October has a reputation for being a volatile month for shares – is this in fact true?
Daily volatility within a year
The standard way to measure volatility is to calculate the standard deviation of returns (in this case these will be daily returns). The following chart plots the standard deviation of the daily returns of the FTSE 100 Index for each trading day of the year for the period 1984 to 2014. For example, the standard deviation of the 30 daily returns on the first trading day of the year since 1984 is 1.37. To smooth the line what is actually plotted is the 5-day rolling average of the daily standard deviations.
It can be seen that the volatility of daily returns fluctuates in a range of approx 0.8-1.2 for the first eight months of the year. It then starts to increase in September and peaks in October before trailing off for the remainder of the year. So, according to this study of daily returns throughout the year, October is indeed the most volatile month.
Daily volatility over 30 years
Having looked at the daily volatility profile for the 12 months of the year, let’s now look at how daily volatility has changed over the past three decades.
The chart below plots the standard deviation of daily returns of the FTSE 100 Index on a 50-day rolling basis for the period 1985-2014.
However, overall levels of daily volatility have not changed greatly over the period. The (50-day rolling) average daily volatility since 1985 is 0.99 and currently stands a bit below that at 0.83. As can be seen, since the spike in daily volatility in 2008, the trend of daily volatility has been down – reverting to the mean daily volatility for the period.
At the time of writing, the 50-day rolling average daily return is 0.058% with a standard deviation of 0.83. This means that in the past 50 days, 16 days (32% of the days) have seen daily changes more than +51 or less than -57 points in the FTSE 100.