Low volatility is past perfect

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Three main subjects in this article: some explanations on historic stock market volatility and how it is derived, an overview of rallies and swoons both in the 21st and the 20th century and finally a discussion on the trend of volatility since the start of the 21st century.

Volatility is calculated using a time series of index (or stock price) close values. It is defined as the standard deviation on the series of percentage day-to-day variations. When considering all day-to-day variations, we obtain one single historic volatility, which – while illustrative – raises a mainly academic interest. 

The key example to studying historic volatility is the Dow Jones Industrial index. Data for a public series available on Yahoo Finance go back to Oct 1, 1928. Hence they contain all information on the 1929 stock market crash and the subsequent 1930′s economic depression.

For this series, we have calculated all day-to-day variations at the close (Dvar) and made a statistical analysis on their distribution. Hereby you find the results:

 

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The red curve (normal Gaussian function) gives but a poor fit to the observed frequency column plot of day-to-day variations. For the geeks: the distribution is leptokurtic. What does this mean? Tiny variations are more frequent than the normal (Gaussian) distribution suggests. Small to average variations are less frequent and – most importantly – you find fatter tails: excessive variations are far more frequent than suggested by the normal distribution.

This is something to keep in mind: the Black&Scholes formula for option valuations has been mathematically derived assuming a normal distribution function: a Gaussian random walk of variations. Therefore the B&S model, seems built on rather shaky ground.
 

Distribution Graph 

Fig 1: Distribution of day-to-day percentage variations of the DJIA since Oct 1, 1928. The interval [-12%, 12%] only leaves aside 6 observations.

Extreme observations: rallies and swoons

Graphing volatility

Long term annualized volatility (in percentage, red on the right axis) and DJIA closing data in blue on the left axis.

Volatility discussion

The surge of US stock market volatility upon the outbreak of the Covid-19 pandemic has eclipsed that of the 2008 financial crisis. Yet if we go into more detail on last few years, the days of low stock market volatility ended early 2018 when US FED funds rates were being hiked and credit markets started tightening. As primary dealers no longer were able to market federal US ten year bonds, the FED stepped in and reversed policy. Quantitative tightening to compensate for the QE from 2008 till 2014 was suddenly off the table. Yet volatility did not slide to its appeased 2017 level. The trade war with China with escalating tariffs, the Brexit saga in Europe against the back scene of climate disasters and refugee flows all caused minor surges of volatility. Nevertheless, the FED balance sheet expansion and the funds rate gradually reduced to near zero cranked up stock markets. Very high valuations are what also fueled the sudden surge of volatility as the Covid pandemic hit the markets.

The rapid recovery of stock markets after the pandemic is the result of credit expansion and exploding sovereign deficits, not of a general recovery of corporate earnings. Both the second wave of corona infections and the risk of a disorderly ‘changing of the guard’ upon contested US presidential elections are major reasons for concern. Low stock market volatility now is past perfect and it doesn’t look as if volatility will soon subside.

The dot-com bubble spooked the markets in 2000, with the 9/11 terrorist attacks causing another blow and surge in volatility. The unwinding of the tech bubble caused repetitive minor surges in volatility on the DJA (while Nasdaq suffered its major setback). Volatility was to appease during subsequent years as economic growth resumed (2004-2006).

Yet low interest rates also caused real estate prices to surge, with loose mortgage credit policies and repacking real estate debt in CDO’s (securization) which started to be a growing concern in 2007. Volatility started rising well before the 2008 financial crisis hit the markets.

Again volatility was rising prior to the crash, as was the case more recently. The major difference being that the recent rise of volatility was caused a number of events not related to the cause of the major crash, whereas in 2007-2008 a succession of aberrations set the stage for the ultimate collapse.

After stock markets pulled themselves together in 2009, the sovereign debt crisis built up in Europe: remember the acronym ‘PIGS’ countries, for highly indebted EU member states (Portugal, Italy, Greece and Spain). The ‘I’ was later doubled to include Ireland after the ‘Celtic tiger’ lost its teeth with a major recession. The overextended construction boom and hot real-estated markets were aggravating the crises in Ireland and Spain. After 2012 days of low volatility returned.