Meet the Greeks

Hang around any professional options trading desk and it will only be seconds before you hear the terms Delta, Theta, Gamma, or Vega. No, they are not reminiscing about their good old fraternity or sorority days (Go Delta Sigma Phi!).

These are all symbols for mathematical explanations of how options prices behave when something changes. They provide additional tools for understanding the price action of options and can greatly enhance your own trading performance.

Bottom line: they are all additional ways to make money trading options.

The best part about the Greeks is that they are all displayed on your online options trading platform FOR FREE! So, if you can read a number off a screen, you gain several new advantages in the options trading world. That’s not a lot to ask.


The simplest and most basic Greek symbol to comprehend is the Delta. An option delta is a prediction of how much the option price will change relative to a change in the underlying security.

Here, it is easiest to teach by example. Let’s go back to our (AAPL) June 17, 2016 $110 strike call option. Let’s assume that (AAPL) shares are trading at $110, and our call option is worth $2.00.

If (APPL) share rise $1 from $110 to $111, the call options will rise by 50 cents to $2.50. This is because an at-the-money call option has a delta of +0.50, or +50%. In other words, the (AAPL) call options will rise by 50%, or half of the amount of the (AAPL) shares.

Let’s say you bought (AAPL) shares because you expect them to rise 10% going into the next big earnings announcement. How much will the above-mentioned call options rise?

That’s easy. A call option with a delta of 50% will rise by half the amount of the shares. So, if (AAPL) shares rise by 10% from $110 to $121, the call options will appreciate by half this dollar about or by $5.50. This means that the call options should jump from in price from $2.00 to $7.50, a gain of 375%.

By the way, did I mention that I love trading options?

(AAPL) June 17, 2016 $110 strike call option

50% delta X $11 stock gain = $5.50

$2.00 option cost + $5.50 option price increase = $7.50

Now let’s look at the Put option side of the equation. Let’s assume that Apple is about to disappoint terribly in their next earnings report, and that the stock is about to FALL 10%.

We want to buy the (AAPL) June 17, 2016 $110 strike put option which will profit when to stock falls. Remember, put options are always more expensive than call options because investors are always willing to pay a premium for downside protection. So, our put options here should cost about $4.00.

If we’re right and Apple shares tank 10%, from $110 to $99, how much will the put options increase in value?

We use the same arithmetic as with the call options. An at-the-money put options also has a delta of 0.50, or 50%. So, the put options will capture half the downside move of the stock, or $5.50. Add this to our $4.00 cost, and our put option should now be worth $9.50, a gain of 237.5%.

Did I happen to tell you that I love trading options?

(AAPL) June 17, 2016 $110 strike put option

50% delta X $11 stock decline = $5.50

$4.00 option cost + $5.50 option price increase = $9.50

Let’s consider one more example, the short position. Let’s assume that Apple shares are going to fall, but we don’t know by how much, or how soon.

It that case, you are better off selling short a call option than buying a put option. That way, if the stock only falls by a small amount, or goes nowhere, you can still make a profit.

When you sell short an option, your broker PAYS you the premium which sits in your account until you close the position.

Short positions in options always have negative deltas. So, a short position in the (AAPL) June 17, 2016 $110 strike call option will have a delta of -50%.

Let’s say you sold short the (AAPL) calls for $2.00 and Apple shares fell by 10%. What does the short position in the call option do? Since it has a delta of -50%, it will drop by half, from $2.00 to $1.00 and you will make a profit of $1.00.

Here is the beauty of short positions options. Let’s assume that (AAPL) stock doesn’t move at all. It just sits there at $110 right through the options expiration date of June 17, 2016.

Then the value of the call option you sold at $2.00 goes to zero. Your broker closes out the expired position from your account and frees up you margin requirement.

(AAPL) June 17, 2016 $110 strike call option

-50% delta X $11 stock decline means the options drops by half, or from $2.00 to $1.00

Sounds pretty good, doesn’t it? In fact, the numbers are so attractive that a large proportion of professional traders only engage in selling short options to earn a living.

To accomplish this, they usually have mainframe computers, highly skilled programmers, and teams of mathematicians backing them up which cost tens of millions of dollars a year.

However there is a catch.

When you sell short a call option, you are taking on UNLIMITED RISK. The position is said to be naked, or unhedged. Let’s say you sell short the (AAPL) June 17, 2016 $110 strike call option, and (AAPL) shares, instead of falling, RISE from $110 to $200, a gain of $90.

Then the value of your short position soars from $2.00 to $45.00. You will get wiped out. It gets worse. The delta on this option is only 50% for the immediate move above $110. The higher the stock rise, the faster your delta increases until it eventually reaches 100%. You now have a loss that increases exponentially!

This is why many hedge fund managers refer to naked option shorting as the “picking up the pennies in front of the steamroller” strategy.

For this reason, brokers either demand extremely high margin requirement for these “naked” or unhedged short positions, or they won’t let you do them at all.

If you dig down behind many of the extravagant performance claims of other options trading services, they are almost always reliant on the naked shorting of options. They all blow up. It is just a matter of when.

For that reason, we here at the Mad Hedge Fund Trader NEVER recommend the naked shorting of put or call options, no matter what the circumstances.

We want to keep you as a happy, money-making customer for the long term. If you succumb to temptation and engage in naked shorting of options, you will be separated from your money in fairly short order.

(AAPL) June 17, 2016 $110 strike call option

(AAPL) shares rise from $110 to $200

$2.00 short sale proceeds + $90 – $88.00

a loss of 4,400%!!


All options have time value. This is why an option with a one-year expiration date cost far more than one with a one-week expiration date. The theta is the measurement of how much premium you lose in a day. This is what options traders like me refer to as time decay.

The theta on an option changes every day. For example, an option with a year until expiration has a theta that is miniscule. An option that has a single day until expiration is close to 100% since it will lose its entire value within 24 hours if it is out of the money. The closer we get to expiration; the faster theta accelerates. As mathematicians say, it is not a straight-line move.

This is why you never want to hold a long option position going into expiration. The value of this option will vaporize by the day. Unless the stock goes your way very quickly, you will have a really tough time making money.

If you are short an option, this is when you can earn your greatest profits. But you only want to consider a short option position when you have an offsetting hedge against it. That will minimize and define your risk, limit your margin requirement, and keep you from blowing up and going to the poor house. We’ll talk more about that later.

I could go into how you calculate your own thetas, but that would be boring. Suffice it to say that you can read it right off the screen for you online trading platform.

Implied Volatility

While we’re here meeting the Greeks, there is one more concept that I want to get across to make your life as an option trader easier.

You have probably heard the term implied volatility. But to understand what this is, let me give you a little background.

Back in the 1970s, a couple of mathematicians developed a model for pricing options. Their names were Fisher Black and Myron Scholes and they received the Nobel prize for their work. Their equation became known as the Black Scholes Equation.

The Black Scholes equations predicts how much an option should be worth based on the historic volatility of the underlying securities, the current level of interest rates, and a few other factors.

When options trade over their Black Scholes value, they are said to have a high implied volatility. When they trade at a discount, they have a low implied volatility.

Let’s say that a piece of news comes out that a company is going to be taken over. The shares will rocket, and so will the implied volatility of the options.

If you pay a very high implied volatility for a call option, the chances of you making money decline and you are taking on more risk. If you pay too much, you could even see a situation where the stock rises, but the call option doesn’t rise, or even falls.

On the other hand, let’s say you buy a call option that is trading at a big discount to its theoretical implied volatility. You usually find this when a stock has shown little movement over a long period of time.

Chances are that you will get a good return on this low risk position, especially if you pick it up just before a major news event that you have correctly predicted.

At the end of the day, you should attempt to do with implied volatilities what you do with stocks and their options, buy low and sell high.

The Minors

There are a few other Greek letters you may hear about in the options market or find on your screen. For the most part, these are unnecessary most basic options strategies, gamma is well above your pay grade.

Gamma is the name of the most powerful type of radiation emitted when an atomic bomb goes off. It is always fatal. But we won’t talk about that here.

In the options world, gamma is the amount that the delta changes generated by a $1 move in the underlying stock price.

You may hear news reports of funds gamma hedging their portfolio during times of extreme market volatility. This occurs when managers want to reduce the volatility of their portfolios relative to the market.

Vega is another Greek term you’ll find on your screen. All options have a measurement called implied volatility or “vol” which indicated how much the option should move relative to a move in the underlying stock.

Vega is the measurement of the change in that option volatility. When a stock has volatility that is changing rapidly, vega will be high. When a stock is boring, vega will be low.

Finally, for the sake of completeness, I’ll mention rho. Rho is the amount that the price of an option will change compared to a change in the risk-free interest rate, i.e. the interest rate of US Treasury bills.

Back in the 1980s, rho was a big deal because interest rates were very high, with Fed funds rates as high as 13%. Since interest rates have been close to zero for the past eight years, rho has been pretty much useless. The only reason you would want to mention rho today is if you were writing a book about options trading.

With that, you should be fairly fluent in the Greeks, at least in regards to trading options. Just don’t expect this to get you anywhere if you ever plan to take a vacation to Greece.