Interpretation of correlation (coefficient)

Question

In an discussion we were confronted with a very special opinion about correlation in respect of financial assets.

The widely used correlation coefficient is used here to give an idea about how different assets were behaving in the past.

So one came up with the following interpretation:

Correlation coefficient --> Percentage of times the two assets behave in the same way:
+1.00 --> 100%
+0.99 --> 90%
+0.93 --> 80%
+0.79 --> 70%
+0.49 --> 60%
+0.00 --> 50%
-0.49 --> 40%
-0.79 --> 30%
-0.93 --> 20%
-0.99 --> 10%
-1.00 --> 0%

Which, in my opinion, is plain wrong. As far as I remember, an correlation of 0.00 has the meaning "One cannot tell how Asset b will behave in respect of the development of Asset a". Especially the probabilty of "Asset b will not do any significant move" is missing in a 50% chance.

What is the meaning of a "0.00" correlation? How can negative correlation coefficients be interpreted? Is an percentage of times a good way of doing that?

edit:

He used the vectors

a   b
1   1
2   2
3   3
4   4
5   5
6   6
7   5
8   4
9   3
10  2
11  1

To calculate those values in excel, leveraging the correl() function.

Answer 1

I have reproduced what your friend has done. You are right that it is plain wrong. In the image I have given a counterexample of the choice of b values for 50% correct scenario and have illustrated to you that that correlation is not 0 depending on the choice of the values that your b takes for those that do not move the same way. To be polite, the calculation of percentages are utterly wrong and depend on the choice of values b takes to relate that percentage to correlation. Go back to your friend and show him the counterexample. Good luck @Graham Kemp has given you the right explanation

Answer 2

The correlation coefficient measures the strength of linear relation between two variables.

The closer the correlation is to plus-one or minus-one the stronger the linear relationship.   A correlation coefficient of exactly plus-one means there is a perfect, direct, increasing linear-relation.   A correlation coefficient of exactly minus-one means that there is a perfect, direct, decreasing linear relation.

A correlation of zero means there is no linear relation.   Note that this does not exclude the possibility of a non-linear relationship.

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I am not sure how those percentages might be derived.   However, a correlation coefficient of one means that increasing one variable always increases the other by some fixed proportion, and a correlation coefficient of minus one means increasing one variable always decreases the other by some fixed proportion.

However, while a correlation coefficient of zero could mean that the two variables are independent, it need not.   They could be related in a non-linear way.