How does insurance work and why is it so complicated? We will begin to answer these questions and more in a three part series on insurance markets.

Simply put, insurance is the business of buying and selling risk. In many situations, businesses and individuals are risk-averse. This means that they would prefer to pay some amount of money to reduce the amount of uncertainty in a situation.

For example, consider a simple coin flip game. If the coin lands on heads, you receive $100,000. If it lands on tails, you receive nothing. The expected value of your winnings is 50% * $100,000 + 50% * $0 = $50,000

Would you prefer to play that game, or just get a guaranteed $50,000?

Most people would prefer the guaranteed $50,000. What about $49,000?

If you would prefer $49,000 we consider you to be risk averse. You are willing to pay a premium of $1,000 to eliminate the uncertainty in this situation.

Of course, this is a somewhat frivolous example. Instead, let’s consider one of the oldest examples of insurance in the real world: property/home insurance. Modern property insurance goes back to shortly after the Great Fire of London. There was a desire among individuals to reduce the financial risk of losing their homes to fire. And companies (i.e. insurers) were founded to meet this need.

Let’s look at the economics behind this:

Let’s assume someone owns an apartment valued at $500,000 and that the insurer only offers one type of insurance, total insurance. Essentially this insurance will pay for any damage done by fire over the next 5 years.

The probability of loss over that time period is as follows:

• 1% chance of total loss ($500,000 cost)
• 2% chance of minor loss ($100,000 cost)

From the individual’s point of view, their expected loss is 1% * $500,000 + 2% * $100,000 = $7,000. Since the individual is risk-averse they are willing to pay at least $7,000 for the insurance policy, but let’s say the insurer charges around $10,000. This cost can be thought of as three parts:

1. The actual expected payout to the individual = $7,000
2. The risk premium (the cost to the insurer for having additional risk) = $500
3. Overhead and administrative costs of providing insurance = $2,500

In this case, if the individual opts for the insurance coverage, they are willing to pay a $3,000 risk premium over the anticipated $7,000 in damages to insure against the risk of a greater loss. There is an important insight here: Insurers are better equipped to handle risk than individuals. As a result, that $500 risk premium the insurer faces is a lot lower than the $3,000 risk premium the individual is willing to pay. Why is this?

In fact, there are a number of reasons insurance companies can better handle risk (e.g. “floating” premiums until claims need to be paid), but the biggest reason comes down to simple probability.

Think back to the coin flip game from earlier. Imagine that the game is now a 50/50 chance at $10,000 and you get to play 10 times. The expected value is still $50,000. But now would you accept a guaranteed $49,000 over the game? Maybe not. That’s because by playing the game many times, you reduce the uncertainty. Since an insurance company can take on many customers, it can effectively reduce the amount of uncertainty it faces.

Below is a diagram showing the probability distribution of winnings in the coin flip game based on if you play once (individual) or if you play 10 times (insurance company). 

And now we can see what the graph looks like if the game is played 100 times. Here the insurance company would always get between $40,000 and $60,000. So that is very little risk compared to the 50/50 gamble the individual faces.

This very simple result shows how insurance companies are able to manage risk, allowing them to create value which is passed on to consumers. Of course in practice, some (or all) of that value is lost due the overhead costs associated with insurance companies (but that is a much more complicated topic).

One key assumption we are making throughout this post is that insurance companies and individuals have the same information and are aware of how likely a “loss” is to happen. What happens when individuals know more about their potential for loss than the insurer does?

The next post in this insurance series will look at exactly that, and more generally the topic of adverse selection.

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Interested in expanding your business vocabulary and learning the skills Harvard Business School's top faculty deemed most important for any professional, regardless of industry or job title?

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About the Author

Ben is a member of the HBX Course Development Team and works on the Negotiation Mastery and Economics for Managers courses. He has a background in economics and physics and enjoys card games, cooking, and discussing philosophy.

On June 16, Amazon announced that they would be purchasing Whole Foods for $13.7 billion - approximately 27% higher than its current value in the market. After the initial shock wore off, many people began to speculate about whether this was a good decision or not.

In finance, we think about creating value as generating returns in excess of a firm's cost of capital - in other words, for projects and decisions to generate more cash flow over time than they cost today to implement, discounted back to the present.

That's a mouthful of a definition, but even the best projections can't necessarily help us understand if our decisions were successful. This is one place where the stock market – the crowdsourced opinions of thousands of analysts – can be of assistance.

Imagine a market value balance sheet; on the left side, the Assets side, are the market value of the firm's cash and their operating assets. On the right side, to balance, are the market value of the firm's debt and the market value of their equity. Now imagine that the firm makes an investment - they use $1 million dollars in cash and make a $1 million investment in a new asset. Accounting will shift the balance from cash to operating assets and show no change. But did the value of the firm change?

For this, we can look at the other side of the balance sheet - the financing side. Unless new debt is taken on as part of the project, the debt portion should stay the same. Which means that any decision that creates or destroys value for the firm will show up immediately in the market value of equity, which we call "market capitalization." The market capitalization tends to reflect the consensus opinion of decisions instantly, as all of those thousands of analysts respond to firm announcements in real time.

We can think of the purchase of Whole Foods as an investment decision - Amazon took a certain amount of cash and purchased an asset. Was that a value creating or value destroying decision?

In acquisitions, value creation comes from synergies, or ways in which the two companies together are worth more than they are individually. Sometimes, the acquiring company overpays for the acquisition, giving most or all of the synergies to their target. Sometimes they overpay by so much that they destroy value. So what about Amazon? How did they do?

For this, we can look at the market value of their equity. On Thursday, June 15, Whole Foods had a market capitalization of $10.6 billion and Amazon had a market capitalization of $460.9 billion. By the end of trading on Friday, Whole Foods' market capitalization was $13.7 (which makes sense, that's the price they were being acquired at) and Amazon's was $472.1 billion.

That means that the market thinks this acquisition created $14.3 billion in value through synergies (the total combined increase across the two companies) and the synergies were split up by giving $3.1 billion to Whole Foods shareholders and $11.2 billion to Amazon shareholders. 

Clearly, the market felt this was a really good decision (and the market capitalizations of the two companies continued to rise over the next week). In fact, since the synergies at $14.3 billion are more than the purchase price of Whole Foods at $13.7, it can be said that the market thinks Whole Foods is worth twice as much as part of Amazon than it is alone. That's incredible - and it's how the market consensus can tell firms, instantly, whether their decisions created value.

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Want to better understand finance? Interested in developing a toolkit to make smarter financial decisions? Learn more about the HBX course, Leading with Finance.

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I’m definitely more the “English major type,” but I understand why having some business acumen is important. So, rather than always perusing the fiction bestseller list, I sometimes opt for books by lauded economic scholars and business leaders imparting new financial concepts and theories.

I try to grasp as much as I can, but these works tend to be data heavy and pedantic, packed with graphs and economic statistics supporting prescriptive mechanisms to achieve financial targets, so after a few chapters my mind starts wandering. Then I discovered Professor Clay Christensen’s work.

Professor Christensen is one of the world’s top experts on innovation and economic growth—so I decided to read his book, The Innovator’s Dilemma. I was captivated. Professor Christensen’s ideas were both novel and highly practical. After reading The Innovator’s Dilemma, I wanted an even more refined understanding of disruption theories, so taking Professor Christensen’s online HBX course, Disruptive Strategy, seemed like a good idea. It proved to be that and more.

Disruptive Strategy not only afforded me some of the most insightful and exciting business knowledge I have gained to date, but did so in a digestible and compelling way. Professor Christensen infused his course with a lot of what other business materials and teaching tools lacked – stories. He presented his theories of disruptive innovation (which are innovative and compelling in and of themselves) through stories with protagonists that have applied his theories to disrupt and improve their industries—ultimately benefitting both consumers and the economy.

In taking the course, I gleaned a strong sense of the possibilities for good social impact that smart business application can yield. This was the business story I had been looking for and it compelled me to seek greater involvement with Professor Christensen’s work.

That led me to my current position working with The Forum for Growth and Innovation at Harvard Business School. The Forum for Growth and Innovation is a research initiative funded by Harvard Business School and guided by Professor Christensen. The purpose of the Forum’s research activities is to develop and disseminate sound, actionable, and prescriptive theory that general managers can apply in their most critical growth and innovation decisions. In Clay’s words:

"We launched the Forum for Growth and Innovation with the goal of pushing innovation and growth research in new directions, all while keeping an eye on the practical implications for people running actual companies.

Our goal is not so much to teach our community what to think, but rather to continually better understand how to think."

The Forum is currently engaged in the active research phase of collecting insights from alumni and industry experts to produce The Capitalist’s Dilemma book, which will be an expanded an updated iteration of the Harvard Business Review article of the same title. The book is an examination into why capitalists aren’t investing in the kind of innovations that lead to long-term economic prosperity and job growth. 

With the current economic and political climate, the ideas and theories in the book have acquired even greater relevance and urgency. As someone who loves a great story, my hope is the book will serve as a catalyst for re-igniting and re-telling the story of inspiring entrepreneurship that leads to robust economic growth and social good.  

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About the Author

Farsh Askari is a Community Manager for the Forum for Growth & Innovation at Harvard Business School—a research project guided by Professor Clay Christensen. Prior to joining FGI, Farsh served as a Faculty Specialist in the Division of Research and Faculty Development at HBS.

He took both HBX CORe and Disruptive Strategy and holds a Bachelor's Degree in Law and Society from the University of California, Santa Barbara.

Courage is the quality that distinguishes great leaders from excellent managers.

Over the past decade, I have worked with and studied more than 200 CEOs of major companies through board service, consulting, and research as a member of Harvard Business School’s faculty. I’ve found the defining characteristic of the best ones is courage to make bold moves that transform their businesses.

Courageous leaders take risks that go against the grain of their organizations. They make decisions with the potential for revolutionary change in their markets. Their boldness inspires their teams, energizes customers, and positions their companies as leaders in societal change.

The dictionary definition of courage is “the quality of mind or spirit that enables a person to face difficulty, danger, pain, etc., without fear.” Courageous leaders lead with principles–their True North–that guide them when pressure mounts. They don’t shirk bold actions because they fear failure. They don’t need external adulation, nor do they shrink from facing criticism.

"COURAGEOUS LEADERS TAKE RISKS THAT GO AGAINST THE GRAIN OF THEIR ORGANIZATIONS."

Courage is neither an intellectual quality, nor can it be taught in the classroom. It can only be gained through multiple experiences involving personal risk-taking. Courage comes from the heart. As Buddhist monk Thich Nhat Hanh once said, “The longest journey you will ever take is the 18 inches from your head to your heart.”

It takes bold decisions to build great global companies. If businesses are managed without courageous leadership, then R&D programs, product pipelines, investments in emerging markets, and employees’ commitment to the company’s mission all wither. These organizations can slip into malaise and may eventually fail, even if their leaders can move on to avoid being held accountable.

Why do some leaders lack courage? Many CEOs focus too much on managing to hit their numbers. They avoid making risky decisions that may make them look bad in the eyes of peers and external critics. Often, they eschew major decisions because they fear failure. I know, because it happened to me.

In my first year as CEO of Medtronic, I passed up the opportunity to buy a rapidly growing angioplasty company because it faced patent and pricing risks. While those risks proved valid, Boston Scientific bought the company instead, transforming both enterprises and creating a formidable competitor for Medtronic. I didn’t have the courage to accept short-term risk to create long-term gain. It took Medtronic two decades of expensive research and development programs and additional acquisitions to become the leader in this field.

Let’s look at some recent examples of courageous leaders whose actions transformed their companies:

Alan Mulally

When Mulally arrived at Ford, he found a depleted organization losing $18 billion that year and unwilling to address its fundamental issues. To retool Ford’s entire product line and automate its factories, Mulally borrowed $23.5 billion, convincing the Ford family to pledge its stock and the famous Ford Blue Oval as collateral. His bold move paid off. Unlike its Detroit competitors, Ford avoided bankruptcy, regained market share, and returned to profitability.

Mary Barra

In contrast to Mulally, General Motors CEO Rick Wagoner and his predecessors refused to transform GM’s product line, even as the company’s North American market share slid from 50 percent in the 1970s to 18 percent. When the automobile market collapsed in late 2008, Wagoner was forced to ask President George W. Bush to bail the company out. Even so, GM declared bankruptcy months later.

Mary Barra, GM’s CEO since 2014, demonstrates the difference courage can make. Immediately after her appointment, she testified before a hostile Senate investigating committee about deaths from failed ignition switches on Chevrolet Camaros. Rather than make excuses, Barra took responsibility for the problems and went further to attribute them to “GM’s cultural problems.” Three years later, she is well on her way to transforming GM’s moribund, finance-driven culture into a dynamic, accountable organization focused on building quality vehicles worldwide.

Paul Polman

When Polman became Unilever’s CEO in early 2009, he immediately began transforming the company, declaring bold goals to double revenues and generate 70 percent from emerging markets. He aligned 175,000 employees around sustainability, publishing the Unilever Sustainable Living Plan with well-defined metrics the following year. Polman’s efforts in his first eight years returned 214 percent to Unilever shareholders. Nevertheless, Kraft Heinz, owned by Brazilian private equity firm 3G, made a hostile bid to acquire Unilever on February 17, 2017. Polman immediately wheeled into action, convincing KHC to drop its bid two days later. Then he announced seven bold moves to enhance shareholder value without compromising the company’s ambitious long-term plans.

In comparison, Kraft CEO Irene Rosenfeld quickly capitulated when confronted by activist Nelson Peltz in 2012. He wanted to split Kraft’s global business by spinning off its North American grocery products unit, which Rosenfeld wound up leading as an international business renamed Mondelez. Without the ability to access global markets, the old Kraft went into a period of decline, making it vulnerable to 3G’s 2015 takeover; meanwhile, Mondelez is adrift with declining revenues and earnings.

Indra Nooyi

Named CEO of PepsiCo in 2006, Nooyi foresaw the coming shift among consumers, especially the millennial generation, to healthier foods and beverages. She immediately introduced PepsiCo’s strategy “Performance with Purpose,” that focuses on complementing the company’s core soft drink and snack business with healthy foods and beverages. In 2013, PepsiCo was challenged by activist Peltz to split the company, but Nooyi steadfastly refused. Instead, she restructured her leadership team to deliver strong near-term performance while continuing to invest in her transformation strategy.

Nooyi’s arch-rival, Coca-Cola CEO Muhtar Kent, decided instead to concentrate on sugar-based soft drinks while ignoring these obvious trends. As a result, Coca-Cola’s performance has consistently lagged PepsiCo’s. Since 2011, PepsiCo stock is up 70 percent, while Coca-Cola’s has increased only 15 percent.

The courage cohort

There are literally thousands of competent managers who can run organizations efficiently using pre-determined operating plans, but few with the courage to transform entire enterprises.

The courage cohort includes Delta’s Richard Anderson, Starbucks’ Howard Schultz, Xerox’s Anne Mulcahy and Ursula Burns, Nestle’s Peter Brabeck-Letmathe, Novartis’ Dan Vasella, Tesla’s Elon Musk, Amazon’s Jeff Bezos, Merck’s Ken Frazier, and Alibaba’s Jack Ma. They join the growing list of authentic leaders that have made courageous decisions to build great global companies.

To quote poet Maya Angelou, “Courage is the most important of all the virtues, because without courage you can't practice any other virtue consistently.” Boards of directors need to examine their leaders carefully to determine if they have the courage to navigate their organizations through turbulent times while enduring hardship, risk, and criticism to ensure they are building sustainable enterprises.

With more courageous leaders like those cited above, the business world will be able to create enormous value for all its stakeholders.

Bill George is Senior Fellow at Harvard Business School, former Chair & CEO of Medtronic, and author of Discover Your True North.

This article originally appeared on Harvard Business School Working Knowledge, a great resource for anyone interested in learning more about hundreds of business topics. 

Each year almost 50,000 people apply to pitch their start-up businesses on Shark Tank. Only a few hundred of them are invited to Sony Studios for taping. And barely half of them actually appear on television.

Two of the lucky ones were my former Harvard Business School student Nate Barbera and his classmate Des Stolar. How they beat those odds offer great lessons for anyone pitching an idea, seeking investors, or courting potential business partners. Nate and Des’s was promoting their novel product—Unshrinkit—a potion that restores improperly washed wool garments to their original size.

They had developed it as part of an HBS requirement that MBA students launch a company and secure real customers. At the outset Nate and Des were mixing the stuff in their dorm room sinks. Even after finding an outfit to produce and distribute their product, sales online and in stores were small compared to the potential market. To build a real business they needed publicity—and what better way to get it than an appearance on Shark Tank.

Nate and Des did three things right to get on the show.

First, they understood that they had to pitch themselves rather than their product. After all, the show’s producers are in the entertainment business. They need entrepreneurs with distinctive personalities who will spark reactions from the panel of sharks. In reviewing applications, perhaps the producers expected Nate and Des to be stereotypical know-it-all MBA students, though that’s not how they come across at all. He is an earnest engineer and she is warm, confident, and ultra-smart. The sharks clearly would be intrigued by their personal story.

Second, Nate and Des prepared obsessively, reviewing all the prior episodes to see what makes a winning pitch and—even more important—how the sharks interact themselves. Nate and Des also dissected the pros and cons of various offers they might receive. They even drew elaborate decision trees mapping out different ways the process might unfold. Naturally they focused on Lori Greiner, the “queen of QTV,” a great platform for their household product.

Shark Tank tapings are grueling. What we viewers see is radically edited down. Nate and Des were on stage for two hours and three minutes without a break. When you’re in front of the camera, of course, things happen very fast.

Des recalls being peppered with demanding questions from the sharks and the futility of trying to answer them all. Midst it all, she told herself, “If I pretend that I’ve only heard the question that I like and I answer that, maybe just maybe, it will lead to a follow-up question I like even more.”

Once she did that, there was a “domino effect where every single question aligned with the story that Nate and I wanted to present, and they all thought we were doing well.” But then there was a crisis. Des describes it as “the most nerve wracking portion of the entire session.” Lori withdrew, saying, “I love you guys. I like the product. I don’t think the market size is there.”

In the heat of the moment, under the glare of the TV lights, Nate and Des let go of their plan and deftly pivoted. Lori’s statement was crushing, not only because she had been their top choice, but because her knowledge of home goods could sway the opinions of the other four sharks.

Des kept her composure and asked Lori to explain her thinking. Lori admitted that had been a long time since she had last done her own laundry, but she didn’t think many people would make the mistake of mishandling their woolen garments.

The other sharks—sensing that Lori had misjudged the market—started arguing with Lori, confessing that they make mistakes like that all the time. That allowed Nate and Des to step back and let the other sharks convince themselves of the product’s potential value.

In the end, three of them made offers, with Mark Cuban jumping in at the last moment with the best one. Having watched Cuban in all the prior episodes of the show, Nate and Des knew that he doesn’t like to haggle, so after quickly nodding to each other, they happily said yes.

They were glad to get his endorsement, of course, but even more important making that deal ensured that their segment would air—and not just once, but in reruns, too. Since it first appeared, sales of Unshrinkit are way up and it’s now available in Canada and Europe. (Nate and Des's whole story is also a cornerstone case in my HBX Negotiation Mastery course.)

Few of us will make it to national television, of course, but whenever we’re pitching a new idea, we’d be smart to remember that first and foremost we must win people’s confidence and generate excitement. Though we can’t anticipate everything, diligent preparation actually enhances our ability to improvise when things take an unexpected turn.

This article was originally published on LinkedIn Pulse.

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About the Author

Professor Mike Wheeler's current research focuses on negotiation dynamics, dispute resolution, ethics, and distance learning. He is the author or co-author of eleven books, and his self-assessment app—Negotiation360—was released early in 2015. Additionally, Professor Wheeler's new HBX course, Negotiation Mastery: Unlocking Value in the Real World, is now accepting applications.

In statistics, we draw a sample from a population and use the things we observe about the sample to make generalizations about the entire population. For example, we might present a subset of visitors to a website with different versions of a page to get an estimate of how ALL visitors to the site would react to them. Because there is always random variability (error), we don't expect the sample to be a perfect representation of the population. However, if it's a reasonably large, well-selected sample, we can expect that the statistics we calculate from it are fair estimates of the population parameters.

Bias is anything that leads to a systematic difference between the true parameters of a population and the statistics used to estimate those parameters. Here are a few of the most common types of bias and what can be done to minimize their effects.

Bias in Sampling

In an unbiased random sample, every case in the population should have an equal likelihood of being part of the sample. However, most data selection methods are not truly random.

Take exit polling. In exit polling, volunteers stop people as they are leaving the voting place and ask them who they voted for. This method leads to the exclusion of those who vote by absentee ballot. Furthermore, research suggests the people are more likely to gather data from people similar to themselves.

Polling volunteers are more likely to be young, college educated, and white compared with the general population. It's understandable that a white college student will be more likely to approach someone who looks like they could be one of their classmates than a middle-aged woman, struggling to keep three children under control by speaking to them in a language the student does not understand. This means not every person has the same chance of being selected for an exit poll.

Bias in Assignment

In a well-designed experiment, where two or more groups are treated differently and then compared, it is important that there are not pre-existing differences between the groups. Every case in the sample should have an equal likelihood of being assigned to each experimental condition.

Let's say the makers of an online business course think that the more times they can get a visitor to come to their website, the more likely they are to enroll. And in fact, people who visit the site five times are more likely to enroll than people who visit three times, who are – in turn – more likely to enroll than people who visit only once.

The marketers at the online school might mistakenly conclude that more visits lead to more enrollment. However there is are systematic differences between the groups that precede the visits to the site. The same factors that motivate a potential student to visit the site five times rather than once may also make them more likely to enroll in the course. 

Omitted Variables

Often links between related variables are overlooked, or links between unrelated variables are seen, because of other variables that have an impact but haven't been included in the model.

For example, in 1980, Robert Matthews discovered an extremely high correlation between the number of storks in various European countries and the human birthrates in those countries. Using Holland as an example, where only four pairs of storks were living in 1980, the birth rate was less than 200,000 per year, while Turkey, with a shocking 25,000 pairs of storks had a birth rate of 1.5 million per year.

In fact, the correlation between the two variables was an extremely significant 0.62! This isn't because storks bring babies, but rather that large countries have more people living in them, and hence higher birth rates—and also more storks living in them.

Rerunning the analysis including area as an independent variable solves this mystery. Many other (more amusing) spurious correlations can be found at tylervigen.com. While it may not be possible to identify all omitted variables, a good research model will explore all variables that might impact the dependent variable.

Self-serving Bias

There are a number of ways that surveys can lead to biased data. One particularly insidious challenge with survey design is self-report bias. People tend to report salary and education as higher than reality, and weight and age as lower.

For example, a study might find a strong correlation between a good driver and being good at math. However, if the data were collected via a self-report tool, such as a survey, this could be a side effect of self-serving bias. People who are trying to present themselves in the best possible light might overstate both their driving ability and their math aptitude.

Experimenter Expectations

If researchers have pre-existing ideas about the results of a study, they can actually have an impact on the data, even if they're trying to remain objective. For example, interviewers or focus group facilitators can subtly influence participants through unconscious verbal or non-verbal indicators.

Experimenter effects have even been observed with non-human participants. In 1907, a horse named Clever Hans was famous for successfully completing complex mathematical operations and tapping out the answer with his hoof. It was later discovered that he was responding to involuntary body language of the person posing the problems. To avoid experimenter expectancy, studies that require human intervention to gather data often use blind data collectors, who don't know what is being tested.

In reality, virtually all analyses have some degree of bias. However, attention to data collection and analysis can minimize it. And this leads to better models.

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Interested in expanding your business vocabulary and learning the skills Harvard Business School's top faculty deemed most important for any professional, regardless of industry or job title?

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About the Author

Jenny is a member of the HBX Course Delivery Team and currently works on the Business Analytics course for the Credential of Readiness (CORe) program, and supports the development of a new course in Management for the HBX platform. 

Jenny holds a BFA in theater from New York University and a PhD in Social Psychology from University of Massachusetts at Amherst. She is active in the greater Boston arts and theater community, and she enjoys solving and creating diabolically difficult word puzzles.

There’s been a lot written about cognitive biases in the last decade. If you walk into the Psychology section of Barnes of Noble today or browse Amazon for “decision-making,” you’re sure to see a library of books on how irrational humans can be.

In my last two posts, I spoke about two of the most pernicious biases affecting businesses today—confirmation bias and over-confidence. But the most important, and troubling, error we make in our thinking just may be the Fundamental Attribution Error (FAE).

What’s the fundamental attribution error?

The FAE is our tendency to attribute another’s actions to their character, while attributing our own behavior to external situational factors. If you’ve ever chastised a “lazy employee” for being late to a meeting and then proceeded to make an excuse for being late yourself later that same day, you’ve made the FAE. It’s our tendency to cut ourselves a break while holding others 100% accountable for their actions.

But don’t feel too bad—the FAE is perfectly human. And similar to confirmation and overconfidence biases, its impact can be reduced by taking a number of measures.

FAE exists because of the way in which we perceive the world. While we have at least some idea of our own character, motivations, and the situational factors affecting us day-to-day, we rarely know all of the things going on with someone else.

In working with our colleagues, for example, we form a general impression of their character based on pieces of situations, but never see the whole picture. While it would be nice to give them the benefit of the doubt, our brains use limited information to make judgments. And thus we only have their perceived character available to us to chastise them for being tardy to the big corporate strategy review.

Within organizations, FAE causes everything from arguments to firings and ruptures in organizational culture. In fact, it’s at the root of any misunderstanding in which human motivations have the potential to be misinterpreted.

Think of the last time you thought a coworker should be fired or the last time a customer service representative was incompetent. How often have you really tried to understand the situational factors that could be affecting this person’s work? Probably not much.

FAE is so prevalent because it’s rooted in psychology, so completely overcoming it is impossible. However, one tool that I’ve found helpful in combating FAE is gratitude. When you become resentful at someone for a bad “quality” they demonstrate, try to make a list of five positive qualities the person also has—this will help balance out your perspective. 

Another method is to practice becoming more emotionally intelligent. Emotional intelligence has become a buzzword in the business world over the past 20 to 30 years, but all it involves is practicing self-awareness, empathy, self-regulation and other methods of becoming more objective in the service of one’s long-term interests and the interests of others. Practicing empathy, in particular, such as having discussions with coworkers about their opinions on projects and life out of the office, is a good first step.

FAE is impossible to overcome completely. But with a combination of awareness and a few small tools and tactics, you can be more gracious and empathetic with your coworkers.

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Interested in expanding your business vocabulary and learning the skills Harvard Business School's top faculty deemed most important for any professional, regardless of industry or job title?

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This post first appeared on LinkedIn Pulse.

I'll be the first to admit it, for the last 22 days I've been nervous. On Friday, April 21, 2017, I entered a freezing testing center at 2pm. In precisely three hours, I answered 135 questions on Business Analytics, Economics, and Financial Accounting. Today I learned I passed the exam.

Insert sigh of relief.

Why I Joined HBX CORe

Like many folks in the Boise cohort, I first heard about the Harvard Business School HBX CORe immersion program at Boise State University on NPR. In December, I discovered I could earn nine college credits while learning skills needed for a burgeoning startup. Don't get me wrong though, I knew about business operations before joining HBX.

My business education prior to HBX came from hands-on experience, running a community preschool, dabbling in real estate development, non-profit board governance, and managing rental properties. I've always been impressed with the expertise a well-versed MBA graduate brings to the table. But I didn't want to dive into an MBA program following two grueling years of engineering school. That would just be YUCK!

My plan is to work, build, solve problems and eat well. Not get an MBA.

HBX covers the fundamentals of an MBA in just 16 weeks (or less!). In fact, many learners use HBX as a litmus test to see if they have what it takes to pursue an MBA. I personally would hire someone on the spot if they passed HBX. I joined HBX so I could avoid common business mistakes and learn accrual accounting.

What was it like?

First, HBX was not easy. But don't just take my word for it. If you want to join HBX do your homework first. There are several years of HBX graduates all over the globe. Google them. Connect.

HBX CORe is a significant time commitment. For me, HBX occupied 15 to 20 hours each week. You will fail if you think you can swoop in after a long day at work or school and take a couple of quizzes and pass in-between dinner with the kids and a little R&R time. There are faculty and protagonist videos, practice questions, interactive learning tools and peer-to-peer learning and engagement. 

I was particularly shocked by my first "cold call", as I I had to answer a tricky, and rather long question, in one minute. The cold call lasts one minute, including response time, and, at the end of the minute, your response is automatically submitted. Then your classmates review and comment on your quick witted thinking. Just like real life...or Twitter.

My cohort was comprised of roughly 300 participants from around the globe. The diversity of the group was tremendous, ranging from fortune 500 executives to college freshman. Through the HBX platform and social media, we were miraculously fortified, across national borders, as one body of learners. I also got to connect with my equally brilliant "local cohort",  as others in Boise were enrolled in the same program .We were all working to exhaustion but we were in it together—and together is an awesome movement.

I thrive on stress and deadlines. HBX did not disappoint. Some weeks overlapping assignments were due. The project manager in me loved this aspect. It proved to be an exhilarating challenge to meet demanding deadlines.

Five reasons why HBX is CrossFit for the brain:

My arms were getting squishy and my husband suggested I join CrossFit with him. So I did. I've been working on my outside and inside self, I thought I'd share similarities:

1. CrossFit is constantly varied functional movements performed at high intensity. HBX is intense work, questions from quizzes are not like the test, you learn to solve problems from the variation. With CrossFit, you develop a balanced physique. With HBX you develop a balanced understanding of business management.

2. CrossFit is made of the best workouts from gymnastics, weightlifting, running, rowing and more. HBX brings in world renowned subject matter experts who teach the most critical aspects of running a business.

3. CrossFit is data driven, individuals use their own statistics to improve physical performance over time. HBX uses data to show student's baseline scores so that they can improve with vigorous study.

4.  CrossFit is a sport that becomes magnetic when a community comes together to do workouts. I can't imagine HBX without learners connected to each other via the platform. The camaraderie that developed with the crew on Facebook was simply organic after initial connections were made. Without multiple touchpoints to other learners, HBX would just be another (boring) online course. Even my CrossFit group has a Facebook page, it's good for the FOMO's.

5. CrossFit was developed for universal scalability making it an ideal workout for any committed individual. You will get out of HBX what you put into it, my brain feels gigantic, but I still know I have a lot of learning ahead to mastery. Fortunately, I'm able to further my studies on my own time, building on the great platform HBX has helped me form.

Fun CrossFit Fact: RUTH BADER GINSBURG CAN BENCH PRESS 70 LBS AT AGE 84!

Huge hearty thanks to HBX for giving my brain a workout and connecting me to a community of internationally acclaimed thinkers and doers. I'll forever be grateful for this experience.

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Interested in learning more about Business Analytics, Economics, and Financial Accounting? 

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About the Author

Erin Sorensen is an entrepreneur, student, mom and community advocate. When she’s not dreaming and doing, she is working on an Engineering degree at Boise State, volunteering in her neighborhood or enjoying the outdoors with her family. In 2016, Erin received a Dorothy Richardson Resident Leadership Award from NeighborWorks America, which is bestowed annually to eight citizens across the nation in recognition of outstanding community leadership.

In finance, we say that the value of something today is the present value of its discounted cash flows. We use this to value everything, and finance courses (like ours) give examples of valuing projects and businesses.

What is a Bond? A bond is a debt investment in which an investor loans money to an entity (typically corporate or governmental) which borrows the funds for a defined period of time at a variable or fixed interest rate. Bonds are used by companies, municipalities, states and sovereign governments to raise money and finance a variety of projects and activities. Owners of bonds are debtholders, or creditors, of the issuer. Source: Investopedia.com

But what about bonds?

Turns out, bonds can be valued exactly the same way. Bonds, however, can be a bit obscured by finance jargon, so we'll need to break through a bit to figure out their value. 

Let's take an imaginary bond: it has a face value of $1000, an annual coupon of 3%, and a maturity date in 30 years. What does all that mean?

What is means is that the company or country that owes the bond will pay the bond holder 3% of the face value of $1000 ($30) every year for 30 years, at which point they will pay the bond holder the full $1000 face value.

That gives us our cash flows. We have a series of 30 cash flows, one each year of $30, and then we have one cash flow, 30 years from now, of $1000.

Now we need to use our discounting formula:

Cash Flow ÷ (1+r)^t

We have the cash flows and we have the number of years for each of them (called "t" in that equation). We need the "r", which is the interest rate. Which should we use? What we do is we use the current interest rate for similar 30-year bonds today. Since we're making up these numbers for the purpose of this example, it doesn't really matter what we use - we can say it's 5%.

So now we can value the various cash flows. First, we have the coupon payments:

30 ÷ (1+.05)¹ + 30 ÷ (1+.05)²... + 30 ÷ (1+.05)³⁰

And then we have the final face value payment, in thirty years:

1000 ÷ (1+.05)³⁰

Together, these total the price - $692.55. This price will ensure that the bond holder receives an annual return of 5% over the life of the bond.

Now that we have our price, we can play with some of our assumptions to see how things change. What if the prevailing market interest rate were 4% instead of 5%? In that case, the price of the bond would be $827.08. If it were 6% instead of 5%, the price would be $587.06. So, one thing to remember is that the price of a bond is inversely related to the interest rate - when interest rates go up, the price of bonds goes down, and vice versa. When the price of the bond is beneath the face value, we say that the bond is "trading at a discount." When the price of the bond is above the face value, we say the bond is "trading at a premium."

This can be important if you don't want to actually own the bond for 30 years. If you want to hold the bond for 5 years, then you'd receive $30 per year for 5 years, and then you'd receive that price of the bond at that time, which will depend on the current interest rates at the time. This is why, while some long term bonds (like government Treasury bonds) can be considered "risk free" over their full lifetime, they will often vary a great deal in value on a year-to-year basis.

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Want to better understand finance? Interested in developing a toolkit to make smarter financial decisions? Learn more about the HBX course, Leading with Finance.

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This post originally appeared on Fortune.com as part of the Leadership Insiders network. The Leadership Insiders network is an online community where the most thoughtful and influential people in business contribute answers to timely questions about careers and leadership. The question Patrick answered was, “What advice do you have for college graduates entering the workforce?” 

If you are graduating this month or next from a higher education institution, let me congratulate you. Generally speaking, you have increased the odds that your economic prosperity and well-being will be enhanced by this accomplishment.

I am sure you are tired of hearing old goats offer their advice through the written word or lofty commencement addresses, but I’d like to share my thoughts while you have a chance to breathe before entering that next period of your life: the employed adult phase.

Those who came before you know something too

I’m sure you’ve seen plenty of articles in which corporate leaders bemoan the expectations and demands of millennials. I think that many such criticisms of your generation are unfair. That said, I’ve read an equal number of articles about how corporations need to change to accommodate you.

As with most things in life, the truth is in the middle. There is little doubt that you will have the opportunity to shape the way work is conducted. But don’t forget that there are literally centuries of acquired knowledge about how to do things that came well before you were even born. Don’t throw all of those ideas out. Pick the best of your world and the “old” one.

Things won’t go according to plan

This is one I’m sure you’ve heard. But it bears repeating: You are not completely in charge of your own destiny. Finding a passion you didn’t expect, falling in love, getting sick or injured, being fired, losing a loved one, working for a horrible boss—all of these things and hundreds more can derail you. Plan for that.

I’m not arguing that you should expect the worst. But do train yourself to be nimble and comfortable with the idea that where you end up is likely not to be where you originally planned. Expect this in both your work and personal life. Jobs and companies come and go, so dive into what you are paid to do but think about how you would use your skills in another context.

Don’t worship money

I love money as much as the next person. I’d rather have more of it than less of it and you should negotiate like hell to get the best deal for yourself when getting that first “real” job. But never forget that one day you won’t be there. That’s so hard to keep in mind while you are still young. But it’s a truth that’s inescapable.

Experiences are much more important to humans than goods. So when you do get money, save for retirement and take care of your family. But also use some of it to travel with those you love, or skydive, or hike Mount Everest, or learn to fly. When you are taking your last breath, you won’t be saying to those gathered around you, “Remember that time I got a bonus and I bought 200 shares of Google?” You’re much more likely to say, “Remember the time we watched the sunrise from Haleakala on Maui?”

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