2p - 1 = x

“We try to think like Fermat and Pascal would if they’d never head of modern financial theory.”
Charlie Munger

In his book The Warren Buffett Portfolio, Robert Hagstrom does an excellent job outlining his thoughts on the focus investment strategy and the psychology of investing. But two chapters in his book in particular caught my attention.

The sixth chapter is titled The Mathematics of Investing. Hagstrom discusses probability theory and the important role it plays in Buffett’s and Munger's decision process. In one example, Buffett takes us through his thinking when he purchased a significant stake in Well Fargo in 1990 just as the West Coast was in the midst of a recession and banks with exposure to residential and commercial mortgages were thought most vulnerable. Wells Fargo’s stock had declined from $86 to $57. An approximately 50% decline.

But this was a bank that was earning $1B pretax at the time. Even if its entire loan portfolio – not just the real estate loans – were hit severely, the bank would still break even. Buffett reasoned that " a year like that ... would not distress us". Other risks existed but Buffett assigned a low probability to those as well. In the end, Buffett figured the odds of making money on the shares were on the order of 2:1 providing him with his Margin of Safety. The shares continued their decline after he bought them and were up only 5% the next year. But in 1992 and 1993 the shares appreciated 34% and 73% respectively, followed by more gains in subsequent years. Not bad.

Another interesting tool introduced by Hagstrom is the Kelly Optimization Model, 2p – 1 = x. It suggests that if you know the probability of success (p), you bet the percentage of your capital (x) that will maximize return. So if you think the probably of buying Coca Cola (NYSE: KO) has only a 55% chance of giving you above average returns over the next decade, you should invest 10% of your portfolio in the stock. It is not clear if Buffett uses this formula in his thinking, but he certainly makes a big bet when he likes his chances. Consider that in 1988 – when he began building a position in Coca Cola – Capital Cities/ABC, GEICO, Coca Cola and the Washington Post comprised 36%, 28%, 21% and 12% of his portfolio respectively.

The eight chapter introduces the concept of the market as a complex adaptive systems. The market has many agents (people) who have their own partial views and biases. They interact with other agents, none of them in control of the market, accumulate experiences and adapt to the constantly changing environment. Such a system is impossible to predict and forecast, especially in the short-term. Buffett says, “We have long felt that the only value of stock forecasters is to make fortune tellers look good.” In other words, don’t worry about price fluctuations, just focus on the economics of the business you are investing in and be assured that in the long-run, the market will reward companies that create shareholder wealth. Of course, all of this assumes you have done your homework and you are buying stock at a reasonable Margin of Safety.