Overestimating Conjunctive Probabilities and Underestimating Disjunctive Probabilities

Here's an interesting finding from cognitive bias researchers (like Tversky and Kahneman): people tend to overestimate conjunctive probabilities and underestimate disjunctive probabilities.

This theory could explain why investors are (over)confident that a company they've bet on will succeed. As Kahneman explains in Thinking, Fast and Slow:

"Biases in the evaluation of compound events are particularly significant in the context of planning. The successful completion of an undertaking, such as the development of a new product, typically has a conjunctive character: for the undertaking to succeed, each of a series of events must occur. Even when each of these events is very likely, the overall probability of success can be quite low if the number of events is large. The general tendency to overestimate the probability of conjunctive events leads to unwarranted optimism..."

I'll bet that when people think of a plan that only needs seven things to succeed, each with a 90 percent chance of success, they essentially mentally average the probabilities to come up with a roughly 90 percent conjunctive probability. When at that point, it's actually more likely than not (0.9^7=0.48) that the plan will not succeed!

So, looking at an investment like Molycorp, the backers need to be able to make a conjunctive probability assessment. The company needs to make many systems work along a chain from ore to refined product. Some of those systems, like the hydrochloric acid plant and the leach tanks, have had what are now longstanding, intractable problems. My skepticism last November about Molycorp's ability to produce (see 1,2,3), not to mention the price that rare earth metals would bring, seems in retrospect like a good conjunctive probability assessment.

In contrast, people underestimate disjunctive probabilities, as Kahneman explains:

"A complex system, such as a nuclear reactor or a human body, will malfunction if any of its essential components fails. Even when the likelihood of failure in each component is slight, the probability of an overall failure can be high if many components are involved."

It seems like judging failure is almost always going to be disjunctive (many possible causes) and success almost always conjunctive. Add in people's existing biases for optimism, and you can see why investors are mostly bulls and bears are so rare.

The Optimism Bias

An excerpt from The Optimism Bias

"[T]hese precise regions — the amygdala and the rACC — show abnormal activity in depressed individuals. While healthy people expect the future to be slightly better than it ends up being, people with severe depression tend to be pessimistically biased: they expect things to be worse than they end up being. People with mild depression are relatively accurate when predicting future events. They see the world as it is. In other words, in the absence of a neural mechanism that generates unrealistic optimism, it is possible all humans would be mildly depressed."

Discussed at the Niederhoffer blog

"It explains also why crashes catch by surprise the optimistic herd, that continues to look positively into the future although all the elements are there to understand that things are very bad. Only a few 'mildly depressed' investors manage to sail macro and micro events maintaining a good understanding of what is going on."

Another Review of The Outsiders - And the "Ninth Outsider"

"Y0ungmoney" wrote a review that builds very nicely off of my reviews of The Outsiders:

"Like Market Wizards, The Outsiders is popular because it's inspiring rather than because it's informative. The book doesn't provide nearly enough detail for readers to determine why the capital allocation decisions it chronicles were successful. It also has methodological problems reminiscent of Jim Collins' Good to Great but even worse-- Thorndike's approach involves a lot of survivorship bias, and he doesn't subject his outsider CEOs to any kind of control group.

As part of my investing research, I recently came across a CEO who's much younger than Thorndike's outsiders but uses the same capital-allocation strategy they did. One can think of him as an honorary ninth outsider."

Study: "Why do people choke when the stakes are high?"

"A new study by researchers at the California Institute of Technology suggests that when there are high financial incentives to succeed, people can become so afraid of losing their potentially lucrative reward that their performance suffers. The researchers also found that the more someone is afraid of loss, the worse they perform."

Cognitive Defect Responsible For Optimism Identified

Here is a fascinating paper in Nature Neuroscience, "How unrealistic optimism is maintained in the face of reality". From the abstract:

"Unrealistic optimism is a pervasive human trait that influences domains ranging from personal relationships to politics and finance. How people maintain unrealistic optimism, despite frequently encountering information that challenges those biased beliefs, is unknown. We examined this question and found a marked asymmetry in belief updating. Participants updated their beliefs more in response to information that was better than expected than to information that was worse. This selectivity was mediated by a relative failure to code for errors that should reduce optimism. Distinct regions of the prefrontal cortex tracked estimation errors when those called for positive update, both in individuals who scored high and low on trait optimism. However, highly optimistic individuals exhibited reduced tracking of estimation errors that called for negative update in right inferior prefrontal gyrus. These findings indicate that optimism is tied to a selective update failure and diminished neural coding of undesirable information regarding the future."

This was published in October. Now I can tell the permabulls and people who didn't learn from 2008 that there is something literally wrong with their brain.

"Trials and Errors: Why Science Is Failing Us"

From the latest Wired,

"[C]auses are a strange kind of knowledge. This was first pointed out by David Hume, the 18th-century Scottish philosopher. Hume realized that, although people talk about causes as if they are real facts—tangible things that can be discovered—they’re actually not at all factual. Instead, Hume said, every cause is just a slippery story, a catchy conjecture, a “lively conception produced by habit.” When an apple falls from a tree, the cause is obvious: gravity. Hume’s skeptical insight was that we don’t see gravity—we see only an object tugged toward the earth. We look at X and then at Y, and invent a story about what happened in between. We can measure facts, but a cause is not a fact—it’s a fiction that helps us make sense of facts."

Unexpected Equity Tail Risk

It pays to know the statistical distributions of the things you deal with!

The Favorite-Longshot Bias

Empirical studies of horse race betting in the U.S., the UK, and Australia have established the so called favorite-longshot bias. Studies find that on average, bets on longshots lose much more than do bets on favorites. This means that longshots are overbet and favorites are underbet. By using a large data set of pari-mutuel harness horse races, we show that the favorite-longshot bias exists in Germany as well. We provide evidence that there is bias not only for simple win bets, but also for other types of bets as well, and that the bias is a time- and track-invariant phenomenon. The bias is consistent with the assumption of the (local) love of risk of the betting audience.