I'm sort of at a loss, my book doesn't seem to explain it well.

Here is the question:

The standard deviation of stock returns for stock A is 40%. The standard deviation of the market return is 20%. If the correlation between Stock A and the market is 0.70, what is Stock A's beta?

Any help is appreciated! :)

I think the answer is:

beta coefficient for the I-th stock= (the standard deviation of the I-th stock's return/the standard deviation of the markets return) (the correlation between the I-th stock's return and the return on the market).

= .40/.20 (.70)= 2 (.70)= 1.4 beta

could someone let me know if I'm off? Ty in advance :)