Market returns in odd and even weeks

This is a strange one. 

The following chart shows the value of two portfolios:

  • Odd Week Portfolio: this portfolio only invests in the FTSE 100 in odd-numbered weeks, and is in cash for the even-numbered weeks.
  • Even Week Portfolio: this portfolio only invests in the FTSE 100 in even-numbered weeks, and is in cash for the odd-numbered weeks.

The portfolios started investing at the beginning of 2010 with values of 100.

The weeks are numbered according to the ISO 8601 numbering system, whereby the week containing the first Thursday of the year is designated the first week of the year (this is also called the European week numbering system).

Odd v Even Week FTSE 100 Portfolios [2010-2015]

The divergence  in performance in the two portfolios is quite striking. By the end of November 2015 the Odd Week Portfolio would have had a value of 155, and the Even Week Portfolio a value of 74. And, as can be seen, the divergence has increased significantly in the last few months (since August 2015).

It may not be possible to exploit this phenomenon due to trading costs, but it is certainly rather bizarre.

Has this been a long-term phenomenon?

Odd v Even by decade

The following chart shows the FTSE 100 average returns for odd and even weeks for the past few decades. For example, from 1984-1989 the average return in odd weeks was 0.19% and for even weeks 0.41%,

Average FTSE 100 returns in odd and even weeks by decadeAs can seen, there has been no consistent relationship between odd and even week returns. In the decade 2000-2009, even weeks were on average stronger than odd weeks, whereas this decade the relationship has reversed – and, as mentioned above, for the moment the divergence is increasing.

While there is no obvious (or, for the moment, non-obvious) explanation for this weekly phenomenon, such weekly effects have been seen elsewhere – for example, the FOMC Cycle.

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FTSE 100 ratio of up/down days

Is there necessarily a close correlation between the ratio of up/down days in a year and the overall annual return of the FTSE 100 Index?

The following chart plots the ratio of up/down days of the FTSE 100 Index in each year and its annual returns since 1984.

For example, in 1985 (the second set of bars in the chart) there were 253 trading days, of those the Index was up on 136 days (53.7% of total trading days). This percentage figure is normalised by deducting 50% and plotted as 3.7% on the chart. In 1985 the Index increased 15% which is shown in the orange bar to the right.

The final year in the chart, 2015, has been highlighted with a grey box (partly to indicate that there are still a few trading days left in the year at the time of writing).

Ratio of up-down days and annual returns of FTSE 100 Index a

A quick glance indeed shows that positive return years are usually accompanied  by a positive ratio of up/down days. In other words, when the index has risen on more days than it has fallen in a year the index tends to be up overall in the year, and vice versa.

The largest annual return for the FTSE 100 Index (1989) was accompanied by the largest positive up/down ratio (9.3%); while the lowest annual return for the FTSE 100 Index (2008) was accompanied by the lowest up/down ratio (-6.5%). (NB. the Y-axis scale has been truncated in the chart to aid legibility; the annual returns  in these two extreme years were: 1989: +35% and 2008: -31%.)

So far, so unsurprising, but there are some interesting features to note here:

  • In the final run up to the dot-com crash (1995-1999), one can see that while the annual returns were, generally, increasing each year, the up-/down ratio was in fact decreasing. This divergence might have been early indicator of trouble.
  • There is a definite bias for the up/down ratio to be positive (i.e. for the market to be up on more days than it falls), and when the ratio is negative it is quite small (in only two years has the ratio been less than -2%: 2002, 2008).
  • The greatest divergence in any year was in 1991 when the up/down ratio was marginally negative (the Index fell on 127 of the 253 trading days), and yet the Index ended the year up 16%. Oddly, the previous year, 1990, the up/down ratio had been identical, but the Index ended the year down 12%.
  • The up/down ratio and annual returns for the FTSE 100 have only diverged (i.e. had opposite signs) in five years: a run of three years 1991-1993, then 2014 and, so far, 2015.
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Weekly market returns and volatility

Previously we’ve looked at the daily volatility of the FTSE 100 Index (here and here), in this article we will look at the average weekly returns and volatility of the Index.

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.

Weekly mean returns of the FTSE 100 Index by decade

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.)

Standard deviation of rolling 10-week returns of the FTSE 100 Index [1984-2015]

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.

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FTSE 100 and FTSE 250 Quarterly Review – December 2015

After the close on 2 December 2015 FTSE Russell confirmed the following changes to the FTSE 100 and FTSE 250 indices. The changes will be implemented at the close Friday, 18 December 2015 and take effect from the start of trading on Monday, 21 December 2015.

FTSE 100

Joining: DCC, Provident Financial, Worldpay Group

Leaving: G4S, Meggitt, Morrison (Wm) Supermarkets

FTSE 250

Joining: Assura, Hastings Group Holdings, Ibstock, Renewables Infrastructure Group

Leaving: Foxtons Group, Hunting, Kaz Minerals, Petra Diamonds, Premier Oil

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Does the Santa Rally exist?

The Santa Rally holds that the market is strong at the end of the year (around Christmas). Is this true?

The market is strong in December

The following chart shows the average returns of the FTSE 100 Index for each of the 12 months for the period 1980-2014.

Santa Rally [2015] 01

Over this period the average return of the FTSE 100 Index in December has been 2.0% (the second strongest average month return after April).

OK, so the average return in December is high, but is this attributable to just a few strong years?

To answer this, the following chart plots the proportion of December month returns that were positive over the same period (1980-2015).

Santa Rally [2015] 02

By this measure, December  is the strongest month in the year for the FTSE 100. In the 35 years since 1980, the Index has risen in 28 years (80%).

The market strength in December can be seen in more detail in the following chart, which plots the actual return of of the FTSE 100 for each December since 1980.

Santa Rally [2015] 03

The Index has only fallen significantly in December in four years since 1980. Until last year (2014), the Index had been on an 11-year winning streak.

When does the Santa Rally start?

So, December is strong for the FTSE 100. But is it possible to determine more precisely when the Santa Rally starts?

The following chart plots the cumulative average daily return of the Index throughout the year (more information about this chart).

Santa Rally [2015] 04

On average the UK market is strong from the start of November (this is a feature of the Sell in May effect). But we can also see an acceleration of the market at the very end of the year. To analyse this further the following chart plots the cumulative average daily return of the Index for December (i.e. the same chart as the above, but zoomed in on December).

Santa Rally [2015] 05

From this we can see that, on average, the market is flat for the first 10 trading days of December, after which it rises strongly. So, we can say that the Santa Rally starts on the 10th trading day of December.

How has this played out in recent years?

The following chart plots the FTSE 100 Index for the last two months of each year for the ten years since 2005. (The index values have been re-based to all start at 100.) The shaded area to the right indicates the final two weeks of the year.

Santa Rally [2015] 06

Yes, it’s something of a mess. So perhaps we can’t draw any strong conclusions. However, one can observe a slight tendency in most years for the market to rise in the final fortnight.

What is the cause of the Santa Rally?

Short answer: we don’t know?

There is no definitive explanation for this effect. Although various reasons have been proposed, including: fund managers window dressing their portfolios, positive sentiment in the market caused by the festive season which is accentuated by low trading volumes, anticipation of the January Effect, and tax reasons (NB. “tax reasons” are often cited in the absence of any definitive explanation).

Conclusion

  1. The UK stock market does tend to be strong in December (although it wasn’t in 2014).
  2. Stocks accelerate upwards from the tenth trading of December (which in 2015 will be 14th December). It is this last hurrah of the market – in the final fortnight – that can be called the Santa Rally.
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Volatility of daily market returns through year

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.

Average volatility of daily returns of FTSE 100 Index through year [1984-2014]

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.

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Average market behaviour in July (2015)

The following chart plots the average performance of the FTSE 100 Index during July since 1984.

Average month chart - July (2015)

As can be seen, historically the market tends to rise for the first week, is flat for the following two weeks, falls in the fourth week, but then ends strongly in the final few days.

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FTSE 100 and FTSE 250 Quarterly Review – June 2015

After the close on 3 June 2015 FTSE Russell confirmed the following changes to the FTSE 100 and FTSE 250 indices. The changes will be implemented at the close Friday, 19 June 2015 and take effect from the start of trading on Monday, 22 June 2015.

FTSE 100

Joining: Inmarsat

Leaving: Aggreko

FTSE 250

Joining: Aldermore Group, Auto Trader Group, B&M European Value Retail, John Laing Group, Onesavings Bank, Shawbrook Group, Wizz Air Holdings, Woodford Patient Capital

Leaving: BlackRock World Mining Trust, De La Rue, Imagination Technologies Group, Infinis Energy, Law Debenture Corp, Personal Assets Trust, RPS Group, Soco International

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First trading day of June

Next Monday will be the first trading day (FTD) of June.

Since 1984 the FTSE 100 Index has on average risen 0.21% on the June FTD, with the month’s return being positive in 55% of years.

The following chart shows the returns for every June FTD since 1984.

First trading day of June (1984-2014)

 

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Last trading day of May

Tomorrow will be the last trading day (LTD) of May.

Since 1984 the market has on average risen 0.02% on the LTD of May, with positive returns in just 48% of all years, which makes it one of the weaker month LTDs in the year.

The following chart shows the FTSE 100 Index returns for every May LTD since 1984.

Last trading day of May (1984-2014)

 

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