# The portfolio parable

Recall the crucial line in the parable: “For whosoever has, to him shall be given and he shall have more abundance; but whosover has not, from him shall be taken away even what he has.” Scholars have contorted themselves to find the Christian interpretation to this. We need not worry about that but simply acknowledge that, in sociological terms, the parable describes how the rich get richer and the poor get poorer. Alternatively – and approaching investment matters – the parable deals with the process known as ‘preferential attachment’.

Everywhere in finance and business we come across preferential attachment. It’s where winners take almost all. Graphically, it is illustrated by those fashionable long-tail distributions where the tail of the chart is disproportionately significant. Its best-known application is the Pareto distribution, better known as the 80:20 rule.

On a chart of a Pareto distribution, 80 per cent of the area under the chart’s line will belong to just 20 per cent of whatever variable is shown along the horizontal axis. So, biblically speaking, 80 per cent of the wealth belongs to 20 per cent of masters who reap where they soweth not; topically, 80 per cent of a stock market’s value will be concentrated into 20 per cent of its listed companies; and prospectively, 80 per cent of the efficacy for treating Covid-19 will come from 20 per cent of whichever vaccines are approved.

I could choose almost any law related to preferential attachment to discuss the merit of big portfolios. But let’s focus on Price’s Square Root Law, named after David de Solla Price, a British scientist who died in 1983. In researching scientific papers, Price spotted that a very small number of academics wrote a high proportion of the papers. His distilled this down to the formula that, for any variable, half of the output will be generated by the square root of the number of inputs.

This has massive implications. Imagine a company with 10 sales people. Price’s law says half the company’s sales will be generated by just three employees (roughly the square root of 10). That’s reasonable, but imagine a bigger company with a sales force of 100. The law now tells us that just 10 people will generate half the sales. Yet this also means their output will be the same as all the other 90. Ten stars and 90 duffers in the sales team – how’s that for a department ripe for a shake-up?

It’s not that simple – and certainly not when you apply the principle to investing. First, let’s confirm that Price’s law fits equity returns. The table shows how much market value was added by the components of the FTSE 100 index in each of the past three calendar years. True, 2018 does not really count because the index fell 12 per cent and only 25 components made year-on-year gains; interestingly, however, the worst-performing 10 accounted for 64 per cent of losses. More relevant, in 2017 the index rose 7 per cent, its 100 components added £920bn of value and its top 10 added £475bn or 52 per cent of that. In 2019, the best 10 accounted for 45 per cent of the £379bn of market value added.

 Price's law in action Change in value (£bn) 2019 2018 2017 FTSE 100 index 379 -464 920 10 biggest winners 171 46 475 Winners % of total 45 na 52 Source: FactSet

So both results were close to what Price’s law predicts. Returns are concentrated, which means – for the purposes of investment success – it is vital to pick the winners and run with them. Therein lies the difficulty – how can investors be confident of doing this? Can they really rely on their stock-picking skills? One thing is certain – a concentrated portfolio makes the task much tougher. Sure, it will still have winners and those winners will distribute their returns much in the way that Price’s law predicts. The problem is that, from the perspective of the whole market, these winners might actually be losers. Simultaneously, the smaller a portfolio, the greater the chance it will miss out on the likes of Apple (US:AAPL) or AstraZeneca (AZN) just lately.

From a global outlook, that blunt truth has applied to investors who focused on UK equities these past few years. From a UK perspective, it applies to those who focused on income stocks. Conversely, the more holdings in a portfolio, the better the chance that it will hold mega winners. True, the bigger the portfolio, the more the impact of the winners will be diluted, but only to begin with. Their impact will rise as a function of the growing success of the winners. That’s what preferential attachment does.

You can see where this is heading – towards holding managed funds in preference to individual stocks; then towards index trackers in preference to managed funds. It’s what the faithful servant would have done.