use corporate funds to pay for individual perks. One of the most famous and well documented of these is RJR Nabisco in the early 1980s. As chronicled in Barbarians at the Gate, the CEO of that time, Mr. Ross Johnson, used corporate money to host lavish parties, hang out with celebrities, and build an air force of expensive private jets.5

One cause of these excesses was the fact that neither Mr. Johnson, nor his board of directors, had much stake in the company stock. In fact, Mr. Johnson owned 0.05% of the company stock, and this represented a small part of his total wealth. At a key point in my class, I ask my students to calculate Mr. Johnsons share of the $21 million purchase price of one jet in the RJR air force. So, what is 0.05% of $21 million?

In one such session I picked a student-who had not volunteered-to provide the figure. He reached over for his calculator. I said, Excuse me, but dont you have two degrees from MIT? He said yes. And arent those degrees in course six (electrical engineering and computer science), one of the toughest and most mathematical areas of MIT? Yes, he answered. And you still need a calculator for this simple calculation? The student said that yes he did need a calculator.

Most people, even those with analytical abilities sufficient to excel at MIT, are not good at even basic calculations. The calculator can readily provide the figure for Ross Johnsons $10,500 (0.05% of $21 million) contribution to RJRs jet fleet. For other problems that our brains do not solve well, however, the solution is not so simple. Consider the following two problems taken from the book Mean Genes, which I coauthored with my friend, Professor Jay Phelan of UCLA.6

Puzzle 1. Chinese families place a high value on sons, yet the Chinese government exerts extreme pressure to limit family size. Lets assume that the chance of having a girl is exactly 50%, but every couple stops having babies once they have a son. So some families have one son, some have an older daughter and a son, some two older daughters and a son, and so on. In this scenario, what percentage of Chinese babies will be female?

Puzzle 2. Imagine that you are a doctor and one of your patients asks

to take an HIV test. You assure her that the test is unnecessary as only one woman out of a thousand with her age and sexual history is infected. She insists, and sadly the test result indicates viral infection. If the HIV test is 95% accurate, what is the chance that your patient is actually sick?

As with Linda the bank teller, almost everyone gets these two problems wrong, and I could pose many other brainteasers that would also trip up most people.

In fact, when doctors and staff at the Harvard Medical School were asked the question about the HIV test, the most common answer they gave was a 95% chance that the patient was sick.7 The correct answer is under 2%. Similarly, as long as the chance of having a baby girl in each pregnancy is exactly 50%, the population will also have 50% girls. This is true regardless of any rule on when to stop having babies. If you are interested in detailed analysis of these sorts of problems, I suggest that you read the risk chapter of Mean Genes. The key message for this book is that most people have trouble doing mathematical calculations.

Sound investing is based on mathematical analysis that is far more complicated than the problems we just discussed. At the core of every investment is a set of costs and benefits that need to be predicted over many years and in many scenarios. Coming up with the correct price for IBM stock or for our own house involves some serious math!

All of us who get even simple problems wrong are in good company. Not only do Harvard doctors make huge mistakes on these problems, so do the most sophisticated people in the world. One of my buddies, Chris, has both undergraduate and doctoral degrees from MIT in physics. His research on lasers is so secretive that he cannot reveal the sponsor of his work. In other words, he is a twenty-first century rocket scientist (for Val Kilmer fans, watch Real Genius to understand this brainy culture). In spite of all his ability and training, Chris admitted that he got the HIV problem wrong.

So we arent built to do mathematical calculations, and relatively simple problems trip up MIT rocket scientists. The news gets even worse. The second big problem we face in investing is that we are systematically

overconfident. We are bad at doing the calculations required to analyze investments, and simultaneously we are unaware of our shortcomings.

Our overconfidence comes in many flavors. When people are asked to rank themselves compared to others, the average rating is always above average. For example, far more than 50% of people rank themselves in the top half of driving ability, although that is a statistical impossibility.8 When couples were asked to estimate their contribution to household work, the combined total routinely exceeded 100%.9

Myriad studies have documented this bias in our self-analysis, but my favorite remains an old study that asked men to rank themselves according to athletic ability. How many men do you think put themselves in the bottom half of male athletic ability? I suspect that you know the answer-not a single man who was surveyed reported that he had below-average athletic ability.10

Our overconfidence extends beyond self-analysis to our views of the world. Lets take a simple test: How many people were employed by Wal-Mart in January, 2004, around the world? Without looking up any information, write down a specific estimate. That may not seem fair, as different people know more or less about Wal-Mart.

To make the question fair, in addition to your guess, write down an upper-bound and a lower-bound number. Pick these bounds so that you are 90% sure that the actual number of employees is between your extreme high and your extreme low guesses.

If you answer 10 questions of this sort, nine of the answers should fall between your upper and lower bound. Do you have your three numbers for Wal-Mart? Your best estimate of the correct number, and lower- and upper-bound numbers?

Well get to the correct answer in a moment. Under exactly these sorts of conditions, when people are asked 10 such questions, they usually get between two and four questions wrong.11 This poor performance comes even after they have been told to give estimates wide enough to get only one of the 10 questions wrong.

People fail in this guessing game because they place too much confidence in their own estimates. Actually I ought to say that we fail, as I