Is there empirical evidence of a “Santa Claus
Rally”?
A Warning About Market Truisms
As an investor, I’m absolutely sick of market
myths and unverified beliefs.
Other investors seem to be allergic to critical
thinking and analysis. Myths such as “a stock
having a low P/E ratio means it’s good” are
pervasive in the industry, and newcomers who
want to get started are deafened and defeated by
all of the noise from people that don’t know
better.
For example, if you’re an investor, you have
probably heard of the “Santa Claus Rally”.
Investopedia defines it as “a sustained increase in the stock market that
occurs around the Christmas holiday on Dec
25”.
The existence (or lack thereof) of this
phenomenon is another example of stock market
truism. While it “makes sense” that the market
might go up for Christmas, is there any
actual evidence
of such a rally actually existing?
My job is to find out.
Performing quantitative analysis
To find out whether the Santa Claus rally is a
real thing, I’m going to perform statistical
analysis. Here’s exactly what I’m doing.
Gathering and Preparing the Data
To perform this analysis, we will do the
following:
-
Gather daily returns data for Dec 25 to Jan 2
from 2020 to 2023.
-
Separate the daily returns into two groups:
holiday period and non-holiday period for each
year.
-
Compute the number of trading days, mean
return, and standard deviation for both
periods.
To gather this data, we can use an online
platform like NexusTrade, to query and compute
the data using natural language.
Using NexusTrade to fetch and compute the
data
NexusTrade is an AI-Powered financial analysis
tool. Using its AI-Powered Stock Screener, we
can fetch and compute all of the data needed to
perform our analysis.
Behind the scenes, NexusTrade runs an advanced
SQL query to perform the computation. If we
wanted to be more confident in our results, we
could analyze the SQL query to make sure its
fetching the correct data.
WITH
years AS (
SELECT year
FROM UNNEST(GENERATE_ARRAY(2000, 2023)) AS year
),
daily_returns AS (
SELECT
EXTRACT(YEAR FROM DATE(date)) AS year,
date,
adjustedClosingPrice,
LAG(adjustedClosingPrice) OVER (ORDER BY date) AS prev_price,
CASE
WHEN (EXTRACT(MONTH FROM date) = 12 AND EXTRACT(DAY FROM date) >= 25)
OR (EXTRACT(MONTH FROM date) = 1 AND EXTRACT(DAY FROM date) <= 2)
THEN TRUE
ELSE FALSE
END AS is_holiday_period,
SAFE_DIVIDE(
(adjustedClosingPrice - LAG(adjustedClosingPrice) OVER (ORDER BY date)),
LAG(adjustedClosingPrice) OVER (ORDER BY date)
) * 100 AS daily_return
FROM `nexustrade-io.universalstockfundamentals.price_data`
WHERE
symbol = 'SPY'
AND DATE(date) >= '2000-01-01'
AND DATE(date) <= '2023-12-31'
),
period_stats AS (
SELECT
year,
is_holiday_period,
COUNT(*) AS trading_days,
AVG(daily_return) AS avg_daily_return,
STDDEV(daily_return) AS stddev_daily_return,
SAFE_DIVIDE(
AVG(daily_return),
NULLIF(STDDEV(daily_return), 0)
) AS return_per_risk
FROM daily_returns
WHERE daily_return IS NOT NULL
GROUP BY year, is_holiday_period
)
SELECT
y.year,
MAX(CASE WHEN is_holiday_period THEN trading_days END) AS holiday_trading_days,
MAX(CASE WHEN NOT is_holiday_period THEN trading_days END) AS non_holiday_trading_days,
MAX(CASE WHEN is_holiday_period THEN avg_daily_return END) AS holiday_avg_return,
MAX(CASE WHEN NOT is_holiday_period THEN avg_daily_return END) AS non_holiday_avg_return,
MAX(CASE WHEN is_holiday_period THEN stddev_daily_return END) AS holiday_stddev,
MAX(CASE WHEN NOT is_holiday_period THEN stddev_daily_return END) AS non_holiday_stddev,
MAX(CASE WHEN is_holiday_period THEN return_per_risk END) AS holiday_return_per_risk,
MAX(CASE WHEN NOT is_holiday_period THEN return_per_risk END) AS non_holiday_return_per_risk
FROM
years y
LEFT JOIN
period_stats ps
ON
y.year = ps.year
GROUP BY
y.year
ORDER BY
y.year;
Once we have our data ready, we can continue our
analysis by forming our hypothesis.
Our Initial Hypotheses
In order to determine whether there is evidence
of a Christmas rally, we have to perform a
statistical test.
In statistical testing, we have two hypothesis:
the
null hypothesis
and the
alternative hypothesis.
The
null hypothesis
is a statement asserting that there is no
difference between variables, and any observed
result is due to random chance. In this case, it
would be the following:
The mean returns for the holiday period are
equal to the mean returns for the non-holiday
period
In contrast, the alternative hypothesis is the
opposite. It is a statement that contradicts the
null hypothesis, asserting that there is a
difference between variables that is not due to
random chance. In this case, the alternative
hypothesis would be:
The mean returns for the holiday period are
different from the mean returns for the
non-holiday period.
In order to determine if our returns are
different, we need to perform a statistical
test.
Performing the Two-Sample T-Test
To evaluate the existence of a Santa Claus
Rally, we apply a two-sample t-test comparing
the mean returns of the holiday period (Dec
25–Jan 2) to the non-holiday period within the
same timeframe for each year.
A table with the mean return, standard
deviation, and sample size during the
holiday and non-holiday period
Steps:
-
Utilize Key Metrics: Retrieve the mean, standard deviation, and
sample size for each group (holiday and
non-holiday) from earlier.
-
Conduct the Test: Use Python to compute the t-statistic,
comparing the mean differences relative to the
variation in returns.
-
Assess Significance: Determine the p-value to assess whether
observed differences are statistically
significant at a chosen confidence level
(e.g., 95%).
Once we have the data from the LLM, we can
finish this analysis using a simple Python
script.
import pandas as pd
from scipy.stats import ttest_ind
data = {
"year": list(range(2000, 2024)),
"holiday_avg_return": [0.0541, -0.4332, -0.0310, 0.9496, 0.0055, -0.4470, 0.1552, -0.5075, 0.6417, 0.4176,
0.0226, -0.1741, 0.0161, 0.7062, -0.4062, -0.1861, -0.2410, -0.0604, 1.4561, 0.0605,
0.4514, 0.1868, -0.0252, 0.0881],
"non_holiday_avg_return": [-0.0269, -0.0326, -0.0837, 0.0869, 0.0437, 0.0283, 0.0591, 0.0336, -0.1637, 0.1006,
0.0628, 0.0210, 0.0633, 0.1016, 0.0619, 0.0136, 0.0530, 0.0814, -0.0427, 0.1120,
0.0816, 0.1020, -0.0690, 0.0966],
"holiday_trading_days": [4, 5, 5, 5, 6, 4, 4, 4, 5, 5, 5, 4, 4, 5, 5, 5, 4, 4, 5, 5, 5, 5, 4, 4],
"non_holiday_trading_days": [247, 243, 247, 247, 246, 248, 247, 247, 248, 247, 247, 248, 246, 247, 247, 247, 248,
247, 246, 247, 248, 247, 247, 246]
}
df = pd.DataFrame(data)
holiday_returns = df["holiday_avg_return"]
non_holiday_returns = df["non_holiday_avg_return"]
t_stat, p_value = ttest_ind(holiday_returns, non_holiday_returns, equal_var=False)
print(t_stat, p_value)
With this script, let’s analyze our results.
Interpreting the Results
The output of our two-sample t-test is as
follows:
(0.8277042939072898, 0.41598212361269926)
-
T-Statistic:
This value measures the size of the difference
relative to the variation in your sample data.
A higher absolute value indicates a greater
difference between the groups.
-
P-Value: This
indicates the probability of observing the
results, or something more extreme, if the
null hypothesis is true.
In our case:
-
P-Value (0.4160) > Significance Level
(0.05): This means we fail to reject the null
hypothesis.
What Does This Mean?
The statistical analysis shows that there is
no significant difference
between the mean returns during the holiday
period (Dec 25–Jan 2) and the non-holiday period
in the years from 2000 to 2023.
In other words, the supposed “Santa Claus Rally”
does not have a statistically significant impact
on stock returns during this period.
This is extremely important because it
highlights an important fact with investing –
just because something seems true does not mean
it is.
Discussion
Now, let me be clear. Just because we failed to
reject the hypothesis
does not mean the Santa Claus rally does not
exist.
All it means is that based on the data, we don’t
have any evidence to suggest that it does exist.
The perceived increase in market returns during
this period can easily just be due to chance or
other factors. Investors should be wary of
buying stocks just because they think that
stocks are supposed to go up in December.
This leads to the main point of this article –
in investing,
don’t believe everything you read
online.
Just because something appears to be true does
not mean it is. This analysis shows that there
is little evidence for a Christmas rally, and
that investors should be wary of making
decisions based on its existence.
This article also shows the power of using
objective data for stock market analysis. By
using NexusTrade, we can gather objective data
in order to better inform out stock trading
decisions.
I hope that this article has taught you
something — if you hear advice and it seems
sound, it’s all over the internet, and has
“reasoning” for being true, it doesn’t mean that
it actually is. You should
always conduct
your own research when making financial
decisions.
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