Probabilistic Thinking and the 80/20 Rule

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Sep 10, 2007
Peter Lindmark of Lindmark Capital shares his study of Probabilistic Thinking in investing. Successful investors think in terms of probabilities, as Charles Munger noted in his 1994 lecture to the University of Southern California, “Buffett…automatically thinks in terms of decision trees and the elementary math of permutations and combinations…”


Probabilistic Thinking and the 80/20 Rule


The human brain is inherently bad at dealing with probabilities. This is largely evident in the field of investing where investors try to handicap companies as potential investments, especially in the face of uncertainty. Investors should strive to improve their cognition of probabilities and operate with a frame of mind that helps to compensate for our wiring at birth. As well, investors need to avoid information overload, a few key variables is all one needs to handicap the odds of an investment’s success or failure.


Successful investors think in terms of probabilities, as Charles Munger noted in his 1994 lecture to the University of Southern California, “Buffett…automatically thinks in terms of decision trees and the elementary math of permutations and combinations…” Mr. Munger prescribes that everyone should understand elementary probabilities such as permutations and combinations, as well as decision trees, which are taught in middle school or earlier. For those who wish to learn more or refresh their memory there is a list of books on probabilistic thinking at the end of this article. As well, there is plenty of information available on the internet.


In Robert Rubin’s excellent book, In an Uncertain World, he provides an explanation on thinking in a probabilistic manner: “Probabilistic thinking is a highly conscious process. Imagine the mind as a virtual legal pad, with the factors involved in a decision gathered, weighed, and totaled up. To describe probabilistic thinking this way does not, however, mean that it can be reduced to a mathematical formula, with the best decision jumping automatically off a legal pad. Sound decisions are based on identifying relevant variables and attaching probabilities to each of them. That’s an analytic process but also involves subjective judgments. The ultimate decision then reflects all of this input, but also instinct, experience, and “feel”.” If investors embrace this probabilistic thought process prescribed by Mr. Rubin they will have a huge leg up on their competition. Mr. Munger thinks that if one does not learn this probabilistic form of thinking then a person will “go through a long life like a one-legged man in an ass-kicking contest.”


"Most investors strive fruitlessly for certainty and precision, avoiding situations in which information is difficult to obtain. Yet high uncertainty is frequently accompanied by low prices. By the time the uncertainty is resolved, prices are likely to have risen. Investors frequently benefit from making investment decisions with less than perfect knowledge and are well rewarded for bearing the risk of uncertainty. The time other investors spend delving into the last unanswered detail may cost them the chance to buy in at prices so low that they offer a margin of safety despite the incomplete information." Margin of Safety, Seth Klarman


Our minds crave certainty in an uncertain world. Uncertainty is loathed by Wall Street, and potential bargains arise in areas where uncertainty exists. In a situation where an event can bankrupt a company, investors tend to overweight the event as opposed to assigning a probability that more closely reflects reality. This is evident today in the financial stocks due to the present liquidity crunch. Investors frame each investment as though banks will never lend another dollar to subprime borrowers though these borrows make up 13% of the borrowers in the mortgage market in the United States. As well, investors are pricing some securities as though liquidity has permanently dried up. When this current liquidity crisis ends certain equities will rebound sharply due to investors overweighting the probabilities of liquidity issues due to the short-term uncertainty it has caused. That does not mean that all these events are not serious and should not be weighed in investment decisions, only that investors overweight recent vivid evidence and improperly frame it over the long-term.



An example which is quite useful to see how one handicaps investments is to figure what percentage of one’s portfolio a person is willing to invest based on the following hypothetical scenario: A company trades at $100 a share and has a 50% probability of being worth zero and a 50% probability being worth $200 a share. How much of one’s portfolio should an investor put into this scenario? The answer is 25% according to the Kelly criterion. The Kelly formula attempts to maximize one’s net worth, but also maximizes volatility. Investor’s have a difficult time dealing with maximum volatility and trusting their analysis when a company’s value may drop 50% or more before their investment pays off. On the other hand many times investors overweight the probability of success of an investment when the odds of success are actually much lower than those projected.


". . . information generally follows the well-known 80/20 rule: the first 80 percent of the available information is gathered in the first 20 percent of the time spent. The value of in-depth fundamental analysis is subject to diminishing marginal returns." Margin of Safety, Seth Klarman


Investors are analysts and therefore are overly analytical and detail oriented. They spend months processing minute details which ignore the big picture. Creating a four hundred line spreadsheet does not make an investment work out nor provide any more certainty to one’s investment analysis. The more work one does on an investment the more comfortable they feel though their thoughts may not reflect the true probabilities of the investment’s success. A person may feel they have more control of an outcome due to knowing a large amount of information about a particular company.


If a company lies within an investor’s circle of competence, they usually derive all of the relevant variables rather quickly when attempting to handicap the odds of the company’s success as an investment. The quicker investors are able to handicap these odds the more opportunities they have to profit handsomely. This does not mean investors should act irrationally and quickly without doing the work. It is simply a prescription to wait until ideas are a “fat pitch,” a baseball analogy where players wait for a pitch that is in the zone where they have the most likelihood of getting a hit. Unfortunately this is not a business where if one works the hardest on an idea they will be paid the most. It only works to act when you are able to handicap the odds of a particular investment correctly.


Warren Buffett put together a portfolio of twenty securities in South Korea in the matter of a few hours from “turning the pages in a directory.” He was simply “looking for pure value ideas with low ratios and strong balance sheets.” The majority of the work was done in a few hours for each of these companies. All he had to figure out was the probabilities of South Korea avoiding complete obliteration because the price he was paying was so cheap, three times earnings on average. Charles Munger refers to ideas like these as “no-brainers” where the odds of losing money are close to zero. Mr. Buffett stated, “There was almost no chance that you don't make money…unless war breaks out or there's a major disaster, but you run that risk investing anywhere.” If investors stick with these “no-brainer” ideas the majority of the work is done in the first 20% of the time. An investor is simply looking for more value than they are paying for in situations where they can correctly handicap the odds.


Books on probabilities:

• In an Uncertain World by Robert Rubin

• Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb

• Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein

• Elementary Decision Theory by Herman Chernofff & Lincoln E Moses

• Probabilities in Everyday Life by John D. McGervey

• Lady Luck by Warren Weaver

• The Black Swan by Nassim Nicholas Taleb

• Randomness by Deborah J. Bennett