What does standard deviation show?

Standard deviation in mathematics is one of the main indicators characterizing the dispersion of an observed value. The term "dispersion" refers to the dispersion of this observed value relative to some average value. Simply put, dispersion shows how the values ​​obtained as a result of certain actions are located from the average, and standard deviation allows us to estimate how they are distributed. If you want to know how to Find Standard Deviation in R please read here https://hostman.com/tutorials/how-to-find-standard-deviation-in-r/.

All this fully applies to asset prices and other parameters used in trading on financial markets. For example, dispersion will show the difference between the closing price of each bar of the quote chart and the average price for a certain period of time. Using standard deviation, you can estimate how these prices will be located.

The formula for calculating the standard deviation is:

Here:

• n is the number of readings (measurements) of the observed value, for example, closing prices;
• Ci - values ​​of the observed quantity (closing price);
• Ccp is its average value over the period.

Standard deviation in investment

Since standard deviation can be considered a measure of volatility, it can be used to determine the level of risk in investments. This is the approach used in Markowitz's portfolio investment theory.

If an investor invests in a single instrument, the risk is taken to be equal to the standard deviation of returns. To calculate it:

1. Select a period for measuring profitability based on historical data, for example, one year.
2. The asset's profitability is calculated over this interval.
3. Determine the yield for each smaller time interval (for example, a month).

The calculation results can be interpreted as follows:

• If the yield of an instrument is 15% and its standard deviation is 5%, then with a probability of 0.68 the investor will receive an income from 10% to 20% per annum.
• Making a profit in the range of 5-25% is possible with a probability of 0.95.
• The probability of remaining without profit or receiving up to 30% per annum for an investor will be 99.5%.

Important! The investor must understand that the calculation results show the development of events on the selected historical interval. They can be extended to future periods only with a certain degree of assumption - results in the past do not guarantee similar results in the future.

When working with a portfolio of assets, to determine the overall investment risk, the standard deviation is calculated for each instrument, and then the overall value is calculated taking into account the weight of the assets in the portfolio and the relationship (covariance or correlation coefficient) between them. In general, the task of forming a portfolio from a mathematical point of view comes down to choosing the weights of assets in the portfolio in such a way as to obtain the minimum overall risk with the maximum return.

The standard deviation as a risk measure and the beta indicator obtained using it, proposed by Sharpe, are used by investors in solving other problems. For example, this is the calculation of investment efficiency indicators - the Sharpe, Sortino, etc.

Standard Deviation in Trading

In trading, the standard deviation of asset prices is widely used to measure volatility. For traders who use this indicator in trading systems (TS), a standard deviation indicator (StDev) is created, which is included in the delivery set of almost all known trading platforms.

StDev indicator

The standard deviation indicator StDev displays a line in a separate window, the values ​​of which are calculated as the standard deviation of the selected prices from the moving average over a given period. In this case, the formula takes the form:

Here:

• StDev - current value of the standard deviation indicator;
• N - calculation period of the indicator and moving average;
• Ci - the price at each interval of the price chart during the calculation period;
• MA (N, i) - values ​​of the moving average with period N on the price interval.

In the settings, the trader can specify:

• the price at which the indicator is built - Close, Open, High, Low, Median, Typical, Weighted;
• moving average type;
• calculation period.

The indicator line clearly displays the current price volatility. It grows when the market is highly active and decreases when it decreases. The indicator readings do not allow determining the direction of movement, so they are rarely used to generate signals to enter the market or close positions.

Typically, traders use the indicator as follows:

1. In the StDev window, levels of low and extremely high volatility are marked. They are determined empirically by analyzing the indicator chart over a significant time interval in history. The indicator being below the lower level indicates a lull in the market (flat, or a protracted flat correction). The indicator above the upper level indicates excessive volatility of the asset - a powerful price impulse in the direction of the trend or a corrective movement.
2. After the indicator line breaks through the lower level, they look for a moment to enter the market. The direction of entry is in the direction of the price movement, which is identified using other tools, such as oscillators or Price Action patterns.
3. After the indicator line goes above the upper level, they expect a return below it and look for entry points: in the direction of the trend, if the impulse for a breakout was during the correction; against the trend (for a correction or reversal), if the impulse was caused by the trend movement.

Thus, the StDev indicator is rarely used as an independent tool. In most cases, it acts as a supplement to other tools. Another option is to use it when creating indicators.

Standard deviation in other indicators

The most famous tool that uses standard deviation in calculations is Bollinger Bands. In the algorithm, this indicator determines the width of the dynamic price channel (the position of the upper and lower boundaries).

In addition to the calculation period, the settings specify the deviation coefficient, which shows at what distance from the center line (in calculated values ​​of the standard deviation) the channel boundaries are located. The default setting (the coefficient is 2) shows that the price is at least 95% of the time inside the channel.

Standard Deviation in Graphic Analysis Tools

Using standard deviation, traders build one of the types of price channels, which is called the standard deviation channel. This graphic object is also included in almost all modern trading platforms. To construct it, the trader selects only the initial and final candles of the interval on the price chart. The channel centerline and the standard deviation value are calculated automatically. The channel boundaries are located from the centerline at a distance determined by the standard deviation and, as in the Bollinger Bands indicator, the deviation coefficient.

The signal to open a position is obtained by the same principles that are used when working in any price channel : on rebounds or on breaking through the boundaries. In this case, it is possible to fairly accurately estimate the probability of developments. Thus, with a deviation coefficient equal to two:

• the price will remain within the channel with a 95% probability;
• a breakout of the channel boundary is an event with a probability of no more than 5%, which with high reliability indicates the non-random nature of the price impulse on which the breakout was recorded.

Thus, the standard deviation is a useful tool for investors and traders. The former use it to determine the risks of investing in individual assets and their portfolios, the latter measure the volatility of prices on the market, build trading systems. Indicators and graphical objects built on its basis allow you to get reliable trading signals.

Why do you need a database management system?

For most companies, data is a key asset that determines the success and efficiency of the business. A database management system plays a key role in ensuring that this data is managed effectively. Here are some reasons why a DBMS is essential in modern business:

- Structured data management: A DBMS allows companies to store data in an organized and systematic manner. This ensures easy access to information and simplifies the processes of searching and analyzing data.

- Data Security: An important aspect is to ensure data security. A DBMS allows you to regulate access to data by defining different levels of access for different users. This helps prevent unauthorized access and protect confidential information.

- Faster decision making: The DBMS provides fast and convenient access to data, which allows employees to make informed decisions faster. The reports and analytics provided by the system help identify trends, predict results and optimize business processes.

Types of Database Management Systems

1. Relational Database Management System (RDBMS)
2. Object-oriented database management system (OODBMS)
3. Hierarchical Database Management System (HDMS)
4. Network Database Management System (NDBMS)

Below we will talk in more detail about each of these types of platforms, discuss their features and areas of application.

Relational database management system

A relational database is a collection of data that is related to one another, allowing different data points to be combined to improve usability. A relational database management system is software that manages the storage and sharing of such databases.

An RDBMS organizes data in a relational database by defining functional dependencies between different data points. It ensures that data is stored in an organized manner, making it easier for employees to find and use the information.

The related points can be time, data or logic, and the relationships can be classified as follows:
a) One-to-one: a data point in one table is related to a data point in another table.
b) One-to-many: a data point in one table is related to multiple data points in another table.
c) Many-to-one: multiple data points in one table are related to a data point in another table.
d) Many-to-many: multiple data points in one table are related to multiple data points in another table.

The platform uses Structured Query Language (SQL), which allows users to execute queries and retrieve the information they need. Key features of the system include:
- Storage of large amounts of data
- Fast data retrieval
- Ability to simultaneously access data by multiple users.

Object-oriented database management system

An object-oriented database is a collection of materials presented as objects. In this type, multiple points are combined into one unit, making it easier to find and use information.

An OODBMS is software that stores and manages databases as objects. It allows workers to search for complete objects rather than individual data points, making searches more efficient and faster. This type of database is used for high-performance tasks such as software development and programming that require faster decision making. 

The characteristics of an object-oriented database include:
- Direct relationship between database objects and real-world scenarios, which prevents objects from losing their purpose.
- Object identifier, which allows objects to be quickly accessed and used.
- Support for various data types, such as images, text, and graphics.
 

Hierarchical Database Management System

A hierarchical database is a collection of data organized in a tree structure. In this structure, data is linked and arranged from top to bottom, with the primary data point at the top and secondary data points following in the hierarchy based on their relevance. An example of a hierarchical database is the organizational structure of a business.

An IDBMS is software that stores and manages hierarchical databases. It ensures that the data hierarchy is maintained accurately according to its use in work processes.

Characteristics of a hierarchical database management system include:
- Ease of adding and deleting data in a hierarchy.
- Ease of searching and accessing data in a hierarchy.
- Adherence to a one-to-many relational data model.

Hierarchical databases are widely used in organizations to represent structured data such as organizational charts, product and service classifications, graphical structures, and others.

Network Database Management System

A network database is a collection of data in which each data point is linked to multiple primary and secondary data points. This means that the data is organized in a network where each data point may have multiple relationships with other data points.

A network database is software that stores and manages interconnected data in a network database. It allows you to create and manage complex data structures while providing quick access to information. This software was created to overcome the shortcomings of the hierarchical database model, which does not allow relationships between data points other than the top-down flow.