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Suppose I have 2 stocks and the only thing I know about them is their volatility and that they cointegrate. Let's say vol of stock A is 25% and B is 20%. Will I be able to find a hedge ratio only using the vol of 2 stocks? Assume that they track each other very closely and so mean reversion isn't an issue.

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If your hedge ratio is your least squares beta you would need the covariance to estimate it. –  user2763361 Nov 3 '13 at 9:28
    
Correlation would also help. For a minimum variance hedge ratio, $$h= \rho \sigma_A / \sigma_B$$. See: en.wikipedia.org/wiki/… –  dmanuge Nov 5 '13 at 2:10
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