What does it mean if the correlation coefficient is positive, negative, or zero?


The correlation coefficient is a measure that determines the degree to which the linked movement of two variables. The most common correlation coefficient, generated by the product-moment Pearson correlation, can be used to measure the linear relationship between two variables. However, in a non-linear relationship, the correlation coefficient may not always be a suitable measure of dependence.

The range of values for correlation coefficient -1.0 to 1.0. In other words, values cannot exceed 1.0 or less than -1.0 through correlation of -1.0 indicates perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation. At any time the correlation coefficient, denoted as R, is greater than zero, it is positive relationship. Conversely, any value less than zero is a negative relationship. A value of zero means that there is no relationship between two variables.

In financial markets, correlation coefficient is used to measure correlation between two securities. When the two stocks, for example, to move in the same direction, the correlation coefficient is positive. Conversely, when two stocks move in opposite directions, the correlation coefficient is Negative.

If the correlation coefficient of two variables is equal to zero, this means that there is no linear dependence between the variables. However, this is only for a linear relationship; it is possible that variables have a strong curvilinear relationship.

If the value of R is close to zero, typically between -0.1 to +0.1, the variables have no linear dependence or very weak linear relationship. For example, suppose that prices for coffee and computing machinery are observed and the correlation is +.0008, which means that there is no relationship, or connection, between two variables.

A Positive Correlation

Positive correlation if the correlation coefficient (R) is greater than 0, means that both variables move in the same direction, or correlate. If R +1 indicates that two variables are compared to a perfect positive relationship; when one variable moves above or below the other variable moves in the same direction with the same magnitude.

The closer the R value is to +1 the stronger the linear dependence. For example, suppose that the value of oil prices is directly related to the cost of plane tickets, with a correlation coefficient of +0.8. The relationship between oil prices and prices has a very strong positive correlation, as this value is close to +1. So if the price of oil decreases, prices follow in tandem. If the price of oil increases, so does the price of plane tickets.

In the table below we compare one of the largest banks in the U.S. Houston JPMorgan chase & co. (JPM) with financial data in select spdr (xlf). As you can imagine Morgan should have a positive correlation with the banking sector as a whole.

We see the correlation coefficient (bottom chart) currently at .7919, which is close to , which indicates a strong positive correlation. A reading above .50 usually indicates a strong positive correlation.

Understanding of the correlation between two stocks or a stock and its industry can help investors to assess whether the stock is trading relative to its partners. All kinds of securities, including bonds, sectors, and etf can be compared to the correlation coefficient.

Negative Correlation

Negative correlation if the correlation coefficient (R) less than 0 and indicates that both variables move in the opposite direction. In short, any value between 0 and -1 means that two securities move in opposite directions. When R 1, the relationship is perfectly negative correlation; in short, if one variable increases, the other variable decreases of the same magnitude, and Vice versa. However, the degree to which two securities are negatively correlated, may change over time and are almost never correlated all the time.

For example, suppose a study is conducted to evaluate the relationship between the ambient temperature and heating bills. The study concludes that there is a negative correlation between the prices in the accounts for heating and the outdoor air temperature. The correlation coefficient is calculated as -0.96. This strong negative correlation indicates that as the temperature decreases outside, the price of heating bills will increase and Vice versa.

When it comes to investing, the negative correlation does not necessarily mean that the securities should be avoided. The correlation coefficient may help investors diversify their portfolio by including a mix of investments that have negative or insignificant correlation with the stock market. In short, while reducing risks of volatility in the portfolio, sometimes opposites attract.

Bottom Line

The correlation coefficient can be a useful definition of the relationship between investment and the market generally or other securities.

This type of statistics is useful in many ways in Finance. For example, it may be helpful in determining how well a mutual Fund behaves compared with its underlying index, or it can be used to determine how mutual behaves in relation to another Fund or asset class. By adding low or negative correlation with a mutual Fund to an existing portfolio, the diversification benefits.

Do you know why questions of correlation for investment? Read 4 reasons why market correlation matters.

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