Probabilty of negative return the higher the smaller the standard deviation?

[christinefin]

Assume two stocks have normally distributed returns. The smaller the standard the deviation the more concentrated. So for instance the probabilty of of negative return is higher when the standard deviation is smaller? But both curves integrate to the same value - 1 ?

 

[christinefin]

Unfortunately I can’t delete my question. This is a complete wrong formulation of my actual question and by now my problems is solved. I apologize!!

 

[busprof]

Just for the sake of instruction, I’ll assume that the problem read “assume that both stocks have an expected return of -1%”, and solve it anyways.
The stock with a lower standard deviation of returns has a mean return that is “further away” from zero in statistical terms (i.e. in terms of number of std deviations from zero). Therefore, the right-tail of its distribution (i.e. the area above zero) is larger. In other words, the probability of a return above zero (a positive return) is greater).
Since the total probability adds to one, this means that the probability of a negative return is smaller for the stock with a lower standard deviation.