Introduction
Every day I actually see how many points the DAX, the S&P 500 or the Dow Jones move up or down. Ultimately, however, I have never understood exactly how the points are calculated, and after coming across wild theories on the Internet such as "the DAX automatically rises by 100 points every day", I thought it was time to look into the subject.
And I would like to share my research with you in this article.
1. fundamentals
Index points are the unit of measurement used to indicate the current level of a stock market index. An index point is independent of any currency. A share index summarizes the performance of selected shares and calculates an overall value, which is then given as a number of points. The calculation method is not standardized and differs from index to index, which is why we have to note that the Dow Jones and the DAX, for example, cannot be directly compared using the number of points. So far so theoretical.
2 How is the DAX calculated?
The DAX comprises the 40 largest listed companies in Germany. It was launched in 1988 and opened at 1163.52 points. But now the calculation:
The calculation is based on the free float market capitalization, which means that only the actual freely tradable shares of a company are taken into account. In the DAX, each company is weighted according to the proportion of its free float market capitalization in relation to the total value of all companies included in the index. In order to keep volatility low, Deutsche Börse imposes a cap whereby a company may not account for more than 15% of the DAX. Changes in the proportion of a company's free float shares are only adjusted quarterly. This means that if a major shareholder buys or sells shares and the number of freely tradable shares therefore changes, the proportion is adjusted every quarter. The dividends are mathematically reinvested in the DAX and the DAX is therefore a performance index. There is no direct formula that we can apply, but in simplified terms the formula is
DAX = (price x number of shares in free float) ÷ divisor.
This divisor is determined by the German stock exchange and is there to absorb capital measures (share splits). Unfortunately, the divisor is not easily accessible to the public and is constantly being adjusted.
So unfortunately I can't calculate the DAX itself, but basically the index points represent a portfolio that invests in the 40 companies broken down by free float market capitalization (including dividends). Any theories that the DAX is subject to arbitrary measures such as "100 points per day" are therefore nonsense.
3 How is the Dow Jones calculated?
The Dow Jones Industrial Average (Dow Jones for short) is one of the oldest share indices in the world and comprises 30 large, major US companies. In contrast to the DAX, the Dow Jones is not based on market capitalization, but is price-weighted. This means that shares with a higher share price have a greater influence on the index score - regardless of the size of the company. A company with a share price of USD 300 therefore has a greater impact on the Dow Jones than a company with a share price of USD 50, even if the latter has a larger market capitalization. Dividends are not reinvested in the Dow Jones, which is why it is a price index. The formula is simplified:
Dow Jones = sum of the share prices of the 30 companies ÷ divisor
Here, too, there is a divisor that is adjusted in the event of capital measures in order to ensure the continuity of the index. Due to the way it is calculated, the Dow Jones is not as representative of the entire US market as other indices, but historically enjoys a great deal of media attention.
4 How is the S&P 500 calculated?
The S&P 500 is a much broader-based index than the Dow Jones. It comprises the 500 largest listed US companies, which are weighted according to their free float market capitalization - similar to the DAX. This makes the S&P 500 a very good reflection of the US market as a whole. The calculation is therefore based on how large the freely tradable market capitalization of a company is in relation to the total value of all companies included in the index. Companies with a larger market capitalization (such as Apple, Microsoft or Amazon) have a greater influence on the index movement. There is no cap on the S&P 500 and the 5 largest companies already make up 20-25% of the entire index. The S&P 500 is a price index, which means that dividends are not reinvested. The simplified formula is
S&P 500 = (sum of weighted market capitalizations) ÷ divisor
A divisor is also used here to neutralize capital measures. Analysts and fund managers consider the S&P 500 to be one of the most important and informative indices worldwide, as it covers a wide range of sectors and company sizes.
Even though I am unfortunately unable to calculate the individual indices myself, as the divisor literally throws a spanner in the works, I have still learned a few new things and hope that you have been able to share in them...
HG Small investor
PS: If you have a few points left on getquin, I'd be delighted too...
Sources
https://www.boerse.de/grundlagen/index-grundlagen/Berechnung-von-Indizes
https://www.hsbc-zertifikate.de/dam/jcr:b9b5c32f-ad2d-407a-ae4f-208d9e5ef394/202406_so_wird_der_dax_berechnet.pdf
https://www.flatex.de/boersenwissen/aktien-und-indizes/dow-jones/
https://www.sparkasse.de/pk/ratgeber/finanzglossar/dax.html
https://www.hermoney.de/boerse-geldanlage/etf/indizes-berechnung/
https://de.m.wikipedia.org/wiki/DAX
https://www.deutsche-boerse.com/dbg-de/media/news-stories/explainers/DAX-Index-Benchmark-und-Barometer-f-r-die-deutsche-Wirtschaft-148654
And some more... (Just ask me for specific sources)
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