Definition
Correlation refers to the statistical relationship between two or more variables that ranges between -1 and 1, where -1 signifies a perfect negative relationship, 0 suggests no relationship, and 1 indicates a perfect positive relationship. On the other hand, covariance measures how much two random variables vary together. It is unbounded and thus, its interpretation isn’t easy or clear-cut compared to correlation.
Key Takeaways
- Correlation is a statistical measure that indicates the extent to which two or more variables move in relation to each other. It provides a scaled understanding of relationships, ranging from -1 (perfect negative relationship) to 1 (perfect positive relationship), with 0 indicating no relationship.
- Covariance is another statistical measure that indicates the direction of the relationship between two variables – positive or negative. However, it does not give the degree of the relationship. Its values are unbounded, and can go from positive infinity to negative infinity.
- Both covariance and correlation are used in portfolio theory to assess the relationship between different assets or investments, providing insights into risk diversification. However, correlation is often favored over covariance since it offers a standardized measure, which allows for more straightforward comparisons and interpretations across different situations.
Importance
Correlation and Covariance are important financial terms used in statistics to measure the relationship and the degree of dependency between two random variables. While both terms provide insight into how two variables might change together, they communicate distinct pieces of information.
Correlation reveals the strength and direction of a linear relationship between two variables, ranging from -1 to 1. It remains unaffected by the scale of values and is standardized making it extensively used to understand the relationship in finance.
Covariance, on the other hand, provides a measure of the degree to which two variables vary together, where a positive number signifies that the variables increase or decrease together, while a negative number indicates they vary inversely. Understanding both concepts is crucial in finance for diverse applications including risk management, portfolio diversification, and in the prediction of future performance.
Explanation
Correlation and covariance are widely used concepts in finance, particularly in portfolio theory, to measure the relationship between the returns of different assets. Their primary purpose is to understand how different securities move in relation to each other, which is essential in risk management and diversification of investment strategies. Investors and financial analysts use correlation and covariance to create diversified portfolios by combining assets that have a negative or low positive correlation—this can help to reduce the overall risk.
Covariance serves as a tool to determine the directional relationship between the returns on two different securities. It indicates how two stocks tend to vary together. If one stock tends to increase when the other increases, the covariance would be positive.
Conversely, if one stock tends to decrease when the other increases, the covariance would be negative. Correlation, on the other hand, standardizes the measure of interdependence between two variables and ranges between -1 and 1. If the correlation is 1, the two securities move in perfect sync with each other; if -1, they move in exactly the opposite directions.
If it’s 0, it indicates that the securities’ price movements are unrelated. Please note that while correlation indicates the strength and direction of a relationship between two variables, it does not indicate causation.
Examples of Correlation vs Covariance
Stock Market Analysis: Analysts in the finance industry often use both correlation and covariance to understand the relationship between different stocks in a portfolio. Covariance measures how two stocks move together (either in the same or opposite directions), while correlation measures the strength and direction of this relationship. A positive high correlation indicates that the two stocks tend to rise and fall together, while a negative correlation means that they move inversely. On the other hand, covariance might reveal if the stocks move together but does not provide the strength of the relationship.
Investment and Risk Management: An investor with a diversified portfolio might utilize correlation and covariance to assess the risk profile. For instance, they might want stocks in their portfolio that have a negative or low correlation to reduce the risk. Let’s say, investor has stocks from Tech and Pharmaceutical sector where Tech sector returns show a low correlation or negative covariance to returns from Pharma sector. This means when Tech sector returns are not performing well, it might be offset with the returns from Pharma sector.
Real Estate and Economic Factors: Let’s consider the correlation and covariance between real estate prices and interest rates. Covariance might demonstrate that these two variables move in opposite directions, i.e., when interest rates go up, real estate prices tend to go down. The correlation would show the strength of this relationship. A high negative correlation indicates a strong inverse relationship, meaning that an increase in interest rates is very likely to lead to a decrease in real estate prices. This kind of information can be crucial in deciding when to invest in real estate.
Frequently Asked Questions: Correlation vs Covariance
What is Correlation?
Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate in relation to each other. A positive correlation indicates the extent to which those variables increase or decrease in parallel; a negative correlation indicates the extent to which one variable increases as the other decreases.
What is Covariance?
Covariance is a measure of how much two random variables vary together. It’s similar to correlation but differs in the following ways: covariance can take on any value while a correlation is limited: -1 to +1, covariance is affected by the change in scale, if all the value of one variable is multiplied by a constant and all the value of another variable are multiplied, by a similar or different constant, then covariance is changed.
What is the difference between Correlation and Covariance?
The difference between correlation and covariance lies in the range and interpretation of their values. Covariance can take any value from -∞ to +∞ while Correlation values lie between -1 and +1. Covariance indicates the direction of the linear relationship between variables whereas Correlation on the other hand measures both the strength and direction of the linear relationship between two variables.
How are Correlation and Covariance used in finance?
Both correlation and covariance are used in portfolio theory. Covariance is used to calculate the variance of a portfolio’s returns, while correlation is used to diversify a portfolio. A perfect positive correlation (+1) implies that as one security moves, either up or down, the other security will move in lockstep, in the same direction. Alternatively, perfect negative correlation means that if one security’s price moves in one direction, the other security moves in the exact opposite direction.
Related Entrepreneurship Terms
- Scatter Plot
- Standard Deviation
- Variable Relationships
- Statistical Analysis
- Risk Diversification
Sources for More Information
- Investopedia: This is a comprehensive financial education website providing information on everything from investing and retirement planning to mortgage, tax and credit debt.
- Finance Formulas: This is an educational website that provides different kinds of financial formulas, explanations and calculations.
- Corporate Finance Institute (CFI): CFI is a leading provider of online financial analyst certification programs with courses for individuals at all skill levels.
- Khan Academy: Khan Academy is a non-profit educational organization that provides free online courses in many disciplines, including finance.
