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Beware the flaw of averages – with Andrew Elliott

A basic average can be a starting point for any analysis but, warns Andrew Elliott, it is an unsatisfactory measure of the centrality of any set of numbers and can mask the diversity and range that underpins it

17/08/2021

Juan Torres Rodriguez

Juan Torres Rodriguez

Fund Manager, Equity Value

Roberta Barr

Roberta Barr

Head of Value ESG Analyst

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Did you hear the one about the statistician who put his feet in an oven and his head in a fridge and said: “On average, I feel quite comfortable”? Of course you did – it is a very old joke but still an above-average way of starting an article on the dangers of taking averages at face value. As we noted some years ago, here on The Value Perspective, ‘average’ is a simple word that masks a significant degree of complexity.

The thing is, as our latest podcast guest Andrew Elliott – the author of Is That a Big Number? And What are the Chances of That? –  points out, at the start of any analysis, an average is often all you have. “As a starting point, an average is better than nothing so I would never suggest you ignore one out of hand,” he continues. “It is just that you then immediately run into problems, such as skewed distribution.

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Take for example, distributions of income or wealth in society, which tend to have very long tails – in other words, you have lots of people with lower incomes and relative few people with very high incomes, who nevertheless pull the average up. It is like the old joke that holds that most people have more than an average number of arms because the average number of arms has to be slightly less than two.

“By the same token, most people earn less than the average income – and so, increasingly, we look to measures like the median income as a better measure of what is typical than the pure mathematical average. Not only is that ‘arithmetic mean’ not always a good measure of the centrality of any set of numbers, it can also disguise the range of variability within the set.”

Misleading picture

In What are the Chances of That?, Elliott highlights the work of proto-statistician John Graunt, who was one of the first people to analyse mortality rates and causes of death in Britain. Working in London in the 17th Century, he calculated the average age of death was around 35 years old – but, as Elliott points out, that one number conjures up a very misleading picture.

“An average age of death of 35 might give you the idea there were no old people in that society,” he continues. “That is entirely untrue, of course, because the figure is skewed by the fact, roughly speaking, one-third of children at the time died before their sixth birthday. Graunt actually reckoned some 7% of people in 17th Century Britain lived beyond 70, so a not-insignificant number were living to twice the average.

“And so the average has given you the wrong picture – of everyone dying around 35, rather than a significant number dying very young and then most people dying at, say, 50, 60 or 70. Rather than helping you think in terms of the diversity and range of a situation, the average masks that and makes you think of a homogenous whole – that everybody in the group is the same.

Peaks and lows

“Similarly, say you are designing websites – you cannot aim to cater for ‘the average number of visitors’. You need to know potential peaks of traffic to ensure the system can cope with those and you need to know when you might be able to wind the system down so you are not wasting resources. So the average is a good starting point – it can indicate you are numerically in the right ballpark – but you quickly need more information.”

Elliott’s call to think well beyond averages holds echoes of a key tenet of value investing – building in a ‘margin of safety’. As we noted in Three principles Warren Buffett says underpin all value investing, there are so many things to be wrong about when valuing a business, it surely makes sense to have some sort of buffer in place in case some of your assumptions turn out to be wrong.

After all, as Buffett has argued, if you were driving a 9,800lb lorry, you would feel comfortable enough driving across a high bridge built to carry 30,000lb vehicles – and rather less so if the bridge was only built to carry 10,000lb ones. In a similar vein, investors ought to be looking at companies trading at large discounts to their underlying value – and then have the patience to allow Mr Market catch up with their view of that value.

Author

Juan Torres Rodriguez

Juan Torres Rodriguez

Fund Manager, Equity Value

I joined Schroders in January 2017 as a member of the Global Value Investment team and manage Emerging Market Value. Prior to joining Schroders I worked for the Global Emerging Markets value and income funds at Pictet Asset Management with responsibility over different sectors, among those Consumer, Telecoms and Utilities. Before joining Pictet, I was a member of the Customs Solution Group at HOLT Credit Suisse.  

Roberta Barr

Roberta Barr

Head of Value ESG Analyst

I am an investment analyst for the Global Value Team, having joined Schroders in 2016 as part of the graduate programme. After spending a year as an investment analyst for the Quantitative Equity Products team, I realised my affinity for the deep value investment mindset and joined the Global Value Team in 2017 and manage Global Sustainable Value. Prior to working for Schroders, I studied mathematics at Oxford University.

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