Probability Theory
It is a vast oversimplification, but not an overstatement, to say that the stock market is an uncertain universe. In this universe are hundreds, even thousands of single forces that combine to set prices, all of which are constantly in motion, any one of which can have a drastic impact, and none of which is predictable to an absolute certainty. The task for investors, then, is to narrow the field, to identify and remove that which is the most unknown, and to focus on the least unknown. And that...
The El Farol Problem
El Farol is a bar near the Santa Fe Institute that used to feature Irish music on Thursday nights. Brian Arthur, who is now the Citigroup Professor of Economics at the Institute, was born and raised in Belfast and enjoyed going to El Farol to listen to his favorite music. But there was one slight problem. Occasionally, El Farol was packed with rambunctious drunks whom Arthur wished to avoid. The chore of having to decide, week after week, whether to go to the bar led him to formulate a...
Investing in Wells Fargo and CocaCola
In October 1990, Berkshire Hathaway purchased 5 million shares of Wells Fargo amp Company, investing 289 million in the company at an average price of 57.88 per share. 15 With this purchase, Berkshire became the largest shareholder of the bank, owning 10 percent of the shares outstanding. It was a very controversial move. Earlier in the year, the share price had traded as high as 86, then dropped sharply as investors abandoned California banks in droves. At the time, the West Coast was in the...
Charles Munger Partnership
Warren Buffett is often called the world's greatest investor, and that title is richly deserved. However, the outstanding record that Berkshire Hathaway has earned over the years comes not only from Buffett but from the wise counsel of Vice Chairman Charles Munger. The one regret I have about The Warren Buffett Way was underserving the important role Charlie has had in Buffett's thinking and Berkshire's fortune. Although Berkshire's investment performance is assigned to its chairman, we should...
John Maynard Keynes
Most people recognize John Maynard Keynes for his contributions to economic theory. In addition to being a great macroeconomic thinker, Keynes was a legendary investor. Proof of his investment prowess can be found in the performance record of the Chest Fund at King's College in Cambridge. Prior to 1920, King's College investments were restricted to fixed-income securities. However, when Keynes was appointed the Second Bursar, in late 1919, he persuaded the trustees to begin a separate fund that...
The Kelly Optimization Model
Each time you set foot inside a casino, the probability of coming out a winner is pretty low. You shouldn't be surprised we all know the house has the best odds. But one game, if played correctly, gives you a legitimate chance to beat the house blackjack. In a worldwide best seller called Beat the Dealer A Winning Strategy for the Game of Twenty-One, Edward O. Thorp, a mathematician by training, outlined a process for outsmarting the casino. 20 Thorp's strategy was based on a simple concept....
The Mathematics of Investing
We try to think like Fermat and Pascal would if they'd never heard of modern finance theory. Charlie Munger As a boy, Warren Buffett was always fascinated with numbers. We already know he invested in common stocks at a young age, but not many people realize that his relationship with numbers goes much further and much deeper than balance sheets and income statements. When he wasn't thinking about the stock market, young Buffett was tackling other mathematical puzzles. Once he decided to...
The Tortoise and the Hare
In 1986, V. Eugene Shahan, a Columbia University Business School alumnus and portfolio manager at U.S. Trust, wrote a follow-up article to Buffett's ''The Superinvestors of Graham-and-Doddsville. In his piece, titled Are Short-Term Performance and Value Investing Mutually Exclusive Shahan took on the same question that we are now asking How appropriate is it to measure a money manager's skill on the basis of short-term performance He noted that, with the exception of Buffett himself, many of...