# Index with negative gamma

I understand the principal of being gamma negative or positive, but what I struggle to understand is that how can we say that an index options for example SPY is gamma negative ? how do we do this calculations ?

We can see here $QQQ short gamma now, how do we calculate this ? this is from spotgamma* • Do you understand how a stock can have negative gamma? – LazyCat Apr 21 at 20:03 • Where are you seeing that "SPY is gamma-negative"? – D Stanley Apr 22 at 2:17 • @noob2 Sorry, Im not clear i meant options on an index or any underlying... – heuveny Apr 22 at 19:52 • @LazyCat I mean options ... – heuveny Apr 22 at 19:54 • You write "an index for example SPY is gamma negative". Do you mean an option on an index? – Bob Jansen Apr 22 at 20:06 ## 2 Answers An index itself doesn‘t have any gamma. Even for the options on an index (spot? futures? ETF?) it‘s a zero sum game since for every long position you have a matching short position. Now it gets a bit more interesting if you look into the type of players that trade options. Very simplified you have two main players. Firstly, there are real money investors buying downside protection & selling upside. Naturally they buy puts as hedges but won‘t further delta hedge those. On the other side of the trade you have market makers (MM) who take that flow to generate income. Since the MM is not using options to create a view, they will hedge their risk for every option that the sell/buy. The type of chart that you’re looking at is based on this very simplified assumption that all puts are sold and calls bought by the MM (and thus delta hedged). Hence for every put, they will sell some of the underlying and for every call the will buy some. If you aggregate the net delta exposure by strike (bucket) you will eventually end up with a chart like yours. This is sometimes referred to gamma imbalance (remember this from a JPM publication). Using a bit of maths, the \$ Gamma per contract is: $$\Gamma_{\\\} = \Gamma_{BS} \times F \times S$$

Where $$F$$ is your contract multiplier (often 100) and $$S$$ the spot price.

Rinse and repeat for every contract and scale the \\$ Gamma by the open interest of every option in the chain. Then simply subtract call gamma from put gamma and there you go!

Now obviously this gross simplification limits the usefulness of such a chart. Nonetheless it‘s a fun exercise and might show a thing or two. There are more sophisticated approaches where you‘d identify for every trade whether its a dealer buying or selling. This could be done via an IV approach where you mark each trade relative to its fair value (dealer buys cheap and sells rich). That‘s a lot of data to process though and requires some proper thought.

Some people make a living out of selling gamma exposure data in a ready made and easily digestible format (not me!). I do recommend having a look at the „white paper“ from above link.

"how can we say that an index options for example SPY is gamma negative ?"

I believe the chart shows an estimate of dealers' net gamma position for QQQ as a function of price. It is not the gamma for a single option on an index.

This kind of analysis has been discussed elsewhere, and I believe previously on StackExchange.

• It is not the gamma for a single option on an index, but the aggregate over all strikes and all expirations (I believe) at various hypothetical levels of the QQQ index (on the x axis). The red line shows the QQQ index level when the chart was drawn (about 341). – noob2 Apr 22 at 21:53
• Yup - subject to SpotGamma's assumptions about direction of flows (etc). I believe there are better ways to calculate these estimates, which Benn Eifert has discussed publicly. – user42108 Apr 22 at 22:37
• Nice guy, that Benn fellow. – noob2 Apr 22 at 22:38