Sunday, April 12, 2009

Quantology Revisited: The Negative Convexity Implications Of Delta-Hedging

I thank readers who provided tremendous insights on the market illiquidity post. However, one point that nobody mentioned, which may very well be at the heart of the problem, has to do with the issue of negative convexity from a delta-hedging perspective. Zero Hedge had previously discussed the implications of this very peculiar phenomenon two months ago in the context of CDO trend chasing in the CDS market and how negative convexity (especially in illiquid markets) leads to explosive and self-fulfilling rallies on either side.

I thank an anonymous reader for presenting the missing piece of the puzzle, and taking the convexity argument one step further from merely structured finance to the entire market. I welcome responses and apologize for the thematic wonkiness, however there is only so much simplification that can be presented. But a simplified attempt: we have crossed into territory where the negative convexity consequences of delta hedging will keep on pushing the market in a straight line in whatever direction it is moving until we see a violent reversal and the delta hedge breaks due to lack of vol to "feed it", which will be, in the parlance of our times, the market's epic fail.
What is good for GS is good for US... Young analysts, just starting in GS the London office not too long ago were told that delta hedging of equity derivatives books can account for up to 30% of market volumes. TD's data clearly demonstrates that vanilla, slow money are being swamped by quant props.

Delta hedging of GS, DB, BNP and other dealers listed/OTC equity derivatives books could be what others construe as a 'sinister plot' to goose up US markets. OTC derivatives are many times bigger than listed and often hedged on listed markets. Clearly many books got caught short upside gamma and that will force them to buy indices and individual names as market goes up. The higher the market goes, the more they need to buy. Markets are getting too small for all the large players to operate efficiently. All of them need to get smaller or some will die.

TD's ideas and data can be taken further and what started as low level liquidity provision issues expanded into market neutral quant problems and spilled in derivatives creating a self-feeding process. More quant problems leads to further short covering, higher markets, further delta hedging, more vanilla, slow money getting sucked in and ever sunnier CNBC commentators and Time magazine contributors. Until, as TD puts it, it doesn't.

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James said...

The equity market is totally scrwed up. I dont see how veteran traders can deny that fact.

This is the most credible explanation of whats going on.

Anonymous said...

Beating the dead horse?

Yea we all agree the market is overbought. Your shorts will payout this week. But don't expect a large drop.

Anonymous said...

are you suggesting that otc derivative buyers are long gamma but do not dynamically hedge and otc derivative dealers are short gamma but do dynamically hedge?

Anonymous said...

In summary, the market will go up until/unless it goes down.

Chris Beanie said...

So what exactly are you saying?

A crash is coming?

Eric Hirschberg said...

With recent high vol levels in many asset classes, it makes sense that most prop books would be positioned short vol (short convexity). That in and of its self is not a problem.
I believe the problem lies in the abnormally high covariance between asset classes do to the credit breakdown and its effect on ability to finance all assets. This raises the overall volatility and decreases the marginal utility of holding any particular asset with respect to all assets.

So the overall risk rises, even if no single risk increases! So normally constructed books of risk now have characteristics approaching individual asset risks.
I don't believe it is possible to hedge the risk of temporal correlation like the kind we are seeing today.

It does set up the possibility of some serious long gamma game playing around options expirations, which we should be seeing more of.

fourthestate said...

After a lot of reading on zerohedge, I'm still completely befuddled as to what the right policy prescription should be. Maybe I'm just dense for which I ask everyone's forgiveness. Any ideas or guidance...about policy prescriptions, not my denseness?

Anonymous said...

As an options trader I have to point out a large flaw which was basically mentioned above: for every option on index components or index or convertible bond or synthetic option position (with gaps, youd rather be synth short!), at any given point one party who is short gamma will be buying on the way up, but the counterparty will be selling on the way up.

Increase of vol --> increase of hedging, which is increased volume. The fact that its ONLY 30% is somewhat surprising to me.

Eric Hirschberg said...


Don't be short vol around expirations. The imbedded short convexity option is not priced for the tail risk that might occur.

Anonymous said...

plus why is negative gamma big after big stock moves? seems like it would be less as most options are now very otm or itm.

Anonymous said...

TD, I love your blog and agree with almost everything you say. But, I always come back to the same issue with those worried about bad debt; what gives anyone confidence that our government will stop printing money? Papering over the debt is fully underway, there has not been a single blink. Not in 20 years if you really go back and look.

What difference does another half trillion CMBS problem make, or even more. In for a penny, in for a pound, and the US government is all in. Preserving the value of a dollar is just not on the agenda. I've looked repeatedly for a very long time and it's not there.

This is not a debt crisis any more. It's a currency/inflation crisis. If it takes the market a while to acknowledge that, I can wait.

Anonymous said...

I think this is rubbish and you sound like a sore loser grasping at straws. There is little difference if dealers/MMs are short gamma or if shorts (be they implied short of the benchmark weight or short via borrowed stock) get stopped our or squeezed in, or if longs buy directly i the cash market or via deltas from dealers. Demand for stock - whether in the cash or OTC market - is demand for stock. Whinging doesn't change the reality of buying, or the mechanism by which is translates into cash-market volume.

It also sounds as if you are anthropomorphizing onto some nefarious manipulator, phenomena that are more easily and obviously explained by chaotic processes and what were deeply oversold markets.

You should tread carefully on both accounts (public whinging and anthropomorphizing) else your otherwise reasonably-good credibility will suffer.

Anonymous said...

tyler, seriously stop anthropomowhatevering. as anon says there is no explainig for "simple chaotic processes"... it makes sense to not think about anything in the market as it is all pure chaos. may god have mercy on all our souls for trying to make sense of how GS makes money instead of flipping a coin every day.

and definitely stop whining, although am not sure where exactly you do that... but stop it or anon will keep coming back more and more to discredit your credibility with ludicrous and nonsensical statements.

Anonymous said...

Anon @ 12:36 - I think what he is saying is that we have gotten to a market where 40% of the volume comes from a few quant shops trading with each other, as the volume goes down then they are forced to get down to a more manageable size and cover delta neutral positions, this forces the players with large option books to hedge and make the move even bigger as they buy or sell in the direction of the move, this then causes the hedgies to further dump positions causing more delta and gamma hedging. So the thesis here is not that the market has gone up because there is like you say a fundamental demand for equities but because those few firms playing with themselves are getting too big and running out of enough liquidity to be efficient. This could mean that if no vanilla institutional money comes in to buy, the momentum will end and then the market will drop which will cause the option players to then start unwinding hedges and selling further. Wash, rinse, repeat.

Anonymous said...

ZH - following up on anon at 12:36 - just shut up until you say something i agree with. that way your credibility with me will keep on growing in perpetuity. just let me know in advance what you are posting so i can put the barney frank seal of approval on it.

Anonymous said...

Don't beat T up too bad.

This is still one of the best blogs / sources of informed opinions on the Internet. I'm glad the club leader can take a punch.

Whacky markets heat up the discourse.

Anonymous said...

Market liquidity is drying up. One of the biggest providers of market liquidity is sec lending and major institutions both public and private pensions are either reducing or ending their progams. With unanticipated losses in collateral pools and being forced to mark those losses to market in their financial (for the first time)many plans are deciding that the small return is not worth the huge risk on the total portfolio of assets lent. Some funds have 2-3% hits on total plan assets from these so called dollar-in dollar-out funds.

Bobby and Jean the amateur world travelers said...

Not matter what way you look at these events they are the "Market". If quants are manipulating the prices to the upside, this is the market. The market is bigger than any of these funds combine as the herd will not stop the price increases until they are no longer justified. Once we hit that inflection point the market will correct and crush through the prior lows. Eventually it will be oversold just as it was over bought and we will see ourselves in another rally (over a year from now) until it rolls over again and breaks lows.

By that point in time we will have an actual gauge of what this recession or depression will look like, we will have an understanding of tax receipts look like, deficits look like and what long term bond rates are at. This is a process and during the whole process deleveraging or delfation will slowly take heed and out power the FED/central banking actions.

If the market was manipulated by the powers that be then then then by the end of the year we will be back to OCT 2007 levels. The Trailing PE will be over 200 and goldilocks will be back. The market is bigger than those who can influence, lets just say the influencers are no more than the starter to the rally, the sheeple keep it going.

The quant story makes sense and eventually this will roll over because there will be no more emotion left to keep it going. Greed will turn to fear as many will lock in profits and fear will turn to greed as short sellers come back with vengeance.

Anonymous said...

The entire stock market is traded on a black box computer program. I worked on the floor of NYSE for Goldman. I handled many many program trades and massive block trades. Goldman front runs the programs for its own acct. Research GATA. Not only do the "Presidents Working Group on Financial markets, and counter-party risk management group" control all aspects of the markets through "program trades" and "quants" They completely control the Gold and Silver markets under the pretense of National Security. Doesnt it arouse any curiosity in any of your mids how the US Govt can nationalize FNM,FRE,BSC,AIG,etc..etc.. and the barometer of financial market health (GOLD) goes lower??? The system is the MOST MASSIVE PONZI SCHEME EVER. Madoff aint got nothing on GS,JPM, US FED, CFTC, and White House!!!

Jason said...

To me this seems like a poker game...the pros depend on new, dumb money to play, otherwise they're just taking each others money, and the house take eventually eats everyone's stack. When the dumb money leaves, the game's over.

Unknown said...

I don't buy that delta-hedging argumentation. I got an impression that neither Tyler Durden nor any of the commentators have ever done delta-hedging.

If liquidity dries up, then those dependent on liquidity will be out of business. No delta-hedging story is needed as a complication to arrive this conclusion.

Actually that has already happened to a part of my business, thus the story is a little bit late too. If Tyler Durden has a time machine and he sends this story back one year in time, the date for publishing will be better, even if late then too.

admin said...

My Sunday Night Coffee post is up. This is my weekly market forecast -

Anonymous said...

I think anon at 12:32 makes a valid point, but it needs futhrer discussion. If the market move higher is the result of short vol players hedging gamma, then the key to when this move will peter out is knowing how close on average we are to the strike price of the call option or call option substitute the prop desks are. For example, lets say the prop desks were short calls in JPM with strike of 30 and a near term expiration date (for explantory purposes, I am obviously picking one option to represent the comlete structure of the otc derivative books, which I know are far more complex). Assume for whatever reason that the other side of the derivatives book (the long call holder) is not gamma hedging. As long as JPM is well below 30, an upside move doesn't require much buying. As it passes through 30 substanitally more buying is needed, but once it is well above 30, the bulk of the hedging is done. So if you assume that the bull run is self reinforcing gamma hedging, the question is how close are we to the quants derivitaive books being above strike (in the money)? Any insights appreciated.

Anonymous said...

With all of our quantitative sophistication, the market will trend lower for longer just like they had during the great depression and other severe bears. There is no amount of manipulation possible to offset fundamentals, temporal currents of asset deflation, and the fact that there are truly fewer market participants due to all of the blow-ups. I know this is the time to buy and I have been doing this on a highly selective basis, but on the flip side I am treading cautiously and have put 1/3 of my portfolio into pure cash, and took half of that and went long a short fund. Trust me that was not easy and I wanted to cry. My short ETF position got me feeling uneasy. But that's exactly how it should feel. I don't want to get to comfortable doing this or over confident because you will be wrong once. Call me crazy.

March can not possibly be the bottom. World GDP is still falling and monetizing the debt (a.k.a printing money) will not reverse the fact that world GDP is falling but instead just devalue our own currency with the global aggregate remaining the same. We don't live in a fiat based money system but instead a credit based money system with a fiat component tacked onto it. Even if it were pure fiat, you have to lend in order for the money multiplier affect to take root and the banks are not.

I don't wish losing money on anyone so there's my two cents.

In Debt We Trust said...

A simpler explanation consists of 2 words:

Max pain.

Anonymous said...


Anybody think the market could just trend sideways ad nauseam?

Anonymous said...

If I understand the post, there are around, a shadow, mysterious and gruesome world of huge positions in OTC infraworld derivatives. These positions can not obtain hedging in the shadow world, in their own world, and the players depend on the open, vanilla, daylight listed market for their hedging maneuvers.

Maybe the OTC market has become too large to be hedged in an, comparatively small, open market with low liquidity or volume.

This does not define a particular direction but would do the system more unstable and movements mors sudden.

(I apologize for my horrid english)

Anonymous said...

While some of you are trying to dish on Tyler, don't forget one small thing...

There is no limit to OTC Deriv contracts that can be entered into. However, there IS a limit to the amount of underlying issuances they can be based on (GS/GE/GM/C stock is a finite amount for all intents and purposes).

Most deriv pricing formulas implicitly assume infinite ability to delta hedge the book. While I haven't looked into the matter enough to determine if that will drive price in one way or another till they meet a greater opposing force, it is something to consider that you have more and more and more dealers trying to delta hedge off of a finite supply of stock.

Just imagine some ridiculous numbers. Say that there are 100,000 shares of XYZ stock and you have 100 million of derivative contracts using it as an underlyer (requiring deltahedge).

Now imagine that you have a trillion in OTC's with XYZ as reference. Delta hedging requirements have doubled with no change in the underlyer. You're definitely going to see that affect the vol/price patterns of XYZ.

GS751 said...

lol this is a big difference between delta hedging a plain vanilla on a liquid exchange and delta hedging on OTC derivative using a liquid exchange.

Anonymous said...

oh irony of irony.
why human beings always try to attach rationality to the irreversible irrationality.

and then, later, they silently try to convince themselves that it's not their fault.

Rhys said...

These large players need to read "The Power of Small" ( ) if they don't want to get crushed by their lumbering inefficiency. Paying more attention to smaller things would have prevented us from getting into this mess.