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How does one calculate the investment of a zero initial investment asset, specifically a variance swap?

In this asset the payoff is given by the difference between the realized variance in a certain maturity and the agreed swap rate, multiplied by a certain notional amount. If the swap rate is the fair market expectation of the realized volatility (similar to the forward price in a future contract) and given that the payoff is a zero sum game, there should be no place for an initial payment (I am unaware if this is how these instruments are actual traded, please clarify this if you have more information).

I am aware that these instruments may have margin requirements but I am unaware if that would be a value for the initial investment or how margins are defined for that matter.

My goal is to replicate artificially the payoffs of such an instrument and I would like to know if it is possible to express this information as returns.

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please define what you mean "return". Once this is clearly defined, we should have some ideas for the computations. –  Gordon Aug 1 at 20:34
    
Well, good point. Something comparable to log return of equity, for instance. I know these are different asset classes but something which would be comparable to that. Alternatively, something which would make the analysis of an investment strategy "correct" by practitioner standards but which is disconnect from investment volume (I. E. Regardless of 1 dollar or 100) –  sasstudent Aug 1 at 20:35

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