why people say vol swap is short vol of vol?
Say we consider a simple vol swap with 3% strike with two days maturity here: scenario1: realized vol is 2% on day1 and 4% on day2 scenario2: realized vol is 1% on day1 and 5% on day2 in both scenarios, same mean for vol but scenario2 has higher vol of vol.
In scenario2, vol of vol is higher and vol swap payoff is higher.
That means vol swap is actually long vol of vol, right? Did I miss something here?