In finance and investments, correlation is a statistical measure that calculates the degree to which two equities or securities move in relation to one and the other. This measurement is very useful in portfolio management, and it is calculated as the correlation coefficient in advanced portfolio overseeing. The value of the correlation coefficient is expected to fall between -1.0 and +1.0 after it has been computed.
A Little More on What is Correlation
We earlier stated that the correlation coefficient is expected to be between -1.0 and +1.0. Correlation can be of three types; the perfect positive correlation, the negative correlation, and the neutral correlation. When the correlation coefficient is equal to 1.0, then it is said to be a perfectly positive correlation. However, when it’s -1.0, then it’s is a negative correlation. In a situation where the correlation coefficient is 0, it simply means that there’s no relationship between the two compared securities.
For instance, the S&P 500 index which is a perfect example of a large cap mutual fund usually has a correlation of 1.0. This is a perfect positive correlation. Other smaller mutual funds however have correlations close to the 0.8 levels, thus they’re positive, but cannot be called perfect. On the other hand, negative correlation is commonly found in put options and their underlying stocks. This is because as the stock price increments, the put option falls and vice versa. This action is usually more direct than the positive correlation and it carries high magnitude too.
Examples of Correlation
The calculation of correlation is very useful to investors, traders and security analysts, as it serves as an important factor in determining the risk reduction rewards of diversifying a portfolio.
Let’s say for instance that a trader wishes to calculate the correlation between the following data sets:
C: 41, 19, 23, 40, 55, 57, 33
D: 94, 60, 74, 71, 82, 76, 61
The trader in this case will need to follow three steps. First, he’d have to add all the value of C to get Sum (C), as well as add up the values of D to arrive at Sum (D). After this, he’ll need to multiply each C value with its subsequent D value and then add them together to get the sum of C and D.
SUM(C) = (41 + 19 + 23 + 40 + 55 + 57 + 33) = 268
SUM(D) = (94 + 60 + 74 + 71 + 82 + 76 + 61) = 518
SUM(C,D) = (41 x 94) + (19 x 60) + (23 x 74) + … (33 x 61) = 20,391
Next, this trader will be required to take each value of C and square it get SUM (C^2). Same thing applies to D.
SUM(C^2) = (41^2) + (19^2) + (23^2) + … (33^2) = 11,534
SUM(D^2) = (94^2) + (60^2) + (74^2) + … (61^2) = 39,174
Using the idea that there exists seven observations, n, the trader can use the formula below to solve for the coefficient.
r = (n x (SUM(C,D) – (SUM(C) x (SUM(D))) / SquareRoot((n x SUM(C^2) – SUM(C)^2) x (n x SUM(D^2) – SUM(D)^2))
Thus, his correlation is given below
r = (7 x 20,391 – (268 x 518) / SquareRoot((7 x 11,534 – 268^2) x (7 x 39,174 – 518^2)) = 3,913 / 7,248.4 = 0.54.