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Where to focus

The underlying reason is that the story of the pandemic is told not only in the tabloid narrative of heart-broken families and frontline heroines, but also in cold-hearted statistics. There is the morbid interest in the daily death tally. Beyond that, ratios, and growth rates abound. In the media, references to, say, reproductive rates, infection-fatality rates and case-fatality rates (not quite the same thing) themselves seem to grow exponentially (something else we’ve learnt about).

Yet one measure of which we have heard little – and which investors must grasp in general and preferably in detail – is the Pareto distribution, or its looser variation, the Pareto principle; both are named after a 19th century economist, Vilfredo Pareto.

Give it time, however. The Pareto principle – also known as the 80/20 rule – says that, in any situation, 80 per cent of the output will be driven by 20 per cent of the inputs. Therefore, the principle also has an important corollary – that the other 80 per cent of inputs produce just 20 per cent of the output.

Intuitively, we know this will apply to the pandemic. So, in the UK, 80 per cent of fatalities will come from just 20 per cent of the population, most especially if it is divided by age, but also if split by region, by socio-economic group, or almost any category you care to think up. The maths of a Pareto distribution can take the relevant data and add the appearance of precision with a nice chart showing an exponential growth curve. And wherever a dotted horizontal line is drawn to show where 80 per cent of the output has accumulated, it will line up with just a small proportion of the inputs.

What will apply to the pandemic applies to companies. I would bet that, give or take, 80 per cent of profits at Tesco (TSCO) come from just 20 per cent of its stores; that 80 per cent at Diageo (DGE) come from 20 per cent of its product lines and so on. It also applies to stock-market values. As I write – and to be precise – 80 per cent of the FTSE All-Share index’s £2.2 trillion value comes from 64 of its 433 components (that’s actually 15 per cent).

It will apply to our own investment portfolios, too. Year after year, the lion’s share of added value in the Bearbull Income Fund comes from comparatively few holdings. And it will apply over a long period. A lifetime’s investment returns will be concentrated into a few exceptional years stemming from a few mega winners. The reverse will also apply. Losses will be concentrated into very few years (or even months) we wished we had never experienced, or stocks we wished we’d never heard of.

Turn the maths of Pareto on its head and it becomes clearer how, as size increases, more output is extracted from less input. Its maths uses a square-root law which says that half the output comes the square root of the input. So, in a portfolio of 10 stocks half the return will come from three of them (the square root of 10 rounded). Increase the portfolio size to 80 and half the return comes from just nine holdings. In other words, the really productive portion drops from 33 per cent of the total to 11 per cent.

Roughly speaking, practice follows theory. For the All-Share index, theory says 50 per cent of its market value will come from 21 of its 433 components. In fact, just 13 stocks currently comprise half its value; in other words, just 3 per cent by number comprise 50 per cent by value.

But here’s the hitch with the Pareto principle, which might be caricatured as ‘the marketing team’s dilemma’. The team knows full well that eight of its 10 marketing plans produce little return and that two of them bring home the goods. The trouble is, though, the team has little idea which are the winners and which the duffers.

Transfer that notion to the grim world of lockdown and the implications are miserable. Pareto tells us that eight out of every 10 social-distancing measures bring little benefit. Meanwhile two will hold the keys to near normality; the trouble is, neither epidemiologists, healthcare specialists nor politicians seem to know which ones they are.

Investors face a similar dilemma. Maths can tell us which fifth of our portfolio has generated four-fifths of its gains and which fifth has delivered a similar proportion of its losses. But it won’t tell us whether they will produce a repeat performance in the future. Should we assume momentum – that the stars will continue to be stellar? Or mean regression – that the stars will fade and the dogs will stir?

That, however, is where good old-fashioned analysis comes in. Critical thinking is needed, focusing on the likely reasons that made the stars shine – do their businesses have ongoing merits or were they just the happy recipients of a one-off re-rating? True, by its nature, such analysis can only arrive at tentative conclusions. The merit of the Pareto principle is that it tells us where to concentrate our efforts and it will do that time and again.