Gamma, Gamma, Gamma: A Move after Midnight (6 min read)

Thorsten Roland Wegener spent twenty years trading equity derivatives and was a partner at Bear Stearns. Currently, he teaches as well as cooking, driving, and cleaning lots.

His biggest professional achievement? Introducing Capital Guaranteed Products and High Yield Reverse Convertibles to the German Market, beating several public funds in the category fresh funds raised.

Hobbies? History, Science Fiction, Politics (isn’t this all the same?)

Thorsten Roland Wegener can be contacted here.

 

With the S&P 500 and almost every other major index at critical junctures, loading up on gamma could be a smart move. But what is it? 25 years ago you might’ve gotten away without knowing. But the so called ‘Greeks’ (the risk parameters used in option trading) have outgrown their infant shoes and are no longer regarded as an exotic pastime. In fact, even seasoned speculators have come to terms with them.

Well, owning gamma is like employing a high-end butler – it’s the Alfred to Bruce Wayne. He’s always there when you need him, no questions asked, with the champagne for the guests and the escape route for Batman. The only downside is cost of his services. So you’d better make use of him.

Markets move and so do option prices on instruments on those markets. If you own a call on an Index like the S&P500 and the market moves upwards, so mostly does your option price (OK not always, but that’s material for another column). The higher the probability becomes that you will make money with your derivative instrument, the more expensive this instrument becomes. Analogue, a lowering in the odds of making money, is reflected in decreasing prices.

So far, we are in a pain-free, neutral world of high finance where we only busy ourselves with observing price changes. However, once you are long or short an option position your frame of reference changes. If you own options – calls or puts, it doesn’t matter – something wonderful happens once the underlying market on those options starts moving. If the market moves in your direction, for example you are long a call option and are confronted with a rising market, you are always a bit ‘more long’ than you were to begin with. If the market goes against you, you end up being a little ‘less long’.

 

Now let us assume that when you bought the call option you did the opposite trade in the underlying asset to hedge or offset your initial position. If the market goes up, you make money on your call and lose it on your short underlying position. If the market falls, you lose money on your long call, but you will make money on your short underlying position. Checking your unrealized P&L on both positions in your portfolio you will now notice the following: in the first scenario (rising markets), your call option position made more money than you have lost on your short underlying position. That’s Alfred serving the champagne. But it gets better. Even the downward scenario will not leave you stranded out of pocket. The long call option will have lost less money than you gained by being short the underlying in a falling market. That’s Alfred leading you out of harm’s way – or even better, delivering the utility belt with the gadgets you need to fight another day.

That’s long gamma, but it comes at a price – literally. You have to pay the premium for the option to be in this enviable position and this premium disappears over time. Slowly, at first; very fast once you approach expiration. This disappearing bit of your option price is the time value of an option and you have to earn it by using your gamma, we will say trade the heck out of it when the market starts moving and you have the opportunity to rebalance your portfolio, taking advantage of the profit generating properties of being long gamma. That’s the equivalent of keeping Alfred busy.

 

How Are You Going to Achieve That? Let’s step back into our example:

The market did move – again it doesn’t matter in which direction – and now your position of underlying and option shows a theoretical, unrealized profit, generated either by the option position or the underlying position. To lock this profit in, we have to rebalance our positions by using the underlying to neutralize our portfolio, either by buying some shares, futures, or bonds, etc., or by selling them. We don’t trade the options. These, after all, contain the desirable gamma we paid for and we tend to use them a bit longer. Once neutralized, we wait for another move in either direction to repeat this transaction and realize more P&L. As long as the market keeps moving, we are happy because the time value we lose on our option position will have materialized in our realized P&L through ‘scalping’ (that’s the technical term) our gamma long position. We would then eventually conclude this trade by selling the option position and cleaning out our position in the underlying.

This will always work under two conditions. One, you haven’t paid too much for the option. I.e., you’ve kept Alfred on a sensible wage. This was reflected in the price of the call or put through the implied volatility you encountered in the market when you bought. Two, you actually used your gamma to earn the loss of time value. The time value you are paying is the rental price for gamma. So make sure you only trade long gamma in markets where you anticipate some big moves to cover the rent. That is, you’re keeping Alfred busy.

This leaves us with a couple of questions. Is a move about to occur in the major indices? And if it is, is the magnitude of the move already priced into the option market and so preventing us from earning the rent for our gamma?

 

With the VIX trading around a relatively modest level of 15% as of writing, and pretty much everybody being fearful of a large correction in the S&P 500, some things don’t stack up. Either we see a big move – in which case the options are priced far too cheaply and being long gamma is a must. Or the option valuation represented through the VIX is correct and we shouldn’t expect Armageddon. In this case the loss of time value of your long gamma position will bleed you dry before the scalping makes you rich.

I can say one thing for sure. Whenever I was long gamma I did not suffer from sleepless nights. Sure, you might pay some premium to insure your portfolio and that might seem like a waste of money at the time, but I have never heard anybody complaining that his or her house did not burn down even though they had paid for fire insurance. In other words, if you can afford Alfred’s services, hire him.

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