# Seasonality of the US Industrials Sector

01 July 2022We continue to study seasonal patterns of changes in the value of financial instruments by sectors of the US stock market.

Today we will focus on the industrial sector.

We will identify the seasonal trends of the S&P 500 Industrials and examine the trading signal based on its seasonal patterns.

The industrial sector index - S&P 500 Industrials - includes 73 companies, prominent representatives of which are:

Changes in the exchange rate of the US industrial sector index (S&P 500 Industrials) have pronounced seasonal manifestations. And a trading signal based on the seasonal patterns of the index is profitable.

Historical data of S&P 500 Industrials index quotes:

- Timeframe - МN (month);
- Period: October 1989 - September 2021;

There are 384 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 1989 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.

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**Analysis of the obtained results **

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**Seasonal changes in the S&P 500 Industrials 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 22 years, so we get 21. Of these 21 months, a price growth has been noted on the basis of 11 months. That is, the share of growth cases has been 52%.*

*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, four months (March, May, July and November) 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 March and November changes over 10 years is directed upwards, which satisfies the last criterion for identifying seasonality.

The 10-year trend of changes in May and July is directed downwards, which confirms the assumption of a seasonal downtrend in prices.

Thus, with some confidence, we can say that the index of the industrial sector tends to grow in March and November, and to decline in May and July.

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 industrial sector index (S&P 500 Industrials) at the beginning of March and November and selling it at the end of these months, as well as selling the index at the beginning of May and July, followed by buying are presented in the diagrams:

So, the rate of return of buying the S&P 500 Industrials index at the beginning of March and selling it at the end of the month was -0.7% with an average rate of return of profitable transactions and a drawdown of 3.4% and 5.7%, maximum rate of return and drawdown of 7.4% and 19.7% respectively.

The rate of return of buying at the beginning of November and selling at the end of the month was 4.1% with an average rate of return of profitable transactions also 4.1% (all transactions are profitable), a maximum rate of return of 14.4% and zero average and maximum drawdown.

The rate of return of index selling at the beginning of May and buying it at the end of the month was -0.1% with an average rate of return of profitable transactions and drawdown of 3.7% and 3.2%, maximum rate of return and drawdown of 8.1% and 6.8%, respectively.

The rate of return of selling at the beginning of July and buying at the end of the month was -0.8% with an average rate of return of profitable transactions and drawdown of 2.3% and 3.4%, maximum rate of return and drawdown of 7% and 7.9%, respectively.

The share of profitable positions in March was 54.5%, in May - 45.5%, in July - 45.5%, in November - 100%.

The S&P 500 Industrials index tends to rise in March and November and to decline in May and July.

Changes in the market value of the US Industrials Index are subject to seasonal fluctuations.

**The effectiveness of trading signals based on the seasonal patterns of the S&P 500 Industrials index has been revealed in November.**

Detailed results are shown in the Appendix:

*Seasonality of the US Industrials sector.xlsx*

See also:

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