Three seasonal anomalies

The short answer is no. Before February this year, the previous time the market had alternated the sign of weekly returns for six consecutive weeks had been in 2015. It’s a pattern that occurs roughly once a year.

However, while extended runs of alternating week returns may be fairly rare, there is an odd characteristic of week returns. The chart below shows the value of two portfolios, defined as follows:

1. Odd Week Portfolio: this portfolio only invests in the FTSE 100 in odd-numbered weeks, and is in cash for the even-numbered weeks.
2. 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 choice of week numbering system (ie, which week is defined as the first week of the year) is arbitrary, but the system used here is 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).

The divergence in performance in the two portfolios is quite striking. Having started with values of 100 in 2010, by November 2017 the Odd Week Portfolio would have had a value of 187, compared with a value of 75 for the Even Week Portfolio. The change in value of the Even Week Portfolio has changed little from 2015, whereas the Odd Week Portfolio has grown strongly recently.

While there is no immediately obvious explanation for this weekly phenomenon, such weekly effects have been seen elsewhere – for example, the Federal Open Market Committee (FOMC) cycle.

According to a 2016 paper[1] a strategy that bought the S&P 500 in the even weeks after FOMC announcements and sold in the odd weeks, would have seen a 650 per cent return since 1994, against a market return of 505 per cent for the period. The opposite strategy (ie, buying in odd weeks) would have had negative returns. And this effect is not limited to the US market, a similar return profile related to the FOMC cycle can be found in developed and emerging markets.

Returning to the odd/even week anomaly in the UK market, does this offer an easy way to make money (ie, simply hold the market in odd-numbered weeks)?

Unfortunately, not necessarily. The above analysis did not factor in the transaction costs (eg, commission, bid-offer spread) of implementing such a strategy. This is rectified in the next chart, which plots the Odd Week portfolio including transaction costs this time against the FTSE 100 Index.

As can be seen, the performance of the Odd Week portfolio is dramatically affected by the inclusion of transaction costs, such that it now significantly underperforms the Index.

Shame, that was looking good for a while!

The difference between statistical and economic significance

Coming across a market anomaly can be exciting, ­with the prospect of low-risk profits. However, the above is a good example of why it is important to understand the difference between an anomaly being statistically significant and one that is economically significant.

An anomaly is a distortion in a financial market that would appear to contradict the Efficient Market Hypothesis. A statistically significant anomaly is one that has passed various statistical tests that indicate the results are probably not due to chance. And an economically significant anomaly is one that can be profitably exploited. In other words, just because an anomaly is statistically significant doesn’t mean you can make money from it.

The issue here is transaction costs, which includes commission costs, the bid-offer spread, and market impact cost. The latter is often particularly important in the case of anomalies. Strategies that seek to exploit anomalies need to be executed in a minimum size to be economically interesting, but sometimes the trade size can be large enough to move the market thereby reducing – and in some cases eliminating – the price anomaly.

So, a big question in this field is whether anomalies exist after taking into account transaction costs. And this question attracts fierce debate. An academic paper will be published with results that show almost no anomalies survive transaction costs (ie, very few anomalies can be profitably exploited). In reply, papers will appear that criticise the first paper’s assumptions and calculations, arguing that certain anomalies (eg, that of momentum) easily survive transaction costs.

There is no easy answer here. But it can be said that, to a certain extent, transaction costs differ between market participants, so each trader needs to carry out their own assessment of the impact of their transaction costs.

Therefore, because of transaction costs, certain observed day and week anomalies will be difficult to exploit. So, let’s look at a longer time frequency.

Turn of the month effect

A recent academic paper[2] makes the rather remarkable claim that “since July 1926, one could have held the US value-weighted stock index (CRSP) for only seven days a month and pocketed the entire market excess return with nearly 50 per cent lower volatility compared with a buy-and-hold strategy”. These seven days straddle the turn of the month.

What might cause this behaviour?

The paper argues that it is the month end liquidity needs of US institutions, pension funds, mutual funds, any that have month-end distributions. For example, the following chart taken from the paper shows the proportion of US pension payment dates around the turn of the month (day T denotes the last trading day of the month). And because settlement in the US is T+3, institutions have to sell at least three days in advance to ensure they have the necessary liquidity for the end of the month. Then, at the beginning of the month, institutions look to invest recently received dividends which puts demand pressure on stocks over the first few days. (And, yes, some pension funds are now changing their distribution dates to get out of synchronisation with their peers!)

Generally, the paper found that the turn of the month anomaly has become more pronounced as mutual funds’ assets under management (AUM) has increased as a proportion of the overall stock market. The paper’s authors also found that the anomaly exists in other developed markets and was more pronounced in countries with larger mutual fund sectors.

So, is this behaviour found in the UK market? The following chart plots the average day returns of the FTSE All-Share Index for the 10 days around the turn of each month since 1970. The days studied are the five last trading days of the month, from ToM(-5) to ToM(-1) (the latter being the last trading day of the month), and the first five trading days of the following month, from ToM(+1) to ToM(+5).

For comparison the average day return for the Index for all days is 0.03 per cent. As can be seen, the six days around the turn of the month (ie, the three days before and three days following) have average returns significantly higher than the average return for all days.

Chart 5 below replicates for the UK market the one found in the Etula paper: it plots the cumulative returns of the FTSE All-Share Index for the six days around the turn of the month (TOM: T-3 to T+3) against the cumulative returns of the index for the rest of the month (X-TOM) for the period 2003-17. The FTSE All-Share Index is added as a benchmark. All series are rebased to start at 100. 

By 2017 a TOM portfolio would have had a value of 349, and an X-TOM portfolio a value of 61. Which does suggest (as the paper found for the US market) that all the market’s gains come in just a few days around the turn of the month.

For comparison, the buy-and-hold FTSE All-Share portfolio would have had a value of 213 by the end of the period. So the TOM would have significantly outperformed the Index, because on average the market had negative returns during the X-TOM part of the month. Which is quite a result! In addition the TOM portfolio would have had 50 per cent less volatility than the index.

In this case, the strategy is statistically significant, and also economically significant for portfolio values over approximately £20,000. Let’s look now at a strategy with an annual frequency.

At the end of each year the Bounceback Strategy buys the 10 FTSE 350 stocks that have performed the worst that year. It then holds them for three months and liquidates the portfolio at the end of March. So, the strategy trades just twice a year: on 31 December when it buys the 10 worst-performing FTSE 350 stocks of the year, and then three months on 31 March when it sells all the stocks.

The table below lists the 10 worst-performing FTSE 350 stocks in 2016. These 10 stocks were picked to form the 2017 Bounceback Portfolio. The final column in the table gives the returns for each stock for the period Jan-Mar 2017. For example, Capita shares fell 56.0 per cent in 2016, and then rose (bounced back) 6.3 per cent in the first three months of 2017. For reference, the performance of the FTSE 350 Index is also shown for the same periods.

As can be seen, the majority of the bounceback stocks outperformed the Index in the first quarter of 2017.

On average the Bounceback Portfolio stocks had a three-month return of 8.6 per cent, compared with a FTSE 350 Index return of 2.9 per cent for the same period. So, an equally-weighted portfolio of the 10 bounceback stocks would have outperformed the FTSE 350 Index by 5.7 percentage points over the target first three months of 2017.

The following chart shows the comparative performance of the portfolio and the FTSE 350 Index for each year since 2003.

The Bounceback Portfolio has outperformed the FTSE 350 Index by an average of 11.3 percentage points each year since 2003. And in that period the portfolio has underperformed the index only twice (in 2013 and 2015).

Exploiting market anomalies offers the potential to improve the timing of moving money in and out of the market, and also to pick up a few percentage points in performance. But don’t forget that not all anomalies can be exploited profitably.

[1] Cieslak, A. (2016). Stock Returns over the FOMC Cycle.

[2] Etula, Erkko and Rinne, Kalle and Suominen, Matti and Vaittinen, Lauri, Dash for Cash: Month-End Liquidity Needs and the Predictability of Stock Returns (May 17, 2016).