Financial risk is an unavoidable part of life. On the 23rd of June, 2016, the United Kingdom voted to leave the European Union in a national referendum. An immediate reaction from financial markets saw the UK’s currency, the pound sterling, fall by more than 10% against the US dollar. This means, for example, that a British tourist who could convert £100 to $150 before the referendum, would only get $133 for their money after it. Financial risk occurs for everyone, not just those with large investment portfolios.

Understanding financial risk requires being comfortable with percentages, given the ubiquity with which percentages are used to normalize price changes across different assets, currencies, and to standardize price changes for investors of all different sizes. What does it take to recover to break-even from a 10% loss? A 10% gain seems like it would do it. But that would be wrong, and demonstrates the danger of downside financial risk. It actually takes an 11.1% gain to recover to break-even after a 10% loss.

This quirk of percentages is best demonstrated by converting into currency returns, which we are more familiar with. It’s true that a $10 gain will fully recover a $10 loss, but this is not the case for returns of +10% and -10%. Suppose a stock is initially at $100, where does it end up after a gain of 10% and a loss of -10%? The 10% gain increases the stock’s value to $110, before the -10% loss reduces the value by $11 to $99 – for a total loss of $1 or 1%.

Research that I have conducted, published in the journal Judgment and Decision Making, shows that this aspect of financial risk is widely misunderstood. People have a default and strong incorrect intuition that positive and negative percentage returns of a given magnitude exactly break-even. Actually it’s always the case that a return of –x% more than wipes out a return of +x%, producing an overall loss.

But what’s the danger of this? The example with returns of +10% and -10% shows that assuming the equal percentage returns cancel out overestimates of final value by only 1%. This error becomes increasingly inaccurate as the size of percentage returns increase. The final return from percentage returns of +50% and -50% is a painful -25% (An initial value of $100 increases to $150, before falling in half to $75). And what about returns of +100% and -100%? In this case the total return is -100% as the stock becomes worthless ($100 increases to $200, before falling to $0).

My research demonstrates that people are largely insensitive to the size of the percentage movement. Many people incorrectly think that returns of +x% and –x% cancel out, whatever the size of x, despite the disastrous overestimation for high values of x. The result is that many people may overestimate their ability to tolerate financial risk. Financial assets do often fall by such large amounts, and can be difficult to come back from. The US stock market fell by 43.7% from 2000 to 2003, requiring a return of 77.5% to break-even, and also fell by 50.8% from 2007 to 2009, requiring a subsequent return of 103.4% to break-even. And individual stocks can and do suffer -100% falls, with the bankruptcy of Lehman Brothers being one example.


What other factors increased the likelihood of someone getting the right answer? Participants with some level of household investments were better than non-investors, although investors still frequently got the wrong answer. The financially literate were more likely to get the right answer, as were people high in numeracy. It probably wasn’t a case of low motivation, as offering a financial incentive to one group of participants also did not lead to a reduction of the break-even error. The answer may lie in how people psychologically process percentage returns. It is natural to try and treat the percentages simultaneously, whereas the correct response involves performing the percentage changes in sequence, and updating the stock’s value in between the two numerical operations. I found that a debiasing instruction telling participants to do just that helped, and that this instruction worked by getting participants to deliberate more and think longer about the problem.

The many ways that financial risk can occur in our constantly changing economy – with the UK’s vote to leave the European Union being just one recent example – suggests that we would all benefit by deliberating more about the potential financial risks we’re exposed to.


Dr. Philip Newall is a behavioral scientist who researches financial decision making.