The effectiveness of a hedge is determined by:

The effectiveness of the hedge is solely determined by the correlation between the position being hedged, and the position being used as the hedge. A hedge can be perfect when correlation is 1, and will be less than perfect when it is anything other than 1.The effectiveness of the optimal hedge is given by the formula √(1-ρ2), where ρ is the correlation between the two. Therefore Choice 'a' is the correct answer. Standard deviations affect the hedge ratio, not the effectiveness of the hedge.

(Note: In other texts, hedge effectiveness is explained to be measured by ρ2, which is essentially the same as √(1-ρ2), both expressions being functions of ρ. You can use either, being aware that one measures the variance explained, and the other is a measure of the unexplained variance.)