Portfolio volatility with options

[FT123]

Hi all,
What approaches are available for calculating overall portfolio volatility that account for option positions in a portfolio of both equity and options?

 

[S2000magician]

It’s no different that evaluating the volatility of any other portfolio: use the variances of the returns on all of the constituent securities and the covariances (or correlations) of returns for every pair of securities. If you have positions in a stock and options on that stock, the correlation of returns will be strongly positive for calls and strongly negative for puts.

 

[FT123]

Thank you much for the response! So the value of the option is just added as the asset amount in the standard formula? Eg if you are long two naked calls trading at 2.00 each without any other position in the underlying your asset value is 400 and standard dev and cov of the underlying with the other assets is used in the generic portfolio vol equation?

 

[S2000magician]

Yup.

 

[FT123]

And if you are effectively short an asset via options, or say in this case long two puts at 2.00 each do you enter -400 as the asset value? If you use the price behavior of the underlying for correlation which in this case has a positive correlation to other stocks in the portfolio, but are effectively short the asset via your option position, I imagine you’d have to get the negative sign into the cumulative variance calculation somehow (?)

 

[S2000magician]

Positive weight, negative expected return, negative correlation of returns (probably).