When it comes to investing, a

For example, suppose a study is conducted to assess the relationship between outside temperature and heating bills. The study concludes that there is a negative correlation between the prices of heating bills and the outdoor temperature. The correlation coefficient is calculated to be -0.96. This strong negative correlation signifies that as the temperature decreases outside, the prices of heating bills increase (and vice versa).
When it comes to investing, a negative correlation does not necessarily mean that the securities should be avoided. The correlation coefficient can help investors diversify their portfolio by including a mix of investments that have a negative, or low, correlation to the stock market. In short, when reducing volatility risk in a portfolio, sometimes opposites do attract.
For example, assume you have a $100,000 balanced portfolio that is invested 60% in stocks and 40% in bonds. In a year of strong economic performance, the stock component of your portfolio might generate a return of 12% while the bond component may return -2% because interest rates are rising (which means that bond prices are falling).
Thus, the overall return on your portfolio would be 6.4% ((12% x 0.6) + (-2% x 0.4). The following year, as the economy slows markedly and interest rates are lowered, your stock portfolio might generate -5% while your bond portfolio may return 8%, giving you an overall portfolio return of 0.2%.
What if, instead of a balanced portfolio, your portfolio were 100% equities? Using the same return assumptions, your all-equity portfolio would have a return of 12% in the first year and -5% in the second year. These figures are clearly more volatile than the balanced portfolio's returns of 6.4% and 0.2%.
Linear Correlation Coefficient
The linear correlation coefficient is a number calculated from given data that measures the strength of the linear relationship between two variables: x and y. The sign of the linear correlation coefficient indicates the direction of the linear relationship between x and y. When r (the correlation coefficient) is near 1 or −1, the linear relationship is strong; when it is near 0, the linear relationship is weak.
Even for small datasets, the computations for the linear correlation coefficient can be too long to do manually. Thus, data are often plugged into a calculator or, more likely, a computer or statistics program to find the coefficient.
The Pearson Coefficient
Both the Pearson coefficient calculation and basic linear regression are ways to determine how statistical variables are linearly related. However, the two methods do differ. The Pearson coefficient is a measure of the strength and direction of the linear association between two variables with no assumption of causality. The Pearson coefficient shows correlation, not causation. Pearson coefficients range from +1 to -1, with +1 representing a positive correlation, -1 representing a negative correlation, and 0 representing no relationship.
Simple linear regression describes the linear relationship between a response variable (denoted by y) and an explanatory variable (denoted by x) using a statistical model. Statistical models are used to make predictions.
 
Simplify linear regression by calculating correlation with software such as Excel.
In finance, for example, correlation is used in several analyses including the calculation of portfolio standard deviation. Because it is so time-consuming, correlation is best calculated using software like Excel. Correlation combines statistical concepts, namely, variance and standard deviation. Variance is the dispersion of a variable around the mean, and standard deviation is the square root of variance.
Finding Correlation Using Excel
There are several methods to calculate correlation in Excel. The simplest is to get two data sets side-by-side and use the built-in correlation formula: