# Poor maths skills lead to investors underestimating financial losses

Do you understand percentages? This appears to be a simple question, but a new study shows that a disturbing number of people’s instinctive understanding of this important concept is wrong - not ideal when talking about investing!

The study was carried out by Phillip Newall, a behavioural science PhD at Stirling Management School, on close to 3,500 people, and it showed that a misunderstanding of percentage losses versus percentage gains causes an underestimation of how much is needed to recover a loss - even to just break even.

Here is one of the questions. Feel free to answer it yourself:

• “Suppose a stock increases 10% in year one, decreases by 10% in year two, and does not pay any dividends for the duration. Is the stock’s final value more than, equal to, or less than its initial value?”

Later a second question was asked, this time with different numbers:

• “Suppose a stock increases 50% in year one, decreases by 50% in year two, and does not pay any dividends for the duration. Is the stock’s final value more than, equal to, or less than its initial value?”

What did you get? The correct answer for both questions is “less than its initial value”. Here’s how it works.

• If you have £100 and this increases by 10%, you will have £110 in total after year one.
• In year two the investment decreases by 10%. What is 10% of 110? Divide £110 by 100 to get 1%, which is £1.10, and then multiply this by 10 to give an £11 loss.
• Now take £11 from £110 and you get your answer, £99, which is less than the £100 that you started with.

In maths, the answer could be written as follows:

£100 + 10% = £110
10% of £110 = £11 ((110/100) * 10)
£110 - £11 = £99

More than half (50.8%) of participants answered both questions wrong. Three in ten (33.9%) got both right, and the rest, 15.3%, got one right and one wrong.

Further experiments based around the same question form took the values to extremes (100%), added financial incentives, allowed for more time before answering and screened for people with enough financial nous to look after their own investments. The results improved as you would expect, but not by significant amounts.

The issue is summed up nicely in the introduction to the study, which states:  “while returns of +10% and –10% result in a total return of –1%, a return sequence of +50% and –50% results in a total return of –25%.”

### Other ways that investors make mistakes

Understanding how people view and operate within finance - often at odds to logic and rationality - is a relatively new concept in the field, earning one of its main proponents, Daniel Kahneman, a Nobel prize in 2002.  He wrote his first paper to tackle this concept in 1980.

Other biases and odd behaviours that can be applied to economics include:

• loss aversion, which Moneywise editor Moira O’Neill looked at in her piece 'The emotional journey of the (not so) smart investor'.
• status quo bias, whereby a person wants things to stay the same amidst a changing world;
• sunk cost fallacy, which describes how people ‘chase good money after bad’, investing in something further simply because they already have done prior;
• gambler’s fallacy, which is used to talk about the idea that past results affect future. For example, if you toss a coin three times and get heads-heads-heads, the probability of getting heads again is still ½. However, those who fall for gambler’s fallacy will believe that getting tails is more likely.