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I would like to know a way to compute returns when the total PnL of a strategy can become negative. For example: Total PnL day 1: 100 Total PnL on day 2: -20 Total PnL on day 3: 30

I have that kind of PnL when implementing systematic selling of straddle/strangle on FX options. As I would like to perform a statistical analysis on the return series such as the Bootstrap Reality Checkof White, I need to be able to compute daily returns for each strategies. However, the fact that the PnL can become negative distort the analysis.

Any ideas ? Thanks :)

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    $\begingroup$ It is true that the value of an option position (in isolation) can go negative, whch makes it impossible to compute percentage returns. But in real life if you are selling a straddle your broker will require that you have enough cash or other collateral in the account to insure that even under reasonably unfavorable scenarios the value of your account stays positive. If the account value ever goes to zero they will close your account. $\endgroup$
    – nbbo2
    Jul 10 at 12:18

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Why don't you use an absolute return series, e.g. 100, -120 and 50, based on your given figures? White's reality check, permutation checks etc. will work with this type of return series just as well as with log returns (which I presume is the thrust of your question, i.e. you can't take the log of a negative number).

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