A lunar landing?
April 27, 2020

A lunar landing?

Neville Pike. UK Equities Product Director, Henley Investment Centre

The challenges faced in financial markets are like nothing that any of us have ever seen before. We can try and run playbooks learned from previous recessions and from previous market collapses, but nothing comes close. Neville Pike looks at how this time it is different. Very, very, different.

Nothing new in the above statement. Many people have made similar points.

So, in an attempt to actually quantify just how different it is, we can turn to statistics. I have taken from Bloomberg the daily movement in the FTSE All-share Index since 24 April 1988 – exactly 32 years ago today.

The standard deviation across the population of 8,086 observations is 1.02% – in simple terms this means that just over 2/3rd of the time, the daily movement in the FTSE All-share Index is within the range +/- 1.02% either side of a daily average of 0.02%. Around 95% of the time the daily movement would be expected to be within 2x standard deviations, i.e. +/- 2.04%. And 99.7% of the time within 3x standard deviations, i.e. +/- 3.06%.

Nothing revolutionary. Standard GCSE maths. Maybe A/S level.

But looking at markets over the recent period of the crisis, and in particular over the two-month period from 24 February to 23 April, in the context of the long run standard deviation, serves to illustrate exactly how statistically anomalous the recent period is.

Table 1 below shows the number of days during this 43 trading-day period in which the actual recorded daily movement was in excess of 3x Standard Deviations, together with the approximate frequency that this might be normally expected, using a statistical model of a “normal distribution”.

Table 1

Std Deviations Actual number of days Expected frequency (approximate)
>3 7 Yearly
>4 4 Every 43 years
>7 1 Every 1.07 Billion years
>8 1  
>10 1  

Source: Bloomberg, as at 24 April 2020. 

A 3-standard deviation event might be expected to occur (100%-99.7%) = 0.3% of the time, or roughly once a year. There were no fewer than 7 such instances in the 43-day period.

A 4-standard deviation event would statistically be expected to occur only once in 43 years … a very full career in the City (mine is 37 years and counting). There were 4 such instances in the 43-day period.

Beyond that, there was a 7-standard deviation event, an 8x, and even a 10x standard deviation event. To put into context, in a normal distribution, a 7-standard deviation event would only be expected once every 1.07 billion years. Trying to calculate 8x and 10x; my computer gave up.

Clearly this isn’t normal. And also serves to illustrate why models – of many kinds – that rely on statistical analysis of historical data, don’t appear to work right now.

I read yesterday an excellent blog from the European team on the challenges of “Interpreting factor risk”. Looking at the above Index data helps further illustrate further why risk models built on regression analysis must be struggling to explain relative performance based on stock specifics, and why factors (very probably “blind factors”) appear to have gained so much in importance.

Note, that is not to decry the usefulness of models, far from it; they have probably never been more useful than they are now. But understanding the statistical abnormalities helps a fundamental-based active manager to calibrate the model and so make for better-informed and better-balanced, long-term decisions.

So why start at 24 April 1988? Daily data exists on Bloomberg back to 1 January 1985, but extending back by a further two-and a bit years (and thereby incorporating the crash of 1987) barely moves the statistical dial. 32 years ago today, on 24 April 1988, the UK tabloid paper The Sunday Sport ran the following story on the front page: World War 2 Bomber Found on Moon.

This is probably what an 8 standard deviation event looks like.

For a 10 standard deviation event, it would probably need to have been piloted there by Elvis.

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