# Bottom Line: Seasonality of the Broad US Stock Market

05 July 2022Today, we are completing a series of studies on seasonal patterns of changes in the value of financial instruments by sectors of the US stock market.

And in conclusion, let's look at the US stock market as a whole, without breaking down by sector.

We will identify the seasonal trends of the S&P 500 stock index, examine the trading signal based on its seasonal patterns, and draw up a dynamic investment plan.

Changes in the market value of the S&P 500 have pronounced seasonal manifestations. And a trading signal based on the seasonal patterns of the index is profitable.

Historical data of S&P 500 index quotes:

- Timeframe - МN (month);
- Period: February 1970 - September 2021;

There are 620 values in total.

**To identify the presence of seasonality, we will use the following criteria:**

1. The share of cases of positive or negative monthly changes for the period under review is more than 53%.

2. The ratio of the average value of positive monthly changes to the average value of negative monthly changes:

- greater than 1, when the share of positive monthly changes is greater than 53% (see point 1);
- less than 1, when the share of negative monthly changes is greater than 53% (see point 1).

3. Linear trend in the distribution of monthly changes over the past 10 years:

- upward trend, when the share of positive monthly changes is greater than 53% (see point 1);
- downtrend, when the share of negative monthly changes is greater than 53% (see point 1).

If all three conditions are met, we will talk about the presence of seasonality in the price changes of a financial instrument.

The section of historical data from 1970 to 2010 will be the base period on which we will identify seasonal patterns in value changes. If such patterns are identified, they will be used as signals to buy or sell in the tested section of history from 2011 to 2021. Thus, we will check the effectiveness of the identified trading signals based on seasonal patterns.

**Analysis of the obtained results **

** **

**Seasonal changes in the S&P 500 index (price changes per month, in %)**

*Explanation for the final lines:*

*1) In the first line, the share of cases of positive changes was calculated based on the analysis of monthly price changes. On the example of January, it looks like this: we take all the months "January" for 41 years, so we get 40. Of these 40 months, a price growth has been noted on the basis of 21 months. That is, the share of growth cases has been 53%.*

*2) In the second line, we compare the average value of all positive monthly changes with the average value of negative changes.*

*If the value obtained is greater than 1, then the price passes more points in the growth months than in the months of declines.**If the value obtained is less than 1, then in the months of decline the price passes more points than in the months of growth. In the case of the month "January", the value is less than 1.*

So, six months (February, March, April, August, November and December) meet two of the three criteria for pronounced seasonality.

Let's check these months according to the third criterion - the direction of the linear trend of the distribution of monthly changes for 2000-2010:

So, the linear trend of changes in February, March and November for 10 years is directed upwards, which satisfies the last criterion for identifying seasonality.

The 10-year trend of changes in August is also directed upwards, but refutes the assumption of a seasonal downtrend in prices.

The linear trend of April and December changes over 10 years is directed downwards, which does not satisfy the last criterion for identifying seasonality.

Thus, with some confidence, we can say that the S&P 500 index tends to grow in February, March and November.

These seasonal patterns we will use as a trading signal for testing on historical data sampling from 2011 to 2021.

We will evaluate the trading signal according to the following criteria:

**The****rate of return**reflects the relative change in the quotes of financial instruments in percentage. A positive value of the rate of return indicates the profitability of the strategy, negative - about the loss.

The rate of return (R) of a financial instrument is calculated using the formula:

**R = Σ P (%) / n,**

where:

n is the number of transactions;

P (%) – the percentage of change in the quote of a financial instrument at the time of fixing a position, is calculated as follows:

for buy positions

P (%) = (position closing price - position opening price) / position opening price * 100%

for sell positions

P (%) = (position opening price - position closing price) / position opening price * 100%

- The
**average rate of return of profitable transactions (AR)**includes the rate of return of only profitable transactions, as a percentage:

**AR = Σ D (+) / n,**

where:

n is the number of profitable transactions;

D (+) – rate of return of profitable transactions.

**Average drawdown (AD)**reflects the average loss when closing losing transactions for the entire trading period, as a percentage. The lower the value of the average drawdown, the lower the losses, and the better the trading signal works.

**AD = | Σ D (-) / n |**

where:

n is the number of losing transactions;

D (-) – rate of return of losing transactions.

**Maximum rate of return (MaxR)**is the maximum profit from closing successful transactions for the entire trading period, as a percentage. The higher the maximum rate of return value, the better the trading signal works.

**MaxR = max (R)**

**Max drawdown (MD)**is the maximum of losses when closing unsuccessful transactions for the entire trading period, in percent (minimum profitability). The lower the value of the maximum drawdown, the better the trading signal works.

**MD = | min (R) |**

**Share of profitable positions (SPP)**shows the share of profitable trading positions from the total number of positions, as a percentage. The higher the DPP, the more profitable trades are made.

**SPP = number of profitable positions / total number of positions * 100**

The results of the strategy of buying the S&P 500 index at the beginning of the months: February, March, November and selling it at the end of these months are presented in the diagrams:

So, the rate of return of buying the S&P 500 index in early February and selling it at the end of the month was 1.3% with an average rate of return of profitable transactions and a drawdown of 3.3% and 4.2%, maximum rate of return and drawdown of 5.4% and 8.7 % respectively.

The rate of return of buying the index at the beginning of March and selling it at the end of the month is close to 0 with an average rate of return of profitable transactions and a drawdown of 3.1% and 3.7%, and maximum rate of return and drawdown of 6.3% and 13.1%, respectively.

The rate of return of buying the index at the beginning of November and selling it at the end of the month was 2.5% with an average rate of return of profitable transactions and drawdown of 3.2% and 0.2%, maximum rate of return and drawdown of 9.9% and 0.3%, respectively.

The share of profitable positions in August was 72.7%, in October - 54.5%, in November - 80%.

Thus, the signal based on the seasonal patterns of the S&P 500 index is profitable in February and November.

Let's summarize the seasonal trends of the US stock market as a whole and by sector. At the same time, we will filter out the results with a rate of return of less than 1%.

In ** February**, the following sectors tend to grow:

- Consumer Discretionary
- Materials

In ** April**, the information technology sector tends to grow, the real estate sector - in

**,**

*March***and**

*June***.**

*July*

** November** is a growth month for the sectors:

- Industrials
- Consumer Discretionary
- Information Technology
- Telecom Services

The US stock market tends to grow in February and November as a whole.

At the same time, the growth of the industrial sector outpaces the growth of the stock market as a whole in November.

The S&P 500 index tends to grow in February, March and November.

**Changes in the market value of the US stock market index are subject to seasonal fluctuations.**

**The effectiveness of the trading signal based on the seasonal patterns of the US stock market has been revealed in February and November.**

During the year, the following sectors of the US stock market tend to grow:

- in February: Consumer Discretionary, Materials;
- in March: Real Estate;
- in April: Information Technology;
- in June: Real Estate;
- in July: Real Estate;
- in November: Industrials, Consumer Discretionary, Information Technology, Telecom Services.

Detailed results are shown in the Appendix:

*Seasonality of the Broad US Stock Market.xlsx*

See also:

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