I suppose the key point, in order to help find an answer your question, appears to be what "partly derived" means. 

Well, X is Profit and Y is Profitability and has been calculated from Profit

How was Y (profitability) derived from X (profit)? If a scatter plot of Y on X shows no clear relationship, that, I guess, provides an explanation you are seeking!

I agree that you should start by looking more closely at the relationship between X and Y, and a scatterplot would be a useful tool. It seems odd that they would be unrelated when profitability has been derived from profit.

Thank you very much for your responses. A scatter plot between X and Y is quite scattered, signifying the un-relatedness between the two. This is understandable. However, what concerns me more that A positively determines both X and Y. Should the fact that both have a common determinant, coupled with the fact Y has been derived from X be ground for atleast correlatedness, if not dependence between X and Y.

That A +vely determines both X and Y could happen despite X and Y being unrelated. I suspect that the extent to which A determines X and the extent to which A determines Y may be quite different - as may be seen from the estimates of beta in the two cases.    

I agree with Subash and Paul that it would possible to get the pattern you suggest if the correlations between A and X & Y were both small. If you think in terms of a Structural Equation Model (in this case, a simple path model) with arrows from A to both X and Y, then the implied correlation between X and Y is the product of the separate correlations between A and X and A and Y.

But I still wonder how profits and profitability are not correlated. The only thing I can think of is that you either multiplied or divided profit by something that was random with regard to profit in order to produce profitability.

And as for multivariate versus multivariable, I understand the distinction, but I know that sociologists routinely refer to multivariate analyses when there are multiple independent variables. I associate the other terminology with psychology.

Perhaps you should go back and think about what the CONCEPTS Profit and Profitability are. Profit relates to the past. Profitability relates to the future. You can have a business with great PROMISE of profit (profitability)UNDER NORMAL CIRCUMSTANCES but due to random events (e.g. a drought) ending with very little profit. So, depending on the time frame and the other covariates you are using, the two might be very little correlated. Check this link.

http://financenmoney.in/profit-vs-profitability/

Thank you very much all for sharing you insights. They will be very valuable in further analysis and building argument.