# Risk management tools for long term Gamma/Vega sellers subject to margin calls

TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you in a margin call. Which model can help you to size the liquidity buffer to overcome these risks while allowing for acceptable returns over capital?

Background

For a while, I've investigated which trading strategies retail options traders use to steadily make meaningful profits by selling Gamma on European index options. So, before the actual question, I would like to share with you some of my findings. I stress the point of being "retail" because there are perks and flaws different than the ones belonging to professional players (like hedge funds):

• usually, transaction costs are a serious problem. This means, for instance, that the frequency of Delta hedging shall be low. Moreover, synthetic exposures to Vega such as those provided by proper long/short positions along the whole chain are unworkable. Even an Iron Condor could be too expensive for some moneyness, that is, its payoff doesn't properly reward the risks taken when you subtract transaction costs from the final expected gain;
• there is no lifeboat. If your mark-to-market current loss exceeds your current margin requirements and you don't have a liquidity buffer, the game is over even if your sold options are still OTM;
• market liquidity is almost never a problem. It's hard to find a strike with a reasonable moneyness where the market maker isn't buying or selling an amount suitable to your needs. Therefore, you're never supposed to give some market makers a call to trade OTC.

So, according to my research, the natural selection kept alive only a small fraction of Gamma sellers. This Darwinian process killed those who took the shortcut of the proverbial "Picking Up Nickels In Front Of A Steam Roller" by keeping themselves too close to the crushing machine, that is, selling high Gamma options (even with "wings" properly hedged, e.g. vertical spreads). As you already know, bid-ask spreads make this short-term game unfair and Delta hedging cannot work while you're approaching the so-called "pin risk". In short, if you systematically sell short-term Gamma to harvest some variance risk premium, you end up... dead. That's what I've seen to occur with a scary frequency.

This pushed the survivors to move to longer maturities: they saw how much easier was to hedge the Delta and the Gamma, while at the same time keeping transaction costs low. However, there's no free lunch:

• those who set aside a lot of buffer capital found out that time decay is a negligible source of profits when you're far from the expiration date, thus they found out that a Treasury bill would have given them better returns;
• those who set aside only a small multiple of the margins required by their brokers met their new horrible reality: as soon as the implied volatility term structure makes a spike, Delta and Gamma neutrality means nothing and they blow up anyway;
• even with enough capital set aside and a meticulous Delta management, there's no way you can deal with a gargantuan opening gap unless already hedged somehow.

This triggered another natural selection round. The (few) survivors put together the puzzle pieces and - according to my research - the highest survivability rate so far has been achieved by those who roughly trade like this:

1. start on a medium or long-term implied volatility skew setup which allegedly makes bode for a mean reversion. Two easy examples: (1) rolling skew time series as difference between constant moneyness implied volatility time series; (2) large difference between implied risk neutral density and historical density. Generally speaking, playing with percentiles can show something worth trying;
2. open a simple even-legs vertical spread, e.g. short 95% Put and long 90% Put. The long protective option is a necessary evil because you cannot forecast gargantuan opening gaps;
3. don't reset Delta to zero already. Instead, overhedge it to make it slightly negative: as implied volatility is usually correlated with underlying negative returns, you would want a slightly negative Delta to partially hedge Vega in case of an implied volatility spike and a market drop.

You could end up with a very simple position like this (Delta -5% is just an example, you should run some regression analysis about the implied volatility-negative returns beta):

Question

From a broader perspective, it's clear what these traders are striving to do: homemade high yield bonds. They're always seeking for a fixed income because of their risk aversion, and this sounds more natural to them than small bleedings followed by uncommon large returns.

Ok, it seems easy, right? Wrong! Aside from blatant risks (e.g. Delta hedging open at least a "wing" downward), here comes the hard part: if you have $$M$$ dollars and one of those trades requires $$m dollars margin, how many of those trades can you open with your broker to optimize the trade off between returns and risks?

Possible insights

It seems that the main variable here is: margins volatility. If you can estimate a density for $$m$$, you can optimize the use of your capital buffer. Margins can be calculated according to many metodologies, but according to my investigations almost every possible algorithm involves stress testing (see examples from Interactive Brokers):

1. unfavourable set of underlying movements;
2. unfavourable set of implied volatility spikes (or unfavourable risk neutral density tails enlargement, if you're working under a model free framework);
3. portfolio re-pricing;
4. $$m$$ is the loss under the worst case scenario.

Trying to quantitatively shape retail traders' rules of thumb led me to assume some usage of Extreme Value Theory applied to scenarios that have already been stressed. If the margin required by the broker was like a Value-at-Risk, here the problem would be to estimate an Expected Shortfall.

Moreover, I found out that using risk neutral density instead of stochastic or local volatility could simplify the job. For example, if you stick to a lognormal mixture framework (see Lognormal-mixture dynamics and calibration to market volatility smiles), a shock scenario doesn't need to disturb SDE's parameters neither to alter a volatility surface in a consistent (and arbitrage free) manner: just inflate the tails, shift the weighted mean(s) and rebuild your stressed chain to get the new worst case prices. A stress test scenario could be sparingly described just by five parameters (two standard deviations, two means, one weight) instead of a whole set of perturbed volatilities.

As you can see, I grope around in the dark. Any effective tool will be the answer.

• Even professional Gamma sellers with long track records are not always able to avoid disaster in this business reuters.com/article/us-usa-fund-volatility/… – Alex C Sep 12 '18 at 20:08
• @AlexC, here comes the point that a retail trader shouldn't suffer the liquidity issues that have (officially) decimated LJM Partners in the attempt to raise cash for their broker. Moreover, this stresses the point that with enough buffer capital available they could have survived... at the expense of annual return, of course. – Lisa Ann Sep 12 '18 at 20:43