Investors, when selecting securities for their portfolio, often encounter situations where, for instance, the price movements of several stocks are identical. Essentially, the dynamics of such assets demonstrate a close connection (correlation) between them. Including a set of such correlated instruments in an investment portfolio can lead to a significant increase in both returns and risks. The correlation coefficient helps assess the depth of this connection.

**From this article you will learn:**

**The fundamental principles of correlation and its significance in financial markets.****Practical strategies for using correlation to forecast price movements.****How correlation aids in portfolio diversification and risk mitigation.**

## Understanding Correlation

Correlation is a statistical concept that shows the relationship (mutual influence) between two random variables. Since the movements of security prices in the stock market are largely similar to the behavior of random variables (although not entirely), many patterns of statistical analysis work well with them.

In practice, correlation in working with securities allows one to estimate the likelihood of synchronous price movements of two assets, such as stocks or a stock and an index. This means that with strong correlation, when the price of one stock rises, the other will also increase. Conversely, when an index falls, the correlated stocks will also decline.

Correlation is a statistical concept that shows the relationship (mutual influence) between two random variables. Since the movements of security prices in the stock market are largely similar to the behavior of random variables (although not entirely), many patterns of statistical analysis work well with them.

In practice, correlation in working with securities allows one to estimate the likelihood of synchronous price movements of two assets, such as stocks or a stock and an index. This means that with strong correlation, when the price of one stock rises, the other will also increase. Conversely, when an index falls, the correlated stocks will also decline.

## Correlation Coefficient

The degree of interdependence of variables (in the case of the stock market – security prices, index values, etc.) is depicted by the correlation coefficient. It can take any value in the range from -1 to 1. Chaddock’s scale for the coefficient values interprets the connection between the observed values as follows:

- 0 – 0.3 – very weak;
- 3 – 0.5 – weak;
- 5 – 0.7 – moderate;
- 7 – 0.9 – high;
- 9 – 1 – very high.
- 0 – complete absence of connection;
- 1 – absolute interdependence.

When the coefficient is less than 0, it indicates a negative (inverse) correlation. For the stock market, this means that the prices of the analyzed assets move in opposite directions: when the price of one rises, the other falls, and vice versa.

### Formula for Calculating the Correlation Coefficient

In statistics, the correlation coefficient is calculated using the values of covariance and the standard deviation of the analyzed variables. For working with securities, the following form of this relationship is used:

In this equation:

R_{1,2} – the correlation coefficient between the prices of the 1st and 2nd assets;

P_{1i} , P_{2i} – the prices of the assets at the i-th observation interval (e.g., the closing price on the i-th day).

P_{1}_{с} , P_{2}_{с} – the average prices over the entire study period, which includes n observation periods.

This relationship is known as Pearson’s formula. In practice, it is somewhat inconvenient because it requires the calculation of average values. Its variant, which uses only the price data at each i-th observation period (asset prices), has the form:

The first version of the formula becomes more convenient if, in addition to asset prices, one uses the values of a technical analysis tool such as the moving average with a period equal to n. This approach allows for the simple implementation of a custom indicator for trading platforms that will reflect the correlation dynamics. It can generate an interesting set of trading signals.

## Using Correlation in Trading and Investing

Understanding correlation and its quantitative assessment (coefficient) is successfully used by both traders, who extract speculative profit in the stock market, and investors.

### Correlation in Trading

In short-term securities trading, the concept of correlation is used to predict the price of certain assets. The essence of the strategy is to find instruments with a high correlation coefficient but with price changes lagging over time.

In this case, the trader waits for the price change of the first asset (called the leader or guide) and makes a trade in the same direction for the second asset.

### Correlation for Investors

In investing, correlation is used when forming and reviewing investment portfolios as a tool for asset assessment, diversification, and hedging.

- Pearson’s Formula is well-suited for assessing the correlation of the returns of individual securities with the returns of the portfolio (simply replace prices in the equation with returns). In this case, the effectiveness of each individual instrument and its contribution to the overall financial result can be evaluated. Such analysis helps eliminate securities that do not meet set goals and risk levels. Additionally, the reverse task allows for predicting portfolio returns with a high degree of probability.
- Correlation is widely used in the search for suitable assets for diversification. Portfolio theory suggests that the best choice is securities with zero correlation, so investors must look for assets with low correlation coefficients. This typically leads to the formation of a set of instruments from different industries and even countries, significantly reducing investor risks even during crises.
- Securities with Negative Correlation Coefficients are used for mutual hedging. In this case, with the correct selection of weights, the loss from one asset is fully compensated by the profit from the second. Moreover, due to the dynamics of both the prices of the securities and the correlation itself, a positive overall result can be achieved.

Thus, correlation and its coefficient should be part of every investor’s toolkit. What may seem like complex equations at first glance can be easily calculated even using Excel. Proper use of correlation can enhance portfolio efficiency, reduce investment risks, and even generate substantial profits in short-term trading.