The psychology of probability

Behavioral biases

The chance of winning versus losing

In this post we look at the problem investors have assessing probabilities.

Does this matter? Here’s what Warren Buffett said at the Berkshire Hathaway Annual Meeting in 1989: “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.”

Howard Marks weighs in on the same subject:

“While in investing we generally aren’t offered explicit odds, the attractiveness of the proposition is established by the price of the asset, the ratio of the potential payoff to the amount risked, and what we perceive to be the chance of winning versus losing.

Superior investors may be superior because they can figure out which companies are likely to be winners. But the best investors I know also have a sense – perhaps innate and instinctive- for situations where the proposition is too favorable relative to the underlying fundamentals. It might be a company whose securities are cheap enough to more than compensate for it poor prospects, or one where the future is exceptionally bright , but its securities aren’t price high enough to charge fully for that potential.” Memo to Oaktree Clients, 2020.

When we have to rely on our innate sense or instincts there’s a lot that can go wrong. What I’m going to focus on in this post is errors of intuition and the fact that humans are not particularly good intuitive calculators of probability. Let’s look at some simple examples that make the point.

Unlikely events – gains

When we intuit probabilities, unlikely events are considerably over weighted. Kahneman gives as an example a choice between a 98% chance of winning $520,000 and a 100% chance of winning $500,000. In spite of the fact that the expected value based on probabilities is $509,600 for the first option, most people will choose option two. Their Decision Weight as Humans is different from the Probability Weight based on rational choice. In the real world the second option is the result of our tendency to be risk averse where there is a high probability of gain.

Conversely, we tend to be risk seeking where there is a low probability of gain. The classic situation is lotteries. The chances of winning are remote. But humans tend to ignore the real probabilities with lotteries.

Many investors think they are smarter than people who play the lottery. But, think about it. The base rate of success amongst tech IPOs is extremely tiny. We would like to believe each one is the next Facebook or Amazon. At one time Microsoft was a tech IPO. The chances of investors picking the next FAANG at the IPO stage is extremely slim. The chances of any new tech IPO turning into an Apple is also slim in the extreme. Investors must not be beguiled by the story.

Is there a time to throw the Hail Mary pass? Is there a time for the high risk golf shot over the lake and bunker to a small sloping green? It depends on what’s to be gained and what lost. If it’s the last chance to win the game or match, it may be worth it.

In investing, I can’t think of an occasion when you would be well advised to take a flyer. There would never be enough to be gained. I can’t imagine Warren Buffett doing it. The chances of picking Apple as a future winner when it was an IPO were about as slim as winning the lottery.

Unlikely events – losses

The reverse is the case with losses. We tend to be risk seeking where there is a high probability of a small loss and risk averse where there is a low probability of large loss. An example of the latter would be fear of losing where there is, say, a 5% chance of losing $10,000. In this case most people become risk averse. (Kahneman, 2011)p.317.

Rare events

Unpleasant rare events pose a particularly difficult problem for psychologists. It seems that Humans tend to either over weight them or ignore them. Take global warming and hurricanes. We are not talking here about the possible connection between global warming and hurricanes. We are talking about them individually. Let’s say we live in Florida. Scientists can give us reasonable probabilities of each having an impact on our lives. If asked to estimate the chances of each impact occurring Floridians will tend to overestimate the chances of hurricane impact and ignore global warming.

This is relevant for investors. Take the example of stock market bubbles and their inevitable bursting. True bubbles in the stock market, and I’m not referring to ordinary bull markets, occur only rarely. They may occur only once every twenty or thirty years. The bursting of a stock market bubble is seared in every investors’ memory. For ten or fifteen years after such an event investors will overweight the probability of a bubble and its bursting. Every bull market will be identified as a bubble, erroneously. Then memories fade. New investors come into the market who have never experienced a real bubble and its bursting. In this era investors will underweight or even ignore completely the possible existence of a bubble and the risk of it bursting in a panic.

These have been just a few examples of our human frailties in assessing probabilities.

The ever present problem of uncertainty

To move forward we have to have a clear idea of where we can and where we cannot calculate probabilities.

Investors always face uncertainty. As Keynes puts it: “By ‘uncertain’ knowledge… I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty… the sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention…About these matters, there is no scientific basis on which to form any calculable probability whatever. We simply do not know!” (Bernstein, 1996)p.229. (emphasis added)

Bottom line

With this in mind, let’s come back to Howard Marks’ formulation:  “the attractiveness of the proposition is established by the price of the asset, the ratio of the potential payoff to the amount risked, and what we perceive to be the chance of winning versus losing.” I think we can add Warren Buffett’s admonition that we are only interested in investing in the ‘seven footers’ (superb companies) and we will only do it at a very attractive price versus fair value. This is how we reason probabilities. At the same time we must always keep in mind that biases are always at work distorting our intuited assessment; things like unlikely events, rare events, etc.

How confident can we be when we reason probabilities?

The answer must be that we have enough confidence to make an investment commitment. Can we be certain we are right? Of course not. Are we on stronger ground if we are convinced we are right? Not really.

“Subjective confidence in a judgment is not a reasoned evaluation of the probability that this judgment is correct. Confidence is a feeling, which reflects the coherence of the information and the cognitive ease of processing it.” (Kahneman, 2011)p.212.

Unfortunately, when we intuit probabilities, the amount and objective quality of the evidence does not count in deciding how confident we are in our conclusion. This subject is canvassed in my post: The frailty of high conviction ideas

Last word

John Maynard Keynes, who really was the first behavioral economist, wrote: “Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits – of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.” (Keynes, 1936,2007)p.161. (emphasis added)

In other words, much of what we do as investors is driven by animal spirits. We better have a good check on them; which is where the gap-to-edge rules of the Motherlode come in. As well, we should always follow what Ben Graham called sound principles of operation. These are discussed in Part 4: Principles of Operation.

Other posts on investment psychology

This post is part of a series. Readers are invited to read Investment psychology explainer for Mr. Market – introduction This will give you a better understanding of some of the terms and ideas and give you links to other posts in the series.

Want to dig deeper into the principles behind successful investing?

Click here for the Motherlode – introduction.

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