Introduction

1) Preliminary remark
A stock market bon mot says "Buy in November and Sell in May" often similarly in a variation also "Sell in May but remember to come back in September". What both statements have in common is that the summer months should be avoided. In the Anglo-American world, this approach is often summarized as "Halloween Effect" or "Halloween Indicator". In the following, we will speak of HI in this publication.

Surprisingly, this HI has so far been neglected in scientific financial research. A search at "SSRN" and "Research Gate", two online databases for scientific papers as a result for the HI or its variants (see above) only yielded about a dozen hits whereas a search for "Momentum Strategy", for example, yielded several hundred hits (as of February 28, 2019).

On the one hand, this article gives an overview of the original HI and reviews some of the postulated core statements. On the other hand, a portfolio is used to show which results the HI achieved in a simulated portfolio including transaction costs and slippage and whether the HI is more of a "trick or treat" in itself and can deliver what it promises in live use.


1.2) The original entry and exit rules of HI

On the first trading day in November, a security or a basket of securities is bought (since this is immediately after October 31st, the day of Halloween in the USA, the HI received its designation).
On the first trading day in May, the previously purchased stock is sold again.
Thus the months June to October are omitted.

1.3) Seasonality
The basic assumption for this approach is based on the observation of seasonal patterns in financial markets, which, according to seasonality advocates, suggest that over longer periods of time there are "stronger and weaker months" in some financial markets.
Figure 1 illustrates this seasonality using the S&P500 future over ten years as an example. The thin black line represents the S&P500 future on a daily closing price basis and the grey, thicker line represents the seasonal pattern over ten years. In fact, this very simplified, seasonal representation shows that over a period of ten years, prices tend to rise from November to April, whereas from May to July a sideways phase is more likely to be observed, only to rise again from around mid-July.

 

 

Figure 1 - Seasonality S&P500 Future

Source: TRADEofficer and TaiPan Lenz+Partner

 

On his website "www.seasonalcharts.de" Dimitri Speck has presented a study on the S&P500 future and the seasonality over a period of 30 years, but with data from 1982 to 2012, and comes to the following conclusion, which can be seen in Figure 2 With his calculation method and over a different period of time, it can also be deduced that from the end of October to the end of May/beginning of June, prices tend to rise and from June to mid/end of October they tend to show weakness. Although a problem of seasonality is already evident here, namely different calculation methods and a change in seasonal patterns over different periods, leads to different results.

 

Figure 2 - Seasonality S&P500 Future

Source: www.seasonalcharts.de Dimitri Speck

 

In summary, it can nevertheless be assumed that seasonal patterns exist in principle and can therefore represent a valid basic assumption for the HI.

 

  • Scientific studies

 

2.1) Study situation
Responsible for the scientific work at the HI are, among others, Sven Bouman and Ben Jacobsen with their paper from 2001/2002 (1), Edwin Maberly and Raylene Pierce from 2003/2004 (2), Sandro Andrade, Vidhi Chhaochharia and Michael Fuerst from 2013 (3) and especially the work of Cherry Zhang and Ben Jacobsen with an update of the original study by Bouman and Jacobsen from 2018 (4).

To reproduce all these works exhaustively would go considerably beyond the scope of this article, so that reference must be made to self-study.

2.2) Summary
In summary, however, it can be said that all of the above-mentioned studies have in common that they demonstrate or confirm the existence of a positive return effect of the HI, not only for individual countries or only for very specific periods of time, but over larger time windows and a multitude of securities and investment countries.
In particular, the latter study by Jacobsen and Zhang from October 2018, with an update on the state of research, examines the entire global equity index market and finds a "striking robustness of the HI with an average 4% higher return during the months of November to April compared to the months of May to October...and, for longer periods such as 5 or 10 years, a probability of outperformance compared to a buy and hold strategy of 80% and 90% respectively. (Jacobsen and Zhang, p. 28, op. cit.)

  • Backtest In

    order to be able to present the results of the HI, we first have to present the procedure of our backtest.

    1) Preliminary remark Backtest

A backtest is an evaluation of a strategy (hypothesis) using data and concrete and objective rules.
First, a hypothesis and data are required. The hypothesis and the corresponding data are then combined with rules such as entry and exit, possible further conditions such as filters, stops, profit targets, etc. to form a model logic. This in turn is then (pre-)tested with historical data, first in an in-sample test (training data) and, if necessary, optimized (configuration/trails), and then finally tested once in an out-of-sample test without optimization. Afterwards, the results are checked to see if they are promising enough to be verified. If the verification was successful, the results will be published and only after that the strategy can be transferred to a trading system.

Figure 3 shows this procedure.

 

Figure 3 - Flowchart

Source: TRADEofficer

3.2) Software
We use C#, C++ and Python as well as Microsoft Excel for backtesting and presentation of the results. Third party programs used for verification purposes are
Wealth-Lab from MS123 LLC, NinjaTrader from NinjaTrader LLC, Captimizer from Logical Line GmbH and Investox from Knöpfel Software GmbH for stocks, futures and ETFs as well as AlgoNet Explorer from THJ Systems Ltd and LiveVol from Cboe for options.

3.3) Hypothesis
The hypothesis is an assumption that is tested without drawing conclusions beforehand.

3.4) Data

3.4.1) Data origin and data validation
The data for the backtesting process is provided by us, for US securities by the New York Stock Exchange (NYSE), for US Future by the CME Group, for options by the Cboe and for all other data (Europe, rest of the world) and for verification purposes, by Quandl, using a second data source.

3.4.2) Data preparation and data quality
The historical data was read in once and the current and future data is updated daily from the data sources, processed and stored in a proprietary database.

3.4.3) Data history and markets
In our proprietary database, we have a data history, some of which goes back to the 1990s, covering all markets worldwide, but with a focus on data from the 1990s and 2000s for the USA and Germany.

3.5) In-sample
In-Sample is the training data part and describes the data used for the learning phase of the backtest or for the configuration or optimization (trail).

3.6) Number of trials / avoidance of backtest overfitting
The number of trails indicates how many iterations of the optimization took place. This helps to avoid backtest overfitting.
Otherwise, if one optimizes long enough, it is always possible to find a variant for a past, known partial data set for which a rule set has worked excellently. For additional self-study we would like to refer to the paper by David Bailey, Jonathan Borwein, Marcos Lopez de Prado and Qiji Zhu from the year 2013, which deals with this problem in detail.


3.7) Out-of-Sample
The out-of-sample is the one-time data test or the part of the data that lies outside the sample and is no longer subject to optimization (trails).

3.8) Verification
The verification is the proof that the result of a first complete backtest is confirmed by at least one other independent authority and thus the truth of the first backtest is proven or not.

In our company, this verification is carried out by at least one of the third-party programs mentioned in section 3.2.

3.9) Backtest evaluation

3.9.1) Gross profit
A fixed amount is used in the gross profit evaluation.

3.9.2) Portfolio Simulation
In portfolio simulation, a percentage of the current capital is used.

3.9.3) Benchmark
The benchmark should be sensibly chosen as the tested market. The S&P500 is useful for a backtesting of individual US stocks.

3.10) Transaction costs and slippage
Finally, the transaction quotas and slippage must also be taken into account in the back test.

  • Backtest of the original HI approach according to Bouman and Jacobsen over 3 years

    After the HI has now been explained and the backtest procedure clarified, the backtest will now be carried out over a period of the last three years from 01.01.2016 to 31.12.2018 on the basis of the original set of rules.


4.1) Entry
Entry is on the first trading day in May for the Open.

4.2) Exit
The exit will take place on the first trading day in November for the Open.

4.3.) Stops and profit targets
There are no stops or winning goals.

4.4) Filters or modifications
There are no filters or modifications.

4.5) In-Sample
The period for the In-Sample is from 01.01.2000 to 31.12.2015

4.6) Number of trails
The number of trails is 0, since there is no optimization in the original set of rules.

4.7) Out-of-Sample
The period for the out-of-sample is from 01.01.2016 to 31.12.2018

4.8) Markets
For the back test and its comparability of the results, the shares included in the Dow Jones Industrial Average are used. The benchmark used is the S&P500 in the form of the SPY ETF, which tracks the index almost 1:1.

4.9) Setting for the backtest
We use a portfolio simulation with a portfolio of USD 100,000.00 and a share of the individual position of 3.33% as well as for the transaction costs per half turn USD 1.00 and one of slippage of 0.1%.

4.10) Result 3 years from 01.01.2016 to 31.12.2018
The result of the backtest of the original approach on 31.12.2018 shows the following results, which are shown in Figure 4 and 5.


Figure 4 - Key figures
Source: TRADEofficer

Figure 5 - Capital curve with S&P500 SPY
Source: Tradeofficer


4.11) Conclusion
We see that although the HI in the original rulebook generated a positive geometric return of 2.53% in the period from January 1, 2016, to December 31, 2018, with a maximum draw down of 20.43%, we would have had a worse performance than with a buy and hold strategy in the S&P500 SPY and therefore could not outperform (see black line S&P500 SPY vs. blue line Equity in Figure 5).

The presentation of the analysis of longer time periods such as 5, 10 and 20 years would also go considerably beyond the scope of this article (if interested, we would be happy to provide the results).

In summary, however, it should be mentioned that no outperformance was achieved in these studies even for periods of 5 and 10 years. And thus the statement claimed by Jacobsen and Zhang, that an 80% or 90% probability of outperformance for any index market over 5 or 10 years, at least for the Dow Jones Average Index and an investment in its individual securities, cannot be confirmed by backtests under real conditions and taking into account transaction costs and slippage.
For example, the two authors Jacobsen and Zhang themselves write in their paper that in the period from October 1998 to April 2017 there is only a 45% probability of beating a buy-and-hold strategy in the USA in the out-of-sample (see p. 44, "The Halloween Indicator, 'Sell in May and Go Away': Everywhere and All the Time", 2018).
However, over much longer periods of 20 years and beyond, the original HI actually outperforms the S&P500 SPY, in some cases significantly.

  • Improvement with modifications possible?

    In a further step we would like to investigate whether a better performance of the HI is possible if we introduce some modifications. For this purpose, we will use the basic set of rules and apply filters and optimizations. The process that leads to the results remains the same as described above and therefore we will only concentrate on the differences and evaluate the results in the end.

    1) Pre-filter S&P500
    We introduce a pre-filter, which means that an entry in accordance with the known entry logic may only occur if the price of the S&P500 index is above its 200-day simple moving average (SMA).
    Otherwise, no entry at all takes place.

    5.2) Filter SMA200
    Furthermore, a filter is introduced on the respective single value. This means that before an entry can be made as described above, the respective individual share must have a price trend above its SMA200. If this is not the case, this share will not be bought on the first trading day in November of a year.

    5.3) Stop In
    addition, a stop in the form of a trailing stop of 10 percent is introduced.

    5.4) Price target
    In addition, a price target in the form of a 25 % trailing stop is also introduced.

    5.5) Number of Trails in the In-Sample
    The number of Trails in the In-Sample was 4. One each for Prefilter, Filter, Stop and Price Target.
    To understand why the trail number is 4 and not a multiple of it, the following explanation:
    When optimizing the SMA, for example, we started with our standard SMA200 and used it once in our backtest. This means that exactly one trail is required for this characteristic.
    On the other hand, if we were to start an optimization run, i.e. "search for the best SMA in the in-sample within a range from SMA50 to SMA300", then this would already be 251 trails, since 251 runs are tested by the software - namely SMA50, SMA51, etc. - and for each individual run the software determines which results occurred in the in-sample and then uses the best result. And this is a multiple optimization process and therefore has to be stated in a serious backtest consideration, although unfortunately this is rarely the case in the financial industry.

    5.6) Result

    The result of the backtest with the modifications is shown in figures 6 and 7.



    Figure 6 - Key figures
    Source: TRADEofficer


    Figure 7 - Capital curve with S&P500 SPY
    Source: Tradeofficer

    5.7) Conclusion
    As we can see, even with this modification we do not outperform the S&P500. However, the geometric return has increased to 3.88% and the maximum drawdown has decreased significantly to only 5.61%. At the same time, the profit factor has also risen significantly to 7.66, and at the same time, transaction costs and slippage have fallen due to the lower number of trades. Furthermore, the liquidity released by the lower number of trades gives us the opportunity to consider further useful additions.
    Similar to the conclusion described above in section 4.11), there is no outperformance even over longer periods of 5 or 10 years. By contrast, periods of 20 years or more result in a clear outperformance.

  • Further modifications possible?

    Further modifications can be made. A useful addition to the modified HI is the implementation of an option strategy, for example, which can be used to generate additional returns using option writer transactions.
    However, a more aggressive approach with short trades during the "weaker months" from May to October, or during this period of investment of free liquidity in fixed or time deposits or in bonds etc., as well as a combination of these, would also be conceivable.

  • Conclusion

    The implementation of the original HI as an admixture to a multi-strategy trading system is not necessarily suitable, at least with its original set of rules, if it is to be applied in shorter periods of time. This is all the more true for the use in "real life" and with real funds, as then the investor is not necessarily willing to accept the sometimes violent maximum drawdown phases.
    By contrast, by means of sensible modifications, HI in a modified form is more of a treat than a trick.

 

Bibliography:

  • Sven Bouman and Ben Jacobsen "The Helloween Indicator, Sell in May and Go Away: Another Puzzle", 2001/2002
  • Edwin Maberly and Raylene Pierce "Stock Market Efficiency Withstands another Challenge: Solving the 'Sell in May / But after Halloween' Puzzle", 2003/2004
  • Sandro Andrade, Vidhi Chhaochharia and Michael Fuerst "Sell in May and Go Away Just Won't Go Away, 2013
  • Cherry Zhang and Ben Jacobsen, "The Halloween Indicator, 'Sell in May and Go Away': Everywhere and All the Time", 2018
  • David Bailey, Jonathan Borwein, Marcos Lopez de Prado and Qiji Zhu, "Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance", 2013