The following chart shows the volatility of various markets so far in 2017.
Not difficult – or surprising – to spot the most volatile market here.
Since 1984, when the FTSE 100 Index was introduced, the mean weekly return of the index has been 0.13%. In other words, when the index is at the 6000 level, the average change in the index in a week has been 8.1 points. However, this single figure masks how the mean return of the index has changed by decade – this is shown in the following chart.
In the 1980s the mean weekly return was 0.29%, which then fell to 0.22% the following decade (which marked the end of the 20-year asset boom). In the 2000s, the mean weekly return fell to a negative -0.01, and so far this current decade the mean has been 0.08%.
Although the current decade’s mean weekly return has been 0.08%, the standard deviation is 2.1 (standard deviation is a common way of measuring volatility). This means that with the index at the 6000 level, for 32% of weeks the weekly change has been greater than -122pts or +131pts.
How has this weekly volatility changed over the years?
The following chart plots the standard deviation of weekly returns of the FTSE 100 Index on a 10-week rolling basis for the period 1984-2015. (A rolling 10-week calculation is used to smooth out the chart a bit.)
As can be seen, there have been some obvious spikes in volatility – notably during the 1987 crash and credit crunch in 2008. But overall the general level of weekly volatility of the index has not changed significantly in the last three decades.
In fact the average standard deviation since 1984 has been 2.1 – so the current level of weekly volatility is pretty much exactly at the mean level for the past 30 years. And, at the risk of getting too iterative, the standard deviation of the mean of the standard deviations of the rolling 10-week returns of the index is moderately low at 1.1; meaning that for 68% of all 10-week rolling periods the volatility is between 1.0 and 3.9.
Extract taken from the The UK Stock Market Almanac.
A previous post looked at the average cumulative stock market returns throughout the year January to December. Beyond simple mean returns, it can also be interesting to look at how the market’s daily volatility changes throughout the year.
The following chart shows the (5-day moving average of the) standard deviation of the daily returns throughout the year for the FTSE 100 Index from 1984 to 2015. In plain English: the chart plots the range of daily fluctuations of the FTSE 100 index for each trading day throughout the year.
It can be seen that the volatility of daily returns is fairly even for the first eight months of the year; it then starts to increase in September and peaks in October before trailing off fairly significantly for the remainder of the year. So, according to this study of daily returns throughout the year, October is the most volatile month.
Extract taken from the newly published The UK Stock Market Almanac 2016.
October has a reputation for being a volatile month for shares – is this in fact true?
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.
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.
The chart below was created by taking the 300 FTSE 350 companies that have seven or more year’s historic price data and then using regression analysis to calculate the slope of the regression line and the R-squared for each of the 300 companies’ year end share prices for the last ten years. These 300 pairs of figures (i.e. a gradient figure and R2 for each company) were then plotted on a scatter chart (below).
The above chart is interesting. A line of best fit has been drawn which has a positive slope, which indicates that shares with higher returns tend to also have higher R-squareds (i.e. lower volatility around the trend line).
This is a Good Thing – this is what investors want: shares with high returns and low volatility.
Shares are therefore attractive in the top-right quadrant of the chart above (i.e. shares with positive returns and R2 over 0.5). An example would be Rotork (circled in the chart) with a slope gradient of 2.82 and R2 of 0.91 for its year end share prices since 2004..
To identify shares in the top-right quadrant we can calculate the multiple of the slope gradient and R2 and rank shares in descending order by this value.
The following table shows the top 20 shares in the FTSE 350 Index as ranked by this multiple of slope gradient and R2. This is, in effect, a ranking of the highest-return/lowest-volatility shares for the past ten years, and as such they might be regarded as the best trending shares over that period.
|Company||TIDM||Slope||R2||Slope x R2|
|Personal Assets Trust||PNL||13.05||0.83||10.84|
|Randgold Resources Ltd||RRS||6.26||0.73||4.55|
|Reckitt Benckiser Group||RB.||3.00||0.90||2.70|
|British American Tobacco||BATS||2.65||0.96||2.54|
In a previous article we looked at very large one-day market falls, in this article we will add to the study very large one-day market gains.
First, the following chart plots the very large one-day market gains with the losses for the period 1984-2014. As before, “very large gains” is defined as daily returns over two standard deviations away from the average return; in this case that is over +2.2%.
As can be seen, there is a certain symmetry here: periods of large one-day gains seem to accompany periods of large one-days falls. This is not too surprising – a large bounceback often follows a large fall.
However, the two are not always closely synchronised. For example, although in the 30 years under study 169 days can be defined as very large one-day gains, only 26 of those large-gain days days were on days after large falls. In fact, those 169 large-gain days followed days whose average return was only -0.21% (to be compared with -2.2% which is the minimum threshold for a day to be defined as a very large fall).
It would be good to understand when these periods of higher volatility happen with respect to the prevailing market. The following chart plots the very large one-day moves and superimposes the absolute level of the FTSE 100 Index.
Putting Black Monday in 1987 to one side, from 1984 to 1997 the market displayed relatively few large one-day moves. Their frequency increased from 1997 and saw a particular high frequency during the Asian financial crisis of 1998. An interesting observation is that the frequency of large one-day moves peaks coincident with market bottoms, and not market tops. So, this can be seen in 2003, 2009 and Sep 2011
The following chart is the same as the above, but the periods of increased large one-day move frequency have been highlighted with grey boxes.
The following chart shows the comparative performance of the market in the 20 days following respectively a large one-day rise or fall. The Y-axis is the percentage move from the close of the index on the day of the large move. For example, by day 5 the index has risen 0.8% above the index close on the day of the large fall.
As can be seen, in the 20 days following a large fall the index has tended to rise strongly and steadily. In the 5 days following a large market rise the index tends to fall back losing some of its one-day gain, but the index then tends to recover and after 20 days has almost regained the level reached by the very large one-day rise.
Other articles on large one-day returns.
Analysis of the behaviour of the FTSE100 Index for very large one-day falls.
Since 1984 there have been 189 very large one-day falls, where “very large fall” is defined as a move more than two standard deviations beyond the average daily change in the index. In other words, a very large fall is any decrease over -2.19%.
The following chart plots just these very large one-day falls.
The following table shows the ten largest one-day falls in the FTSE 100 Index since 1984.
The following chart shows how on average the index behaves in the days following a very large fall. The Y-axis is the percentage move from the close of the index on the day of the large fall. For example, by day 5 the index has risen 0.8% above the index close on the day of the large fall.
Other articles on large one-day moves.
How do shares prices react after a very large fall or rise in prices on one day? Do prices reverse some or all of the change quickly? Most of the academic papers on large one-day price changes address the issue of whether price reversals do occur and, if they do, the extent and duration of the reversal and in what circumstances they happen.
This article presents a brief review and listing of academic papers on large one-day price moves.
In 1985 De Bondt and Thaler (1985) proposed the overreaction hypothesis, which states that most people overreact to unexpected and dramatic news events. With respect to stocks, this overreaction can cause large one-day changes in share prices, which are then followed by a reversal.
Atkins and Edward A. Dyl (1990) found that after large one-day price changes, especially in the case of declines, the market reversed quickly, but the widening of the bid-ask spread made it difficult to exploit this. A little later Turner and Weigel (1992) found no evidence of short-term market reversals after large one-day price moves. This was followed a couple of years afterwards by the, so far, most cited work on the topic Cox and Peterson (1994), which argued that any observed short-term price reversals were due to changes in the bid-ask spread. They further observed that shares with large falls continue to perform badly beyond the short-term. In other words, the overreaction hypothesis doesn’t hold.
This was largely supported by Park (1995) a year later, who found that price reversals disappeared on the following day if the average of the bid-ask prices was used. After the following day, however, the paper did find systematic abnormal reversal returns. Wong (1997) found that prices tend to rise after large one-day advances and fall after large one-day declines (i.e. no reversals), which supported Cox and Peterson (1994) and not De Bondt and Thaler (1985).
From 2001, some papers started taking a more nuanced view of this by analysing the type of news that had caused the large price move. Pritamania and Singal (2001) found that if the news relates to earnings or analyst recommendations then the 20-day abnormal returns become much larger ranging from 3% to 4% for positive events and about -2.25% for negative events. This trend of analysis was continued by Larson and Jeff Madura (2003), who found that there was overreaction to strong price rises in the absence of news (defined as news appearing in the WSJ), but no overreaction to price rises accompanied by news.
Fehle and Zdorovtsov (2003), cut straight to the chase to analyse whether money could be made in the case of large one-day declines. They found that stocks did overreact in this situation, that the subsequent reversals could be profitably traded and that trading profits were correlated with the size of the fall. Further, following on from the above, they found that the reversals were greater for those stocks with no concurrent associated news. This was consistent with Daniel, Hirshleifer and Subrahmanyam (1998) and Hong and Stein (1999).
Sturm (2003) focused on the asymmetry of reactions: finding that large price decreases are followed by positive returns (i.e. reversal), but large price increases do not drive positive or negative abnormal returns. Ma, Tang and Hasan (2005) found a difference in behaviour between markets with strong evidence of price overreactions for Nasdaq stocks but not NYSE. This was followed by Zawadowskia, Andor and Kertész (2006) who did find significant reversal behaviour but that, while widened bid-ask spread for NYSE stocks eliminated profit potential, this was not the case for Nasdaq stocks where the bid-ask spread was unchanged offering the potential for significant short-term profits.
With respect to the UK market, Mazouz, Joseph and Joulmer (2009) found continuation, rather than reversal, behaviour after large moves. And then Gu (2013) found that the market does usually reverse its direction in the day after the large move.
[Papers listed in reverse date order; ♠ indicates major paper.]
Predictability of Big Day and Profitability Thereafter
Authors [Year]: Anthony Yanxiang Gu 
Journal [Citations]: Journal of Accounting and Finance , 13(5), pp63-73
Abstract: Significantly higher volume in a few day window combined with significantly higher opening may signal a big up day. Negative relationships between return and volume over a three-day window may signal the danger of a big down day. Opening prices of all the big down days are significantly higher than the day’s low and close, and opening prices of all the big up days are significantly lower than the day’s high and close. The market usually reverses its direction in the day after the big day. A strategy is developed for excess returns.
Do large falls in the market tend to happen on certain days of the week?
The following chart shows the frequency distribution by day of the week for the 100 largest daily falls in the FTSE 100 Index over the period 1984-2013.
The following chart looks at the weekday distribution of large falls over a longer period (1969-2013) for the FTSE All-Share Index.
Obviously, the UK market follows the US market, especially for large market moves. So, it is interesting to look at what happens in the US market.
The following chart shows the frequency distribution by day of the week for the 100 largest daily falls in the S&P 500 Index over the period 1950-2013.
Other articles on day of the week anomalies.