# The Half-of-the-Month Effect in the Stock Markets

08 June 2022We continue to study various stock market anomalies. Today, the next step is to study the half-of-the-month effect.

The half-of-the-month effect is as follows:

- The stock market shows the main growth during the first half of the month

- During the second half of the month, the market demonstrates near-zero or negative dynamics

Explanations for the half-of-the-month effect are closely related to another calendar anomaly, which is **the turn-of-the-month effect**. The main argument in favor of the existence of these stock market anomalies comes down to the *liquidity hypothesis*: the appearance at the end of each month (as well as in the first days of the next month) in the financial system of a large amount of free cash, due to which the price of stock assets grows in the following days.

In the second half of the month, there is a liquidity deficit in the market. Until the time for the payment of wages and other incomes to the population comes, stock assets do not have enough “fuel” for growth.

Fluctuations in the level of liquidity of the financial system are logically quite consistent with the half-month effect. Let's see how the effect will manifest itself in the global stock markets, where the frequency of cash flows in the economy can vary significantly.

The average growth of world stock indices in the first half of the month exceeds the results of the second half of the month.

Historical data of quotes of world stock indices:

- US: Dow Jones 30, S&P 500, NASDAQ 100
- Germany: DAX 30
- France: CAC 40
- Japan: Nikkei 225
- UK: FTSE 100
- Russia: MICEX, RTS

Timeframe - D (daily)

Period - from 1990 to February 2022. For indices with the start of trading after 1990, respectively, from the start of trading to February 2022.

A total of 8,117 values, 386 complete months.

## Strategy

**Entering the market** - **buying** the index at the opening of the first trading day of the month.

**Exit from the market** - **selling **the index at the close of the 15th day of the month.

If the 15th day of the month is a holiday/day off, exit from the market will be at the close of the last trading day before the 15th.

We will evaluate the results of the strategy according to the following criteria:

**The average rate of return**reflects the relative change in quotations of financial instruments in percentage. A positive value of the average rate of return indicates the profitability of the strategy, a negative one indicates a loss.

The average rate of return (D) of a financial instrument is given by the formula:

**D = ****Σ P (%) ****/ n,**

where:

n is the number of transactions;

P (%) – the percentage of change in the quotation of the financial instrument at the time of fixing the 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 total rate of return (TD)**is the sum of the returns from all transactions. The greater the value of the total rate of return, the greater the profit brought by the signal during its testing period.

**Maximum drawdown (MaxDD)**is the maximum loss in percentage terms from fixing losing trades for the entire testing period. The smaller the value of the maximum drawdown, the better the trading signal works.

**MaxDD = | min ( DD**_{1}**: DD**_{n }**) |**

**DD**_{n }**= TD**_{n }**– max ( TD**_{1}**: TD**_{n }**)**

where:

n - the number of transactions;

D - rate of return;

TDn - total rate of return of n transactions;

DD_{n} – drawdown at the time of closing the nth transaction;

MaxDD – max drawdown.

Further, the results of the strategy using the half-of-the-month effect are compared with the results of the second half of the month:

**Entering the market** - **buying** the index at the opening of the first trading day of the month after the 15th day.

**Exit from the market** - **selling **the index at the close of the last trading day of the month.

## Analysis of the obtained results

Consider the results of the strategy for each considered index:

The study has shown a clear presence of the half-of-the-month effect in the dynamics of the **Dow Jones index**. On average, for the first half of the month, the index shows a growth of 0.61%, while for the second half - only 0.14%. In other words, the first half of the month, on average, provides more than 81% of the Dow Jones index total growth.

For the **S&P 500 index**, a pronounced half-of-the-month effect has also been revealed: an average growth of 0.45% in the first half of the month against 0.27% in the second half. More than 62% of the S&P 500 growth falls in the first half of the month.

**NASDAQ**, like its neighbors in the American market Dow Jones and S&P 500, shows the best result in the first half of the month: an average growth of 0.65% against 0.3% in the second half. 68% of all growth falls in the first half of the month.

At the same time, NASDAQ shows the best result in the first half of the month both in terms of rate of return and maximum drawdown: in the first half, the maximum drawdown is 67.2% compared to 116.87% in the second half of the month.

The German **DAX 30** shows results that are in direct contrast to the US indices. Here, the average rate of return for the 2nd half of the month is much better: 0.32% compared to 0.09% in the 1st half. The first half of the month accounts for only 22% of the growth.

The maximum drawdown for DAX 30 is also much better in the 2nd half of the month: 42.31% vs. 61.79%.

The French market index **CAC 40** shows a severe growth bias in favor of the 2nd half of the month: 0.42% against 0.02%. Only 4.5% of the growth falls in the first half of the month.

The maximum drawdown data is also very indicative: 38.34% in the 2nd half of the month against 113.03% in the 1st half. According to all analyzed indicators, the 2nd half of the month for CAC 40 is better than the 1st.

The Japanese **Nikkei 225**, like the DAX 30 and CAC 40, shows the best result in the 2nd half of the month: an average rate of return of 0.33% versus 0.03% in the 1st half. Only 8.3% of growth on average falls in the 1st half of the month.

The maximum drawdown also shows a clear advantage of the 2nd half of the month for the Nikkei 225: 35.14% compared to 81.09% for the 1st half.

The **FTSE 100** shows the most even distribution of returns among all the considered indices: 0.09% in the 1st and 0.06% in the 2nd half of the month. 60% of the growth falls in the 1st half of the month and 40% - on the 2nd.

Despite the lower rate of return, in this case the 2nd half of the month has almost half the maximum drawdown: 34.13% versus 61.11%.

The **MICEX index** demonstrates a clear advantage in the 1st half of the month in terms of average rate of return: 1.08% versus 0.21% in the 2nd half. More than 83% of the growth falls in the 1st half of the month.

At the same time, the maximum drawdown differs slightly in this case: 87.43% and 91.24%, which also confirms the strength of the half-of-the-month effect for the MICEX index.

For the **RTS index**, the 1st half of the month completely exceeds the 2nd both in terms of rate of return (1.25% versus -0.1%) and maximum drawdown (98.54% versus 179.58%), confirming the half-of-the-month effect hypothesis.

The half-of-the-month effect has clearly manifested itself in the example of 6 out of 9 considered indices. The exception has been the DAX 30, CAC 40 and Nikkei 225 indices, for which the second half of the month has turned out to be much better.

At the same time, for NASDAQ, MICEX and RTS, the half-of-the-month effect not only provides greater rate of return, but also reduces the maximum drawdown.

**The effectiveness of applying the half-of-the-month effect for trading Dow Jones, S&P 500, NASDAQ, FTSE 100, MICEX and RTS indices has been identified.**

Detailed results are shown in the Appendix:

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