Year of the horse - Annexe

This document serves as an annexe to the article entitled "Year of the horse", published on the 26th of February 2026. Its purpose is that of a supporting paper, providing additional figures and calculations, as well as providing a more robust defence of the methodology used and the assumptions made therein.

Data collection

The first step was to collect the daily close prices for the S&P 500 index, from the 20th of January 1928 to the 13th of February 2026. The data were obtained from the Yahoo Finance API, which provided the date, open price and close price. The data set only started differentiating the open and close price from 1962 onwards, but since we are only concerned with the closing price, this was not an issue. We will call this data set "SP500".

The second step was to collect the start and end date for every Chinese lunar year stretching back to the same date. Such information is readily available throughout the internet and was easy to acquire. We will call this data set "CNY".

Calculating the average return per zodiac animal

With our two data sets in hand, the next step was to create a column with the daily close price of the S&P 500 at the end of every lunar year. To achieve this, we use a simple XLOOKUP function in order to return a result whenever the dates from CNY match those in SP500. Of course, the dates in CNY do not always correspond to days for which we have daily price data. For example, should the lunar year end on a Saturday, Sunday, or bank holiday, SP500 will not be able to provide a price. This was in fact the case for the latest lunar year, ending on the 16th of February 2026, which was a Monday, but happened to fall on President's Day, meaning US stock markets were closed. To account for these differences, we insert a "-1" in the fifth argument in our XLOOKUP function, in order to return the last available match.

Using this function, we can populate a new column with the closing price for the end of every lunar year. From this, calculating the change from the previous year is trivial. We now have the yearly return of the S&P 500 according to the Chinese lunar calendar:

Year start	Year end	Zodiac	Close	Change (%)
23/01/1927	20/01/1928	Rabbit	17.48	/
23/01/1928	09/02/1929	Dragon	24.44	39.82
10/02/1929	29/01/1930	Snake	22.35	-8.55
30/01/1930	16/02/1931	Horse	17.34	-22.42
17/02/1931	05/02/1932	Sheep	7.78	-55.13
06/02/1932	25/01/1933	Monkey	7.10	-8.74
26/01/1933	13/02/1934	Rooster	11.22	58.03
14/02/1934	03/02/1935	Dog	9.05	-19.34
04/02/1935	23/01/1936	Pig	13.91	53.70
24/01/1936	10/02/1937	Rat	18.17	30.63
11/02/1937	30/01/1938	Ox	10.55	-41.94
31/01/1938	18/02/1939	Tiger	12.40	17.54
19/02/1939	07/02/1940	Rabbit	12.22	-1.45
08/02/1940	26/01/1941	Dragon	10.45	-14.48
27/01/1941	14/02/1942	Snake	8.62	-17.51
15/02/1942	04/02/1943	Horse	10.43	21.00
05/02/1943	25/01/1944	Sheep	11.88	13.90
26/01/1944	12/02/1945	Monkey	13.68	15.15
13/02/1945	01/02/1946	Rooster	18.64	36.26
02/02/1946	21/01/1947	Dog	14.97	-19.69
22/01/1947	09/02/1948	Pig	14.31	-4.41
10/02/1948	28/01/1949	Rat	15.20	6.22
29/01/1949	16/02/1950	Ox	16.99	11.78
17/02/1950	05/02/1951	Tiger	22.20	30.67
06/02/1951	26/01/1952	Rabbit	24.55	10.59
27/01/1952	13/02/1953	Dragon	25.74	4.85
14/02/1953	02/02/1954	Snake	25.92	0.70
03/02/1954	23/01/1955	Horse	35.44	36.73
24/01/1955	11/02/1956	Sheep	43.64	23.14
12/02/1956	30/01/1957	Monkey	44.91	2.91
31/01/1957	17/02/1958	Rooster	41.11	-8.46
18/02/1958	07/02/1959	Dog	54.37	32.25
08/02/1959	27/01/1960	Pig	56.72	4.32
28/01/1960	14/02/1961	Rat	61.41	8.27
15/02/1961	04/02/1962	Ox	69.81	13.68
05/02/1962	24/01/1963	Tiger	65.75	-5.82
25/01/1963	12/02/1964	Rabbit	77.57	17.98
13/02/1964	01/02/1965	Dragon	87.58	12.90
02/02/1965	19/02/1966	Snake	92.41	5.51
20/02/1966	08/02/1967	Horse	87.72	-5.08
09/02/1967	29/01/1968	Sheep	93.35	6.42
30/01/1968	16/02/1969	Monkey	103.61	10.99
17/02/1969	05/02/1970	Rooster	85.90	-17.09
06/02/1970	26/01/1971	Dog	95.59	11.28
27/01/1971	14/02/1972	Pig	104.59	9.42
15/02/1972	02/02/1973	Rat	114.35	9.33
03/02/1973	22/01/1974	Ox	96.55	-15.57
23/01/1974	10/02/1975	Tiger	78.36	-18.84
11/02/1975	30/01/1976	Rabbit	100.86	28.71
31/01/1976	17/02/1977	Dragon	100.92	0.06
18/02/1977	06/02/1978	Snake	89.50	-11.32
07/02/1978	27/01/1979	Horse	101.86	13.81
28/01/1979	15/02/1980	Sheep	115.41	13.30
16/02/1980	04/02/1981	Monkey	128.59	11.42
05/02/1981	24/01/1982	Rooster	115.38	-10.27
25/01/1982	12/02/1983	Dog	147.65	27.97
13/02/1983	01/02/1984	Pig	162.74	10.22
02/02/1984	19/02/1985	Rat	181.33	11.42
20/02/1985	08/02/1986	Ox	214.56	18.33
09/02/1986	28/01/1987	Tiger	275.40	28.36
29/01/1987	16/02/1988	Rabbit	259.83	-5.65
17/02/1988	05/02/1989	Dragon	296.97	14.29
06/02/1989	26/01/1990	Snake	325.80	9.71
27/01/1990	14/02/1991	Horse	364.22	11.79
15/02/1991	03/02/1992	Sheep	409.53	12.44
04/02/1992	22/01/1993	Monkey	436.11	6.49
23/01/1993	09/02/1994	Rooster	472.77	8.41
10/02/1994	30/01/1995	Dog	468.51	-0.90
31/01/1995	18/02/1996	Pig	647.98	38.31
19/02/1996	06/02/1997	Rat	780.15	20.40
07/02/1997	27/01/1998	Ox	969.02	24.21
28/01/1998	15/02/1999	Tiger	1230.13	26.95
16/02/1999	04/02/2000	Rabbit	1424.37	15.79
05/02/2000	23/01/2001	Dragon	1360.40	-4.49
24/01/2001	11/02/2002	Snake	1111.94	-18.26
12/02/2002	31/01/2003	Horse	855.70	-23.04
01/02/2003	21/01/2004	Sheep	1147.62	34.11
22/01/2004	08/02/2005	Monkey	1202.30	4.76
09/02/2005	28/01/2006	Rooster	1283.72	6.77
29/01/2006	17/02/2007	Dog	1455.54	13.38
18/02/2007	06/02/2008	Pig	1326.45	-8.87
07/02/2008	25/01/2009	Rat	831.95	-37.28
26/01/2009	13/02/2010	Ox	1075.51	29.28
14/02/2010	02/02/2011	Tiger	1304.03	21.25
03/02/2011	22/01/2012	Rabbit	1315.38	0.87
23/01/2012	09/02/2013	Dragon	1517.93	15.40
10/02/2013	30/01/2014	Snake	1794.19	18.20
31/01/2014	18/02/2015	Horse	2099.68	17.03
19/02/2015	07/02/2016	Sheep	1880.05	-10.46
08/02/2016	27/01/2017	Monkey	2294.69	22.05
28/01/2017	15/02/2018	Rooster	2731.20	19.02
16/02/2018	04/02/2019	Dog	2724.87	-0.23
05/02/2019	24/01/2020	Pig	3295.47	20.94
25/01/2020	11/02/2021	Rat	3916.38	18.84
12/02/2021	31/01/2022	Ox	4515.55	15.30
01/02/2022	21/01/2023	Tiger	3972.61	-12.02
22/01/2023	09/02/2024	Rabbit	5026.61	26.53
10/02/2024	28/01/2025	Dragon	6067.70	20.71
29/01/2025	16/02/2026	Snake	6836.18	12.67

The next step is to average these values across each zodiac animal using a simple AVERAGEIF function:

Zodiac	Average return (%)
Dragon	9.9
Snake	-1.0
Horse	6.2
Sheep	4.7
Monkey	8.1
Rooster	11.6
Dog	5.6
Pig	15.5
Rat	8.5
Ox	6.9
Tiger	11.0
Rabbit	11.7

Calculating volatility per zodiac animal

The next step is to calculate the volatility over every lunar year. This first requires establishing a suitable metric against which we can actually quantify volatility. Finding the high and low of a given year and dividing by its mean gives us the relative spread of each period, which is somewhat useful for illustrating the size of the overall trading range, but fails to describe how much the results cluster around the mean.

A more useful measure of volatility is to calculate the standard deviation across a given year, which tells us exactly how grouped together or spread out the daily close prices are. Using a STDEV.S function in combination with a FILTER function, we are able to calculate the standard deviation for each lunar year by filtering price data by date range. We now have the standard deviation for each period, but these results do not account for the huge difference in absolute values over time. A standard deviation over a 10-point range is obviously going to be smaller than the standard deviation over a 1,000-point range. To account for this, we simply divide the standard deviation by the mean, thereby normalising the results. This figure is called the coefficient of variation, also known as normalised root-mean-square deviation (NRMSD), which is often used in economic models and represents a measure of the extent of variability in relation to the mean of a given data set. We are content that this is an adequate description of volatility as we wish to model it.

Full results presented below:

Year start	Year end	Zodiac	Change (%)	Spread (%)	NRMSD (%)
23/01/1927	20/01/1928	Rabbit	/	/	/
23/01/1928	09/02/1929	Dragon	39.82	20.78	10.81
10/02/1929	29/01/1930	Snake	-8.55	28.68	13.81
30/01/1930	16/02/1931	Horse	-22.42	28.44	16.38
17/02/1931	05/02/1932	Sheep	-55.13	41.29	23.98
06/02/1932	25/01/1933	Monkey	-8.74	35.81	18.28
26/01/1933	13/02/1934	Rooster	58.03	37.62	19.76
14/02/1934	03/02/1935	Dog	-19.34	15.98	7.68
04/02/1935	23/01/1936	Pig	53.70	26.63	15.20
24/01/1936	10/02/1937	Rat	30.63	14.64	7.82
29/01/2025	16/02/2026	Snake	12.67	13.23	6.08

Averaging our coefficient of variation values across each zodiac animal, we obtain the following table:

Zodiac	Average return (%)	Spread (%)	NRMSD (%)
Dragon	9.9	10.2	5.06
Snake	-1.0	12.7	6.10
Horse	6.2	15.7	8.15
Sheep	4.7	14.1	7.36
Monkey	8.1	12.9	6.34
Rooster	11.6	13.7	6.83
Dog	5.6	13.1	6.99
Pig	15.5	11.7	5.64
Rat	8.5	15.2	7.70
Ox	6.9	15.4	8.25
Tiger	11.0	16.0	7.84
Rabbit	11.7	11.9	5.71

We now have a quantified measure of volatility, per animal. The next step is to ascertain whether or not the spreads in average returns and average volatility are meaningful. With a low of -1.0 and a high of 15.5, the spread in average returns looks significant. Likewise, with a low of 5.06 and a high of 8.25, we have what looks like a reasonably wide spread in volatility. Alas, looks can be deceiving. We need to determine just how significant these spreads really are.

One way of doing this is to perform a permutation test. The purpose of performing such a test is to see what the results would be if we attributed the yearly results to a random animal instead of to its actual animal. To achieve this, we create a column that randomly assigns a zodiac sign to each year, and then calculate results according to these random signs. We then collect the spread in average returns and coefficients of variation to see how they measure up against our original data set.

As per the above table, for average returns, we have a minimum of -1.0 and a maximum of 15.5, giving us a spread of 16.4. For the coefficient of variation, we have a minimum of 5.06 and a maximum of 8.25, giving us a spread of 3.19.

Running the permutation test over many cycles, we compare the obtained spreads against these results. Predictably, the randomly calculated spreads are significantly higher than our original results. Put differently, if we were to assign zodiac animals to random years, we would likely obtain a higher spread in average returns and in volatility, per animal, than what we actually got. This tells us that there is no correlation whatsoever between the performance of the S&P 500 index and the Chinese lunar calendar.

This confirms what we would realistically expect. US stock markets have historically followed cyclical patterns that are shorter than the 12-year zodiac cycle, blurring the results over the lunar calendar. More broadly speaking, there is little reason to expect an American stock market index to correlate to the Chinese lunar calendar, and it indeed does not.

Nikkei 225

This is where things get a little more interesting. We repeat the exact same steps for the Japanese Nikkei 225 index as we did for the S&P 500. Firstly, the return of the Ni225 according to the lunar calendar:

Year start	Year end	Zodiac	Close	Change (%)
29/01/1949	16/02/1950	Ox	109.6	/
17/02/1950	05/02/1951	Tiger	119.43	8.97
06/02/1951	26/01/1952	Rabbit	184.27	54.29
27/01/1952	13/02/1953	Dragon	409.42	122.18
14/02/1953	02/02/1954	Snake	357.71	-12.63
03/02/1954	23/01/1955	Horse	371.04	3.73
24/01/1955	11/02/1956	Sheep	427.57	15.24
12/02/1956	30/01/1957	Monkey	572.07	33.80
31/01/1957	17/02/1958	Rooster	533.85	-6.68
18/02/1958	07/02/1959	Dog	689.97	29.24
08/02/1959	27/01/1960	Pig	953.93	38.26
28/01/1960	14/02/1961	Rat	1581.64	65.80
29/01/2025	16/02/2026	Snake	56806.41	45.59

The next step is to average these values across each zodiac animal using a simple AVERAGEIF function:

Zodiac	Average return (%)
Dragon	23.0
Snake	10.3
Horse	0.3
Sheep	4.2
Monkey	12.4
Rooster	17.0
Dog	3.9
Pig	16.8
Rat	20.3
Ox	1.9
Tiger	4.8
Rabbit	20.4

As noted in the main article, the spread in average returns is significantly greater than those found in the S&P 500.

Using the same methodology as for the S&P 500 data set, averaging our coefficients of variation across each zodiac animal, we obtain the following table:

Zodiac	Average return (%)	Spread (%)	NRMSD (%)
Dragon	23.0	17.9	8.27
Snake	10.3	18.2	9.01
Horse	0.3	14.7	7.91
Sheep	4.2	12.1	6.64
Monkey	12.4	13.7	6.61
Rooster	17.0	13.7	7.34
Dog	3.9	11.6	5.30
Pig	16.8	15.2	7.70
Rat	20.3	23.6	12.22
Ox	1.9	14.1	6.81
Tiger	4.8	14.7	6.93
Rabbit	20.4	15.7	7.86

As per the above table, for average returns, we have a minimum of 0.3 and a maximum of 23, giving us a spread of 22.7. For the coefficient of variation, we have a minimum of 5.30 and a maximum of 12.22, giving us a spread of 6.92.

We run the same permutation test as above, randomising zodiac animals per year. This time, we notice a difference. For the average returns, the randomly calculated spreads are typically higher than our spread of 22.7, suggesting that just as with the S&P 500, the average return of the Nikkei 225 does not correlate with the lunar calendar.

However, when calculating spreads in volatility, we quickly notice that the randomised spreads are lower than our original spread of 6.92. Put differently, if we were to assign zodiac animals to random years, we would likely obtain a lower difference in volatility than what we actually got. This tells us that there is in fact a correlation between the volatility in the Nikkei 225 and the Chinese lunar calendar. As stated in the main article, a possible explanation to this lies in the longer economic cycles that dominated the Japanese financial sphere after the second world war, but if that is the case, it is odd that the same correlation does not appear in the average return of the index.

Conclusion

Whether or not the Chinese lunar calendar actively influenced sentiment on the trading floor of the Tokyo Stock Exchange over the decades would be almost impossible to prove. It is nevertheless interesting that volatility in the Nikkei index does appear to correlate with the Chinese Zodiac, even when the performance of said index does not.

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