Allowing compounding to extend over the long term is, therefore, crucial to investment success, but what this means in practice can be somewhat counter-intuitive. Rather than chasing higher returns, defensive strategies and avoiding loss are actually far more important when seeking to create higher returns over time. Warren Buffett captures the truth of this in his two rules of investing: ‘Rule number one: never lose money. Rule number two: don’t forget rule number one.’

The quantitative truth behind this folksy quote can be illustrated by imagining two different funds. In one, the manager averages 15 per cent a year for nine years, but loses 12 per cent in the tenth year; in the second fund, the manager returns an average of 12 per cent a year for ten years. At first glance, it seems somewhat surprising that the second fund provides a higher return for investors.

This example also illustrates one of the problems investors face: the goal of having more wealth in the long term and the desire to maximise the amount of time spent feeling happy about performance can be competing aims. In the example given, an investor in the second fund may have felt unhappy at underperforming their peers for more than nine years (often, unhappy enough to switch manager at just the wrong time, before the first fund suffered a loss), but eventually ended up wealthier than their peers in the apparently more exciting returning fund, which offered years of outperformance.

How do we know that the second fund has the better outcome?