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I understand that VIX futures are usually in contango and so a portfolio that holds futures with a weighted average expiration of 30 days will "roll" down to equal the VIX index at maturity.

This is usually given as the reason why XIV makes money most of the time.

But a portfolio that holds VIX futures with a weighted average expiration of 30 days has to keep adjusting its weightings as time passes, adding more weight to the 2nd future. This means that although the falling value of the front contract reduces this weighted average, the purchase of more 2nd month futures pushes up the weighted average.

So are we saying that the loss from the fall in value in the first contract is greater than the gain in weighted average from moving into higher valued 2nd month options?

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  • $\begingroup$ I'm not sure I understand. Take an equity future contract on a stock which pays dividends and zero rates. Typically, this would result in the forward curve being in backwardation: the future price $F(t,T)$ will be lower than $S_t$ at all times $t$ (due to expected divs) and converge to $S_T$ at time $T$. But this does not mean that you know for sure that $F(T,T) - F(0,T) = S_T - F(0,T) $ (P&L at expiry $T$ of being long the future at time $t=0$) will be positive. It all depends on the path of the stock price. $\endgroup$ – Quantuple Nov 2 '17 at 9:23
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I found the answer.

The loss in value is due to the fact that the portfolio of 1st and 2nd month futures itself loses value before it is readjusted. So when the readjustment is made (at the end of the day or however frequently it happens) to maintain a 30-day weighted average, a very small (but not insignificant) amount of money is lost.

It is not due to the fact that the 2nd month contract is more expensive, but rather due to the fact that both the 1st and 2nd month contracts lose value for the interval they are held for before each rebalancing.

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