Thread by @bennpeifert

Thread on variance swaps, the good, the bad, and the ugly. Sorry for the delay on this one, New York was too much fun and I didn't have time.

https://twitter.com/mikeandallie/status/1889352614216692192

Variance swaps are very simple. You buy a certain amount of notional at a specified level of implied variance with a specified maturity; you recieve floating (actual realized variance) and you pay fixed (the price you agreed on).

By convention, variance swaps are traded in vega notional (exposure per volatiity point). So I might buy $1 million vega of SPX Mar25 variance at 20. That translates into $1m / 2 / 20 = 25,000 variance notional units (using the chain rule from calculus).

If I buy that swap at 20 and realized volatility over the life of the swap is 21, my floating leg earns 21^2 * 25,000 and my fixed leg pays 20^2 * 25000, and I make $1.025 million, very close to my vega notional.

It's not exact because I bought variance, which is convex with respect to volatility (it's vol squared!). If volatility doubles, my vega exposure in the swap will double. So a variance swap is very leveraged into the tails. Buy at 20 and realize 80, make 150x your initial vega

Sometimes -- and always, in the case of single-name equities -- variance swaps come with caps, typically at 2.5x their initial strike, which determine the maximum possible realized volatility that can be used in the calculation of the payoff. This truncates the extreme tail

THE GOOD: variance swaps are neat and elegant things with a special place in the hearts of derivatives quants. The simple static replication of a variance swap using vanilla options is as beautiful as finance results come. @EmanuelDerman wrote the classic

emanuelderman.com/more-than-you-…

In particular, you can replicate a variance swap with a strip of vanilla put and call options on the same underlying with weights inversely proportional to the square of the strike price (so buying more downside puts than upside calls)

They became widespread as a way to trade exposure to volatility in large part because of this, because banks viewed them as mostly straightforward to price and hedge. (I say mostly because the extreme tails may still be hard to hedge... I'll come back to that)

For clients who want pure exposure to volatility, they are very convenient, you don't need to mess with trading a bunch of options and trying to delta hedge every day and rebalance strikes, just buy variance at 20, and if it realizes 21, make roughly 1x your vega

A volatility pair trade in variance swaps is sometimes viewed as super convenient, just fire and forget, result driven only by realized volatility, no rebalancing needed. Very common among volatility relative value PMs.

A manager may want to own variance in order to have a highly convex payout in the event of a major market meltdown and variance spike. They might own it outright; to make it even more of a tails trade, they might buy it against a volatility swap and size it up

So that the trade is locally vega neutral, paying some small negative carry, but becomes extremely long volatility in a major volatility spike

THE BAD: variance swaps are highly leveraged into the tails because they're convex in volatility, so people on the short side of variance swaps often blow up, sometimes seling tails purposely but sometimes just not really thinking about it.

Some people think about it. Variance swaps always trade at a premium to volatility swaps (at least 1-2 points in equity index) and ATM vol (at least 2-3 points) so the return stream of selling variance tends to be very attractive in normal market environments

I didn't know this but an old equity derivatives sellside trader was telling me Hodor sold a ton of S&P variance at 12 in 2006 and lost $60 million in addition to all the other fun stuff he was doing

https://x.com/bennpeifert/status/1888456375078158542

AIMCO sold a ton of uncapped variance against capped variance and lost $3 billion in 2020; Malachite also sold lots of it (among many other things) and lost 300% of their AUM, incurring massive losses to their bank counterparties
institutionalinvestor.com/article/2bsx55…

Sometimes people blow up on tail events in varswap positions without even really intending to be short tails. Even if you're long one variance swap and short another vega neutral, you are massively exposed to a blowup where your RV trade underperforms

https://x.com/bennpeifert/status/1880789268228108636

If you have a view on the relative value of volatility, it usually is a view about the center of the distribution, not about the far left tail. It's very dangerous to put it on using a structure that doubles your exposure every time that volatility doubles

THE UGLY: variance swaps do have a very beautiful theoretical replication. However, in many cases it's hard or impractical to fully replicate the tails, because (depending on the underlying) options may not be listed for extreme low strikes, or no one may want to sell them to you

So a bank that deals a lot of variance swaps to its customers may be warehousing millions and millions of vega of variance replication basis risk (short variance, long the replicating strip as best as possible)

This basis trades at a discount or premium driven by the supply and demand for variance swaps. Banks can only warehouse so much of this risk, it's not a pure arbitrage because you may be underhedged in the extreme tails, and the basis can always blow out more on you

For a while during the risk recycling boom of the mid-2010s, banks marketed variance replication basis packages to clients where the client would sell variance and buy an auto-delta-hedged package of options that replicated variance between some lower and upper strike

Note that is just very explicit tail risk selling (you're naked short the options in the part of the replication strip that is outside the range). People did them who liked carry and liked sounding smart. Those trades blew up catastrophically in March 2020

There are many variations on variance swaps that have been popularized over the years, sometimes starting from a risk recycling and intermediation framework, always leading to more blowups. Here's a thread on corridor variance swaps

https://x.com/bennpeifert/status/1597222504057053184

What else interesting did I miss? Reply with your favorite variance swap accident stories.

As always if you are glad I'm around posting derivatives lore for you say thank you to Honey, wouldn't be if not for her. Her second novel coming out soon!

"Benn, what do you do on your birthday?" yes I just answered that question now didn't I

oh and thank you to @mikeandallie for the topic suggestion. one of the masterminds of the only put selling strategy ever that actually WAS basically free money 🥳