In Haug's pricing book, bleed-offset vol is simply one day theta divided by vega. He says you can have a negative offset-vol (in the case of positive theta) but for a plain long option the offset-vol is negative (since it's a negative divided by a positive). So if I own a call, and the bleed-offset vol is -0.50, how am I supposed to interpret that? I would think it should be positive (not negative) since an increase in vol will offset the theta.