Behavioural Finance – Heads or tails? Don’t gamble on a small sample
Very rarely does the clink of a coin tossed clumsily in the air play into financial decisions. Rather, they tend to be made based on examples from somewhat abstract financial concepts. A recent award-winning satirical research paper gives us a simple — and entertaining — way of illustrating a cognitive bias, referred to as the representative heuristic, and its consequences. All it takes is a coin flip or two…
Don’t take a small sample size at face value
Spring marks the consultation period for Nobel Prize nominations and candidates. It’s also the season for its parody, the quirky “Ig Nobel” Prize1 (derived from the word “ignoble”), to award publications that “make people LAUGH, then THINK”.
One 2024 Ig Nobel Prize winner in particular offers a much-needed dose of light-heartedness at a time of turbulence on the financial markets. A study on probability based on coin flips addressed the question of whether a coin tossed into the air is more likely to land with the head side or tail side facing upwards. The experiment revealed that 50.8% of the time, the coin landed on the same side it was facing to start off with.
The probability of a coin landing “heads or tails” is a perfect example of the representativeness heuristic. If a coin lands tails three times in a row, and someone is asked to predict the fourth toss, usually they will either assume it will be tails again, continuing the streak, or they will guess heads, the thinking being that the results will even out. We are naturally inclined to refer to historical coin flips, even though each one is independent and a sample size of just earlier tosses is very little to go by.
Drawing conclusions based on an insufficient sample size is the very definition of the representative heuristic, first described by Tversky and Kahneman. It leads us to make decisions based on very limited input wrongly assumed as representative. It makes us overlook real probabilities in favour of misleading generalisations and stereotypes.
Our researchers bypassed the bias by using a sample of 350,757 coin tosses carried out by 48 different researchers using the coins of 46 different currencies. This resourceful methodology (which confirmed the intuitive result of a near 50/50 split) rightfully earned the experiment an Ig Noble Prize.
Don’t be short-changed by poor financial decisions
The representative heuristic has a very real impact on our financial decisions.
When choosing a mutual fund (UCITS), investors often place too much emphasis on past performance in their investment decisions. Despite the standard disclaimer that past performance does not guarantee future performance, it’s tempting to base our reasoning on past gains. Unfortunately, as financial markets frequently remind us, one year or even one month can differ wildly from another. Beyond risk profile, the type of underlying asset, the processes and the investment team, the key selection criterion lies in the fund’s ability to mitigate market downturns and harness upswings to deliver strong long-term performance. It may be better to consider outperformances well beyond recent years. We can apply the same logic to selecting a stock or even an asset class: you can’t generalise or extrapolate a trend based on just a few short months, and you run a very real risk of being “short-changed”.
Corporate finance, exemplified by mergers and acquisitions, are is also affected by the representativeness heuristic. When valuing a company using comparable transactions (based on acquisitions/sales of similar unlisted companies) or comparable publicly traded companies (based on their market valuation), achieving true comparability in terms of size, nationality, profitability, development stage, etc. is very challenging. The evaluator must find a sample large enough to be representative, while also trying to balance sample size with relevance. There's a real risk of falling into the representativeness trap, as the quest for maximal comparability could disproportionally reduce the sample size.
And lastly, from an insurance perspective, decisions around your personal protection may also fall prey to the representativeness heuristic. Just because you haven’t been exposed to any adverse events (natural disasters, health issues, a death in the family, etc.) over a given period of time doesn’t mean you shouldn’t take out insurance and a personal protection plan.
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Now that we’ve taken the mystery out of the representative heuristic, how about flipping the 350,478th coin?
1www.improbable.com
2 “Fair Coins Tend to Land on the Same Side They Started: Evidence from 350,757 Flips”, František Bartoš, Eric-Jan Wagenmakers, Alexandra Sarafoglou, Henrik Godmann et al.
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