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Coming to get you

At least Covid-19 has answered one question about the equity markets I’ve pondered these past two or three years – where have all the bad times gone? And it had a corollary – why are equity markets so placid?

They aren’t any more. The 9.5 per cent fall in the FTSE All-Share index for February was a stomach-churner, the steepest month-on-month drop since October 2008, which was also the most recent month that UK equities fell at least 10 per cent.

That’s worth some reflection. To find a worse month than February 2020, you have to go back more than 11 years, almost to another era; a time when the collapse of Lehman Brothers threatened to bring down much of Wall Street and forgotten figures such as Girls Aloud, Sarah Palin and Alistair Darling as chancellor of the Exchequer were in the news. Somehow, it seems unnatural that equity markets could go for so long without putting the frighteners up confused traders and cowering investors. And, quite possibly, it is.

The past 10 years or so have, indeed, been freakishly docile. Since October 2008, the All-Share’s average monthly return is 0.4 per cent with volatility (measured by the standard deviation) of 3.6 per cent around that average. Over the full 33 years for which I have data readily available, the average monthly change in the All-Share isn’t much different at 0.5 per cent, but volatility is about a fifth higher at 4.3 per cent and, as that stat is derived from a much longer period, it should be a better indicator.

In none of the past 11 years have there been more than two monthly falls of over 5 per cent and in 2014, 2016 and 2017 there were no drops of this magnitude (over the 36 months in question, the biggest fall was 3.1 per cent). Yet take the period from the start of 1987 and 5 per cent drops have happened at an average of once every nine months. Put another way, during 11 years when there should have been 14 falls of 5 per cent or more there have been just 10. So the question isn’t so much ‘where has all the volatility gone?’ as ‘when will it return?’

The table below helps answer this question. It takes the All-Share’s monthly returns since January 1987 and slots them into eight bands of standard deviation away from the mean (four plus and four minus). The theory of normal distribution tells us that, if stock market returns are the same as flipping coins (ie, there is no connection between one month’s returns and subsequent months), then returns would be symmetrically distributed around their average, with their frequency in each band diminishing with travel away from the mean. And if calculus were used to smooth that banded variation from the mean into a line, it would be the classic bell-shaped curve.

 

Not quite normal
FTSE All-Share index (% ch per month, Jan 1987 - Feb 2020 )
 Range (%)Actual frequencyTheoretical frequency
+4 St Dev13.4 to 17.711
+3 St Dev9.1 to 13.469
+2 St Dev4.8 to 9.14254
+1 St Dev0.5 to 4.8167135
-1 St Dev0.5 to -3.8113135
-2 St Dev3.8 to -8.15454
-3 St Dev-8.1 to -12.4139
-4 St Dev-12.4 to -16.721
Ave month (%)0.47Best month (%)13.9
St dev'n (%)4.3Worst month (%)-26.6
Source: S&P Capital IQ  

 

Especially since the US sub-prime meltdown, we all know that the theory of normal distribution, on which much financial modelling rests, fails at crucial moments. Markets – much like weather systems – thrive on the feedback and self-reinforcing loops that normal distribution can’t cope with; in particular, it can’t spot the extreme events that feedback produces.

The table makes that point nicely. Normal distribution is there or thereabouts in reflecting stock market reality, but it only predicts 10 extreme monthly dips since January 1987 whereas reality has served up 15. Even over a 30-year period where the market is generally moving up, an additional five hits where something around 10 per cent is lost each time will have a big impact on long-term performance.

Reality is also logical to the extent that lousy months will tend to cluster together since markets take time to grasp and adjust to really bad situations. Not for nothing, perhaps, did two of the worst months in the sample run consecutively when the All-Share fell 13.4 per cent then 12.1 per cent in September and October 2008. That year also saw two other falls on the wrong side of 7 per cent.

All of which makes one think that we have been getting away with it these past 10 years. But that won’t last. It may not come today, or even next month. But, sometime soon, reality is coming to get you.