U.S. Tax Day

Tax Day in the United States refers to the day by which individuals must submit income tax returns to the federal government.

In the past Tax Day has moved around a bit, but since 1955 it has been fixed at 15 April. Although there are exceptions due to the close proximity of the Emancipation Day holiday in Washington State D.C. Such that since 2007 when 15 April falls on a Friday then Tax Day is moved to the following Monday, and when 15 April falls on a weekend Tax Day is moved to the following Tuesday.

This year, 2017, 15 April is a Saturday and so Tax Day will be Tuesday, 18 April.

It is probably not too controversial  a claim that most people dislike filling in forms and paying taxes. Could this dislike affect individual investors attitude to risk around the time of Tax Day and. if so. could that in aggregate be sufficient to influence equity returns around this period?

Let’s see…

The following chart plots the proportion of weeks that saw positive returns in the S&P 500 Index for the two weeks before Tax Day and for the one week following Tax Day for all years since 1955. For example, the S&P 500 had positive returns in the week two weeks before Tax Day in 69% of years since 1955.

S&P 500 in weeks around Tax Day [1955-2016] - Positive week returns

As can be seen, over the three-week period there was a moderate decline in the proportion of positive weekly returns.

The following chart looks at the same period and weekly frequency, but plots the average weekly returns.

S&P 500 in weeks around Tax Day [1955-2016] - Average week return

Here we can see relatively high returns two weeks before Tax Day, although this overlaps with the start of April which is usually a strong period for equities anyway. The week leading up to Tax Day is relatively weak, and then there’s something of a small relief(?) rally in the week following Tax Day.

Let’s now focus in on the days around Tax Day.

The following chart plots the proportion of days that saw positive returns in the five days around Tax Day. For example, since 1955 the S&P 500 Index has seen positive returns on Tax Day itself (TD(0D)) in 67% of years.

S&P 500 in days around Tax Day [1955-2016] - Positive day returns

Historically we can see that returns have been depressed leading up to Tax Day, with the strongest returns in the 5-day period seen on Tax Day itself.

The following chart looks at the same period and daily frequency, but plots the average daily returns.

S&P 500 in days around Tax Day [1955-2016] - Average day return

The same behaviour profile can be seen as in the previous chart. The weakest average daily returns in the period have been seen on the trading day two days before Tax Day. While the strongest average daily returns have been on Tax Day itself (with an average daily return ten times the average daily return for all days since 1955).


The results here are not strong, but there is some evidence that equities are relatively weak in the days immediately before Tax Day, but the market is strong on Tax Day itself.

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United States presidential inauguration day

The United States presidential inauguration day used to be on 4th March, but in 1937 the Twentieth Amendment changed the date of inauguration day to 20 January. If that day is a Sunday, inauguration day is moved to 21 January.

Has this day had any significant effect on the stock market?

Let’s see.

The following chart plots the daily returns for the S&P 500 Index for inauguration day (ID) in the years from 1953 to 2009. Note: the chart only includes inauguration days for first terms (on the grounds that the market most likely knows what to expect with second-term presidents).

US president inauguration days (first term) [1953-2009] 1

As can be seen shares have been weak on inauguration days. Since the 1963 inauguration of Lyndon B. Johnson the S&P 500 has been down on every inauguration day.

The following chart plots the average daily returns for the S&P 500 Index for the trading day before inauguration day, the day itself and the day after.

US president inauguration days (first term) [1953-2009] 3

Since 1953 the average daily return for the S&P 500 on inauguration day has been -1.1%. For the day after ID the average daily return is 0.7%, so there does seem to be a partial relief rally afterwards.

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A very average start to 2017

The following chart plots the daily returns of the FTSE 100 Index for the nine days around Christmas and New Year.

The blue bars plot the average daily returns of these days for the period 2000-2016. The orange bars plot the daily returns for the last nine days.

FTSE 100 Index daily returns around Christmas and New Year [2017]

As can be seen the actual daily returns for the last nine days have been on the whole pretty close to the average daily returns seen for the last 16 years..

  • Strong returns have been seen on the trading days following Christmas and New Year.
  • After the first day after New year, returns have trailed off (days 8 and 9 in the chart).
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Tuesday reverses Monday

Do market returns on Tuesdays reverse those on Monday?

We first looked at this in 2013 (in this article), so time to see if anything has changed.

First, the following updates the chart to 2016 plotting Tuesday returns for the FTSE 100 Index split by whether the previous day’s returns were positive or negative. Two time periods are considered: 1984-2016 and 2000-2016.

For example, for the longer period, the average return on Tuesday when Monday was up is 0.02%, while the average Tuesday return when Monday was down is 0.09%.

FTSE 100 returns on Tuesdays when Monday was up-down

While the figures have marginally changed from the previous study in 2013, the overall finding is the same: namely that the theory that Tuesday reverses Monday does not seem to hold. Since 1984 it has done so when Monday returns have been negative, but not when they have been positive. 

As in the 2013 study, the theory has been valid for the market since 2000.

The previous study suggested that further analysis might include a filter on the size of the Monday returns. This is done in the following chart, where Tuesday returns are only considered if Monday’s returns were beyond a certain threshold (i.e. of a certain size). The (arbitrary) threshold chosen was 1 standard deviation for Monday’s returns.

FTSE 100 returns on Tuesdays when Monday was up-down (1SD filter)

It can be seen that limiting the analysis of Tuesday returns to just large movements on Monday (i.e. beyond 1 standard deviation) does help the reversal theory. In this case, if the market rises on Monday, then on average it falls the following day (albeit a pretty small average fall), and if the market falls on Monday, the market rises (fairly strongly) on the Tuesday.

Let’s now look at how the theory has been holding up in recent years.

Recent years

The following chart is similar in design to the previous charts, but this time it plots the reversal results for the discrete years 2013 – 2016.

FTSE 100 returns on Tuesdays when Monday was up-down [2013-2016]

First, when the market is up on Monday, all four of the past four years has failed to support the reversal theory as Tuesday has followed with positive returns as well. When Mondays are down, in three of the past four years Tuesdays have seen positive average returns (the exception being 2015).

Exploiting the reversal effect

OK, so how to exploit this?

The following chart plots the cumulative value of a portfolio that invests in the FTSE 100 just on Tuesdays when the previous day saw negative returns. For the rest of the time it is in cash.

In the 2013 study a variant portfolio was also considered, that as well as going long Tuesdays following negative Mondays also went short Tuesdays following positive return Mondays. There’s currently not much point in considering this as the reversal effect is not working for positive Mondays.

So, instead the variant second strategy studied here is as above (i.e. long Tuesday following a negative Monday) but with a 1 standard deviation filter applied to the Monday return (i.e. the strategy only goes long on Tuesday if the Monday negative return is a greater than 1 standard deviation return).

Strategies exploiting the Tuesday reversal effect [2000-2016]

Since 2000 it can be seen that the simple long Tuesday strategy out-performs the benchmark buy-and-hold FTSE 100 portfolio. The variant 1SD strategy only marginally out-performs the simple long Tuesday strategy, but does so with with a greatly reduced volatility.


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Day of the week grid

We have previously looked at data to see if there are any discernible patterns in market returns by day of the week. The following table presents another way of studying this.

The table shows the daily returns of the FTSE 100 Index for every day so far in 2016 (up to last Friday, 28 Oct). Positive returns are highlighted in green, negative returns in red. (White cells indicate a market holiday.)

Day of the week grid [2016 wk43]


  1. So far in 2016 the longest run of positive (or negative) returns for a day started in the 10th week of the year when day returns for eight consecutive Wednesdays were positive.
  2. For 11 weeks, the day returns on Fridays were the opposite sign to that on the previous day (Thursday). This run ended last Friday (when both Thursday and Friday saw positive returns).

Other articles looking at returns on days of the week.

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Last trading day of October

Next Monday will be the last trading day (LTD) of October.

Historically, the last trading day of October has been the strongest LTD of any month in the year. Since 1984 the market has on average risen 0.46% on the LTD of October, with positive returns in 69% of all years.

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

FTSE 100 last trading day of October [1984-2015]

As can be seen on the chart the market only fell twice on the October LTD in the 19 years from 1984 to 2002. One possible reason for this may have been that November is the start of the strong six month period of the year (this is part of the Sell in May effect), and investors could have been buying equities at this time in anticipation of that.

However, in recent years this pattern of behaviour has changed. Quite dramatically so – in the last seven years the market has only risen once on the October LTD. Last year (2015) the FTSE 100 Index was down 0.5% on the last trading day of October.

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High, Low, Close

Analysis of the daily close  of the FTSE 100 Index and the day’s high and low. 

The following table shows the frequency with which the FTSE 100 closes within a certain percentage of the high (or low) of the day. For example, since 1985 the FTSE 100 Index has closed within 10% of its daily high 20.8% of all days, and it has closed within 1% of its low 5.6% of all days.

  10% 5% 1%
Top (%) 20.8 15.1 9.8
Bottom (%) 14.5 9.6 5.6

It’s interesting to note that for one in 10 days the index closes within 1% of its high for the day.

The following day

Continuing this analysis of where the index closes relative to the Hi-Lo range of the day, the following table shows the performance of the FTSE 100 Index on the following day.

For example, on the days when the index closes within 10% of its low for the day on average the index return is -0.005% the following day; and when the index closes within 1% of its high for the day on average the index return is 0.167% the following day.

  10% 5% 1%
Top (%) 0.111 0.132 0.167
Bottom (%) -0.005 0.001 0.013


The above is an extract from the Harriman Stock Market Almanac 2017.

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Sell Rosh Hashanah, Buy Yom Kippur

In 1935, the Pennsylvania Mirror referred to a Wall Street adage, “Sell before Rosh Hashanah; buy before Yom Kippur”. Recently an academic paper quoted this article and set out to establish if the adage was true and still valid today.

The theory is that the market is weak during the approximately seven trading-days gap between the Jewish New Year (Rosh Hashanah ) and the Day of Atonement (Yom Kippur). To test this theory the authors studied the results of short-selling the Dow Jones Industrial Average on one of the three days before Rosh Hashanah and buying back on one of the three days following Yom Kippur. They analysed the nine different combinations of trade dates, i.e. selling on the third day before Rosh Hashanah (R-3) and buying back on the day after Yom Kippur (Y+1), R-3 and Y+2, R-3 and Y+3, R-2 and Y+1 etc. The period tested was 1907 to 2008.

The paper found that the mean returns for the DJIA for the nine trade dates considered ranged from -0.47% for R-3 and Y+2 (i.e. shorting three days before Rosh Hashanah and covering two days after Yom Kippur) , to -1.01 for R-2 and Y+1.

In other words, they found that the market had indeed been weak between the two Jewish holidays, and that five of the nine scenarios yielded statistically significant results. They checked to see if this Jewish Holiday Effect might have diminished in recent years and found that the effect over 1998-2008 was actually stronger for six of the nine trade scenarios than for the prior period 1907-1998.

So, what’s the reason for this?

The authors of the paper found that this was not a result of the influence of other anomalies (e.g. the weekend effect), nor was it the result of data outliers. One Wall Street trader gave the traditional explanation that people of the Jewish religion “wished to be free (as much as possible) of the distraction of worldly goods during a period of reflection and self-appraisal.” Of course Jewish traders are only a small part of the market, but at the margin their withdrawal from the market over this period may increase volatility and risk and thus discourage others from trading, and then the arbitrage traders exploiting the effect can make it self-fulfilling.

Is this a peculiarity of just the US market, or is the effect present in other markets?

The above cited paper starts by quoting a 9 September 1915 New York Times article titled “The London Market Quiet – Jewish Holiday Causes Small Attendance on the Exchange”, the newspaper reported that money and discount rates on the London Stock Exchange were “easy today” and attendance at the exchange was low due to the Jewish holiday of Rosh Hashanah.

So, might this effect still be in force in the London market today?

The following chart shows the mean returns for the FTSE 100 Index for the nine combinations of trade dates (as above) for the period 1984-2013.

Average FTSE 100 returns for period between Rosh Hashanah and Yom Kippur [1984-2015]

As can be seen, the market was weak for all nine combinations of trade dates over the Rosh Hashanah to Yom Kippur period. The weakest combination was for selling on the third day before Rosh Hashanah and buying back on the second day after Yom Kippur (T2) when the mean return has been -1.3%.

The Jewish Holiday Effect would therefore seem to be as strong in the London market as that in New York.

The above is an extract from the Harriman Stock Market Almanac 2017.


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FTSE 100 around FOMC announcements

The Federal Open Market Committee (FOMC) is the monetary policy-making body of the U.S. Federal Reserve System. Since 1981 the FOMC has had eight scheduled meetings per year, the timing of which is quite irregular, The schedule of meetings for a particular year is announced ahead of time [calendar here].

Starting in 1994, the FOMC began to issue a policy statement (“FOMC statement”) after the meetings that summarised the Committee’s economic outlook and the policy decision at that meeting. The FOMC statements are released around 14h15 Eastern Time.

Before 1994 monetary policy decisions were not announced; investors therefore had to guess policy actions from the size and type of open market operations in the days following each meeting. But since 1994 there has been far greater transparency over both the timing and the motivation for monetary policy actions.

This has led to a number of academic papers investigating the influence of these FOMC statements on financial markets. One such paper[1] found large average excess returns on U.S. equities in the 24-hour period immediately before the announcements (an effect the paper called the “Pre-FOMC Announcement Drift”). In other words, equities tended to be strong just before the FOMC statement. Further, these excess returns have increased over time and they account for sizable fractions of total annual realized stock returns. Quantifying this the paper says,

[since 1994] the S&P500 index has on average increased 49 basis points in the 24 hours before scheduled FOMC announcements. These returns do not revert in subsequent trading days and are orders of magnitude larger than those outside the 24-hour pre-FOMC window. As a result, about 80% of annual realized excess stock returns since 1994 are accounted for by the pre-FOMC announcement drift

A quite extraordinary finding!

And the relevance to UK equities is…?

The above quoted paper also found that such pre-FOMC excess returns occurred also in major international equity indices.

Let’s see if that is the case.

The following chart shows the average daily returns for the FTSE 100 Index for the seven days around the FOMC statements for the period 1994-2014. The seven days cover the three days leading up to the statement, the day of the statement itself A(0), and the then the three days after the statement. Given that the FOMC statement is usually released around 18h15 GMT (i.e. after the UK market has closed), A(0) can be taken as occurring in the 24 hours before the statement.

FTSE 100 around FOMC announcements

The result is quite clear, the average daily return for A(0) is 0.33%, over ten times greater than the average daily return on all other days. This does support the claim in the above referenced paper. It might also be interesting to note the weakness in equities on the day prior to the FOMC statement.

[1] David O. Lucca, Emanuel Moench, “The Pre-FOMC Announcement Drift” (2013)

Further articles on the Fed Rate and FOMC announcements.

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Do European stocks follow the US on a daily basis?

Do European stocks follow the lead of the US market from the previous day? In other words if, say, the US market is down one day are European stocks more likely to fall in their trading session the following day?

To test this the following chart plots the daily returns of the S&P 500 Index against the corresponding daily return of the EuroSTOXX 50 Index for the following day.

Europe v US stocks_EuroSTOXX 50 v S&P 500 (n-1) [2000-2016]

There is a positive correlation here, but as can be easily seen it is a very weak correlation. And this observation is supported by the very low R2 of 0.05.

So the immediate answer to the question of whether European stocks follow the US is: only very slightly.

However, the following chart is interesting. This next chart plots the daily returns for the two indices as above, but this time it is the daily returns for the same day. In other words, this time the US market movements come after those in Europe.

Europe v US stocks_EuroSTOXX 50 v S&P 500 [2000-2016]

As can be seen, here the correlation is higher than in the above first case. The R2 = 0.3; which while not statistically very significant is quite a bit higher than in the first case.

So, this might suggest that it is the US market that follows Europe.

Is this the case?

Probably not. Rather it is likely to be a feature of the trading hours of the respective markets. The illustration below shows the trading hours for five exchanges.

NB. Strictly, UK and Swiss stocks are not in the EuroSTOXX 50 Index but the exchanges are included here for reference.

Europe v US stocks_exchange hours

The times referenced here are UTC – which are accurate at the time of writing (in May), but will be shifted one hour when countries switch to Daylight Savings Time. However, for the purposes of the discussion here the times are fine, because what we are interested in is the overlap of trading hours at the end of trading in Europe and the beginning of trading in New York each day.

As can be seen, each day there is an overlap of a couple of hours between the Paris and New York exchanges, and longer for Frankfurt and New York. Each day European markets can be active at their open in the morning (reacting to overnight developments – including US stock movements), then often these markets can tread water for a while waiting for the US market to open in the afternoon. The European markets can then take their lead from the US for the rest of their trading day.

The higher correlation seen in the second chart above is therefore probably reflecting this overlap period when European stocks are influenced by what is happening in the US that same day.

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