2 Outcome Variation Managers can use estimates of variability to make comparisons. Variability is typically measured by listing the range of possible values or by listing the standard deviation (which is the square root of the variance). If you are not comparing outcomes, the standard deviation is not helpful. In contrast, the range can convey useful information even if you are not comparing out- comes. The range helps you see the best-case and worst-case scenarios. To know whether a risk is worth taking, you need to know the size of the risk

range The difference between the largest and smallest values.

standard deviation The square root of a variance.

variance The squared deviation of a random variable from its expected value. (If a variable takes the value 3 with a probability of 0.2, the value 6 with a probability of 0.3, and the value 9 with a probability of 0.5, its expected value is 6.9. Its variance is 5.49, which is 0.2 × [3 – 6.9]2 + 0.3 × [6 – 6.9]2 + 0.5 × [9 – 6.9]2.)

Improvements fail

Expected Profit = $80,000

Improvements succeed

P = 0.6

P = 0.4

Profit = $120,000 P = 0.60

Profit = $20,000 P = 0.40

EXHIBIT 4.1 A Nursing Home

Decision Tree

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 61

and the potential payoff. Few people will want to take a risk if the best pos- sible payoff is small or if the worst payoff is disastrous. On the other hand, if the best payoff is large, some people will be willing to accept significant risks.

To calculate variance, multiply the squared difference between the value of each outcome and the expected value by its probability of occur- rence and then add the resulting products. (Find the appropriate probability of occurrence by multiplying the probability on the “branch” of the outcome by the probability on the preceding branch.) So, in our example, the variance equals 0.15 × ($100,000 − $75,000)2 + 0.45 × ($120,000 − $75,000)2 + 0.10 × ($0 − $75,000)2 + 0.3 × ($20,000 − $75,000)2, or $2,475,000,000. The standard deviation is the square root of $2,475,000,000, which is $49,749.

A standard deviation or variance has meaning only when you are comparing options. If two choices have similar expected values, the one with the higher standard deviation carries a higher risk because a larger standard deviation means that the bad outcomes are either more likely or much worse. For example, a project that has an 85 percent chance of earning $0 and a 15

Profit = $100,000 P = 0.15

Profit = $120,000 P = 0.45

Profit = $0 P = 0.10

Profit = $20,000 P = 0.30

Expected profit of short-term bond = $40,000

Expected Profit = $75,000

Rate cuts

No rate cuts

P = 0.25

P = 0.75

Rate cuts

No rate cuts

P = 0.25

P = 0.75

Improvements succeed

Improvements fail

P = 0.6

P = 0.4

= 0.15 × $100,000 + 0.45 × $120,000 + 0.10 × $0 + 0.30 ×

$20,000

EXHIBIT 4.2 A Nursing Home Decision Tree with the Possibility of Rate Cuts

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Economics for Healthcare Managers62

percent chance of earning $500,000 also has an expected profit of $75,000. The standard deviation for this project is $178,536, confirming its higher risk.

Remember that the point of these calculations is to improve your analysis. The analysis should include an understanding of the size of the risk, how likely it is to occur, and whether it is worth taking. If your target audi- ence, which might include members of the board or nonfinancial managers, is puzzled by your analysis and does not really understand the issues, you have failed to present it effectively. Your audience will not be able to offer useful feedback, and the decision to take or not take the risk will be all yours. Managers could be terminated for taking risks that the board and other man- agers understood and approved. Managers will be terminated for taking risks that the board and other managers did not understand.

4.3.3 Risk Preferences Risk preferences may influence choices. A risk seeker prefers more variability. Someone who gambles in a casino must be risk seeking because the expected payoff from a dollar bet will always be less than a dollar because of taxes and the casino’s take. Likewise, a patient who can expect to live 18 months if she undergoes standard therapy may be a risk seeker. She may prefer a therapy that gives her an expected life span of only 13 months if it increases her chances of significant recovery. The manager of a nearly bankrupt business is likely also a risk seeker. Taking chances, even ones with low expected payoffs, may be the only way to survive.

A risk-neutral person does not care about variability and will always choose the outcome with the highest expected value. Large organizations with substantial reserves can afford to be risk neutral. For example, a firm with $400 million in cash reserves will probably not buy fire insurance for a $200,000 clinic. If the expected loss is $4,000 per year (a 2% chance of a $200,000 loss), the organization’s fire insurance will cost at least $4,400 because of processing costs and insurer profits. On average, the firm will have higher profits if it does not insure this risk, and it can afford not to. Spending $200,000 for a new clinic will not put much of a dent in the organization’s reserves.

A risk-averse person avoids variability and will sometimes choose strategies with smaller expected values to avoid risk. An individual who buys health insurance is likely to demonstrate risk aversion because the expected value of the covered expenses will usually be less than the premium. Insurance premiums must cover the insurer’s expected payout, its cost of operation, and some return on invested capital. Unless a beneficiary’s expected benefits (the insurer’s expected payouts) have been incorrectly estimated, the insurer’s

risk seeker A person who prefers more risk to less. (A risk seeker would prefer a gamble with a 50% chance of getting nothing and a 50% chance of getting $10 to getting $5 for sure.)

risk seeking When a decision maker is willing to accept a lower payoff in order to increase risk.

risk neutral Not caring about risk. (A risk-neutral person would think that getting $5 for sure is as good as a gamble with a 50% chance of getting nothing and a 50% chance of getting $10.)

risk averse Preferring a smaller, less risky payoff to a larger payoff with more variability. (A risk- averse person would choose getting $5 for sure instead of a gamble with a 50% chance of getting nothing and a 50% chance of getting $10.)

risk aversion When a decision maker is willing to accept a lower payoff in order to reduce risk.

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 63

costs and profits will push insurance premiums above expected losses. By definition, someone who will pay an insurance premium is risk averse.

4.3.4 Decision Analysis Decision analysis has three steps, and only one of them is difficult. The steps are setting up a decision tree, identifying the alternative with the largest expected value, and using sensitivity analysis to assess the robustness of the analysis. Setting up a decision tree is the hardest and most important part of decision analysis. Managers gain the most insights but also make the most mistakes in this step. Setting up a decision tree requires six actions:

1. Carefully defining the problem. Often this task is harder than it sounds.

2. Finding alternative courses of action. Serious mistakes are often made here.

3. Identifying the outcomes associated with each alternative. 4. Identifying the sequence that leads to final outcomes, including choice

and chance events. 5. Calculating the probability of each outcome. 6. Calculating the value of each outcome.

Each of these activities is more difficult than it sounds, so deciding whether to do a decision analysis at all should be the first step.

4.3.5 Sensitivity Analysis Whenever the process of setting up and solving a decision tree is worthwhile, performing a sensitivity analysis is equally worthwhile. A sensitivity analysis substitutes different, but plausible, values for the values in a decision tree. Gauging the effects of minor data changes on the results is always helpful. The data are never perfect, and using them as if they were does not make sense.

The decision tree for the nursing facility purchase tells us that the key issue is whether its manager can realize the operational improvements and product line changes that she is contemplating. If she can, the return on equity will be no less than 8.3 percent, no matter what Medicare does. A sensitivity analysis tells us that if she can realize about 70 percent of her projected gains, she can expect a 7 percent return on equity, no matter what Medicare does. What could she do to increase the odds of full improvement? The sensitivity analysis indicates that the gains can fall somewhat short of the manager’s prediction and still hit the target rate of return.

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Economics for Healthcare Managers64

4.3.6 Scenario Analysis Just focusing on the expected value of a risky choice is not a satisfactory way to make a decision. The expected value may not be a possible outcome, and the best possible and worst possible outcomes matter. One solution is to model several scenarios. Typically these models include a worst-case scenario, a most likely scenario, and a best-case scenario. The process of setting up a decision tree helps identify these scenarios.

In exhibit 4.2, the worst case, which is relatively unlikely, yields a profit of $0. The best case, which is the most likely scenario, yields a profit of $120,000. Thus, buying the nursing home has the potential to be profitable and appears to be low risk. The scenario analysis also reinforces the conclu- sion that succeeding in making improvements is vital.

4.4 Managing Risk

Risk sharing and diversification are the only two strategies for managing risk. Buying an insurance policy is the obvious way to share risk, although joint ventures or options can serve the same function. For insurance, consumers pay a fee to induce another organization to share risks. Joint ventures or options share costs and profits with partners.

Diversification can take a number of forms. Horizontal integration (creating an organization that can offer the full spectrum of healthcare ser- vices) is one diversification strategy because some products are likely to be profitable no matter what the environment. All these strategies limit potential losses, but they also limit potential profitability.

4.4.1 Risk Sharing Joint ventures and options are common risk-sharing methods in the biotech- nology and pharmaceutical fields. For example, in 2016 Bayer and start-up CRISPR Therapeutics launched a joint venture to develop new drugs using CRISPR, which edits DNA precisely (Orcutt 2016). The US-based firm Kite Pharma and the Chinese firm Shanghai Fosun Pharmaceutical launched a joint venture to develop and manufacture cancer drugs. The main goals were to give Kite access to the Chinese market (plus additional funds for research) and to give Chinese patients access to advanced medications (BusinessWire 2017). The two firms share product development and marketing decisions.

Biotechnology entails significant risk. Only about 5 percent of interventions that pass toxicity tests get approved for public marketing

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 65

(Schuhmacher, Gassmann, and Hinder 2016), so reducing the costs of research and development represents another motive for joint ventures (ide- ally with a low-cost partner). For example, Amgen reports that it has two joint ventures, ten partnerships, 15 collaborators, and eight acquisitions (Amgen 2017). Its partners include investment firms (e.g., venBio), multina- tional pharmaceutical firms (e.g., Novartis, Dr. Reddy’s Laboratories), small biotechnology companies (e.g., Xencor), and equipment manufacturers (e.g., Illumina). Such partnerships allow Amgen to diversify its portfolio of poten- tial products and reduce its fixed costs. Both strategies reduce risk.

In a different type of joint venture, two physicians and Eastern Long Island Hospital agreed to construct a jointly owned ambulatory surgery cen- ter (Dyrda 2017). The motives for each side are straightforward: Physicians hope to negotiate higher rates because of the hospital’s ownership, and the hospital hopes to have a low-cost site for routine surgeries (which is increas- ingly valuable as value-based payments become more common).

Boston Children’s Hospital and General Electric are producing soft- ware to improve interpretations of brain scans of young patients (McCluskey 2016). This example illustrates another facet of risk sharing. Often the cost that an organization seeks to share is the enormous cost of acquiring a key competency. Working with a knowledgeable partner allows the organization to gain experience. Much time and money are needed to build expertise, and joint ventures can reduce the risk of expending these resources needlessly. Of course the organization must also assess the partner’s likely gains, such as expertise and profits.

4.4.2 Diversification Diversification creates a portfolio of projects or therapies that are not highly positively correlated. Exhibit 4.3 compares investing in a clinic, investing in an emergency department, and investing in a portfolio of 50 percent shares of each. Forecasts of return on investment for the projects depend on whether the growth of accountable care organizations becomes rapid, moderate, or slow. The clinic is a better investment than the emergency department (higher expected profits and lower standard deviation of profits). The portfolio is also a better investment than the emergency department (higher expected profits and lower standard deviation of profits). The portfolio might be a better investment than the clinic for a risk-averse investor (lower expected profits but a lower standard deviation of profits).

Joint ventures can make diversification less risky, as case 4.2 illustrates. But acquisitions and mergers typically increase risk.

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Economics for Healthcare Managers66

Accountable Care Organization Growth

Rapid Moderate Slow

Growth probabilities 0.160 0.700 0.140

Profits Expecteda

Standard Deviation

Clinic 10.0% 4.0% −1.0% 4.3% 3.0%

Emergency department −3.0% 2.0% 13.0% 2.7% 4.5%

Portfoliob 3.5% 3.0% 6.0% 3.5% 1.0%

a Expected profits = P rapid

× Profit rapid

+ P moderate

× Profit moderate

+ P slow

× Profit slow

. b Portfolio profits = 50% of the clinic profits and 50% of the emergency department profits.

EXHIBIT 4.3 Diversification

and Risk Reduction

Diversification by Joint Venture and Acquisition

The University of Pittsburgh Medical Center (UPMC) has international operations in nine countries (UPMC 2017a). It operates cancer centers and a full-service hospital in Ireland; transplantation, radiotherapy, and biotechnology centers in Italy; information technology and cancer centers in the United Kingdom; cancer center consulting in Colombia, Kazakhstan, and Lithuania; transplantation in Singapore; pathology consulting in China; and educational training in primary care in Japan. UPMC is exploring expansion in Cyprus and Qatar. Most of these repre- sent joint ventures with local partners.

UPMC is headquartered in Pittsburgh, where it has a commanding presence. The largest employer in western Pennsylvania, with more than 70,000 employees and nearly $17 billion in revenue, UPMC owns more than 30 hospitals, 600 outpatient sites, a large insurance plan, and a number of other healthcare ventures (UPMC 2017b).

Moody’s Investors Services greeted UPMC’s 2017 diversification with a debt downgrade (Moody’s Investors Services 2017). Rather than

Case 4.2

(continued)

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 67

4.5 Conclusion

The goal of describing, evaluating, and managing risk is improving choices, not identifying perfect choices. No one can make perfect choices. Even when managers have good evidence and make good decisions, bad outcomes can result. More often, though, medical and managerial decisions are made with inadequate information. For example, managers often must make invest- ment decisions long before they know how well technology will work, what volumes will be, and what rivals will do. Even when a manager has access to good information (which will never be the case with innovative choices), the possible consequences of the choices remain uncertain.

Good management, however, can reduce risk and reduce the conse- quences of risk. Managers will avoid some risks because of inadequate payoffs. Managers will share some risks via joint ventures or insurance. And managers will hedge some risks via diversification. A balanced portfolio of projects and lines of business can be profitable in any market environment. Reducing cost variations or reducing fixed costs can cut risk sharply. Finally, a high margin

a joint venture, it was an acquisition. In summer 2017, UPMC bought Pinnacle Health System, a seven-hospital system based in Harrisburg, Penn-

sylvania. This acquisition means that UPMC acquired, built, or other- wise gained access to nine hospitals in 2017, allowing UPMC to sell its health insurance products outside its core western Pennsylvania mar- ket. Moody’s noted that the purchases added integration and execu- tion risk, marked UPMC’s entry into a competitive and rapidly consoli- dating market, put pressure on profit margins, and increased the ratio of debt to equity (Moody’s Investors Services 2017).

Discussion Questions • Why is expansion outside the United States an attractive form of

diversification?

• What are the pitfalls of international expansion?

• What are the potential pitfalls of other diversification efforts?

• Why do small profit margins and a high ratio of debt to equity increase risk?

• What are the main risks that UPMC faces in its Pittsburgh operations?

• Why is buying additional hospitals in Pennsylvania risky?

Case 4.2 (continued)

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Economics for Healthcare Managers68

is a great way to reduce risk. If possible outcomes are a 15 percent return on equity or an 11 percent return on equity, most managers will sleep well.

Exercises

4.1 Five of ten people earn $0, four earn $100, and one loses $100. What is the expected payoff? What is the variance of the payoff?

4.2 You have a 50 percent chance of making $0, a 40 percent chance of making $100, and a 10 percent chance of losing $100. Calculate the expected value and variance of the payoff. How does your estimate compare to the previous exercise?

4.3 You have a 1 percent chance of having healthcare bills of $100,000, a 19 percent chance of having healthcare bills of $10,000, a 60 percent chance of having healthcare bills of $500, and a 20 percent chance of having healthcare bills of $0. What is your expected spending?

4.4 You have a 2 percent chance of having healthcare bills of $100,000, a 20 percent chance of having healthcare bills of $10,000, a 60 percent chance of having healthcare bills of $500, and an 18 percent chance of having healthcare bills of $0. What is your expected healthcare spending? How does it compare to the answer in exercise 4.3?

4.5 You have a 1 percent chance of having healthcare bills of $100,000, a 19 percent chance of having healthcare bills of $10,000, a 60 percent chance of having healthcare bills of $500, and a 20 percent chance of having healthcare bills of $0. What is your expected spending? Would you be willing to buy complete insurance coverage if it cost $3,712? Explain.

4.6 Instead of complete insurance as in exercise 4.5, you have a policy with a $5,000 deductible. What will your expected out-of- pocket spending be? What will your expected insurance benefits be? Assuming that the premium equals 116 percent of expected insurance benefits, do you prefer the policy with a $5,000 deductible or the policy with complete coverage? Explain.

4.7 Your firm, which operates a nationwide system of cancer clinics, has annual profits of $800 million and cash reserves of $500 million. Your clinics have a replacement value of $200 million, and fire insurance for them would cost $5 million per year. Actuarial data show that your expected losses due to fire are $4 million. Should you buy insurance?

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 69

4.8 Your firm rents a supply management system to hospitals. You have received a buyout offer of $5 million. You forecast a 25 percent chance that you will have profits of $10 million, a 35 percent chance that you will have profits of $6 million, and a 40 percent chance that you will have profits of $2 million. Should you accept the offer? Explain.

4.9 You were given a lottery ticket. The drawing will be held in 5 minutes. You have a 0.1 percent chance of winning $10,000. You refuse an offer of $11 for your ticket. Are you risk averse? Explain.

4.10 Your house is worth $200,000. Your risk of a catastrophic flood is 0.5 percent. Such a flood would destroy your house and would not be covered by homeowner’s insurance. Although you grumble, you buy flood coverage for $1,200. Are you risk averse or risk seeking?

4.11 Your firm faces considerable revenue uncertainty because you have to negotiate contracts with several customers. You forecast a 20 percent chance that your revenues will be $200,000, a 30 percent chance that your revenues will be $300,000, and a 50 percent chance that your revenues will be $500,000. Your costs are also uncertain because the prices of your supplies fluctuate considerably. You forecast a 40 percent chance that your costs will be $400,000 and a 60 percent chance that your costs will be $250,000. Use Excel to set up a decision tree for your profit forecast (it does not matter whether costs or revenues come first). How many possible profit outcomes do you have? What is your expected profit?

4.12 Your firm has been sued for $3 million by a supplier for breach of contract. Your lawyers believe that three possible outcomes could occur if the suit goes to trial. One, which the lawyers term highly improbable, is that your supplier will win the lawsuit and be awarded $3 million. Another, which the lawyers term unlikely, is that your supplier will win the lawsuit and be awarded $500,000. The third, which the lawyers term likely, is that your supplier will lose the lawsuit and be awarded $0. You have to decide whether to try to settle the case. To do so you need to assign probabilities to “highly improbable,” “unlikely,” and “likely.” What probabilities correspond to these statements? Going to trial will cost you $100,000 in legal fees. One of your lawyers believes that your supplier will settle for $100,000 (and you will have legal fees of $25,000). Should you settle?

4.13 Why does reducing cost variation reduce risk? Why does reducing fixed cost reduce risk?

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Economics for Healthcare Managers70

4.14 In a week a clinic sees the following numbers of flu cases per day: 1, 2, 2, 4, 6. What is the average for this sample? What is the standard deviation for this sample?

4.15 The following data describe the costs for two pediatric clinics with the same revenue. Calculate the average and sample standard deviation of weekly costs. Which clinic is riskier?

Week Clinic 1 Clinic 2

1 $21,616 $23,041

2 $21,462 $19,382

3 $20,812 $22,156

4 $19,308 $15,757

5 $20,544 $21,145

6 $19,712 $17,867

7 $18,682 $17,767

8 $19,994 $16,514

9 $19,359 $18,553

10 $19,334 $20,330

11 $20,034 $20,166

12 $20,283 $20,131

13 $19,435 $16,275

14 $21,746 $16,200

15 $18,419 $15,171

16 $19,359 $24,460

17 $19,140 $21,365

18 $18,721 $22,551

19 $18,036 $21,534

20 $19,392 $24,215

21 $21,155 $20,933

22 $21,005 $23,774

23 $21,419 $22,121

24 $19,131 $20,901

25 $20,162 $22,200

26 $21,607 $15,182

27 $21,030 $24,725

28 $19,426 $16,239

(continued)

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Chapter 4: Descr ibing, Evaluat ing, and Managing Risk 71

Week Clinic 1 Clinic 2

29 $21,785 $20,137

30 $18,258 $22,673

31 $18,644 $15,545

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