The financial markets’ obsession with round numbers is one of the few irregularities which are consistently valid over time, across time horizons and across asset classes. It can be observed not only in the media headlines, but also in the actual market data.
With yesterday’s S&P500 closing above 2000 for the first time in history, one thing that might have caught your attention is the very pretty closing value of 2000.02. The .02 is just a coincidence. The fact that the first close above 2000 also happens to be so close to the round number level is less so.
Below you can find some simple historical data, showing the days when S&P500 closed above round hundreds for the first time and the days when the Dow Jones Industrial Average closed above round thousands for the first time.
- px_close_prev = index closing value the day before
- px_close = index closing value on the day it first closed above the round number
- above 100 / above 1000 = how many % above the round number level it closed on that day, as % of the previous day closing value
- day_perf = day close to close performance, as % of the previous day closing value
- px_close_next = index closing value the next day
- next_day_perf = next day close to close performance, as % of the current day closing value
Those occurrences when the first close was very close to the round number level are highlighted (green <0.1%; yellow <0.2%) and you can see that they have been quite frequent – just by looking at the values, without calculating any high statistics, it is evident that they are more frequent then they are supposed to be in the world of random.
On just one occasion on S&P500 (the 400 level in 1991) and none on the Dow did the indices close over 1% above the round number level on the first day (remember this when the Dow gets to
18000 19000 next month).
The median for the Dow is 0.17% and for S&P500 it is 0.31%. Furthermore, there have been 4/20 occurrences below 0.05% on S&P500.
One can also argue that not all these round numbers are of equal significance, with e.g. 500, 1000, 1500, 2000 S&P500 and 5000, 10000, 15000 DJIA being the “big ones”.
Of course, much further research can be done in this direction. You can look at the price action before (how the indices behave when approaching a big round number) and after (for example, if the round number level can be used as a subsequent support). When doing proper analysis, the changing historical volatility and/or range should also be taken into consideration. These things are beyond the scope of this quick observation.
Holding VIX futures and options past the close of the last trading day and waiting for the final settlement value to determine your profit or loss is widely considered a gamble. It is impossible to predict how the VIX will change from close to next day open, let alone what the final settlement value will be (and I leave the speculations about if and how much it is manipulated to others).
But trading is about statistics and probabilities and there have already been more than a hundred VIX expirations. In this post, which originated as a follow-up to my earlier tweet, I look at historical statistics of the differences between VIX options and futures final settlement values and spot VIX index closing values on the last days before expiration.
Let’s start with an overview of the last two years. For each VIX expiration you can see the spot VIX index close on Monday (the day before the last trading day), the spot VIX index close on Tuesday (the last trading day), and the final settlement value, as well as the changes from Monday to Tuesday and from Tuesday to final settlement value.
A few observations:
- Majority of changes (both Mon-Tue and Tue-Wed) have been quite small (roughly 3/4 changes smaller than 1 VIX point).
- The changes have been both positive and negative, with no apparent bias to either side (just by looking at the table).
- The most interesting observation: In 5 out of the last 11 VIX expirations the change from Tuesday VIX close to the final settlement value was greater than 1 VIX point.
Let’s look at the whole history of VIX expirations and the summary statistics. I have only included VIX expirations when the final settlement was on Wednesday and the Monday and Tuesday before that were not holidays (as on some past January and February expirations).
There have been 100 such expirations so far (out of 110 total).
Let’s focus mainly on the changes from Tuesday to the final settlement value, which are more interesting for this analysis. Mean and median are not far from zero. The changes are positively skewed and there is very high kurtosis (fat tails). However, most of it can be attributed to one outlier: +9.93 in October 2008 (change from 53 to 63). Without that month in the sample, the skewness and kurtosis would be +0.27 and +0.30, respectively, and the distribution would get quite close to normal.
Which brings us to the idea that maybe we should work with percentage changes rather than VIX point changes. The table is below.
Alternatively, we can eliminate the periods of high VIX from the sample, as there are good reasons for expecting the VIX to behave differently in times of low volatility and in times of high volatility. If we only include the expirations when Monday spot VIX close was below 20, we are left with 62 observations which are perhaps more relevant to the current situation in the markets.
In low volatility times, the skewness and kurtosis are negative, but so small that the distribution can be considered normal. Mean is -0.14 and standard deviation is 0.79 VIX points. Also note the maximum (+1.51) and minimum (-1.89) – no far extremes here.
For the sake of completeness, below you can see the table for percentage changes in VIX<20 times. As expected, the findings are in line with the above.
The most important observations for the low volatility sample are the following:
- Slightly negative mean/median. Final settlement value is slightly more likely to be lower than higher than Tuesday close.
- The distribution is almost normal.
- There haven’t been any outliers much farther than 2 standard deviations from the mean (+2.08 and -2.21 sigma to be precise). This is best visible in the frequency histogram below.
For comparison, here is also the frequency histogram for the all VIX values sample. You can see that except the one huge outlier (not shown in the chart) it is only moderately positively skewed.
The last number, and maybe the most interesting number in the whole post, is the correlation between the Mon-Tue and Tue-Wed point changes. It is -0.01 for all the 100 expirations, but -0.30 for the 62 expirations when VIX closed below 20 on Monday. In other words, in periods of low volatility, when VIX has risen on Tuesday, the final settlement value is slightly more likely to be lower than Tuesday VIX close. But of course, a correlation of -0.30 on a sample of 62 is not a good basis for strong conclusions (furthermore, if we remove April 2013 from the sample, with the changes of -3.31 and +1.50, the correlation becomes -0.21).
With the markets at all-time highs and less than 1/5 of trading days left in 2013, it’s time to look at historical statistics again and see if there is any guidance for the rest of the year. In May, at the height of the “Sell in May and go away” discussion, I published my piece of analysis on that. Let’s now look at a similar “Sell in October and go away” strategy. As usual, we’ll leave the speculations and reasons to other analysts and focus only on hard data.
Average Performance Jan-Oct vs. Oct-Dec
Let’s first look at average performance of the Dow Jones and S&P500 from the beginning of the year to 22 October vs. from 22 October to year end.
We should of course take into account that the period from January to 22 October is more than 4x longer than from 22 October to year end and compare annualized performance.
The year end has shown 2x (median) to 3x (average) higher returns than the period from the beginning of the year to October. Not surprisingly, the results are very similar for the two indices when comparing the same time period (DJIA has much longer history than S&P500).
Worst Year Ends
One figure that deviates from the others is the average year end performance of the Dow when looking at the whole history since 1897. This can be attributed mostly to the Great Depression years (1929, 1930, 1931 all in top 6), but there were other ugly years a hundred years ago. Note that there is only one post-WWII year among the worst 11, which is 1973 (and 1974 is rank 12). The 23 years listed below are the only years when DJIA performance from 22 October to year end was worse than -2%. The worst year end in the last 35 years has been 2007 with -2.23%.
Best Year Ends
Below you can see the 23 best year ends (with consistency being the only reason to choose 23, besides the fact that 23 is exactly 20% of the total number of years 1897-2012).
Double digit positive year end returns were about twice as frequent as double digit negative returns.
Most of the very best years again occurred near the beginning of the previous century, but 3 out of the last 20 years – 1999, 2003, and 2004 – are also represented in the top 23. Fair share would be 5-6, but note that other 6 out of the last 20 years are between rank 24 and 34 – 1995, 1996, 1998, 2000, 2001, 2006. If you are familiar with the history of the stock market and the economy, all these figures make perfect sense.
How Good Years End
For an investor it is much more important to look whether the good year-to-date performance that we have seen this year has any significance for predicting the year end performance. For this we will look at S&P500 data rather than the Dow, as one of the characterstics of 2013 has been a wide performance gap between the two indices (23.03% vs. 18.04%). By 22 October, year 2013 ranks 6th in S&P500 history.
The picture for performance going forward is very similar to what we saw in May. In the years with very strong positive performance until 22 October, it is very likely that the market will keep growing into the year end, although the returns have been in low single digits in most years. There have been five negative year ends among the top 23 years (top 22 without 2013), but none of them worse than -2.09% (1988). Also note that the market was very close to its all-time highs in most of the top years (the third column with mostly red numbers shows 22 October closing value compared to all-time closing high).
Nevertheless, year end performance has been almost as good in other years and YTD performance in October has not been significant for predicting year end return. Average non-annualized S&P500 return from 22 October to year end has been 3.19% for all years and 3.77% in the 22 years with strongest YTD performance. Below you can see the scatter plot.
Another thing that comes to mind when looking at the scatter plot is that big changes (over 5% or under -5%) have been much more frequent on the positive side than on the negative side at year end.
The last chart below shows how much a 100 dollar investment would be worth after 10 years if you stayed invested the whole time (blue line) vs. got out of the market on 22 October and back in at year end (green line). There was no 10-year period when the “Sell in October” strategy outperformed buy and hold.
- It is generally better to stay long the market from 22 October to year end, as this part of year has historically been stronger than the rest.
- YTD performance does not have much predictive power for year end performance.
But of course, the sample is small and this year can be different.
Yesterday the VIX index closed at 17.67, highest since the end of June. This is the 5th major VIX spike YTD. 4 out of the 5 spikes (June being the exception) have had intraday highs within 1.5 VIX points range (17.80 – 19.27) and closing highs within 2 VIX points range (17.01 – 18.99).
In the big June VIX spike you can actually identify three “subspikes” and the first two of them also had their intraday and closing highs within this range, like if there was a resistance in the VIX at these levels. The VIX only broke out of the range 1-2 weeks later and only stayed there for 3 sessions before sharply falling to 12 in July.
You can also find a similar zone at the bottom of 2013 VIX range. It is much narrower (which makes complete sense) and it has also been violated on one occasion in March.
These thoughts of course have little meaning for predicting the future. They just came to my mind when I saw the VIX chart. It is certainly possible that today or the next week the VIX will break out to new highs.
Nevertheless, so far in 2013 a winning strategy would have been to go long volatility when VIX reaches the lower zone and short volatility when it reaches the upper zone. While it sometimes stayed in the 12’s or 13’s for longer time (and staying long VIX of course costs money with passing time, especially when it’s in the 12’s), shorting the spikes would have brought you fast profits (but keep in mind that buying VIX puts is much safer than shorting VIX futures). Alternatively, VIX spikes would have been good signals for going long stocks.
Rather than observing these exact zones, which will certainly become invalid sooner or later, treat the chart as a reminder that volatility and the VIX are mean reverting and it does generally pay to fade extremes.
The markets seem to have recovered from the latest correction, at least for now. S&P500 has not exceeded its early August and all-time high (1709.67), but it is now within 1% (and Monday close was the 4th highest in S&P500 history). The big technical picture is still a long-term uptrend, as the end August low was much higher than the previous one. To confirm the uptrend we would certainly like to see the all-time high improved soon.
Spot VIX Index
The spot VIX index has been in the 14’s, so from a purely mean reverting perspective there is no particular trading opportunity on either side – it can go anywhere (as usual). The tapering story has probably limited spike potential now, save for any surprisingly hawkish rhetorics by Fed officials. Number one risk factor is the geopolitical situation (Syria), but of course the greatest VIX spikes arise from the least expected factors.
In line with the spot, VIX futures have lost a lot from the end August peak. The most important feature of this move has been the lack of steepening, as the futures curve has made an almost parallel downward shift of 1.60-2.80 points (if you ignore the nearest month, the range of the changes is only 1.60-2.60). Volatility expectations for the rest of the year and for spring 2014 have gone down significantly.
Traded volume in VIX futures has stayed off the highs in the recent weeks, although it has recovered from the summer lows. At this time last year the volume was making new historic highs. Not this year, but y/y increase from 2012 remains somewhere around 50-70%.
The VVIX index, which measures implied volatility of VIX options in the same way as the VIX measures implied volatility of S&P500 options, is around 80, roughly the middle of last two months range, like the VIX itself.