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Surviving market madness

Contagion is everywhere. Investors get infected by ideas in much the same way as people get infected by a virus
February 13, 2020

Bet you don’t know what Hollywood A-lister Kevin Bacon has in common with climate-change activist Greta Thunberg? Maybe you should, because the answer is implied in the question. The point is, it’s almost axiomatic that the incredibly well-connected Mr Bacon has a link with almost everyone on the planet. That’s why the notion of ‘six degrees of separation’ – the idea that anyone is no more than six acquaintances away from anyone else – is informally called ‘Bacon’s Law’ after the actor’s seeming ability to have worked with just about everyone else in the movie business. 

Thanks to Ms Thunberg’s elevation to fame, Mr Bacon must be close to her now – surely a ‘Bacon number’ of no more than ‘2’, given the propensity of Hollywood’s glitterati to signal their virtue by lining up with the 17-year-old schoolgirl who made skolstrejk understood globally. Yet what binds the two to this feature is the idea of contagion, currently a subject at the forefront of our minds chiefly because a variation on a familiar virus is galloping across the globe with its own brand of pathological contagion. 

True, as investors, we are more interested in social contagion, and how ideas are spread. But it does not really make much difference. Contagion is contagion whether it is the social sort sprinkled by Ms Thunberg, which has elevated the elimination of anthropogenic climate change into a belief system for millennials, or pathological contagion, which might enable 2019-nCoV to strike a special deal with the Grim Reaper. 

Mr Bacon comes into the story because of his role in explaining the function of social networks in spreading contagion and especially the vital part played by those who are particularly well connected. 

More of that in a moment. Meanwhile, the link between contagion, epidemics and investing is both intuitively obvious and well established. It’s intuitively obvious by the use of terms such as ‘financial mania’ to describe events as far removed as London’s South Sea Bubble of 1720, the scramble for the Bitcoin cryptocurrency that probably peaked in 2017 (although it could come again) or – closer to home – the dash for shares in any number of companies that turned out to be more wishful thinking than commercial reality, from Polly Peck in the 1980s, to Northern Rock in the 2000s and Quindell in the 2010s. 

 

 

Six degrees of separation: What does Greta Thunberg have in common with Kevin Bacon?

 

The madness of crowds

And the link is well established because way back in 1841 Charles Mackay, a Scottish journalist, was seeking a title for his short work about three episodes of financial madness that he labelled “moral epidemics” because they showed “how easily the masses have been led astray and how imitative and gregarious men are even in their infatuations”. Mackay lighted upon a title that has become perhaps the most famous in all financial writing – Extraordinary Popular Delusions and the Madness of Crowds. Instantly, it conjures up the dark forces of social contagion and our imagination does the rest. 

While Mackay’s title captured the feeling of contagion, it took two other Scotsmen to nail down its process in a mathematical model. In the 1920s, Anderson McKendrick, a military doctor and mathematician, and William Kermack, a biochemist, formalised a theory that predicts the transmission of infectious disease that is still widely used and whose application has spread to wherever contagion is possible; in particular, to marketing (including, if you like, the marketing of investment ideas). 

This is the S.I.R. model of epidemiology where S stands for ‘susceptible’, I stands for ‘infected’ (or ‘infective’ – having the ability to infect) and R for ‘recovered’. The model uses calculus to predict what is intuitively simple – that the spread of a contagion within a defined population, which might be a country or just an investment community, depends on the connection between the infected and the susceptible. Specifically, it depends on an infection rate, which is a function of the amount of contact between those two groups and the ease with which the contagion can be spread. What’s especially important is the effect of scale – the bigger a group of susceptibles, the greater the chance that each of them will have contact with infected ones and the more the infection will have the chance to spread exponentially. 

Let’s think that through. Imagine a group of 100 of whom 10 are already infected. Each of those 10 could come into contact with 90 susceptibles and at each contact have the opportunity to spread whatever it is. Therefore, the number of possible contacts where infection could happen is 900 (10 lots of 90) and infection would pass at a probability of ‘x’. So for each susceptible person, the possibility of infection is 9x. 

By contrast, if the group is small – say 10 – then, even if the ratio of infected to susceptibles is the same, the single infected one has only a maximum of nine susceptibles to contact. Correspondingly, for each susceptible the chance of meeting the infected blighter is one in nine. Thus the chance of infection is just 0.9x. 

Another crucial factor is that if the infection rate falls below a threshold, then an epidemic won’t take hold, although the disease will linger on in much the way that some nasty, though minor, diseases linger in the physical world or unfashionable notions linger in the world of ideas. This is important because the potential for contagion remains. In a changed set of circumstances, the minor illness could become a major contagion, a maligned hypothesis could become an accepted belief or a lowly rated share could become a go-go stock (see the box, 'How to survive an investment virus'). 

However, if the infection rate exceeds the threshold, then an epidemic will take hold and – for a while – multiply exponentially, as the 2019-nCoV virus has been doing. In the early stages of expansion there are many susceptibles who can become infected. Thus the number of those infected accelerates rapidly before flattening out and eventually tailing off as fewer and fewer susceptibles are left to become infected or, by analogy, to buy the fashionable investment idea. Simultaneously – and lagging the process of infection – the number of those recovered also grows, starting slowly, then accelerating and evening out. 

We have labelled the infection rate as ‘x’, but epidemiologists use the fancier label, β. What matters is that β depends not just on the amount of contact between the infected and susceptibles, but also on the contagiousness of what’s being passed. In illness, some diseases are easily transmitted, such as the common cold, whose micro-organisms are airborne; others, such as cholera or hepatitis A, are less contagious. 

 

Super connectors

Plentiful data on contagiousness can bring rigour to the β factor used to model the spread of disease. However, when it comes to mapping social contagion, it is closer to guesswork to estimate which fashions, fads and notions will be readily caught and which will remain unnoticed. Yet it is clear that people play the key role in spreading social contagion, and not just any old people, but special ones – this is where Kevin Bacon figures. 

He is what’s labelled a ‘super connector’. To explain, back in the 1960s, an American psychologist, Stanley Milgram, put together what became known as ‘the small-world experiment’. Milgram gave a letter to each of a batch of randomly chosen students with the request that it be sent to a named stranger (usually a stockbroker in Boston), though there was no address. Milgram suggested the students send their letters to someone they thought was most likely to be linked to the stranger and requested that the recipient do the same and so on. He found that, on average, it took six links to deliver the letter. Hence the now-famous notion of six degrees of separation and the after-dinner game where the guests figure out how many links connect, say, your wife to Barack Obama. 

Sure, some of Milgram’s experiments flopped. In one, only 64 out of a batch of 296 letters reached their target. Despite this, he also spotted something especially relevant to social contagion – a high proportion of delivered letters came from just a few links in the chain. These are the super connectors, the Kevin Bacons of this world. Because of their connections, they are among the first to catch what’s starting to go around. And because of those same connections, they have lots of opportunity to pass it on. Diagrammatically, they are the nodes in the network through which a disproportionate number of signals pass. 

It seems feasible that spreading investment ideas should need such super connectors. After all, take a quote from Robert Shiller, the Yale University economist who has devoted a long career to undermining the notion that investors pursue their own self interest with rational objectivity. Back in 1984, when he was building the career that would culminate in winning the 2013 Nobel Prize for economics, Professor Shiller began a paper about the link between share prices and ‘social dynamics’ with the words “Investing in speculative assets is a social activity”. He went on: “Since investors lack any clear sense of objective evidence regarding prices of speculative assets, the process by which their opinions are derived may be especially social.” 

True, some investors may object to the tone of Professor Shiller’s remark, yet his words are consistent with this discussion. They are also consistent with how “ideas and products and messages and behaviours spread like viruses do”, to quote from The Tipping Point, an influential and best-selling book from 2000 by Malcolm Gladwell, a Canadian writer. 

For The Tipping Point, Mr Gladwell drew heavily on academic research; not just that of Stanley Milgram but also – and especially – that of a major influence on sociology in the US, Paul Lazarsfeld, who focused on the importance of a small numbers of key players in the spread of opinions. Lazarsfeld called these people ‘mavens’ from the Yiddish for ‘expert’. Mr Gladwell’s mavens are the sort of sociopaths who naturally sit at the centre of a social hub; they are also bursting with information that they just have to pass on – probably with the precursor “Don’t tell anyone but. . .” – and, for good measure, they are likely to be good salespeople, too. 

 

 

Professor Robert Shiller (left) and Canadian writer Malcolm Gladwell (right) have both written about social contagion

 

Social contagion

The crucial role of mavens in the mass spreading of anything is also consistent with the mathematics of a so-called Pareto distribution. This is named after a 19th century Italian engineer, Vilfredo Pareto, and is caricatured as the 80-20 rule where 80 per cent of the output of whatever is being measured will be driven by 20 per cent of the input. In the context of social contagion, 80 per cent of the ‘infections’ will pass through the 20 per cent of connectors who earn the label ‘super’. 

This seems to be how social contagion spreads. Back in his 1984 paper about social dynamics and stock prices, Robert Shiller assumed the existence of smart-money investors who led low-level investors in the charge for speculative stocks. Something similar was proved in the real world when Ville Rantala, a finance professor at University of Miami’s business school, got access to the data from a police investigation into a large-scale scam in Finland. 

The scam – Wincapita – was an archetypal Ponzi scheme, which ran from 2003 until 2008 with about €100m invested at its peak. Its boss claimed to be dealing in spread bets and currency trading but was simply paying out to existing investors from subscriptions received from newcomers while – of course – claiming wonderful dealing profits. An important feature was that Wincapita was deliberately secretive and expanded only via the personal recommendation of existing members. 

Using data from the police investigation allowed Professor Rantala to make a detailed analysis of the links between Wincapita’s 10,000 members and, in particular, their connections to a few super-connected hubs. He found that the average number of new subscribers sponsored by each member was just below four, but that 2 per cent of sponsors each introduced more than 20 new investors. Plausibly, therefore, that super-connected 2 per cent could have introduced approaching half the total 10,000 subscribers. 

Not just that, but the research showed plenty of evidence of Stanley Milgram’s ‘small-world’ phenomenon. While most investors in Wincapita’s network were directly connected only to their sponsor and one other, they were also only a short distance from a Kevin Bacon figure, a super-connected market maven. The average investor was just two steps away from 21 members – a Bacon number of two – and three steps away from 77. 

It seems that the investors in Wincapita really did what Victorian writer Charles Mackay suggested in his famous book about popular delusions – they thought in herds, they went mad in herds. Whether, as Mackay also suggested, they recovered their senses slowly and one by one, we don’t know. But they did prove it is indeed a small – and contagious – world.