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History and maths

Fast forward one week and the world looks like something out of a Dan Dare adventure. Meanwhile, financial markets have multiple crises to deal with – supply-side, demand-side, financial, monetary, you name it. So the probability bands have shifted downwards. Last week the central band might have pointed to the bottom being around 2700 on the All-Share index – close to where it stands as I write – with that 2500 marker being shaded towards the pessimistic end.

Now, 2500 looks more like a central marker and the notion that the crash will be on the scale of the one UK shares suffered in 1973-74 no longer seems outlandish. In which case, the All-Share bottoming at 1250 – a few days ago a scenario reserved for millenarian loonies – now warrants debate.

I won’t pretend that mathematical rigour lies behind those numbers; they’re intuitive. But the point is that 2020 now looks like 1973-74 in the way that multiple major bearish factors have coincided and morphed into a storm from which there seems no escape. Back then the developed world faced two major threats – inflation driven by the cost of the Vietnam war and oil supply shortages following the Yom Kippur war of 1973. In addition, the UK – then Europe’s sick man – had special problems that, on a bad day, made the threat to British capitalism seem existential.

Some of the headline effects are shown in the table. Output was strong in both 1972 and 1973, despite persistently high inflation (what would today’s political leaders give for real output to rise by 4 per cent then 6 per cent over two years?). But for 15 months, from late 1973 to early 1975, the multiple assault became too much for share prices to bear while inflation continued on its merry way.


When the end was nigh
% change on yearShare pricesInflationReal GDPPer capita GDP
The Yom Kippur War
Spanish flu
Source: Bank of England, FTSE All-Share index 


If a comparison with 1973-74 is tempting, then one with the previous occasion a pandemic got really nasty is irresistible. That takes us back to 1918 and the Spanish-flu pandemic. But the comparison is not that useful since it deals with a very different era from today and not just because the population was exhausted by the effects of the world’s first near-global war. More relevant from an investing perspective, it was a time when stock market investing was very much a minority activity. So the pandemic’s effect on UK securities’ prices was most likely less than today’s and it would be impossible to separate out from other factors, in particular that of faltering national output as the war effort no longer needed to be sustained, and the inflationary effect of the supply shortages that followed.

When the Spanish-flu pandemic was at its worst – 1918 – on average share prices rose by 12 per cent, but that was three points less than inflation (see table). In 1919 there was a similar picture and it was not until 1920 that share prices fell heavily (by 29 per cent), but by that time the pandemic, which had been hushed up by governments anyway, had been forgotten.

It would be nice to think that 2020’s investors could get away with a year-on-year fall of the same magnitude and that would still be quite possible if Covid-19 disappears as quickly as Spanish flu did. After an especially virulent second phase in the autumn of 1918, by November it had pretty well gone for reasons that remain unclear.

If that gives us hope for today, it’s not shared by the epidemiologists who advise the UK’s government. To think through the implications of their view, we must flit elsewhere in 20th century history, although still talk about war. In particular, in 1932, Britain’s prime minister, Stanley Baldwin, made what became a famous speech in the House of Commons in which he said: “It is well for the man in the street to realise that there is no power on Earth that can protect him from being bombed. Whatever people may tell him, the bomber will always get through.”

Fast forward almost 90 years and today’s prime minister – or, at least, the epidemiologists advising him – say something very similar: the virus will always get through.

Baldwin’s speech had a profound effect, helping to mould the doctrine of appeasement. But the point is that his dogmatism – shaped by footage of Italian aircraft flattening villages in Abyssinia and the science fiction of HG Wells – proved wrong. Not only did it fail to prevent war; more important, when the test came, the bombers did not get through. Ultimately, the Second World War was neither won nor lost in the air.

Today’s related question is: will the epidemiologists be right, will Covid-19 always get through or will their forecasts be more like Baldwin’s beliefs? Obviously, we hope they will be as accurate as Baldwin. If so, as spring warms to summer, Covid-19 will become more like Sars or Mers or swine flu – another great pandemic that never quite made it; though, by gosh, it gave us a fright.

The fear is they will be right. Not only would that mean a summer spent without normal life, and that the pressure on many companies would become unbearable; the worst is that, if the epidemiologists are right, then China’s leaders are wrong. If the virus will always get through, then somehow it will get into China again (if it ever left), build into an undetected cluster, then break out. Yet already the party leader and president, Xi Jinping, has enjoyed his victory parade in the streets of Wuhan, the smog is about to descend on Beijing once more as business life resumes and, according to the World Health Organisation (WHO), no new cases have been reported in China since 8 March.

So, if there is a second phase of Covid-19, how will China’s authorities respond? Can the party admit to it? If it doesn’t, can the onslaught be tackled effectively? The potential for a Doomsday scenario lying within that hardly bears thinking about.

True, in this year of outliers hoving into view, that would be the blackest swan. But, because of thoughts such as that, I wouldn’t yet consider putting cash into the equity market. I say ‘wouldn’t’ because the Bearbull income portfolio is – and remains – fully invested and is suffering for it.

Sure, on paper there are some great bargains out there and, if I had a 30-year investment horizon and spare cash I could afford to lose, I might be tempted to put a small amount into each of, say, the 30 worst-hit shares in the All-Share index after throwing in some caveats around profit margins and balance-sheet strength. But an exercise such as that is for the next week or so.


●  Meanwhile, let’s use some mathematics of investment to explain a difficulty relating to how rapidly Covid-19 spreads. Every day the media shrieks that the numbers infected have risen by, say, 20 per cent and the death toll has doubled or whatever, and the public is correspondingly shocked and frightened. Simultaneously, boffins talk of the number they call ‘R’, which, everyone now knows, is Covid-19’s reproductive rate. But they say that R is a tiny number, such as 1.2. If R is so small, the intuitive thought goes, how can the disease spread so fast? It hardly helps when the experts reply: “Well, that’s the exponent acting on its base.”

If we talk in the language of investing, the picture becomes clearer. Take, for example, Italy, where – based on data from the WHO – R equals 1.23. That’s the same as saying infection has been growing at a compound rate of 23 per cent. Any investor will tell you that’s a snappy growth rate. It would cause a share price to double in less than four compounding periods. For investors, compounding periods are normally counted in years. For epidemiologists, they are counted in days. So – give or take – what Warren Buffett achieves with his stock selections in four years, Covid-19 achieves with its victims in four days.

And if Italy’s reproductive rate stays at 1.23, then daily compounding means it will hit 1m cases on 3 April. Meanwhile, so far the UK’s rate is growing less fast – its R is 1.157. That means the UK, with 1,547 diagnosed cases (although it will be much higher by the time you read this) will hit 1m on 1 May. So, as the UK government says, the country is – give or take – three weeks behind Italy.

Now, however, it starts to get silly. If the UK’s R value stays at 1.157, how long before the entire population of 66m or so has the virus? Answer, just 29 days after that – on 30 May. Yet clearly that can’t happen if only because 1m will already have the virus on 1 May and 990,000 of them will be healthy again and immune by the end of the month.

In other words, we know this – the UK’s reproductive rate for Covid-19 will start to slow soon enough. If nothing else, that might mean the English football season is completed before the next one starts. It does not do to relax, however, because it is chilling to consider how many undiagnosed cases there are in the UK, or almost any other country. We can use the maths of compounding to estimate this, too.

The number of new infections in the UK doubles every five days, that’s the effect of R being 1.157, or a compounding rate of 15.7 per cent. Also, for every person who dies today, 100 must have been newly infected on the same day as the unfortunate victim. That’s because the best guess for Covid-19’s mortality rate is one in 100; sure that’s much lower than the UK’s official figures (2.8 per cent), but, as we contest, most of those infected have not been diagnosed. We also know that infection took place about 20 days earlier since Covid-19’s incubation period is about five days and the illness then lasts about 15 days until death. Last, we know that the UK reported 20 deaths on 16 March.

Bring those figures and guesstimates together and we can work out that 20 days earlier the UK started with 2,000 new infections (20 divided by the 1 per cent mortality rate) and that, by the day of the deaths, the number infected had risen to 32,000 since there were four doubling periods.

By contrast, the NHS’s figures report 1,547 confirmed cases, so the official data is likely to be underestimating by a factor of 20. It doesn’t do to be flippant, but I’m reaching for the hand sanitiser even as I type.