The Greek System
Being an options trader can sometimes feel like belonging to a fraternity; some gravitate toward the academic minded, some are athletically oriented, and some of us just go all-out Animal House
Of course, we at ThinkorSwim like to believe we represent the finest brokerage house on the industry’s campus. But wherever you decided to pledge, almost everyone gets introduced to the reigning “Greeks” early in the process.
These mighty Greeks -- delta
, and rho (well rho isn’t so mighty right now with interest rates near zero) -- will be your guides and provide the code for being a lifelong member of good standing in the fraternal order of options.
But before we meet each of these individually -- and learn about their powers, and yes, the tragic flaws they each have -- let’s use another quintessential part of the hazing process: the road trip, which will draw an analogy of how the Greeks can provide a general map of where one’s position is located at a specific time, but can't predict the bumps or detours on the way and can't accurately predict the condition in which you’ll arrive.
So you pack into your father’s mint Cadillac convertible and are blasting across the desert highway toward Vegas. With a full tank of gas, there’s nothing but 300 miles between you and a big payday.
Time to step on the accelerator, set the cruise control at 95 miles per hour, lean back, and count the minutes, approximately 32, before you pull up to the clearing house, I mean casino, and start grabbing at the piles of money.
Those who joined the call options buying in tech names during the pre-2000 Internet bubble must have had similar feelings. They were in the driver’s seat and there was little need to pay attention to know if you’d arrive safely at a profitable destination. Hey, you’re with your Greek brothers who have it all mapped out. You trust them, what could go wrong?
Well, if you’re also an option trader, especially one that has used TOS education and tools, you’d know that the driving conditions could change drastically.
It’s now dark and raining, the gas meter has slipped below “H”, and that classic Caddy-feel is starting to feel like an old, gas-guzzling clunker. This is essentially what happened to the financial markets starting in September 2008.
Suddenly, the gauges on your dashboard take on a different, more important meaning and need to be monitored more closely. The slick road and darkness increases risk, akin to an increase in implied volatility or your vega risk.
A bridge was washed away and the detour goes to a curvy, mountainous road. The 300 miles, or your expiration date, suddenly seem much further away, making theta a more important consideration. This forces you to look at that fuel tank, or your capital and margin requirements, and the costs associated with carrying the position under these new conditions. It’s time to slow down your speed, or reduce your delta, because it’s clear now that you're headed in the wrong direction. It’s time to pull over, reassess the situation, and make an adjustment.
Those Greeks, who had mapped out a clear risk/reward profile and had promised a smooth ride, are now shrugging their collective shoulders and saying “You screwed up, you trusted us.”
But how did they fail? After this long and laborious analogy, let’s drill down and try to learn exactly what the Greeks are, what they aren’t, what their limitations are, and what they have offer.
A Derivative of a Derivative
The components that go into pricing an option are based on factual numbers, while Greeks are strictly theoretical. As such, the Greeks are a derivative and provide a rearview mirror view.
Basic pricing models such as Black-Scholes use five inputs: current stock price, time remaining until expiration, strike price, prevailing interest rates, and implied volatility are known or factual numbers.
Actually, the implied volatility part of the option pricing model is the "X" in the calculation. In essence, IV is the “answer” to the pricing equation. The price of the option is the price, and IV is the result. You can argue they may be wrong until you are blue or broke.
In a sense, the same holds true for the Greeks. They’re derived from the option’s current price and their values are projected based on mathematical models, and as such, they are second derivatives.
In fact gamma, one of the powerful forces, is a derivative of a derivative, in that it’s a measure of how a change in delta will impact the value of the option.
If all of this sounds a bit intimidating, you can take comfort that using a platform such as TOS does most of the heavy lifting for you in that its proprietary software performs the necessary calculations to provide an accurate value for each of the Greeks.
So while Greeks may have their limitations in terms of prediction, they’re not without value for defining risk, and more importantly, helping to make adjustments in dynamic and changing market conditions. A Compass, Not a Map
To beat our car and road trip analogy into the ground, one can consider the Greeks as a compass, rather than a map. Greeks can’t be viewed in isolation of what may be changing terrain. They might point true north, but if there are hills and streams to forge, the path won’t be linear. And non-linear is a crucial and central concept when dealing with options. None of the Greeks are defined in straight line, but rather have slopes and curves.
Delta and gamma share a smile. Vega and theta slope down as expiration approaches. And each is tied to not only the price of the underlying security, but to each other.
The delta, gamma, and vega of an option are vastly different depending on the strike price (out of the money versus in the money) and time remaining.
This ever-changing landscape makes predicting what will happen to the price of a single option or a position involving multiple options a difficult undertaking.
Often the option price doesn’t always appear to move in conjunction with the price of the underlying asset. It’s important to understand what factors contribute to the movement in the price of an option, and what effect they have. In this way, the Greeks can provide a compass and keep you on course.
This doesn’t mean you have to improvise, or make adjustments, which is a way of life for option traders. The Greeks can help you quantify the various risks of every trade you consider, no matter how complex. Know Where You're Going, Not Where You’ve Been
Let’s look at one of the basic adjustments to keep a position delta neutral. The conventional, and believed the most efficient, way to hedge a position is to buy or sell stock against the option owned.
For example, if one buys 10 Apple
(AAPL) $140 calls for $2 a contract when the stock is trading $140, the hedge to get delta neutral would be to sell five shares of the stock. And this will work great because if the stock plummets, you’ll make money, if the stock rallies, you will also make money. This is because the position is long gamma. But the fact that this will be profitable if there’s an extreme move in either direction doesn’t make it an efficient hedge. By definition, a hedged position shouldn’t make or lose money no matter what the price of the underlying is.
Of course there’s no such thing as a perfect hedge and everything comes with a cost. If we flipped the above position around -- sold 10 calls and bought five shares -- it would only be profitable if Apple remained above $139 and below $143.50 a share.
Yes, time decay, or theta, is now working in your favor, but the position is short gamma and, therefore, can have exponentially large losses on a large price.
Option positions have a variety of opportunity and risk exposures, and these risks vary dramatically over time and with market movements. It’s important to understand them and the Greeks can be a good guide. Just don’t give them the keys to your car or the password to your account.