# How to Calculate Correlation of Investment Returns

by Edriaan Koening

When investing, diversifying your portfolio can help reduce your risk exposure. This means having your money in unrelated industries and sectors so that a downturn in one area of the economy doesn't hurt your entire portfolio. Some investments often move together in value, while others move in opposite directions. Correlation measures the movement of one investment relative to a benchmark. The correlation coefficient ranges from -1 to 1, with -1 indicating that they move in opposite directions and 1 suggesting that they always move together.

1. Gather the data of the investment you want to measure, and the benchmark over the period you want to measure. For example, you can choose a stock that you hold and the S&P 500 index, and decide to use a period of one year. The longer the period, the more accurate your result will be. You need the prices and standard deviations.

2. Find the returns of both the investment and your benchmark over the analysis period. For example, if you measure monthly returns over a year, you will have 12 return figures for the investment and another 12 for the benchmark. Deduct the price of the investment at the end of the month by the price of the same investment at the beginning of the month. Then divide the result by the price at the beginning of the month. For example, if a stock is worth \$10 at the beginning of the month and \$15 at the end of the month, then the return is 0.5 (from \$5/\$10).

3. Find the average return figure of both the investment and the benchmark. Do this by adding up all the return figures by the number of returns you have in your sample.

4. Deduct the average benchmark return from the first benchmark return figure, then divide the result by the standard deviation of the benchmark. Do the same calculation with the investment returns -- deduct the average investment return from the first investment return figure, then divide the result by the standard deviation of the investment. Multiply the two results and write down the product. Do the same with every single return figures in your sample. If you collect 12 monthly return figures over one year, then you have to do this 12 times.

5. Add up all the results you get from the calculations in Step 4.

6. Deduct 1 from the number of samples you have. For example, if you take 12 return figures for both the investment and the benchmark, then you will have 11. Divide 1 by this number.

7. Multiply the result from Step 5 by the result from Step 6. This is the correlation coefficient of the investment relative to the benchmark.

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