For many investors, price movements on equity markets have become more tempestuous. Rather than experiencing prolonged phases of turbulence, market players see themselves as being caught up in brief but hefty whirlwinds which regularly leave a trail of damage on markets. Can empiricism, i.e. an analysis of price movements from the past, confirm this assessment?
To answer this question, we examined the distribution of daily price fluctuations on the DAX between 1965 and the present. The result shows that, 78% of the time, prices moved within a „normal“ fluctuation band of daily returns of between – 1.2% and + 1.2% (for friends of statistics: plus / minus one standard deviation). So far, so good.
However, these statistics fail to tell the whole story. Capital market researchers have revealed anomalies in the return data, such as extremely positive and negative daily returns. In statistics, these are referred to as „fat tails“, i.e. the bulky ends in distribution functions. They describe the extremely rare and pronounced price blips. We have defined these blips as daily price gains or losses beyond five standard deviations (or five sigma, not to be confused with General Electric’s Six Sigma management tool). This corresponds to a daily movement of around 6% (1.2% x 5) in one direction or the other.
The result shows that, since 1965, there have „only“ been 96 trading days (or 0.7% of the time) on which DAX prices fluctuated to such a degree. Spread out over the various decades, the distribution of these extreme events has been relatively even since the 1980s when computer trading was introduced on a grand scale and stock exchange trading became much more liquid. The current decade (i.e. 2010 to the present), with 13 extreme movements, is as average as the 1980s and 1990s. Only the years between 2000 and 2009, in which major disruptions such as the 9/11 attack and the Lehman crisis occurred, were far more stressful. We counted 53 five sigma events during this period. The biggest positive sigma event of all time took place in the DAX on 13 October 2008 when the index surged by 11.4%. Meanwhile, the biggest negative sigma event was the virtually unknown crash of 16 October 1989 which was triggered by financing difficulties in the acquisition of a number of US companies.
Compared with this, the price movements of recent years have not been all that turbulent. There is also no reason to alert investors of an approaching „storm season“ because these are also not predictable in the five sigma area. Investors keen to optimize their return „per unit of stress“ would in any case do well to monitor share prices as rarely as possible – and especially not the daily price fluctuations.