Behavioural Finance, Part 4: The Law of Small Numbers

Welcome to Part 4 of our Behavioural Finance series. If you’ve missed the earlier parts of the series, you’ll find our Introduction to Behavioural Finance here, Part 2: Prospect Theory and loss aversion here, and Part 3: Availability and Representativeness here.

I really hope you’re enjoying our Behavioural Finance series so far. In the first three blogs, we’ve covered prospect theory and loss aversion, and availability and representativeness. And the great thing is, we’re only just getting started. Although we won’t be covering all of them, there are a remarkable 188 cognitive biases. It’s little wonder that humans can seem hard-wired to screw things up financially or to make bad decisions over and over again.

While these instincts represent a significant threat to investors, they can be a huge opportunity for great financial planners. It is crucial for a financial planner to understand these biases and how they affect their clients, so they can be well prepared for their clients’ reactions to certain situations. Then they can help them to avoid errors and to focus on making the right decisions over and over again instead. The value of this type of coaching over the longer term can be enormous.

In this week’s post, we look at some more examples of how our ability to estimate probabilities can often be skewed by human instincts, which sometimes leads to unconscious biases and irrational behaviour.

The Law of Small Numbers

The law of small numbers is the name economists give to a very common mistake people make when it comes to making predictions or gauging probability. The simplest example of it is when we toss a coin. Every time we toss a coin there is a 50% chance that it will land on a head and a 50% chance it will land on a tail. However, if we get a run of, say, five straight heads, we might start to feel as if the next time we toss the coin there will be a higher probability of it being a tail. This would be wrong because the outcome of each toss of the coin has no bearing on the next one, so the odds of each toss are still 50/50.

The reason we make this mistake, according to behavioural economists, is that humans tend to put too much faith in small amounts of information. In some situations, this approach might be valid. For example, if you have 10 red balls and 10 black balls in a bag and randomly pick five consecutive red ones without replacing them, the odds of drawing a black one next will increase. But in the case of tossing a coin, each outcome is completely independent of what came before and what will come after. Every time you have an equal chance of getting a head as you do of getting a tail.

There are a number of ways in which the law of small numbers can bias our investing decisions.

The Gambler’s Fallacy

The gambler’s fallacy describes how gamblers might expect, for instance, a number that hasn’t come up on the lottery or on a roulette wheel for a while to be ‘due’. These people are effectively making the same mistake that’s highlighted by the coin-toss example, but on a larger scale: their brain is telling them that they’re dealing with a finite pot of numbers that aren’t replaced once they’re picked. But actually, all numbers are available with every spin of the roulette wheel.

As with other biases, an interesting theory of why our brains do this looks to our evolutionary past. It might have been beneficial to expect that a series of common outcomes would be broken at some point: for example, the hunter who believes their luck will turn around after a series of failures is much more likely to eat than the hunter who gives up.

The Hot-Hand Effect

While in some cases the law of small numbers causes people to underestimate the chances of a particular outcome (as with the likelihood of seeing a run of five heads in the coin toss example), in others, it causes them to overestimate. Economists call this the ‘hot-hand effect’. The name comes from basketball and the mistaken belief among fans and players that the chance of a player hitting a shot is greater following a hit on the previous shot than a miss. It’s as if they believe the player is ‘on a roll’ or ‘in the zone’ and that success will breed more success.

It might seem at first as if the gambler’s fallacy and the hot-hand effect contradict each other, but they both come from the same place. In short, both make the mistake of believing that past events change the probability that a given event will happen in the future. In fact, far from being contradictory, we can imagine a scenario when both the gambler’s fallacy and the hot-hand effect are employed at the same time:

Bob puts his lottery numbers on for the week, being careful to avoid numbers that have recently been drawn [gambler’s fallacy], but he makes sure he gets his ticket from the shop that has sold tickets to more winners than any other in his town [hot hand effect].

The Effect on Investing

So how do these phenomena translate to the everyday way that we approach investing? The gambler’s fallacy and the hot hand effect can be spotted regularly by financial advisers in the behaviour of their clients.

For example, if stock markets go up for a period, as they have done recently, some investors fear that at any minute everything is going to go into reverse. They announce they are not investing anymore as the market is sure to plummet any day now. This could be seen as an example of the gambler’s fallacy – if the stock market has gone up for a while, a fall must be due. If we compare the rising stock market example to how we think about house prices, we get a totally different reaction. When house prices go up, people say they are going to invest in property as it’s a safe bet because prices always go up and they see no reason why this won’t continue – this is the hot-hand effect.

The house price example also touches on another topic we’ve addressed in this series – the availability bias. Because house price crashes are relatively rare, there’s less available information about them out there so we recall them less and fear them less. But that’s not to say they don’t still happen and that the risk shouldn’t be considered properly. If we look at the stock market example again, conversely, if stock markets go down, many investors then worry they are going to sink even lower. They don’t arrive at the conclusion that an upturn is due. As a result, they don’t buy when they should, when the market is low; instead, they wait until it picks up and buy when prices are rising again, missing the opportunity. This reflects aversion to loss which we have also looked at.

There is a great deal of interplay between the biases of behavioural finance. Many of them have their basis in some of our earliest childhood experiences. As Professor Brett Kahr says:

“As every parent knows only too well, newborn infants specialise in what psychologists refer to as “magical thinking”.  In other words, we magically expect that a mummy or a daddy will automatically bring us milk and biscuits, or will cuddle us, or change our nappies, just as they did yesterday, and the day before that.  Great parents will gratify this magical thinking in infants and will respond to the baby’s needs in the most desirous way.

“Regrettably, financial markets do not respond to our wishes as reliably as good mummies or daddies may have done.  Thus, when infantile magical thinking seduces us into believing that ‘all will be well’ with our investments, we run the risk of disappointing ourselves, often hugely so. Therefore, it’s wise to collaborate in a considered way with trusted experts to help protect us from our vulnerability to the infantile thinking which lurks so deeply within our minds.”

Questions to Ask Yourself

How strongly do you agree or disagree with the following statements?

  • I am confident in my ability to time the market when I buy and sell
  • I wouldn’t consider an investment if I’d seen that it had recently dropped in value
  • I worry about making an investment at the wrong time

If you would like some help in planning your ideal financial lifestyle, please feel free to get in touch.

Next post: Anchoring, Herding and Conservatism Bias.

This document is marketing material for a retail audience and does not constitute advice or recommendations. Past performance is not a guide to future performance and may not be repeated. The value of investments and the income from them may go down as well as up and investors may not get back the amount originally invested.

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