Trading Day Of The Week (TDW) on the GBP/JPY

The concept of Trading Day of the Week was introduced by Larry Williams in his trading literature. The idea was applied to commodity trading, particularly treasury bonds and S&P 500 futures, and was later extended to practically any trading instrument. The idea behind TDW is that markets exhibit strong tendencies depending on the day of the week beyond the level that random variations can explain. This is my attempt to replicate the same research, this time on forex pairs.

Some basic information and background on the research:

• The data used on this study was hourly data on the GBP/JPY forex pair downloaded from FXCM’s trading station.
• There are 21,813 data points are updated from 12:00pm 29 December 2004 to 9:00am 27 June 2008. The times are in Manila/Singapore time which is 12 hours opposite New York Time.
• This hourly data was compressed into 1,082 days, the three days in 2004 (29-31 December 2004) were dropped.
• As the forex market has no real opening and close, the turn of the day was used as the marker for opening. So the opening of each day would be the opening of the first hour and the close would be the close of the last hour of the day.
• As the study was to find a bias for a day of the week, each day was classified into the working days (i.e. Monday, Tuesday, etc.). As the forex market opens early in Japan, Sunday appears as a trading day in the data set. Due to the few hours contained in these days, they were dropped from the analysis.
• The performance data of each days are primarily as follows:
  • Profit – is measured as the distance in pips from the opening and close of day. A gain is if the close is higher than the open, while a loss is the opposite.
  • Win Rate – is the percentage of days in the category that registered a positive close.
  • Avg Win – is the total gains of profitable days over the number of profitable days.
  • Avg Loss – is the total losses of losing days over the number of losing days.
  • Win/Loss – is the average win figure over the average loss figure.

All Days Results

Here’s the chart the total profitability of the five days along with their winning percentages:

The actual spread of profits showed a strong tendency for gains to occur on Tuesdays and Wednesdays while a strong tendency for losses showed on Fridays. The winning percentages were strong on Tuesdays, Wednesdays, and Thursdays in excess of 55% while closer to even on Fridays.

Tuesdays are the strongest followed by Wednesdays having larger average wins compared to average losses. Fridays are the weakest with wins at 80% as large as average losses. Combining the average wins and losses to the winning percentages, we can derive the expectancy of each day:

The expectancy shows a marginal performance for Mondays and Thursdays, while Tuesdays and Wednesdays show a slight positive expectancy while Fridays shows a slight negative expectancy.

Per Williams’ methodology, counting the sequence of the days of the week may also yield some insights. For each day, the data was further divided onto the sequence in the month (i.e. First, Second, etc.) they would appear in.

Mondays

Although Mondays in general showed a neutral bias and marginal profitability, the third Mondays in the month show a strong tendency for losses.

With the exception of Second Mondays, average losses tend to be higher than gains on Mondays. The Third, Fourth, and Fifth in particular have average gains that are less than 80% the magnitude of the average losses.

Tuesdays

Tuesdays in general have shown a positive expectancy, and with the exception of Second Tuesdays, all Tuesdays have been at least marginally profitable. The Third Tuesday has shown a strong tendency for gains while the Third and Fourth Tuesdays have had higher than 60% winning days.

All Tuesdays except the Fourth have had larger sized average gains than losses. The Third and Fifth Tuesdays have shown gains as much as 130% of average losses.

Wednesdays

Wednesdays in general have shown a positive expectancy, and with the exception of First Wednesdays which are marginal, all other Wednesdays have shown tendencies for profitability. The Second and Fifth Wednesdays have the strongest profits while the Second, Third, and Fifth Wednesdays have winning percentages around 60%.

The average gains for Fifth Wednesdays were 180% that of the average losses. Second Wednesdays were about equal, while the First and Third Wednesdays showed smaller gains than losses. Fourth Wednesday gains were 124% of losses.

Thursdays

Thursdays in general had a marginal expectancy, however Third Thursdays showed a strong tendency for losses. Fourth Thursdays had a slight tendency for gains as well as a winning percentage higher than 60%.

Average gains for Third Thursdays were a dismal 53% the size of average losses. Fourth Thursdays were 73%. Second and Fifth Thursdays were at least 135% of losses while First Thursdays was roughly equal.

Fridays

Fridays had a negative expectancy in general, and the First, Second, and Fourth Fridays showed tenedencies for losses. The Third Friday was the exception, showing a tendency for profits. Fourth Fridays had a low winning percentage at 48% while Fifth Fridays had a 57% winning percentage.

Except Third Fridays, all Fridays showed gains that were less than 80% of losses, First Fridays had dismal gains that were 53% of average losses.

Comparative Tendencies

Lining up the average win/loss ratios of the days together produces the following chart:

Although each day had a distinct spread of tendencies in win vs. losses, there is a noticable change in tendency on the Thirds of each specific day. For days where gains were larger than average losses, the Third days would have larger losses relative to gains, and vice-versa. Fifth days also generally had larger gains to losses, although these days are rarer in the calendar.

Using the win/loss ratios as a rank, Fifth Wednesdays are a strong candidate for gains, while Third Thursdays and First Fridays were the weakest.

We can also compute expectancy for each day and sequence to produce the following ranking:

Fifth Wednesdays also produce the highest positive expectancy, while Third Thursdays and First Fridays are the lowest.

Insight and Applications

The results of the Day of the Week analysis indicate that there are indeed strong behavioural patterns and tendencies in the specific days that are not explainable by random variation. Although the causes for these tendencies can be many things, one immediate factor I can consider is the effect of options and futures expiration on the price behaviour on Third days, since options expire monthly every Third Friday, while the Third weeks of third months futures contracts are rolled over.

In fact isolating the Options and Futures expiry days from the rest of the data yields a positive expectancy compared to the marginal expectancy for the rest of the days:

There are many possible applications of these daily tendencies to trading:

• Daytraders looking to be more efficient in their trade selection can capitalize on the expectancy and win/loss rankings for directional strategies and can opt to trade only on days which have a strong directional tendency to capture the best ranges.
• Position traders can use daily tendencies to support entry and exit decisions to optimize their strategies. A position trader that has spotted a bullish trend, can use negative tendency days to enter the market a better prices, while a bearish trader looking to go short can use positive tendency days to sell at higher prices in a downtrend.

Of course, the winning percentages presented above confirm that although a bias exists, many times the tendency will not pan out. However with percentages of +/- 5% from a 50/50 chance it can already be a good trading edge, which can be combined with other standard trading approaches and money management strategies to form a complete and robust trading system.