Learning to Think Like Charlie: Mathematics Part 2

To help us learn to think like Charlie Munger (Trades, Portfolio), author Robert Hagstrom wrote “Investing: The Last Liberal Art.” Chapter eight covers the relationship between big ideas in mathematics and practical applications in the field of investment.

Our summary of chapter eight is broken into two parts. The first covered Aesop's fable, "A bird in the hand is worth two in the bush," and how investors like Munger and his partner Warren Buffett (Trades, Portfolio) have made it part of their thinking about cash flow; also, how the concept of discounted cash flow analysis helped change valuation into a quantitative exercise.

Part one also included Blaise Pascal's development of probability theory, and what was to become decision theory and decision tree analysis. Pascal's ideas, along with Bayesian analysis, eventually led to much stronger risk management principles.

Part two of our summary of the chapter begins with Hagstrom describing Sir Francis Galton’s discovery of “regression to the mean.” This principle is also captured by a number of common sayings, including: “What goes up must come down” and even “Pride goeth before a fall.”

Using mathematics and experiments, he demonstrated why big peas did not get infinitely larger and small peas did not get infinitely smaller. The same held for the height of people. Essentially, it is all about the normal distribution, the so-called bell curve.

Turning to contrarians in the stock market, Hagstrom wrote, “They would tell you greed forces stock prices to move higher and higher from intrinsic value, just as fear forces prices lower and lower from intrinsic value, until regression to the mean takes over. Eventually, variance will be corrected in the system.”

While regression to the mean is relatively well understood and practical, why is forecasting with it so difficult? Hagstrom offered three reasons:

1. “Overvaluation and undervaluation can persist for a period longer—much longer—than patient rationality might dictate.”
2. “Volatility is so high, with deviations so irregular, that stock prices don’t correct neatly or come to rest easily on top of the mean.”
3. “Last, and most important, in fluid environments (like markets) the mean itself may be unstable. Yesterday’s normal is not tomorrow’s.”

And, he added:

“In physics-based systems, the mean is stable. We can run a physics experiment ten thousand times and get roughly the same mean over and over again. But markets are biological systems. Agents in the system—investors—learn and adapt to an ever-changing landscape. The behavior of investors today, their thoughts, opinions and reasoning, is different from investors of the last generation.”

To cite a specific example, he offered the S&P 500 Index, which is passively managed. But passive does not mean unchanging; about 15% of companies that comprise the list turn over every year; some 75 companies enter or exit the index. Some exit because their capitalization has fallen or they have been taken over by another company. Most enter the index because they are healthy and growing. Hagstrom noted, “As such, the S&P 500 Index evolves in a Darwinian manner, populating itself with stronger and stronger companies—survival of the fittest.” The mean is continually shifting.

American economist Frank Knight, who founded the Chicago School of Economics, made a distinction between economic risk and uncertainty. He argued that risk covers situations with unknown outcomes, but the range of outcomes is known in advance because of the probability distribution (again, the bell curve).

Uncertainty covers situations in which we know neither the outcome nor what the underlying distribution will be. That makes it both immeasurable and impossible to calculate. Surprise is the only constant.

Knight’s ideas about uncertainty were reinforced by Nassim Nicholas Taleb’s book, “The Black Swan: The Impact of the Highly Improbable” in 2007. According to Taleb, black swan events have three characteristics:

1. They are beyond the realm of regular expectations; nothing in the past suggests they will happen.
2. The impact is extreme.
3. Human nature demands that we search for explanations afterward, to make the event both explainable and predictable.

Examples of such events include the attack on Pearl Harbor in 1941 and the 9/11 attack on the World Trade Center. Both had the requisite characteristics.

Statisticians knew about black swan events before Taleb’s book. They called such an event a “fat tail.” A normal bell curve looks like a bell, being tall and wide in the center and then quickly tapering out at the bottom. The left and right sides of a distribution are known as “tails,” but if a tail balloons rather than flattens, then it’s known as a fat tail. A black swan event, then, is the equivalent of a fat tail event.

We can also call them deviations from the normal distribution; variations of five or more deviations are extremely rare. Hagstrom complained that our language has been debased by many investors, who now believe any minor deviation from the norm can be called a black swan or fat tail.

Mathematics, unlike language, can increase precision and reduce ambiguity. However, we still have trouble predicting the future using numbers from the past. To address this issue, Hagstrom introduced economist and Nobel winner Kenneth Arrow, who wrote, “Our knowledge of the way things work, in society or in nature, comes trailing clouds of vagueness. Vast ills have followed a belief in certainty.”

So there is uncertainty within all predictions, but probability, variance, regression to the mean and fat tails help “narrow the cone of uncertainty that exists in market—but not eliminate it.” Risk management, then, lies in dealing with the matters that can be measured to some extent, and recognizing that we can never eliminate uncertainty.

Hagstrom wound up his chapter on mathematics with this quotation from G. K. Chesterton, a literary critic and author of the Father Brown mysteries:

“The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in the wait.”

Read more here:

• Â Learning to Think Like Charlie: Mathematics Part 1
• Learning to Think Like Charlie: Literature and Critical ThinkingÂ
• Learning to Think Like Charlie: PhilosophyÂ

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