With a few explanatory notes below... https://twitter.com/nonergodicgame/status/1337866554080366596

The payoff of a variance swap is

variance notional x (realized vol ^2 - strike ^2)

Why does a variance swap have delta (instantaneous sensitivity to spot price returns) intraday?

Because its payoff is a function of daily squared returns. Once the underlying starts to move in one direction, the swap accumulates delta in that same direction. That delta grows as the return gets larger, because of the squared thing. d(r^2)/dr = 2*r.

if you're long a variance swap, and the underlying is down 1%, you'd sure rather it went down another 1% (giving you 2% ^ 2 in the payoff function) rather than up 1% (giving you 0) by the end of the trading day

a variance swap can be synthetically and statically replicated by a portfolio of long options, which has the exact same gamma profile (constant as a function of spot price). The variance swap "delta hedges" itself at the end of the day (by virtue of the daily return observations)

if you're managing the replicating portfolio you have to delta hedge it yourself, which speaks to one of @VolatilityStu 's follow up questions (if you are a dealer who is long variance facing a client and short the replicating portfolio to hedge, what do you do on the close?)

the calculation itself here is trivial, its just about taking the derivative of r_t^2 with respect to r_t and getting the various unit scalings right.

typically dollar delta is quoted in market value terms, e.g. -$700 million delta means -$7 million per 1% move

and you animals who quote S&P delta in e-mini contract equivalents, don't @ me, I'm too old for multiplying and dividing numbers in my head