„Timing is everything in life and in golf.“
Arnold Palmer
Numerous studies have confirmed that the global financial market, or at least some of its segments, is impacted by various seasonal patterns and calendar anomalies. Calendar anomaly is a pattern in the behaviour of asset prices that is related to a specific calendar event. It usually has the form of abnormally good or abnormally poor returns recorded during the event window. What is interesting is that no one knows for sure what actually causes the calendar anomalies. For each type of anomaly there usually exists several explanations; however, none of them is generally accepted.
The sheer existence of calendar anomalies is a contradiction of the Efficient Market Hypothesis, according to which all relevant data is already reflected by the current asset price, and thus neither fundamental nor technical analysis can deliver abnormal returns. However, numerous studies have shown that the calendar anomalies can indeed be used to generate abnormal returns. Moreover, some of the calendar anomalies have only a short-term nature, a period of several days, for instance; and some of them are more long-term and may span several months. Another important feature of the calendar anomalies is that they are not permanent. Several studies have shown that over time the frequency of their appearance, as well as their strength, changes.
In this article we will take a closer look at whether and how some of the most famous calendar anomalies affect the most popular gold investment vehicles: the SPDR Gold Shares ETF (GLD), the VanEck Gold Miners ETF (GDX), and the VanEck Junior Gold Miners ETF (GDXJ).
Not all days are created equal. This is what one of the most famous calendar anomalies shows. The day of the week effect is based on the premise that asset returns tend to be notably higher during some days of the week, usually on Fridays, and notably lower during other days, usually on Mondays.[1] According to Keim and Stambaugh, the tendency to abnormally low Monday returns can be traced back to the late 1920s on the US stock market.[2] According to Conine, Giacotto and Tamarkin, the high Friday and low Monday returns can be explained by the pre-weekend optimism of investors that supports Friday market performance and post-weekend depression that negatively impacts Monday performance.[3]
The next chart shows the comparison of average returns recorded by GLD, GDX, and GDXJ, since their inception until the end of 2023. As can be seen, over the investigated period, GLD recorded positive average returns during each weekday, except for Monday. The average Monday return was -0.01%. On the other hand, the highest average returns, as high as 0.11%, were recorded on Fridays. Even more negative average Monday returns (-0.12%) were observed in the case of GDX.
However, unlike GLD, GDX also experienced negative average Thursday returns (-0.03%). The average Friday returns were positive (0.11%), although slightly lower than the average Wednesday returns (0.13%). GDXJ experienced the lowest average returns on Thursdays (-0.09%) and the highest average returns on Fridays (0.09%). In its case, too, the average Monday returns were negative (-0.03%).
Source: Reuters Eikon, Incrementum AG
*Start Date: GLD = 11/2004, GDX = 05/2006, GDXJ = 11/2009
It is important to note that the investigated time periods for each of the ETFs differ, due to the different dates of their establishment, which may at least partially explain the notable differences in the results. It is, however, possible to observe some common features: In all the three cases, the average Monday returns were negative, and in all the three cases the average Friday returns were highly positive. Therefore, it is possible to conclude that the day of the week effect affects GLD, GDX, and also GDXJ.
This finding can hardly be used in long-term investment strategies; however, it may be useful for short-term traders. For example, since its inception, until the end of 2023, GLD generated returns of 330.8%. However, a simple strategy of avoiding Mondays, which means investing in GLD during the rest of the week but staying aside on Monday, would improve the return to 412.1%. GDX and GDXJ have recorded since their inception losses of 16.7% and 62.8% respectively. If one was able to avoid Mondays, the 16.7% loss would turn into a 204.2% profit, and the 62.8% loss would be reduced to a 38.1% one.
The main feature of the turn of the month effect is abnormally high returns recorded when an old month is coming to an end and a new one begins. However, there is not a single rule regarding the exact length of the turn of the month window. Although the existence of this calendar anomaly has been confirmed by numerous studies, the results show relatively big differences, depending on what days are included in the turn of the month window.
According to Ariel, between 1963 and 1981, the majority of US stock market returns were recorded during the turn of the month periods.[4] Ogden believes that the turn of the month effect is attributable to standardisation of payments that leads to higher liquidity around the end of the month.[5] On the other hand, Nikkinen attributes this calendar anomaly to US macroeconomic news release dates that usually fall around the end of the month.[6]
As shown in the next chart, the turn of the Month effect also impacts the gold market and gold mining companies. Because, as mentioned above, there is no generally accepted length of the turn of the month window, the chart compares average returns recorded over the last three days of an old month (Day -3, Day -2, Day -1), the first three days of a new month (Day 1, Day 2, Day 3), and over the remaining days (RoM – rest of the month). As can be seen, all three ETFs tend to record significantly higher returns on the first day of the month. In the case of GLD, the average returns from Day -1 and Day 2 are also higher than the RoM returns. On the other hand, the Day -3 and Day 3 average returns are negative. In the case of GDX, the average RoM returns are close to zero. And although the Day -3 and Day 3 average returns are negative, the Day -2, Day -1, Day 1 and Day 2 average returns are positive, significantly higher than the RoM average returns. For days -1 and 1, the average returns are 0.20% and 0.34% respectively. Even bigger differences can be seen with GDXJ. The Day -3, Day -2, and Day 2 average returns are lower than the RoM average returns of -0.02%. However, the Day -1 and Day 3 average returns are highly positive, and the Day 1 average returns are high, at 0.77%.
Source: Reuters Eikon, Incrementum AG
*Start date: GLD = 11/2004, GDX = 05/2006, GDXJ = 11/2009
As can be seen, for GLD, GDX, and also GDX there is a clear pattern of positive returns recorded on trading days during the turn of the month period. As with the day of the week calendar anomaly, this finding can be useful mainly for some short-term traders.
The month of the year effect means that abnormally high or low returns tend to be recorded during a particular month of the year. Numerous studies have shown that the month of January is atypical for abnormally high positive returns. This phenomenon is called the January effect, and it was first described by Wachtel in 1942.[7] According to Keim as well as Moller and Zilca, the majority of the January returns are concentrated in the first half of the month.[8]
According to Wachtel, the January effect is related to tax-loss selling.[9] Tax-loss selling occurs when investors decide to sell assets at a loss, in order to offset capital gains taxes from other investments. This may lead to a situation when assets that recorded losses on a year-to-date basis experience further declines at the very end of the year. According to Klock and Bacon, the underperforming stocks tend to record abnormal negative returns in November and December and abnormal positive returns in January.[10] On the other hand, Lakonishok et al. as well as Park and Moskalev opine that the January effect is caused by “window dressing”, that is, at the end of the year portfolio managers may try to improve the image of their funds by selling the losers and buying the winners.[11]
The next chart captures average monthly returns recorded by GLD. A strong January effect can be seen, as the average January returns are 3.31%. January is also the most successful month in terms of probability of positive returns, as out of 19 Januaries, 13 were positive. On the other hand, the least successful month, over the investigated period, was March, with 14 negative occurrences in 19 years. However, the average March return of -0.34% is only the third lowest, as May and September have average returns of -0.54% and -0.66% respectively.
Source: Reuters Eikon, Incrementum AG
Similar statistics, but for GDX, are presented in the next chart. Also in this case, the highest average monthly returns were recorded in the month of January. They amounted to 2.74%. However, the average April returns (2.72%) are only slightly lower. When looking at the success rate, 10 out of 17 Januaries were positive, and 9 out of 17 Aprils were positive. It is also important to note that while for GLD the negative months saw similar average returns, for GDX September clearly stands out. There were 12 negative Septembers in 18 years, and the average September return for the 18-year period was -3.03%.
Source: Reuters Eikon, Incrementum AG
The results for GDXJ are shown in the next chart. Most striking is the fact that January has only the third highest average returns (2.52%), as it was outperformed by July (3.19%) and April (4.61%). Also, the January success rate is unimpressive, with 6 positive returns in 14 years.
Source: Reuters Eikon, Incrementum AG
So, the question arises, how much of the difference between GLD, GDX, and GDXJ is explainable by the different time periods examined? During the same 14-year period, GDX recorded 8 and GLD 9 positive Januaries. The worst month for GDXJ is usually September. Similarly to GDX, September shows not only the lowest average return (-5.94%) but also the lowest success rate, as GDXJ recorded a positive September monthly return only in 3 out of 14 years.
The monthly patterns revealed in the charts above indicate some potential for the creation of successful investment strategies. For example, investing in GLD during each month except for the weak 4-month period between March and June would have generated gains of 327.1% between December 2004 and November 2023. During the same period, a simple buy & hold strategy would have generated a gain of 336.5%. However, if one would have been able to generate only some tiny gains during the March–June periods, for example by investing in bonds or money market instruments, the buy & hold strategy would have been beaten.
For GDX, during the June 2006–November 2023 period, a strategy of avoiding the weak 3-month period between August and October would have led to a gain of 180.3%. At the same time, a long-term buy & hold strategy would have generated a 20.2% loss. Similarly, during the period between December 2010 and November 2023, GDXJ’s share price declined by 65.2%. But a strategy of avoiding the weak period of September and November would have generated a gain of 51.9%.
The Halloween effect, also known as “Sell in May and go away” or “Sell in May and return after Halloween” is based on the observation that the markets tend to do much better during the winter half of the year, approximately between the end of October and beginning of May, than during the summer half of the year. According to Bouman and Jacobsen, the Halloween effect can be traced to the British stock market in late 17th century.[12] Although the majority of studies have focused on investigating this calendar anomaly in stock markets, some studies have discovered its presence also in commodity markets.[13]
There is an old myth that says that on Halloween the ghosts chase the bad returns away, and they dare to return only after six months have passed. But there are also Hong and Yu, who opine that the reason for the winter half-year outperformance is the holiday season in combination with low trading activity during the summer months.[14] According to Cao and Wei, the Halloween effect should be blamed on the weather, as during the cold winter months investors are more aggressive, while during the hot summer months they tend to be apathic.[15] Kamstra et al. opine that the reason is Seasonal Affective Disorder, according to which the behaviour of investors is affected by different amounts of daylight in winter and in summer.[16]
The results of the Halloween Effect investigation look very persuasive. The average returns recorded during the winter periods (November–April) are notably higher than the average returns recorded over the summer periods (May–October). In the case of GLD, an average return of 1.20% was recorded during the summer periods, while an average return of 8.10% was recorded during the winter periods. In the case of GDX, the average summer period returns amounted to -4.00%, compared to the average winter period returns of 8.99%, And for GDXJ, the average returns amounted to -5.51% and 3.44% respectively. Thus, the differences between the summer and winter periods equal to 6.71 (GLD), 12.99 (GDX) and 8.95 (GDXJ) percentage points respectively. In all the three cases, the difference is clearly in favour of the winter period.
Source: Reuters Eikon, Incrementum AG
*Start date: GLD = 05/2005, GDX = 11/2006, GDXJ = 05/2010
Investing in GLD only during the winter periods and staying out of the market during the summer periods – which means no summer returns at all – would have led to a gain of 263.9% in the May 2005–October 2023 period. Holding shares of GLD for the whole time would have generated a 324.7% gain. At first look, the buy & hold strategy looks superior; however, the difference wouldn’t be so persuasive if one were able to generate at least some mediocre returns during the summer periods.
The situation looks much better in the case of GDX and GDXJ, where a strategy of simply staying out of the market during the summer periods is clearly superior. During the May 2006–October 2023 period, the share price of GDX declined by 24.8%, but the strategy of investing only during the winter periods would have generated gains of 155.7%. During the May 2010–October 2023 period, GDXJ lost 71.4% of value, while the strategy of holding its shares only during the winter periods would have generated a loss of only 9.5%.
In some fairytales, the magic must be performed at an exact time, under very specific conditions, for it to work. With calendar anomalies, the situation is similar. Fortunately, you don’t have to go with your laptop into the heart of the forest at midnight under the full moon to confirm your trading order. All it takes is to follow some patterns that have been observed over the years; and although the reasons for their existence are not fully clear, the data show that they are simply there.
As shown in this chapter, the calendar anomalies can also be observed in the gold market, represented by the SPDR Gold Shares ETF (GLD), the VanEck Gold Miners ETF (GDX), and the VanEck Junior Gold Miners ETF (GDXJ). Although the results obtained for the three ETFs differ quite notably, it is possible to find several patterns with potential to be utilized as a part of investment strategies. Especially, the month of the year effect and the Halloween effect, due to their longer-term nature, offer several relatively easy ways of generating abnormal returns that beat the simple long-term buy & hold investment strategy.
Probably the easiest way of exploiting a calendar anomaly is to focus on the Halloween effect. All it takes is to purchase gold or gold stocks at the very end of October and sell them at the very end of April. The rest of the time, the money can be held in a savings account, which will generate some additional return. This assumes only two trades per year, so transaction costs should be negligible. The tax impacts obviously depend on the country of residence and its specific tax rules.
However, it is important to be reminded of the well-worn advice that historical results are no warranty of future ones. Moreover, numerous studies have shown that the strength of the calendar anomalies changes over time.
[1] Cross, Frank: “The Behavior of Stock Prices on Fridays and Mondays”, Financial Analysts Journal, Vol. 29, No. 6 (1973), pp. 67–69; French, Kenneth R.: “Stock Returns and the Weekend Effect”, Journal of Financial Economics, Vol. 8, No. 1, (1980), pp. 55–69
[2] Keim, Donald B., & Stambaugh, Robert F.: “A Further Investigation of the Weekend Effect in Stock Returns”, The Journal of Finance, Vol. 39, No. 3 (1984), pp. 819–835
[3] Conine, T., Giacotto, C. and Tamarkin M.: “On Risk-adjusted Returns and the Weekend Effect”, presented at the Financial Management Association Meetings, Toronto, Canada, 1984
[4] Ariel, Robert A.: “A Monthly Effect in Stock Returns,” Journal of Financial Economics, Vol. 18, No. 1 (1987), pp. 621–628
[5] Ogden, Joseph P.: “Turn-of-Month Evaluations of Liquid Profits and Stock Returns: A Common Explanation for the Monthly and January Effects,” The Journal of Finance, Vol. 45, No. 4 (1990), pp. 1259–1272
[6] Nikkinen, Jussi, Sahlström, Petri et al.: “Turn-of-the-month and Intramonth Anomalies and U.S. Macroeconomic News Announcements on the Thinly Traded Finnish Stock Market,” International Journal of Economics and Finance, Vol. 1, No. 2 (2009), pp. 3–11
[7] Wachtel, Sidney B: “Certain Observations on Seasonal Movements in Stock Prices,” Journal of Business of the University of Chicago, Vol. 15, No. 2 (1942), pp. 184–193
[8] Keim, Donald B.: “Size–Related Anomalies and Stock Return Seasonality: Further Empirical Evidence”, Journal of Financial Economics, Vol. 12, No. 1 (1983), pp. 13–32; Moller, Nicholas and Zilca, Shlomo: “The evolution of the January effect,” Journal of Banking & Finance, Vol. 32, No. 3 (2008), pp. 447–457
[9] Wachtel, Sidney B: “Certain Observations on Seasonal Movements in Stock Prices,” Journal of Business of the University of Chicago, Vol. 15, No. 2 (1942), pp. 184–193
[10] Klock, Shelby. and Bacon, Frank W.: “The January Effect: A Test of Market Efficiency,” Journal of Business Behavioral Sciences, Vol. 26, No. 3 (2014), pp. 34–42
[11] Lakonishok, Josef, Shleifer, Andrei et al.: “Window Dressing by Pension Fund Managers,” American Economic Review, Vol. 81, No. 2 (1991), pp. 227–231; Park, Seung–Chan and Moskalev Sviatoslav A.: “The 52–Week High and the January Effect,” Journal of Business & Economics Research, Vol. 8, No. 3 (2010), pp. 43–58
[12] Bouman, S. And Jacobsen, Ben: “The Halloween indicator, ‘Sell in May and Go away’: Another puzzle,” American Economic Review, Vol. 92, No. 5 (2002), pp. 1618–1635
[13] Arendas, Peter: “The Halloween Effect on the Agricultural Commodities Markets,” Agricultural Economics, Vo. 63 (2017, online first)
[14] Hong, Harrison G. and Yu, J.: “Gone Fishin’: Seasonality in Trading Activity and Asset Prices,” Journal of Financial Markets, Vol. 12, No. 4 (2008), pp. 672–702
[15] Cao, M. and Wei, J.: “Stock Market Returns: A Note on Temperature Anomaly,” Journal of Banking and Finance, Vol. 29, No. 6 (2005), pp. 1559–1573
[16] Kamstra, Mark J., Kramer, Lisa A. and Levi, Maurice D.: “Winter Blues: A SAD Stock Market Cycle,” American Economic Review, Vol. 93, No. 1 (2003), pp. 324–343
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