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Maybe I am very wrong. At least one of my friends agree with my view point. I was in a project to find out the optional structure of a butterfly. My goal is to make gamma and vega neutral, and find the optimal weight of the three options. It sounds pretty easy and I can successfully find the optimal weight.So my boss wants to see the portfolio vol. I am of the opinion that I should weight by underlying variance of each individual options (no correlations), and take sqrt of it. However, my boss says I should weight by stdev. Even more weird, for long position, I take +, short position, I take -. Thus my portfolio vol becomes a very small number (even negative probably).Am I crazy or my boss just drank too much last night?

Maybe I did not understand well, but how can you forget about correlations?If you have two contracts in a portfolio with market value MV1 and MV2 and volatilities VOL1 and VOL2 (% volatilities!) I would say that the volatility (%volatility) of the portfolio is:sqrt( MV1^2 * VOL1^2 + MV2^2 * VOL2^2 + MV1*MV2*COVARIANCE)/(MV1+MV2)COVARIANCE=CORRELATION*VOL1*VOL2and the resulting portfolio volatility can get quite high if you mix short and long positions.If you have options on the same underlying CORRELATION=1 or -1 and you can simplify the formula in:(MV1 * VOL1 +/- MV2 * VOL2)/(MV1+MV2)